Educational qualification

Amount given to you for help

Period of time when classes are in session

Period of time

A percentage needed for classes

Monitoring gpa

Your ID number assigned to you

To be accepted

To enroll in school to expand education

Relating to education

Signing up for school

so they are discussing the nature of who is consider a creator? it seems that they consider a craftsman someone who physically makes the piece, and that you are classified as an imitator based on if you replicate the work?

Capitalism may have changed in appearance, but it still depends on profit-seeking companies, wage labor, and inequality. The claim that this system fits human nature because people are inherently selfish is unrealistic since humans have survived and prospered mainly by supporting one another.

Although GDP measures the money value of production it ignores unpaid work mostly done by women and even count useless activities. While it is still useful for economic planning I agree with the author that this does not show true prosperity or well-being and makes me wonder why economists continue to rely on GDP despite its flaws.

this is a add on to how the people are kind and caring

this shows the teamwork and the peoples kindness

the are feeling sorrow for the person and feel pity on that they fell

This shows a change of the world which would also mean a change in the poem.

Here there is an assumption that it is not the object of desire that will lead to weakness rather it is excitement linked with desire that will make the person lose the object of desire. This assumption in my opinion is a little farfetched. There is an acceptance nonetheless that achieving the object of desire will lead to happiness.

Is this what trump is goimg after?

Good fucking lord

It isn't discussed but are the thoughts not there?

When a film or show contains certain traits they’re put under a certain category. Like the genre film nior, it contains thrillers, gangster films, and Detective films.

Films usually become popular based on the genre, but I think in this generation, popularity also comes from people caring more about who's acting in the films rather than what it's actually about.

Interesting how he didn't get credit even though there's documentation that his work was before 1739

I wanted to note that he criticizes all the religions equally through skepticism of their truthfulness. He wonders who's right and who's wrong, which to this day has no answer.

It's interesting to see how Yacob had this religious view in his life even though it feels like such a modern way of thinking.

is this the same type of Christianity that we practice in the United States / what denomination would they fall under?

Reflects one of the tenets of the enlightenment; intresting considering that this occurred before whAt we would consider the start.

Specifically the importance of this even though it gets labeled as "Unskilled"

Freedom of entry and exit

I suspect knowing the language can actually go both ways as far as in demand skills for countries

Cliche but more on the line

And not learning skills that translate neccesarily

Entry level for some of the skills migrants are bringning

But they will bring tons of informal trainings, that is the key part

The formal education cannot be the explanation because these workers don't have that background (formally)

Gendered aqcuisition

What makes this so important?

Schooling and the like

Which is most common of these three? Which has the greatest mobility pathway?

Chain migration?

Question three

I did not know that Tuesday, Wednesday, Thursday, and Friday were derivatives of these Old Germanic deities. It is always fascinating to learn about the cultural exchange and assimilation of people through what is kept or changed in their language. Since it effects more then just words but the entire identity of the people. Who take what is added or changed and make it there own.

I find it intriguing how the physical aspects of the land has so much influence on how a culture and society start. When it comes to Egypt they became reliant on the predictable and annual floods of the Nile. Allowing them to settle a permeant and prominent society that can grow. They were able to make many achievements and have a long lasting impact by building the foundation for many other ancient civilizations.

For me I find it interesting how often in western media and older textbooks there is this narrative bias of Europeans having invented or being smarter then the rest of the ancient world. This is very evident in the idea of Europeans becoming "civilized" and the having the start of agriculture being accredited to them. Despite there now being a lot of evidence that humans developed these ideas independently and within ways that fit their needs.

This is cool to think that different nations thrived by growing different things and if they grew those things and had a good harvest their nations populations would normally grow.

This information is interesting to see that a crop that is rarely planted now because the price of it is useless compared to back then when people grew it and the plant would let them thrive in their cultures.

Seeing how the indigenous people and really most people years ago think that food we ear today and don't even think about it and really appreciate it because were so used to it but reading this I think we sometimes forget how years ago most people didn't have the nicer things and just the simple things like the food we ear can change so much and how I think lots of us take advantage of it now.

This information is really interesting seeing how we still use the culture and intellectual life form the Middle East and Europe today I think is just so amazing. How we can still learn from them now in schools.

Reading about this I find its pretty amazing how seeing how farming started and developed to seeing how the transition from the hunt and gather group to societies more similar to our society now with governments, number systems, and so on and seeing how much things can change.

I think it is pretty crazy how even after 80,000 years ago archaeologists can still find traces of humans and how they moved and traveled from Africa, Asia, and Europe.

another "Arranging"

Race should not be considered in any job anyway.

This makes sense because the programs got banned.

just jewish students?

Talks about Hamas and Not Palestine

This makes me think about how science can reconstruct a person's life story from their bones alone. It makes me reflect on how much information our skeletons contain about our identity.

This is interesting because comparison is something we all do when we go to other places, but anthropology turns it into a systematic method. It makes me wonder if comparisons run the risk of oversimplifying cultures when comparing them?

This caught my attention because it highlights the extreme diversity of human environments. It makes me think about how biology (climate adaptations) and culture (diet, clothing, housing) complement each other to help people survive. It also makes me wonder if our cultural flexibility is more important than biology in explaining human diversity.

Although we can look at previous patterns of evolution, how are researcher's able to determine what patterns they should be looking for as we continue to evolve?

Its interesting to look at the differences in cultural values and morals, especially when it comes to knowing and understanding. For centuries, society has continued to attempt to answer the questions of knowing using both science and religion as a temporary band aid for what we have yet to understand. In no way do I think using these concepts is a negative thing, on the contrary, having something that keeps us content.

I find this interesting in the sense that while it clearly shows Kates interest in anthropology, it also connects to the idea and general theme of sociology. As someone who previously took a sociology course, I look forward to picking up on these minor comparisons in future readings.

Environmental, social, and cultural conditions impact the experience of illness but I also believe being in a group rather than alone can play a part ones illness and thinking.

Una respirazione tranquilla con volumi correnti inferiori allo spazio morto anatomico non introduce affatto gas fresco negli alveoli; solo la parte del volume corrente inspirato (VT) superiore al VD introduce gas fresco negli alveoli. Lo spazio morto può essere ulteriormente aumentato dal punto di vista funzionale se parte del volume corrente inspirato viene convogliato in una zona del polmone che non riceve flusso sanguigno polmonare e quindi non può contribuire allo scambio gassoso (ad esempio, la porzione di polmone distale rispetto a un grande embolo polmonare).

bring structure into life always wins

Important limitation: cash helps immediate needs and choices but doesn’t replace structural policy reforms (e.g., universal health care, housing policy). It’s a partial solution, not a cure-all.

People sometimes accept lower pay short-term if it leads to long-term gains (training, promotion paths). Cash provides the breathing room to make that investment in future earning potential.

Cash lowered barriers to entrepreneurship for Black participants, showing how even modest regular payments can enable risk-taking and opportunity creation for historically excluded groups.

Work hours fell slightly, but not dramatically. Importantly, reduced hours often reflected positive choices (schooling, caregiving, skill-building) rather than inactivity — a nuanced outcome, not a simple “people stop working” headline.

A quick, measurable effect: recipients prioritized essentials (food, housing, transport). This rebuts the stereotype that unconditional cash is frivolously spent — it often covers necessities.

Very high response rates reduce bias from dropouts. When almost everyone answers, we can be more confident the results represent the whole group, not just the most engaged people.

Participants came from different community types (not just one city), which helps the findings generalize better across varied U.S. settings — though it is still limited to two states.

A large sample and multi-year follow-up strengthen the study’s reliability. Because it spans several years (including the pandemic), results reflect effects during a turbulent time — useful but also context-dependent.

This describes the main experimental treatment: a sustained, unconditional monthly payment. “No strings attached” means recipients could spend the money however they chose, so the study measures real-world behavior, not mandated use.

In this equation use ni for nh, and nf for nl

Quiet playtime with Robert the robot

Cosying up by the fire with Lady Penelope - and sometimes Brains, Alan and Tin Tin - by my side

Reading Century 21: Menace From Space by torchlight in the dark while listening to peaceful African music

The warmth and comfort of talking to Lady Penelope at night.

The warm scent of cake coming from the kitchen

Brains resting in the shade of a tree

I found that even the Pittsburgh police didn't want to put down the protests. So, they had to call in a militia that killed 20 strikers and instead of decreasing the severity it instead erupted into a month of destruction because of the militias rifle fire and their bayonets.

A list of privileges that was provided to students by the high school or college

A privilege that has became so common. Even with a good amount of people still behind, schools are always pushing more towards the technological sides. For instance most elementary classes I hear about are filled with chromebooks.

Shows the amount of people who are living a life separated digitally from the rest along with some technologies to watch out for.

I honestly expected this number to be a bit higher, just because of the internet's major dominance. It also makes me wonder if part of this percentage is by choice.

Puts into perspective the numbers some of the companies are producing

I agree with this statement. I say this because so many of of the things we do in real life have something or influence us to do so. How we talk to people, our eating habit, even how we act.

eLife Assessment

This useful study shows that stimuli of a certain size elicit theta oscillations in V1 neurons both in spikes and local field potentials, and monkeys performing a dot detection task on these stimuli show theta rhythmicity in their response times. This replicates previous findings showing rhythmic theta activity in V4 and behaviour when stimuli are presented in the receptive field along with a surrounding flanker stimulus. However, there is incomplete evidence that rhythmicity in neural activity is related to the rhythmicity in behavior, and the mechanisms underlying these oscillations remain unclear.

Reviewer #1 (Public review):

Summary:

The authors add to the body of evidence showing theta rhythmic modulations of neuronal activity and behavior.

Strengths:

Precise characterization of the effects of visual stimulation on theta-induced neuronal oscillations of spiking neurons in V1 and its relevance for behavior.

The manuscript is well-written and clearly presented,

Weaknesses:

The advances are limited over the established body of evidence. Both theta-induced visual oscillations and their relevance for behavior have been firmly established by prior work, including prior work from the authors. There is no major new technique, data, finding, or insight that extends our knowledge in a majorly significant way beyond existing knowledge, in my opinion. I would suggest that the authors re-evaluate the body of existing work to more strongly place their work in the context of existing work. A study that targets fundamental holes or open questions in the field would have been viewed as more impactful.

Reviewer #2 (Public review):

Summary:

Schmid & colleagues test an interesting hypothesis that V1 neurons might act as theta-tuned filters to incoming sensory information, and thereby influence downstream processing and detection performance.

Strengths:

The authors report that circular stimuli elicit theta oscillations in V1 single units and population activity. They also report that the phase of the theta oscillations influences performance in a change detection task.

Weaknesses:

The results are reported in terms of specific stimulus sizes. To truly reflect general-purpose spatial computations in the primary visual cortex, it will be important to establish a relationship between stimulus size and receptive field size.

I have several major concerns that I would like the authors to address:

(1) First paragraph of Results: The results are presented at very specific stimulus sizes: 0.3-degree, 1-degree, 4-degree, and so on. A key missing piece of information is the size of the receptive fields (RFs) that were recorded from. A related missing information is at what eccentricity these RFs were recorded from. Since there is nothing magical about a 1-degree stimulus, any general-purpose computation in the primary visual cortex has to establish a relationship between RF size and stimulus size.

(2) Second paragraph of Results: The authors state that "specific stimulus sizes consistently induced strong theta rhythmic activity: 1{degree sign} in MUA and 2{degree sign} in LFP". What is the interpretation of these specific sizes? Given that the LFP and MUAe reflect different aspects of neural activity, how does one interpret the discrepancy?

(3) Third paragraph of Results: Again related to (1), what is the relationship between the stimulus size that elicited the largest theta peaks and RF size at the population level? (1)-(3) taken together, there seems to be an opportunity to reveal something more fundamental about V1 processing that the authors might have missed here.

(4) Change detection task: It was not clear to me whether the timing of the luminance change, which varied from 500ms to 1500ms, was drawn from an exponential distribution or a uniform distribution. Only an exponential distribution has the property of a flat hazard function, which will be important to establish that the animal could not anticipate the timing of the upcoming change.

(5) Figure 3D: Have the authors tried to fit the data separately for each animal? There seems to be an inconsistency in the results between the 2 animals. The circular data points ('AL') seem positively correlated, similar to the overall trend, but the diamond data points ('DP') seem to have a negative slope.

Reviewer #3 (Public review):

Summary:

This paper investigates changes in brain oscillations in V1 in response to experimentally manipulating visual stimulus features (size, contrast at optimal size) and examines whether these effects are of perceptual relevance. The results reveal prominent stimulus-related theta oscillations in V1 that match in frequency the rhythms of behavioural performance (response speed in detecting targets in the visual display). Phase analyses relate these fluctuations of detection performance more formally to opposite theta phase angles in V1.

Strengths:

The non-human primate model provides unique findings on how brain oscillations relate to rhythms in perception (in two rhesus monkeys) that align well with findings from human studies (as occurring in the theta band). However, theta rhythms in humans are typically associated with fronto-parietal activity in the domain of spatial orienting, attentional sampling, while here the focus is on V1. Importantly, microsaccade-controls seem to speak against a spatial orienting/ attentional sampling mechanism to explain the observed effects (at least regarding overt attention).

Weaknesses:

This study provides interesting clues on perceptually relevant brain oscillations. Despite the microsaccade-control, I believe it remains an open question whether the V1 rhythmicity is of pure V1 origin, or driven by top-down input, as it is conceivable that specific stimuli capture attention differently (and hence induce specific covert attentional (re)orienting patterns). For perceptually relevant (yet beta) rhythmicity over occipital areas that are top-down generated, see e.g., Veniero et al., 2019.

CS 197: Computer Science Research Step 1: Performing a literature search Keep track of how much you’re learning about the design axes as you consume additional papers. Typically, you’re learning the most at the very beginning, and the amount per paper starts going down after five papers or so.

important

need elaboration

need elaboration

eLife Assessment

In this useful study, ectopic expression and knockdown strategies were used to assess the effects of increasing and decreasing Cyclic di-AMP on the developmental cycle in Chlamydia. The authors convincingly demonstrate that overexpression of the dacA-ybbR operon results in increased production of c-di-AMP and early expression of the transitionary gene hctA and late gene omcB. Whilst the authors have attempted to revise the submission, the model proposed in the revised manuscript is still not fully supported by the data presented.

Reviewer #2 (Public review):

This manuscript describes the role of the production of c-di-AMP on the chlamydial developmental cycle. The main findings remain the same. The authors show that overexpression of the dacA-ybbR operon results in increased production of c-di-AMP and early expression of transitionary and late genes. The authors also knocked down the expression of the dacA-ybbR operon and reported a modest reduction in the expression of both hctA and omcB. The authors conclude with a model suggesting the amount of c-di-AMP determines the fate of the RB, continued replication, or EB conversion.

Overall, this is a very intriguing study with important implications however the data is very preliminary and the model is very rudimentary. The data support the observation that dramatically increased c-di-AMP has an impact on transitionary gene expression and late gene expression suggesting dysregulation of the developmental cycle. This effect goes away with modest changes in c-di-AMP (detaTM-DacA vs detaTM-DacA (D164N)). However, the model predicts that low levels of c-di-AMP delays EB production is not not well supported by the data. If this prediction were true then the growth rate would increase with c-di-AMP reduction and the data does not show this. The levels of of c-di-AMP at the lower levels need to be better validated as it seems like only very high levels make a difference for dysregulated late gene expression. However, on the low end it's not clear what levels are needed to have an effect as only DacAopMut and DacAopKD show any effects on the cycle and the c-di-AMP levels are only different at 24 hours.

The data still do not support the overall model.

In Figure 1 the authors show at 24 hpi.

DacA overexpression increases cdiAMP to ~4000 pg/ml

DacAmut overexpression reduces cdiAMP dramatically to ~256 pg/ml)

DacATM overexpression increases cdiAMP to ~4000 pg/ml.

DacAmutTM overexpression does not seem to change cdiAMP ~1500 pg/ml .

dacAKD decreases cdiAMP to ~300 pg/ml .

dacAKDcom increased cdiAMP to ~8000 pg/ml.

DacA-ybbRop overexpression increased cdiAMP to ~500,000 pg/ml.

DacA-ybbRopmut ~300 pg/ml.

However in Figure 2 the data show that overexpression of DacA (cdiAMP ~4000 pg/ml) did not have a different phenotype than over expression of the mutant (cdiAMP ~256 pg/ml). HctA expression down, omcB expression down, euo not much change, replication down, and IFUs down. Additionally, Figure 3 shows no differences in anything measured although cdiAMP levels were again dramatically different. DacATM overexpression (~4000 pg/ml) and DacAmutTM (~1500). This makes it unclear what cdiAMP is doing to the developmental cycle.

In Figure 4 the authors knockdown dacA (dacA-KD) and complement the knockdown (dacA-KDcom) dacAKD decreases cdiAMP (~300) while DacA-KDcom increases cdiAMP much above wt (~8000).<br /> KD decreased hctA and omcB at 24hpi. Complementation resulted in a moderate increase in hctA at a single time point but not at 24 hpi and had no effect on euo or omcB expression. Importantly, complementation decreased the growth rate. Based on the proposed model, growth rate should increase as the chlamydia should all be RBs and replicating and not exiting the cell cycle to become EBs (not replicating). Interestingly reducing cdiAMP levels by over expressing DacAmut (~256 pg/ml) did not have an effect on the cycle but the reduction in cdiAMP by knockdown of dacA (~300 pg/ml) did have a moderate effect on the cycle.

For Figure 5 DacA-ybbRop was overexpressed and this increased cdiAMP dramatically ~500,000 pg/ml as compared to wt ~1500. This increased hctA only at an early timepoint and not at 24hpi and again had no effect on omcB or euo. Overexpression of the operon with the mutation DacA-ybbRopmut reduced cdiAMP to ~300 pg/ml and this showed a reduction in growth rate similar to dacAmut but a more dramatic decrease in IFUs.

Overall:

DacA overexpression increases cdiAMP to ~4000 pg/ml (decreased everything except euo)

DacAmut overexpression reduces cdiAMP dramatically (~256 pg/ml). (decreased everything except euo)

DacATM overexpression increases cdiAMP to ~4000 pg/ml (no changes noted)

DacAmutTM overexpression does not seem to change cdiAMP ~1500 pg/ml (no changes noted)

dacAKD decrease cdiAMP to ~300 pg/ml (decreased everything except euo)

dacAKDcom increased cdiAMP to ~8000 pg/ml (decreases growth rate, increase hctA a little but not omcB)

DacA-ybbRop overexpression increased cdiAMP to ~500,000 pg/ml (decreases growth rate, increase hctA a little but not omcB)

DacA-ybbRopmut ~300 pg/ml (decreased everything except euo)

Overall, the data show that increasing cdiAMP only has a phenotype if it is dramatically increased, no effect at 4000 pg/ml. Decreasing cdiAMP has a consistent effect, decreased growth rate, IFU, hctA expression and omcB expression. However, if their proposed model was correct and low levels of cdiAMP blocked EB conversion then more chlamydial cells would be RBs (dividing cells) and the growth rate should increase. Conversely, if cdiAMP levels were dramatically raised then all RBs would all convert and the growth rate would be very low. When cdiAMP was raised to ~4000 pg/ml there was no effect on the growth rate. However, an increase to ~8000 pg/ml resulted in a significant decrease but growth continued. Increasing cdAMP to ~500,000 pg/ml had less of an impact on the growth rate. Overall, the data does not cleanly support the proposed model.

Author response:

The following is the authors’ response to the current reviews

Reviewer #2 (Public review): 

This manuscript describes the role of the production of c-di-AMP on the chlamydial developmental cycle. The main findings remain the same. The authors show that overexpression of the dacA-ybbR operon results in increased production of c-di-AMP and early expression of transitionary and late genes. The authors also knocked down the expression of the dacA-ybbR operon and reported a modest reduction in the expression of both hctA and omcB. The authors conclude with a model suggesting the amount of c-di-AMP determines the fate of the RB, continued replication, or EB conversion. 

Overall, this is a very intriguing study with important implications however the data is very preliminary and the model is very rudimentary. The data support the observation that dramatically increased c-di-AMP has an impact on transitionary gene expression and late gene expression suggesting dysregulation of the developmental cycle. This effect goes away with modest changes in c-di-AMP (detaTM-DacA vs detaTM-DacA (D164N)). However, the model predicts that low levels of c-di-AMP delays EB production is not not well supported by the data. If this prediction were true then the growth rate would increase with c-di-AMP reduction and the data does not show this. The levels of of c-di-AMP at the lower levels need to be better validated as it seems like only very high levels make a difference for dysregulated late gene expression. However, on the low end it's not clear what levels are needed to have an effect as only DacAopMut and DacAopKD show any effects on the cycle and the c-di-AMP levels are only different at 24 hours. 

These appear to be the same comments the reviewer presented last time, so we will reiterate our prior points here and elsewhere. We do not think and nor do we predict that low c-di-AMP levels should increase growth rate (as measured by gDNA levels), and this conclusion cannot be drawn from our data. Rather, we predict that the inability to accumulate c-di-AMP should delay production of EBs, and this is what the data show. The reviewer has applied their own subjective (and erroneous) interpretation to the model. The asynchronicity of the normal developmental cycle means RBs continue to replicate as EBs are forming, so gDNA levels cannot be used as the sole metric for determining RB levels. We show that reduced c-di-AMP levels reduce EB levels as well as transcripts associated with late stages of development. The parsimonious interpretation of these data support that low c-di-AMP levels delay progression through the developmental cycle consistent with our model.

The data still do not support the overall model.

We disagree.  We have presented quantified data that include appropriate controls and statistical tests, and the reviewer has not disputed that or pointed to additional experiments that need to be performed.  The reviewer has imposed a subjective interpretation of our model based on their own biases.  A reader is free, of course, to disagree with our model, but a reviewer should not block a manuscript based on such a disagreement if no experimental flaws have been identified. 

In Figure 1 the authors show at 24 hpi. 

We also showed data from 16hpi, which is a more relevant timepoint for assessing premature transition to EBs.  In contrast, the 24hpi is more important for assessing developmental effects of reduced c-di-AMP levels.

DacA overexpression increases cdiAMP to ~4000 pg/ml 

DacAmut overexpression reduces cdiAMP dramatically to ~256 pg/ml) 

DacATM overexpression increases cdiAMP to ~4000 pg/ml. 

DacAmutTM overexpression does not seem to change cdiAMP ~1500 pg/ml . 

dacAKD decreases cdiAMP to ~300 pg/ml . 

dacAKDcom increased cdiAMP to ~8000 pg/ml. 

DacA-ybbRop overexpression increased cdiAMP to ~500,000 pg/ml. 

DacA-ybbRopmut ~300 pg/ml. 

However in Figure 2 the data show that overexpression of DacA (cdiAMP ~4000 pg/ml) did not have a different phenotype than over expression of the mutant (cdiAMP ~256 pg/ml). HctA expression down, omcB expression down, euo not much change, replication down, and IFUs down. Additionally, Figure 3 shows no differences in anything measured although cdiAMP levels were again dramatically different. DacATM overexpression (~4000 pg/ml) and DacAmutTM (~1500). This makes it unclear what cdiAMP is doing to the developmental cycle. 

As we have explained in the text and in response to reviewer comments on previous rounds of review, overexpressing the full-length WT or mutant DacA is detrimental to developmental cycle progression for reasons that have nothing to do with c-di-AMP levels (likely disrupting membrane function), since, as the reviewer notes, the WT DacA deltaTM strain had similar c-di-AMP levels but no negative effects on growth/development. If we had not presented the effects of overexpressing the individual isoforms, then a reviewer would surely have requested such, which is why we present these data even though they don’t seem to support our model.  This is an honest representation of our findings.  The reviewer seems intent on nitpicking a minor datapoint that seems to contradict the rest of the manuscript while ignoring or not carefully reading the rest of the manuscript.

In Figure 4 the authors knockdown dacA (dacA-KD) and complement the knockdown (dacA-KDcom) 

dacAKD decreases cdiAMP (~300) while DacA-KDcom increases cdiAMP much above wt (~8000). 

KD decreased hctA and omcB at 24hpi. Complementation resulted in a moderate increase in hctA at a single time point but not at 24 hpi and had no effect on euo or omcB expression.

By 24hpi, late gene transcripts are being maximally produced during a normal developmental cycle. It is unclear why the reviewer thinks that these transcripts should be elevated above this level in any of our strains that prematurely transition to EBs. There is no basis in the literature to support such an assumption. As we noted in the text, the dacA-KDcom strain phenocopied the dacAop OE strain, and we showed RNAseq data and EB production curves for the latter that support our conclusions of the effect of increased c-di-AMP levels on developmental progression.

Importantly, complementation decreased the growth rate.

Yes, since the c-di-AMP levels breached the “EB threshold” at 16hpi, it causes premature transition to EBs, which do not replicate their gDNA, at an earlier stage of the cycle when fewer organisms are present. Therefore, the gDNA levels are decreased at 24hpi, which is consistent with our model.

Based on the proposed model, growth rate should increase as the chlamydia should all be RBs and replicating and not exiting the cell cycle to become EBs (not replicating).

This is a spurious conclusion from the reviewer. As we clearly showed, the dacA-KDcom did not restore a wild-type phenotype and instead mimicked the dacAop OE strain. This was commented on in the text.

Interestingly reducing cdiAMP levels by over expressing DacAmut (~256 pg/ml) did not have an effect on the cycle but the reduction in cdiAMP by knockdown of dacA (~300 pg/ml) did have a moderate effect on the cycle. 

This is again a spurious conclusion from the reviewer. The dacAMut and dacA-KD strains are distinct. As noted in the text and above for DacA WT OE, overexpressing the DacAMut similarly disrupts organism morphology, which is different from dacA-KD. These strains should not be directly compared because of this. This point has been previously highlighted in the text (in Results and Discussion).

For Figure 5 DacA-ybbRop was overexpressed and this increased cdiAMP dramatically ~500,000 pg/ml as compared to wt ~1500. This increased hctA only at an early timepoint and not at 24hpi and again had no effect on omcB or euo.

As we explained in prior reviews, our RNAseq data more comprehensively assessed transcripts for the dacAop OE strain. These data show convincingly that late gene transcripts (not just hctA and omcB) are elevated earlier in the developmental cycle. Again, it is not clear why the reviewer should expect that late gene transcripts should be higher in these strains than they are during a normal developmental cycle. This is not part of our model and appears to be a bias that the reviewer has imposed that is not supported by the literature.

Overexpression of the operon with the mutation DacA-ybbRopmut reduced cdiAMP to ~300 pg/ml and this showed a reduction in growth rate similar to dacAmut but a more dramatic decrease in IFUs. 

As we described in the text, in earlier revisions, and above, the dacAMut OE strain has distinct effects unrelated to c-di-AMP levels and, therefore, should not be compared to other strains in terms of linking its c-di-AMP levels to its phenotype.

Overall: 

DacA overexpression increases cdiAMP to ~4000 pg/ml (decreased everything except euo) 

DacAmut overexpression reduces cdiAMP dramatically (~256 pg/ml). (decreased everything except euo) 

DacATM overexpression increases cdiAMP to ~4000 pg/ml (no changes noted) 

DacAmutTM overexpression does not seem to change cdiAMP ~1500 pg/ml (no changes noted) 

dacAKD decrease cdiAMP to ~300 pg/ml (decreased everything except euo) 

dacAKDcom increased cdiAMP to ~8000 pg/ml (decreases growth rate, increase hctA a little but not omcB) 

DacA-ybbRop overexpression increased cdiAMP to ~500,000 pg/ml (decreases growth rate, increase hctA a little but not omcB) <br /> DacA-ybbRopmut ~300 pg/ml (decreased everything except euo) 

Overall, the data show that increasing cdiAMP only has a phenotype if it is dramatically increased, no effect at 4000 pg/ml.

Yes, this clearly shows there is a threshold - as we hypothesize!  However, these thresholds are more important at the 16hpi timepoint not 24hpi (which the reviewer is referencing) when assessing premature transition to EBs.  We specifically highlighted in our prior revision in Figure 1E this EB threshold to make this point clearer for the reader.  Once the threshold is breached, then the overall c-di-AMP levels become irrelevant as the RBs have begun their transition to EBs.

Decreasing cdiAMP has a consistent effect, decreased growth rate, IFU, hctA expression and omcB expression. However, if their proposed model was correct and low levels of cdiAMP blocked EB conversion then more chlamydial cells would be RBs (dividing cells) and the growth rate should increase.

The only effect should be normal gDNA levels, which is what we see in the dacA-KD.  Given the asynchronicity of a normal developmental cycle in which RBs continue to replicate as EBs are still forming, there is no basis to assume gDNA levels should increase under these conditions for the dacA-KD strain at 24hpi.

Conversely, if cdiAMP levels were dramatically raised then all RBs would all convert and the growth rate would be very low.

We agree. This is what is reflected by the dacAop OE and dacA-KDcom strains, with reduced gDNA levels at 24hpi since organisms have transitioned to EBs at an earlier time post-infection.

When cdiAMP was raised to ~4000 pg/ml there was no effect on the growth rate.

Yes, because it had not breached the EB threshold at 16hpi – consistent with our model!  The reviewer is confusing effects of elevated c-di-AMP at 24hpi when they should be assessed at the 16hpi timepoint for strains overproducing this molecule.

However, an increase to ~8000 pg/ml resulted in a significant decrease but growth continued.

If the reviewer is referring to the dacA-KDcom strain, then this is not accurate. gDNA levels were decreased in this strain at 24hpi when the c-di-AMP levels were increased compared to the WT (mCherry OE) control at 16hpi, indicating this strain had breached the “EB threshold” and initiated conversion to EBs at an earlier timepoint post-infection when fewer organisms were present.

Increasing cdAMP to ~500,000 pg/ml had less of an impact on the growth rate.

It is not clear what this conclusion is based on and what the reviewer is comparing to.  This is a subjective assessment not based on our data.

Overall, the data does not cleanly support the proposed model.

It is an unfortunate aspect of biology, particularly for obligate intracellular bacteria – a challenging experimental system on which to work, that the data are not always “clean”.  The overall effects of increased c-di-AMP levels on chlamydial developmental cycle progression we have documented support our model, and we think the reader, as always, should make their own assessment.

The following is the authors’ response to the original reviews.

Reviewer #2 (Public review): 

This manuscript describes the role of the production of c-di-AMP on the chlamydial developmental cycle. The main findings remain the same. The authors show that overexpression of the dacA-ybbR operon results in increased production of c-di-AMP and early expression of transitionary and late genes. The authors also knocked down the expression of the dacA-ybbR operon and reported a modest reduction in the expression of both hctA and omcB. The authors conclude with a model suggesting the amount of c-di-AMP determines the fate of the RB, continued replication, or EB conversion. 

Overall, this is a very intriguing study with important implications however, the data is very preliminary, and the model is very rudimentary. The data support the observation that dramatically increased c-di-AMP has an impact on transitionary gene expression and late gene expression suggesting dysregulation of the developmental cycle. This effect goes away with modest changes in c-di-AMP (detaTM-DacA vs detaTM-DacA (D164N)). However, the model predicts that low levels of c-di-AMP delays EB production is not not well supported by the data. If this prediction were true then the growth rate would increase with c-di-AMP reduction and the data does not show this.

Thank you for the comments. We have apparently not adequately communicated our predictions and the model. We do not think and nor do we predict that low c-di-AMP levels should increase growth rate, and there is no basis in any of our data to support that. Rather, we predict that the inability to accumulate c-di-AMP should delay production of EBs, and this is what the data show. We have clarified this in the text (line 89 paragraph).

The levels of c-di-AMP at the lower levels need to be better validated as it seems like only very high levels make a difference for dysregulated late gene expression. However, on the low end it's not clear what levels are needed to have an effect as only DacAopMut and DacAopKD show any effects on the cycle and the c-di-AMP levels are only different at 24 hours.

Our hypothesis is that increasing concentrations of c-di-AMP within a given RB is a signal for it to undergo secondary differentiation to the EB, and the data support this as noted by the reviewers. Again, we stress that low levels of c-di-AMP are irrelevant to the model. We have revised Figure 1E to indicate the level of c-di-AMP in the control strain at the 24hpi timepoint that coincides with increased EB levels. We hope this will further clarify the goals of our study. That a given strain might be below the EB control is not relevant to the model beyond indicating that it has not reached the necessary threshold for triggering secondary differentiation.

The authors responded to reviewers' critiques by adding the overexpression of DacA without the transmembrane region. This addition does not really help their case. They show that detaTM-DacA and detaTM-DacA (D164N) had the same effects on c-di-AMP levels but the figure shows no effects on the developmental cycle.

As it relates directly to the reviewer’s point, the delta-TM strains did not show the same level of c-di-AMP. It may be that the reviewer misread the graph. The purpose of testing these strains was to show that the negative effects of overexpressing full-length WT DacA were due to its membrane localization. Both the FL and deltaTM-DacA (WT) overexpression had equivalent c-di-AMP levels even though the delta-TM overexpression looked like the mCherry-expressing strain based on the measured parameters. This shows that the c-di-AMP levels were irrelevant to the phenotypes observed when overexpressing these WT isoforms. For the mutant isoforms, the delta-TM looked like the mCherry-expressing control while the FL isoform was negatively impacted for reasons we described in the Discussion (e.g., dominant negative effect). In addition, at 16hpi, neither delta-TM strain had c-di-AMP levels that approached the 24h control as denoted in Figure 1E (dashed line) and in the text, which explains why these strains did not show increased late gene transcripts at an earlier timepoint like the dacAop and dacA-KDcom strains.

Describing the significance of the findings: 

The findings are important and point to very exciting new avenues to explore the important questions in chlamydial cell form development. The authors present a model that is not quantified and does not match the data well. 

We respectfully disagree with this assessment as noted above in response to the reviewer’s critique. All of our data are quantified and support the hypothesis as stated.

Describing the strength of evidence: 

The evidence presented is incomplete. The authors do a nice job of showing that overexpression of the dacA-ybbR operon increases c-di-AMP and that knockdown or overexpression of the catalytically dead DacA protein decreases the c-di-AMP levels. However, the effects on the developmental cycle and how they fit the proposed model are less well supported. 

Overall this is a very intriguing finding that will require more gene expression data, phenotypic characterization of cell forms, and better quantitative models to fully interpret these findings. 

It is not clear what quantitative models the reviewer would prefer, but, ultimately, it is up to the reader to decide whether they agree or not with the model we present. The data are the data, and we have tried to present them as clearly as possible. We would emphasize that, with the number of strains we have analyzed, we have presented a huge amount of data for a study with an obligate intracellular bacterium. As a comparison, most publications on Chlamydia might use a handful of transformant strains, if any. Given the cost and time associated with performing such studies, it is prohibitive to attempt all the time points that one might like to do, and it is not clear to us that further studies will add to or alter the conclusions of the current manuscript.

Reviewer #2 (Recommendations for the authors): 

Minor critiques 

The graphs have red and blue lines but the figure legends are red and black. It would be better if these matched. 

Changed.

For Figure 1C. The labels are not very helpful. It's not clear what is HeLa vs mCherry. I believe it is uninfected vs Chlamydia infected.

Changed.

WIr müssen diskutieren, ob Establishment wirklich teil von Employers and employeessein soll, oder ob wir das als eigenen Daummy kodieren und dafür Employers and employees in Collective agreements zurückbenennen.

Exploratory kind of reasoning - does it ever emerge? Why are most cohorts either silent or coming up with inadequate ideas?

eLife Assessment

This valuable study revisits the effects of substitution model selection on phylogenetics by comparing reversible and non-reversible DNA substitution models. The authors provide solid evidence that 1) it can be beneficial to include non-time-reversible models in addition to general time-reversible models when inferring phylogenetic trees out of simulated viral genome sequence data sets, and that 2) non time-reversible models may fit the real data better than the reversible substitution models commonly used in phylogenetics, a finding consistent with previous work.

Reviewer #1 (Public review):

Summary:

This is a contribution to the field of developmental bioelectricity. How do changes of resting potential at the cell membrane affect downstream processes? Zhou et al. reported in 2015 that phosphatidylserine and K-Ras cluster upon plasma membrane depolarization and that voltage-dependent ERK activation occurs when constitutively active K-RasG12V mutants are overexpressed. In this paper, the authors advance the knowledge of this phenomenon by showing that membrane depolarization up-regulates mitosis and that this process is dependent on voltage-dependent activation of ERK. ERK activity's voltage-dependence is derived from changes in the dynamics of phosphatidylserine in the plasma membrane and not by extracellular calcium dynamics. This paper reports an interesting and important finding. It is somewhat derivative of Zhou et al., 2015. (https://www.science.org/doi/full/10.1126/science.aaa5619). The main novelty seems to be that they find quantitatively different conclusions upon conducting similar experiments, albeit with a different cell line (U2OS) than those used by Zhou et al. Sasaki et al. do show that increased K+ levels increase proliferation, which Zhou et al. did not look at. The data presented in this paper are a useful contribution to a field often lacking such data.

Strengths:

Bioelectricity is an important field for areas of cell, developmental, and evolutionary biology, as well as for biomedicine. Confirmation of ERK as a transduction mechanism and a characterization of the molecular details involved in the control of cell proliferation are interesting and impactful.

Weaknesses:

The authors lean heavily on the assumption that the Nernst equation is an accurate predictor of membrane potential based on K+ level. This is a large oversimplification that undermines the author's conclusions, most glaringly in Figure 2C. The author's conclusions should be weakened to reflect that the activity of voltage gated ion channels and homeostatic compensation are unaccounted for.

There are grammatical tense errors are made throughout the paper (ex line 99 "This kinetics should be these kinetics")

Line 71: Zhou et al. use BHK, N2A, PSA-3 cells, this paper uses U2OS (osteosarcoma) cells. Could that explain the differences in bioelectric properties that they describe? In general, there should be more discussion of the choice of cell line. Why were U2OS cells chosen? What are the implications of the fact that these are cancer cells, and bone cancer cells in particular? Does this paper provide specific insights for bone cancers? And crucially, how applicable are findings from these cells to other contexts?

Line 115: The authors use EGF to calibrate 'maximal' ERK stimulation. Is this level near saturation? Either way is fine, but it would be useful to clarify.

Line 121: Starting line 121 the authors say "Of note, U2OS cells expressed wild-type K-Ras but not an active mutant of K-Ras, which means voltage dependent ERK activation occurs not only in tumor cells but also in normal cells". Given that U2OS cells are bone sarcoma cells, is it appropriate to refer to these as 'normal' cells in contrast to 'tumor' cells?

Line 101: These normalizations seem reasonable, the conclusions sufficiently supported and the requisite assumptions clearly presented. Because the dish-to-dish and cell-to-cell variation may reflect biologically relevant phenomena it would be ideal if non-normalized data could be added in supplemental data where feasible.

Figure 2C is listed as Figure 2D in the text

There is no Figure 2F (Referenced in line 148)

Reviewer #2 (Public review):

Sasaki et al. use a combination of live-cell biosensors and patch-clamp electrophysiology to investigate the effect of membrane potential on the ERK MAPK signaling pathway, and probe associated effects on proliferation. This is an effect that has long been proposed, but a convincing demonstration has remained elusive, because it is difficult to perturb membrane potential without disturbing other aspects of cell physiology in complex ways. The time-resolved measurements here are a nice contribution to this question, and the perforated patch clamp experiments with an ERK biosensor are fantastic - they come closer to addressing the above difficulty of perturbing voltage than any prior work. It would have been difficult to obtain these observations with any other combination of tools.

However, there are still some concerns as detailed in specific comments below:

Specific comments:

(1) All the observations of ERK activation, by both high extracellular K+ and voltage clamp, could be explained by cell volume increase (more discussion in subsequent comments). There is a substantial literature on ERK activation by hypotonic cell swelling (e.g. https://doi.org/10.1042/bj3090013, https://doi.org/10.1002/j.1460-2075.1996.tb00938.x, among others). Here are some possible observations that could demonstrate that ERK activation by volume change is distinct from the effects reported here:

i) Does hypotonic shock activate ERK in U2OS cells?

ii) Can hypotonic shock activate ERK even after PS depletion, whereas extracellular K+ cannot?

iii) Does high extracellular K+ change cell volume in U2OS cells, measured via an accurate method such as fluorescence exclusion microscopy?

iv) It would be helpful to check the osmolality of all the extracellular solutions, even though they were nominally targeted to be iso-osmotic.

(2) Some more details about the experimental design and the results are needed from Figure 1:

i) For how long are the cells serum-starved? From the Methods section, it seems like the G1 release in different K+ concentration is done without serum, is this correct? Is the prior thymidine treatment also performed in the absence of serum?

ii) There is a question of whether depolarization constitutes a physiologically relevant mechanism to regulate proliferation, and how depolarization interacts with other extracellular signals that might be present in an in vivo context. Does depolarization only promote proliferation after extended serum starvation (in what is presumably a stressed cell state)? What fraction of total cells are observed to be mitotic (without normalization), and how does this compare to the proliferation of these cells growing in serum-supplemented media? Can K+ concentration tune proliferation rate even in serum-supplemented media?

(3) In Figure 2, there are some possible concerns with the perfusion experiment:

i) Is the buffer static in the period before perfusion with high K+, or is it perfused? This is not clear from the Methods. If it is static, how does the ERK activity change when perfused with 5 mM K+? In other words, how much of the response is due to flow/media exchange versus change in K+ concentration?

ii) Why do there appear to be population-average decreases in ERK activity in the period before perfusion with high K+ (especially in contrast to Fig. 3)? The imaging period does not seem frequent enough for photobleaching to be significant.

(4) Figure 3 contains important results on couplings between membrane potential and MAPK signaling. However, there are a few concerns:

i) Does cell volume change upon voltage clamping? Previous authors have shown that depolarizing voltage clamp can cause cells to swell, at least in the whole-cell configuration:

https://www.cell.com/biophysj/fulltext/S0006-3495(18)30441-7 . Could it be possible that the clamping protocol induces changes in ERK signaling due to changes in cell volume, and not by an independent mechanism?

ii) Does the -80 mV clamp begin at time 0 minutes? If so, one might expect a transient decrease in sensor FRET ratio, depending on the original resting potential of the cells. Typical estimates for resting potential in HEK293 cells range from -40 mV to -15 mV, which would reach the range that induces an ERK response by depolarizing clamp in Fig. 3B. What are the resting potentials of the cells before they are clamped to -80 mV, and why do we not see this downward transient?

(5) The activation of ERK by perforated voltage clamp and by high extracellular K+ are each convincing, but it is unclear whether they need to act purely through the same mechanism - while additional extracellular K+ does depolarize the cell, it could also be affecting function of voltage-independent transporters and cell volume regulatory mechanisms on the timescales studied. To more strongly show this, the following should be done with the HEK cells where there is already voltage clamp data:

i) Measure resting potential using the perforated patch in zero-current configuration in the high K+ medium. Ideally this should be done in the time window after high K+ addition where ERK activation is observed (10-20 minutes) to minimize the possibility of drift due to changes in transporter and channel activity due to post-translational regulation.

ii) Measure YFP/CFP ratio of the HEK cells in the high K+ medium (in contrast to the U2OS cells from Fig. 2 where there is no patch data).

iii) The assertion that high K+ is equivalent to changes in Vmem for ERK signaling would be supported if the YFP/CFP change from K+ addition is comparable to that induced by voltage clamp to the same potential. This would be particularly convincing if the experiment could be done with each of the 15 mM, 30 mM, and 145 mM conditions.

(6) Line 170: "ERK activity was reduced with a fast time course (within 1 minute) after repolarization to -80 mV." I don't see this in the data: in Fig. 3C, it looks like ERK remains elevated for > 10 min after the electrical stimulus has returned to -80 mV

Comments on revisions:

The authors have done a good job addressing the comments on the previous submission.

Reviewer #3 (Public review):

Summary:

This paper demonstrates that membrane depolarization induces a small increase in cell entry into mitosis. Based on previous work from another lab, the authors propose that ERK activation might be involved. They show convincingly using a combination of assays that ERK is activated by membrane depolarization. They show this is Ca2+ independent and is a result of activation of the whole K-Ras/ERK cascade which results from changed dynamics of phosphatidylserine in the plasma membrane that activates K-Ras. Although the activation of the Ras/ERK pathway by membrane depolarization is not new, linking it to an increase in cell proliferation is novel.

Strengths

A major strength of the study is the use of different techniques - live imaging with ERK reporters, as well as Western blotting to demonstrate ERK activation as well as different methods for inducing membrane depolarization. They also use a number of different cell lines. Via Western blotting the authors are also able to show that the whole MAPK cascade is activated.

Weaknesses

A weakness of the study is the data in Figure 1 showing that membrane depolarization results in an increase of cells entering mitosis. There are very few cells entering mitosis in their sample in any condition. This should be done with many more cells to increase the confidence in the results. The study also lacks a mechanistic link between ERK activation by membrane depolarization and increased cell proliferation.

The authors did achieve their aims with the caveat that the cell proliferation results could be strengthened. The results, for the most par,t support the conclusions.

This work suggests that alterations in membrane potential may have more physiological functions than action potential in the neural system as it has an effect on intracellular signalling and potentially cell proliferation.

In the revised manuscript, the authors have now addressed the issues with Figure 1, and the data presented are much clearer. They did also attempt to pinpoint when in the cell cycle ERK is having its activity, but unfortunately, this was not conclusive.

Author response:

The following is the authors’ response to the original reviews.

Reviewer #1 (Public review):

Summary:

This is a contribution to the field of developmental bioelectricity. How do changes of resting potential at the cell membrane affect downstream processes? Zhou et al. reported in 2015 that phosphatidylserine and K-Ras cluster upon plasma membrane depolarization and that voltage-dependent ERK activation occurs when constitutive active K-RasG12V mutants are overexpressed. In this paper, the authors advance the knowledge of this phenomenon by showing that membrane depolarization up-regulates mitosis and that this process is dependent on voltage-dependent activation of ERK. ERK activity's voltage-dependence is derived from changes in the dynamics of phosphatidylserine in the plasma membrane and not by extracellular calcium dynamics.

Strengths:

Bioelectricity is an important field for areas of cell, developmental, and evolutionary biology, as well as for biomedicine. Confirmation of ERK as a transduction mechanism, and a characterization of the molecular details involved in control of cell proliferation, is interesting and impactful.

Weaknesses:

The functional cell division data need to be stronger. They show that increasing K+ increases proliferation and argue that since a MEK inhibitor (U0126) reduces proliferation in K+ treated cells, K+ induces cell division via ERK. But I don't see statistics to show that the rescue is significant, and I don't see a key U0126-only control. If the U0126 alone reduces proliferation, the combined effect wouldn't prove much.

We thank the reviewer for constructive feedback. We repeated the experiment including the U0126-only control (5K+U). We updated Fig.1, presenting the newly obtained data with statistical analysis.

Also, unless I'm missing something, it looks like every sample in their control has exactly the same number of mitotic cells. I understand that they are normalizing to this column, but shouldn't they be normalizing to the mean, with the independent values scattering around 1? It doesn't seem like it can be paired replicates since there are 6 replicates in the control and 4 replicates in one of the conditions? 

We apologize for the unclear description. As the reviewer pointed out, the experiments were not paired replicates due to the limited number of conditions that can be conducted as a single experiment. To overcome this problem, we always included a control condition (i.e. 5K) based on which normalization was performed. This is the reason the data in 5K is always 1 and the sample size of 5K is the largest. Data include 100-900 mitotic cells within the imaging frame of 6 hrs. We re-wrote the figure legend (Fig1) and the main text, which hopefully clarified our experimental framework.

Reviewer #2 (Public review):

Sasaki et al. use a combination of live-cell biosensors and patch-clamp electrophysiology to investigate the effect of membrane potential on the ERK MAPK signaling pathway, and probe associated effects on proliferation. This is an effect that has long been proposed, but convincing demonstration has remained elusive, because it is difficult to perturb membrane potential without disturbing other aspects of cell physiology in complex ways. The time-resolved measurements here are a nice contribution to this question, and the perforated patch clamp experiments with an ERK biosensor are fantastic - they come closer to addressing the above difficulty of perturbing voltage than any prior work. It would have been difficult to obtain these observations with any other combination of tools.

However, there are still some concerns as detailed in specific comments below:

Specific comments:

(1) All the observations of ERK activation, by both high extracellular K+ and voltage clamp, could be explained by cell volume increase (more discussion in subsequent comments). There is a substantial literature on ERK activation by hypotonic cell swelling (e.g. https://doi.org/10.1042/bj3090013, https://doi.org/10.1002/j.1460-2075.1996.tb00938.x, among others). Here are some possible observations that could demonstrate that ERK activation by volume change is distinct from the effects reported here:

(i) Does hypotonic shock activate ERK in U2OS cells?

(ii) Can hypotonic shock activate ERK even after PS depletion, whereas extracellular K+ cannot?

(iii) Does high extracellular K+ change cell volume in U2OS cells, measured via an accurate method such as fluorescence exclusion microscopy?

(iv) It would be helpful to check the osmolality of all the extracellular solutions, even though they were nominally targeted to be iso-osmotic.

This is an important point. We conducted several experiments and provided explanations to rule out the possibility that ERK activation can be explained solely by cell volume change. We measured the osmolarity of all solutions used in this paper, which were 296-305 mOsm/L. This information was added to the Material and Methods section (line 387). Under our experimental conditions, ERK activation was not observed with hypotonic 70 % nor 50% osmolarity solution (Fig.S2).

It is therefore unlikely that the main cause of ERK activation upon high K⁺ perfusion is due to cell volume change. We would like to pursue this issue further when we obtain capacity to measure accurate cell volume change in the future.

(2) Some more details about the experimental design and the results are needed from Figure 1:

(i) For how long are the cells serum-starved? From the Methods section, it seems like the G1 release in different K+ concentration is done without serum, is this correct? Is the prior thymidine treatment also performed in the absence of serum?

Only the high K⁺ incubation phase was serum free. We added the following sentence in the main text (line 63) and an experimental diagram was added as Fig1A. “Cells were incubated in the presence of serum except for the phase with altered K⁺ concentration. “

(ii) There is a question of whether depolarization constitutes a physiologically relevant mechanism to regulate proliferation, and how depolarization interacts with other extracellular signals that might be present in an in vivo context.

This is a very important point. However, the significance of membrane depolarization for cell proliferation in vivo is beyond the scope of this study. This important question will be addressed in the future.

Does depolarization only promote proliferation after extended serum starvation (in what is presumably a stressed cell state)?

Cells were cultured in the presence of serum prior to the high K⁺ incubation phase as described above. We added a new figure (Fig1A).

What fraction of total cells are observed to be mitotic (without normalization), and how does this compare to the proliferation of these cells growing in serum-supplemented media? Can K+ concentration tune proliferation rate even in serum-supplemented media?

We included data recorded in serum-supplemented conditions (Fig.1), which showed a high mitotic rate. This is presumably due to the growth factors included in serum. There is no significant difference between 5K+FBS and 15K+FBS.

(3) In Figure 2, there are some possible concerns with the perfusion experiment:

(i) Is the buffer static in the period before perfusion with high K+, or is it perfused? This is not clear from the Methods. If it is static, how does the ERK activity change when perfused with 5 mM K+? In other words, how much of the response is due to flow/media exchange versus change in K+ concentration?

The buffer was static prior to high K perfusion. We confirmed that perfusion alone does not activate ERK (Fig.S2). We added the following sentence to the main text. “We also confirmed that the effect of perfusion was negligible, as ERK activation was not observed upon start of the 5K⁺ perfusion” (line 150).

(ii) Why do there appear to be population-average decreases in ERK activity in the period before perfusion with high K+ (especially in contrast to Fig. 3)? The imaging period does not seem frequent enough for photo bleaching to be significant.

Although we don’ t have a clear answer to this question, we speculate that several aspects of the experimental setup may have contributed to the difference. The cell lines and imaging systems used in Fig.2 and Fig.3 were different. The expression level may be different between U2OS cells and HEK 293 cells: transient expression in U2OS cells in contrast to stable expression in HEK 293 cells. This difference may lead to the different signal-to-noise ratio. The imaging system used in Fig.2 is an epi-illumination microscope excited with a 439/24 bandpass filter and detected with 483/32 (CFP) and 542/27 (YFP), while the imaging system used in Fig.3 is a confocal microscope excited with 458 nm laser and detected with 475-525 (DFP) and LP530 (YFP). These optical setups may also contribute to the different population-average properties before stimulation.

(4) Figure 3 contains important results on couplings between membrane potential and MAPK signaling. However, there are a few concerns:

(i) Does cell volume change upon voltage clamping? Previous authors have shown that depolarizing voltage clamp can cause cells to swell, at least in the whole-cell configuration: https://www.cell.com/biophysj/fulltext/S0006-3495(18)30441-7 . Could it be possible that the clamping protocol induces changes in ERK signaling due to changes in cell volume, and not by an independent mechanism?

We do not know whether cell volume is altered in the perforated-patch configuration. As discussed above, however, the effect of cell volume changes on ERK activity seemed to be negligible, because ERK activation was not observed with hypotonic 70 % nor 50% osmolarity solution (Fig.S2)

(ii) Does the -80 mV clamp begin at time 0 minutes? If so, one might expect a transient decrease in sensor FRET ratio, depending on the original resting potential of the cells. Typical estimates for resting potential in HEK293 cells range from -40 mV to -15 mV, which would reach the range that induces an ERK response by depolarizing clamp in Fig. 3B. What are the resting potentials of the cells before they are clamped to -80 mV, and why do we not see this downward transient?

We set the potential to -80mV immediately after the giga-seal formation and waited for at least 5 minutes to allow pore formation by gramicidin. We started imaging only after membrane potential was expected to have reached a steady state at -80 mV. We now included this sentence in the ‘Material and Methods’ section (line 398).

(5) The activation of ERK by perforated voltage clamp and by high extracellular K+ are each convincing, but it is unclear whether they need to act purely through the same mechanism - while additional extracellular K+ does depolarize the cell, it could also be affecting function of voltage-independent transporters and cell volume regulatory mechanisms on the timescales studied. To more strongly show this, the following should be done with the HEK cells where there is already voltage clamp data:

(i) Measure resting potential using the perforated patch in zero-current configuration in the high K+ medium. Ideally this should be done in the time window after high K+ addition where ERK activation is observed (10-20 minutes) to minimize the possibility of drift due to changes in transporter and channel activity due to post-translational regulation.

We measured membrane potential in the perforated patch configuration and confirmed that there is negligible potential drift within 20 minutes of perfusion with 145 K+ (only 1~5 mV change during perfusion).

(ii) Measure YFP/CFP ratio of the HEK cells in the high K+ medium (in contrast to the U2OS cells from Fig. 2 where there is no patch data).

YFP/CFP ratio data in HEK cells are shown in Fig.S1. As the signal-to-noise level is affected by the expression level of the probe, it is difficult to compare between cells with different expression levels. A higher YFP/CFP value with HEK cells compared to HeLa cells and A431 cells (Sup1) does not necessarily mean that HEK cells have higher ERK activity.

(iii) The assertion that high K+ is equivalent to changes in Vmem for ERK signaling would be supported if the YFP/CFP change from K+ addition is comparable to that induced by voltage clamp to the same potential. This would be particularly convincing if the experiment could be done with each of the 15 mM, 30 mM, and 145 mM conditions.

The experimental system using fluorescent biosensor cannot measure absolute ERK activity and can only measure the amount of change after a specific stimulus compared to the period before the stimulus. In electrophysiology experiments, the pre-stimulation membrane potential was clamped to -80 mV, whereas in the perfusion experiment, the membrane potential was variable in individual cells (-35 to -15 mV). It is therefore difficult to compare the results of electrophysiology experiments with those of the perfusion system. Unlike ion channels, it is currently not possible to plot absolute ERK activity with respect to the overall membrane potential. In the present study, we therefore discussed the change rather than the absolute value of ERK activity.

(6) Line 170: "ERK activity was reduced with a fast time course (within 1 minute) after repolarization to -80 mV." I don't see this in the data: in Fig. 3C, it looks like ERK remains elevated for > 10 min after the electrical stimulus has returned to -80 mV

Thank you for pointing out that our description was confusing. We changed the sentence to clarify the point we wanted to make. It now reads as follows. “ERK activity showed signs of reduction within 1 minute after repolarization to -80 mV.” (line 174)

Reviewer #3 (Public review):

Summary:

This paper demonstrates that membrane depolarization induces a small increase in cell entry into mitosis. Based on previous work from another lab, the authors propose that ERK activation might be involved. They show convincingly using a combination of assays that ERK is activated by membrane depolarization. They show this is Ca2+ independent and is a result of activation of the whole K-Ras/ERK cascade which results from changed dynamics of phosphatidylserine in the plasma membrane that activates K-Ras. Although the activation of the Ras/ERK pathway by membrane depolarization is not new, linking it to an increase in cell proliferation is novel.

Strengths

A major strength of the study is the use of different techniques - live imaging with ERK reporters, as well as Western blotting to demonstrate ERK activation as well as different methods for inducing membrane depolarization. They also use a number of different cell lines. Via Western blotting the authors are also able to show that the whole MAPK cascade is activated.

Weaknesses

A weakness of the study is the data in Figure 1 showing that membrane depolarization results in an increase of cells entering mitosis. There are very few cells entering mitosis in their sample in any condition. This should be done with many more cells to increase confidence in the results.

We apologize that that description was not clear. Due to the limited number of conditions that can be conducted as a single experiment, we always included control condition (i.e. 5K) and performed normalization by comparing with the control condition of the initial 1.5 hrs. Data were from 100-900 mitotic cell counts within 6hr of the imaging time window. We re-wrote the figure legend (Fig1) and the main text.

The study also lacks a mechanistic link between ERK activation by membrane depolarization and increased cell proliferation.

The present study focused on the link between membrane potential and the ERK activity; the mechanistic link between ERK activity and cell proliferation is beyond the scope of the present study. This important topic will be pursued further in subsequent studies.

The authors did achieve their aims with the caveat that the cell proliferation results could be strengthened. The results for the most part support the conclusions.

This work suggests that alterations in membrane potential may have more physiological functions than action potential in the neural system as it has an effect on intracellular signalling and potentially cell proliferation.

Reviewer #1 (Recommendations for the authors):

minor typo:

ERK activity has voltage-dependency with the physiological rang of membrane potential should be "range"

Corrected

Reviewer #2 (Recommendations for the authors):

Small points:

Line 82: rang -> range

Corrected

Line 102: ". they were stimulated" -> ". The cells were stimulated"

Corrected

Figs. 2C, 2D show exactly the same data points and the same information. Please cut one of these figures.

We deleted 2C and added the information in 2D and made new Fig.2C.

For all figs: Please indicate # of cells and # of independent dishes used in each experiment, and make clear whether individual data-points correspond to cells, dishes, or some other unit of measure.

We added the information in figure legends.

Reviewer #3 (Recommendations for the authors):

The authors should repeat the cell proliferation experiments with more cells to strengthen the data. They could also use alternative assays like phosphorylated histone H3 staining for cells in M phase, that might to easier to quantitate.

We repeated the experiment and Fig.1 was replaced with the new Fig.1

The authors should investigate how the upregulation of ERK is driving cells into mitosis. At what point in the cell cycle is activated ERK induced by membrane depolarization having the effect. Is it entry into mitosis or earlier in the cell cycle?

The cells were incubated with a high K+ solution 8-9 hr after G1 release, which is supposed to correspond to G2. These data suggest that mitotic activity is stimulated when ERK is activated at G2. However, we lack conclusive data at present to show the consequence of ERK activation during G2. We therefore cannot pinpoint the stage of cell cycle where depolarization-activated ERK exerts its effect.

The authors refer a lot to the work of Zhou et al 2015 throughout the paper. This is not necessary and is a bit distracting.

We deleted several sentence from the manuscript.

eLife Assessment

This useful paper presents evidence from several experimental approaches that suggest that changes in membrane potential directly affect ERK signaling to regulate cell division. This result is relevant because it supports an ion channel-independent pathway by which changes in membrane voltage can affect cell growth. The reviewers point out that while some experimental results and interpretations are compelling, the strength of evidence is still incomplete and changes to the manuscript are needed to rule out other possible interpretations of the data.

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does he mean, its more for the experience rather than gaining / obtaining something?

I feel like this suggests that gaining a new perspective can open the door to seeing humanity as whole and unified, even while remaining mysterious.

Delta Phenomenon?

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eLife Assessment

This is a fundamental study providing molecular insight into how cross-talk between histone modifications regulates the histone H3K36 methyltransferase SETD2. The manuscript contains excellent quality data, and the conclusions are convincing and justified. This work will be of interest to many biochemists working in the field of chromatin biology and epigenetics.

Reviewer #1 (Public review):

Summary:

In this manuscript, Mack and colleagues investigate the role of posttranslational modifications, including lysine acetylation and ubiquitination, in methyltransferase activity of SETD2 and show that this enzyme functions as a tumor suppressor in a KRASG12C-driven lung adenocarcinoma. In contrast to H3K36me2-specific oncogenic methyltransferases, the deletion of SETD2, which is capable of H3K36 trimethylation, increases lethality in a KRASG12C-driven lung adenocarcinoma mouse tumor model. In vitro, the authors demonstrate that polyacetylation of histone H3, particularly of H3K27, H3K14 and H3K23, promotes the catalytic activity of SETD2, whereas ubiquitination of H2A and H2B has no effect.

Strengths:

Overall, this is a well-designed study that addresses an important biological question regarding the functioning of the essential chromatin component. The manuscript contains excellent quality data, and the conclusions are convincing and justified. This work will be of interest to many biochemists working in the field of chromatin biology and epigenetics.

Comments on revisions:

All previous comments are well addressed, and I enthusiastically support publication.

Reviewer #2 (Public review):

Summary:

Human histone H3K36 methyltransferase Setd2 has been previously shown to be a tumor suppressor in lung and pancreatic cancer. In this manuscript by Mack et al., the authors first use a mouse KRASG12D-driven lung cancer model to confirm in vivo that Setd2 depletion exacerbates tumorigenesis. They then investigate the enzymatic regulation of the Setd2 SET domain in vitro, demonstrating that H2A, H3, or H4 acetylation stimulates Setd2-SET activity, with specific enhancement by mono-acetylation at H3K14ac or H3K27ac. In contrast, histone ubiquitination has no effect. The authors propose that H3K27ac may regulate Setd2-SET activity by facilitating its binding to nucleosomes. This work provides insight into how cross-talk between histone modifications regulates Setd2 function.

Comments on revisions:

(1) Regarding New Figure 2F lane 1, please reference PMID: 33972509 Fig 4D bottom. Setd2-SET is a well-known robust K36 trimethylase. Why, under the authors' conditions, do WT nucleosomes show a significant amount of K36me1 and K36me2 accumulation, whereas K36me3 is not as pronounced? As a comparison, the authors should also report the evidence for the efficiency of each chemical modification that generates K36 methylation mimic.

(2) The bottom panel of Figure 2B does not match the top one; the number of repeats should be indicated in the figure legends.

(3) In Figure 4E, the differences between Setd2-bound WT and acetylated nucleosomes are minimal, as judged by both the decreasing trend of unbound nucleosomes and the increasing trend of bound fractions. This experiment needs to be quantified based on multiple repeats.

Author response:

The following is the authors’ response to the original reviews.

Reviewer #1 (Public review):

(1) Labels should be added in the Figures and should be uniform across all Figures (some are distorted).

We thank the Reviewer for pointing out this issue. As requested, labels have been edited to ensure they are legible and are consistent in font, size, and style.  

Reviewer #2 (Public review):

(1) As for Figure 2F, Setd2-SET activity on WT rNuc (H3) appears to be significantly lower compared to what is extensively reported in the literature. This is particularly puzzling given that Figure 2B suggests that using 3H-SAM, H3-nuc are much better substrates than K36me1, whereas in Figure 3F, rH3 is weaker than K36me1. It is recommended for the authors to perform additional experimental repeats and include a quantitative analysis to ensure the consistency and reliability of these findings.  

We appreciate the Reviewer’s points. We respectfully suggest that these comments may reflect potential confusion around interpreting how different assays detect in vitro methylation, what data can and cannot be compared, and the nature of the different substrates used. 

With respect to point 1 (Western signal significantly lower compared to extensive literature): To the best of our knowledge, it would be extremely challenging to make a quantitative argument comparing the strength of the Western signal in Figure 2F with results reported in the literature. Specifically, comparing our results with previous studies would require (1) all the studies to have used the exact same antibodies as antibody signal intensities vary depending on the specific activity and selectively of a particular antibody and even its lot number, (2) similar in vitro methylation reaction condition, (3) the same type of recombinant nucleosomes used, and so on. Further, given that these are Western blots, we do not understand how one could interpret an absolute activity level. In the figure, all we can conclude is that in in vitro methylation reactions, our recombinant SETD2 protein methylates rNucs to generate mono-, di-, and tri-methylation at K36 (using vetted antibodies (see Fig. 2e)). If there is a specific paper within the extensive literature that the Reviewer highlights, we could look more into the details of why the signals are different (our guess is that any difference would largely be due to the use of different antibodies). We add that it might be challenging to find a similar experiment performed in the literature; we are not aware of a similar experiment. 

With respect to comparing Figure 2B and 2F: We do not understand how one can meaningfully compare incorporation of radiolabeled SAM to antibody-based detection on film using an antibody against specific methyl states. In particular, regarding the question regarding comparing rH3 vs H3K36me1 nucleosomes, we point out that in using recombinant nucleosomes installed with native modifications (e.g. H3K36me1), in which the entire population of the starting material is mono-methylated, then naturally the Western signal with an anti-H3K36me1 antibody will be strong. In Fig. 2b, the assay is incorporation of radiolabeled methyl, which is added to the preexiting mono-methylated substrate. In other words, the results are entirely consistent if one understands how the methylation reactions were performed, how methylation was detected, and the nature of the reagents.

(2) The additional bands observed in Figure 4B, which appear to be H4, should be accompanied by quantification of the intensity of the H3 bands to better assess K36me3 activity. Additionally, the quantification presented in Figure 4C for SAH does not seem accurate as it potentially includes non-specific methylation activity, likely from H4. This needs to be addressed for clarity and accuracy. 

We thank the reviewer for this comment. The additional bands observed in Figure 4B represent degradation products of histone H3, not H4 methylation. This is commonly seen in in vitro reactions using recombinant nucleosomes, where partial proteolysis of H3 can occur under the assay conditions.  

(3) In Figure 4E, the differences between bound and unbound substrates are not sufficiently pronounced. Given the modest differences observed, authors might want to consider repeating the assay with sufficient replicates to ensure the results are statistically robust.

In Figure 4E, we observe a clear difference between the bound and unbound substrate. To aid interpretation, we have clarified in the figure where the bound complex migrates on the gel, while the unbound nucleosomes migrate at the bottom of the gel. The differences are indeed subtle, which we highlight in the text.  

(4) Regarding labeling, there are multiple issues that need correction: In the depiction of Epicypher's dNuc, it is crucial to clearly mark H2B as the upper band, rather than ambiguously labeling H2A/H2B together when two distinct bands are evident. In Figure 3B and D, the histones appear to be mislabeled, and the band corresponding to H4 has been cut off. It would be beneficial to refer to Figure 3E for correct labeling to maintain consistency and accuracy across figures. 

Thank you for pointing this out. To avoid any confusion, we have delineated the H2B and H2A markers and indicate the band corresponding to H4.

(5) There are issues with the image quality in some blots; for instance, Figure 2EF and Figure 2D exhibit excessive contrast and pixelation, respectively. These issues could potentially obscure or misrepresent the data, and thus, adjustments in image processing are recommended to provide clearer, more accurate representations. 

Contrast adjustments were applied uniformly across each entire image and were not used to modify any specific region of the blot. We have corrected the issue of increased pixelation in Figure 2D. 

(6) The authors are recommended to provide detailed descriptions of the materials used, including catalog numbers and specific products, to allow for reproducibility and verification of experimental conditions. 

We have added the missing product specifications and catalog numbers to ensure clarity and reproducibility of the experiments.

(7) The identification of Setd2 as a tumor suppressor in KrasG12C-driven LUAD is a significant finding. However, the discussion on how this discovery could inspire future therapeutic approaches needs to be more balanced. The current discussion (Page 10) around the potential use of inhibitors is somewhat confusing and could benefit from a clearer explanation of how Setd2's role could be targeted therapeutically. It would be beneficial for the authors to explore both current and potential future strategies in a more structured manner, perhaps by delineating between direct inhibitors, pathway modulators, and other therapeutic modalities. 

SETD2 is a tumor suppressor in lung cancer (as we show here and many others have clearly established in the literature) and thus we would recommend avoiding a SETD2 inhibitor to treat solid tumors, as it could have a very much unwanted affect.  Our discussion addresses a different point regarding the relative importance of the enzymatic activity versus other, nonenzymatic functions of SETD2. We believe that a detailed exploration of the therapeutic potential of inhibiting SETD2 would be better suited in a review or a more therapy-focused manuscript.

eLife Assessment

This study identifies novel approaches to improving transgene expression in the injured mammalian myocardium through a combination of a tissue regeneration enhancer element and engineered AAVs - specifically, a liver-detargeting capsid, AAV.cc84, and an in vivo library screen-selected AAV-IR41. The evidence is convincing, and the AAV vectors are of fundamental value to the field of cardiac gene therapy. Future research exploring how to combine the features of AAV.cc84 and AAV-IR41 could yield an even more promising vector for therapeutic use.

Reviewer #1 (Public review):

In this manuscript, Wolfson and co-authors demonstrate a combination of an injury-specific enhancer and engineered AAV that enhances transgene expression in injured myocardium. The authors characterize spatiotemporal dynamics of TREE-directed AAV expression in the injured heart using a non-invasive longitudinal monitoring system. They show that transgene expression is drastically increased 3 days post-injury, driven by 2ankrd1a. They reported a liver-detargeted capsid, AAV cc.84, with decreased viral entry into the liver while maintaining TREE transgene specificity. They further identified the IR41 serotype with enhanced transgene expression in injured myocardium from AAV library screening. This is an interesting study that optimizes the potential application of TREE delivery for cardiac repair.

Comments on revisions:

The authors are responsive and have addressed my concerns.

Reviewer #2 (Public review):

Summary:

In this manuscript by Wolfson et al., various adeno-associated viruses (AAVs) were delivered to mice to assess the cardiac-specificity, injury border-zone cardiomyocyte transduction rate, and temporal dynamics in the goal to find better AAVs for gene therapies targeting the heart. The authors delivered tissue regeneration enhancer elements (TREEs) controlling luciferase expression and used IVIS imaging to examine transduction in the heart and other organs. They found that luciferase expression increased in the first week after injury when using AAV9-TREE-Hsp68 promoter, waning to baseline levels by 7 weeks. However, AAV9 vectors transduced the liver, which was significantly reduced by using an AAV.cc84 liver de-targeting capsid. The authors then performed in vivo screening of AAV9 capsids and found AAV-IR41 to preferentially transduce injured myocardium when compared to AAV9. Finally, the authors combined TREEs with AAV-IR41 to show improved luciferase expression compared to AAV9-TREE at 7, 14 and 21 days after injury.

Overall, this manuscript provides insights into TREE expression dynamics when paired with various heart-targeting capsids, which can be useful for researchers studying ischemic injury of murine hearts. While the authors have shown the success of using AAV9-TREEs in porcine hearts, it is unknown whether the expression dynamics would be similar in pigs or humans, as mentioned in the limitations.

Strengths:

Important contribution to the AAV gene therapy literature.

Comments on revised version:

My concerns have been adequately addressed.

Reviewer #3 (Public review):

Summary:

The tissue regeneration enhancer elements (TREEs) identified in zebrafish have been shown to drive injury-activated temporal-spatial gene expression in mice and large animals. These findings increase the translational potential of findings in zebrafish to mammals. In this manuscript, the authors tested TREEs in combination with different adeno-associated viral (AAV) vectors using in vivo luciferase bioluminescent imaging that allows for longitudinal tracking. The TREE-driven luciferase delivered by a liver de-targeted AAV.cc84 decreased off-target transduction in liver. They further screened an AAV library to identify capsid variants that display enhanced transduction for infarcted myocardium post ischemia reperfusion and myocardial infarction. A new capsid variant, AAV.IR41, was found to show increased transduction post I/R and MI.

Strengths:

The authors injected AAV-cargo several days after ischemia/reperfusion (I/R) injury as a clinically relevant approach. Overall, this study is significant in that it identifies new AAV vectors that can be used to deliver promising genes as potential new gene therapies in the future. The manuscript is well-written and the data are also of high quality.

Weaknesses:

The authors have addressed my previous concerns.

Author response:

The following is the authors’ response to the original reviews.

Reviewer #1 (Public review):

In this manuscript, Wolfson and co-authors demonstrate a combination of an injury-specific enhancer and engineered AAV that enhances transgene expression in injured myocardium. The authors characterize spatiotemporal dynamics of TREE-directed AAV expression in the injured heart using a non-invasive longitudinal monitoring system. They show that transgene expression is drastically increased 3 days post-injury, driven by 2ankrd1a. They reported a liver-detargeted capsid, AAV cc.84, with decreased viral entry into the liver while maintaining TREE transgene specificity. They further identified the IR41 serotype with enhanced transgene expression in injured myocardium from AAV library screening. This is an interesting study that optimizes the potential application of TREE delivery for cardiac repair. However, several concerns were raised prior to publication:

Major Concerns:

(1) In Figure 1, the authors demonstrated that 2andkrd1aEN is not responsive to sham injury after AAV delivery, but Figure 3 shows a strong response to sham when AAV is delivered after injury. The authors do not provide an explanation for this observation.

This discrepancy is due to the timing of AAV delivery. In Figure 1, AAV was delivered 60 days prior to IVIS imaging and cardiac injury, allowing time for the baseline level of AAV transgene expression to reach a plateau. From this baseline level, we were able to measure fold change in luminescence signal before and after cardiac injury. In Figure 3, AAV was delivered 4 days after cardiac injury. Luminescence in the heart was measured 3 days later (day 7), when the baseline of AAV transgene expression is still building. The data from Figure 1C-D inform us that the 2ankrd1aEN response to cardiac injury peaks within the first week and returns to baseline levels after 5-7 weeks. In Figure 3E, we show that 2ankrd2aEN provides a baseline level of expression that is present in sham hearts and reaches its plateau after 6 weeks. In contrast, I/R injured hearts show enhanced expression in the first 3-4 weeks, corresponding with the dynamics of 2ankrd1aEN’s response to injury observed in Figure 1C. We have now included a phrase in the revised manuscript on p. 7, paragraph 1 to clarify.

(2) In Figure 4, a higher GFP signal is observed in all areas of the heart of the IR41-treated mouse compared to AAV9. The authors should compare GFP expression between AAV9 and IR41 in uninjured hearts and provide insights into enhanced cardiac tropism to confirm that IR41 is MI injury enriched, not Sham as well.

We sought to address this question with the experiments presented in Figure 5. We treated sham mice with AAV9 and IR41 containing 2ankrd1aEN. Figure 5D showed IR41 delivered more vector genomes to the sham heart on average, though not with a p-value less than 0.05 compared with AAV9. In Supplemental Figure 5B, IR41 also provided higher luminescence at day 7 post-sham but was comparable at day 14 and day 21. These data suggest IR41 might increase heart tropism in healthy hearts, but IR41’s effect is most dramatic when delivered to injured hearts, where cardiac vector genomes are highest (Figure 5D). We have now included a sentence in the revised manuscript on p. 8, paragraph 2 to clarify.

(3) The authors should clarify which model is being used between myocardial infarction (MI) and Ischemia-reperfusion (IR) throughout the figures, as the experimental schemes and figure legends did not match with each other (MI or IR in Figure 1A, 1D, 3A, and 3E). Both models cause different types of injuries. The authors should explain the difference in TREE expression in both models.

We have revised the figures to specify the model, where I/R or MI is used.

(4) In Figure 2, the authors use REN instead of 2ankrd1aEN to demonstrate liver-detargeting using AAV cc.84. Is there a specific reason?

Our data in Figure 1 informed us that off-target liver expression is more specifically an issue for REN compared to 2ankrd1aEN. Baseline levels of luminescence in the heart could not be as clearly marked due to off-target expression in the liver, which was showcased in Figure 2B with AAV9 delivery to sham mice. As discussed above, 2ankrd1aEN provided stronger baseline levels of expression of the heart which could be more clearly marked in IVIS images for tracking fold changes over time. For these reasons, we sought to explore how incorporation of the AAV.cc84 capsid could be utilized to minimize off-target liver expression. We have now included a sentence in the revised manuscript on p. 5, paragraph 3 to clarify.

Reviewer #2 (Public review):

In this manuscript by Wolfson et al., various adeno-associated viruses (AAVs) were delivered to mice to assess the cardiac-specificity, injury border-zone cardiomyocyte transduction rate, and temporal dynamics, with the goal of finding better AAVs for gene therapies targeting the heart. The authors delivered tissue regeneration enhancer elements (TREEs) controlling luciferase expression and used IVIS imaging to examine transduction in the heart and other organs. They found that luciferase expression increased in the first week after injury when using AAV9-TREE-Hsp68 promoter, waning to baseline levels by 7 weeks. However, AAV9 vectors transduced the liver, which was significantly reduced by using an AAV.cc84 liver de-targeting capsid. The authors then performed in vivo screening of AAV9 capsids and found AAV-IR41 to preferentially transduce injured myocardium when compared to AAV9. Finally, the authors combined TREEs with AAV-IR41 to show improved luciferase expression compared to AAV9-TREE at 7, 14, and 21 days after injury.

Overall, this manuscript provides insights into TREE expression dynamics when paired with various heart-targeting capsids, which can be useful for researchers studying ischemic injury of murine hearts. While the authors have shown the success of using AAV9-TREEs in porcine hearts, it is unknown whether the expression dynamics would be similar in pigs or humans, as mentioned in the limitations.

The following questions and concerns can be addressed to improve the manuscript:

(1) From the IVIS data, it seems that the Hsp68 promoter might not be "normally silent in mouse tissues," specifically in the liver (Figure S1B). Are there any other promoters that can be combined with TREEs to induce cardiac-injury specific expression while minimizing liver expression? This could simplify capsid design to focus on delivery to injured areas.

Indeed we found the Hsp68 promoter does provide low levels of baseline expression, especially in the liver of mice. The Hsp68 promoter was initially chosen due to its permissive nature allowing for assessment of expression directed by TREEs. Many or most groups use the Hsp68 promoter for enhancer tests in mice, but we agree that other permissive promoters might have lower baseline levels of expression and might have the benefit of smaller size. We have not rigorously tested other permissive promoters in our experiments.

(2) Why is it that AAV9-TREE-Hsp68-Luc wane in expression (Figure 1C and 1D), whereas AAV.cc84-TREE-Hsp68-Luc expresses stably for over 2 months (3E)? This has important implications for the goal of transience in gene delivery.

Please see our response to reviewer 1’s comment #1 above.

(3) AAV-IR41 was found to transduce cardiomyocytes in the injured zone. However, this capsid also shows a very strong off-target liver expression. From a capsid design perspective, is it possible to combine AAV-cc84 and AAV-IR41?

This approach is in theory possible as these epitopes are structurally distinct. However, since the mechanism (receptor usage) is currently unknown, it would not be possible to predict whether the properties are mutually exclusive. Further, we would need to ensure that combining modifications does not impact vector yield. We can explore such features with next generation candidates as we continue to improve the platform. We have now included a sentence in the revised manuscript on p. 9, paragraph 3, mentioning the possibility of combining the two capsid mutations.

(4) It would be helpful to see immunostaining for the various time points in Figure 5. Is it possible to use an anti-luciferase antibody (or AAV-TREE-Hsp68-eGFP) to compare the two TREE capsids?

We were not able to do immunostaining of luciferase expression, because the biopsied hearts were used to quantify vector genomes via qPCR. We have previously reported results of immunostaining of EGFP expression directed by 2ankrd1aEN in I/R-injured mouse hearts (Yan et al., 2023), which we expect to match the expression seen in these experiments.

Reviewer #3 (Public review):

Summary:

The tissue regeneration enhancer elements (TREEs) identified in zebrafish have been shown to drive injury-activated temporal-spatial gene expression in mice and large animals. These findings increase the translational potential of findings in zebrafish to mammals. In this manuscript, the authors tested TREEs in combination with different adeno-associated viral (AAV) vectors using in vivo luciferase bioluminescent imaging that allows for longitudinal tracking. The TREE-driven luciferase delivered by a liver de-targeted AAV.cc84 decreased off-target transduction in the liver. They further screened an AAV library to identify capsid variants that display enhanced transduction for myocardium post-myocardial infarction. A new capsid variant, AAV.IR41, was found to show increased transduction at the infarct border zones.

Strengths:

The authors injected AAV-cargo several days after ischemia/reperfusion (I/R) injury as a clinically relevant approach. Overall, this study is significant in that it identifies new AAV vectors for potential new gene therapies in the future. The manuscript is well-written, and their data are also of high quality.

Weaknesses:

The authors might be using MI (myocardial infarction) and I/R injury interchangeably in their text and labels. For instance, "We systemically transduced mice at 4 days after permanent left coronary artery ligation with either AAV9 or IR41 harboring a 2ankrd1aEN-Hsp68::fLuc transgene. IVIS imaging revealed higher expression levels in animals transduced with IR41 compared to AAV9, in both sham and I/R groups (Fig. 5A)". They should keep it consistent. There is also no description for the MI model.

We have adjusted figure labels and main text to ensure the injury model is described correctly.

We have also addressed all additional Recommendations for the authors, which requested minor modifications to figures like error bars and image annotation.

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eLife Assessment

This important study provides a conceptual advance in our understanding of how membrane geometry modulates the balance between specific and non-specific molecular interactions, reversing multiphase morphologies in postsynaptic protein assemblies. Using a mesoscale simulation framework grounded in experimental binding affinities, the authors successfully recapitulate key experimental observations in both solution and membrane-associated systems, providing novel mechanistic insight into how spatial constraints regulate postsynaptic condensate organization. The conclusions are supported by solid strength of evidence and the findings are of broad significance for both computational and experimental biologists

Reviewer #2 (Public review):

This is a timely and insightful study aiming to explore the general physical principles for the sub-compartmentalization--or lack thereof--in the phase separation processes underlying the assembly of postsynaptic densities (PSDs), especially the markedly different organizations in three-dimensional (3D) droplets on one hand and the two-dimensional (2D) condensates associated with a cellular membrane on the other. Simulation of a highly simplified model (one bead per protein domain) is apparently carefully executed. Based on a thorough consideration of various control cases, the main conclusion regarding the trade-off between repulsive excluded volume interactions and attractive interactions among protein domains in determining the structures of 3D vs 2D model PSD condensates is quite convincing. The novel results in this manuscript should be published.

Comment on the revised manuscript:

The authors have adequately addressed all my previous concerns. The manuscript is now much improved, ready for publication as a version of record.

Reviewer #3 (Public review):

Summary:

In this work, Yamada, Brandani and Takada have developed a mesoscopic model of the interacting proteins in the postsynaptic density. They have performed simulations, based on this model and using the software ReaDDy, to study the phase separation in this system in 2D (on the membrane) and 3D (in the bulk). They have carefully investigated the reasons behind different morphologies observed in each case, and have looked at differences in valency, specific/non-specific interactions and interfacial tension.

Strengths:

The simulation model is developed very carefully, with strong reliance on binding valency and geometry, experimentally measured affinities, and physical considerations like the hydrodynamic radii. The presented analyses are also thorough, and great effort has been put into investigating different scenarios that might explain the observed effects.

Weaknesses:

The biggest weakness of the study, in my opinion, has been a lack of more in-depth and quantitative physical insights about phase separation theories. In the revised version, the authors have added text to point the interested reader to the respective theories, and have included a qualitative assessment of their findings in the light of said theories. This better positions their discussion. I still believe the role of entropic effects need more attention, which can be the subject of future studies.

The authors have revised their Introduction and added text to the Discussion, to enrich their view on the attractive and repulsive forces as well as mixing entropy. This version better covers the physics of phase separation.

I appreciate the added discussion about the different diffusive behavior in the membrane in contrast to the bulk (i.e. the Saffman-Delbrück model). This paves the way for future studies, including realistic kinetics of the studied system.

Author response:

The following is the authors’ response to the original reviews.

Reviewer #1 (Public review):

Summary:

This study uses mesoscale simulations to investigate how membrane geometry regulates the multiphase organization of postsynaptic condensates. It reveals that dimensionality shifts the balance between specific and non-specific interactions, thereby reversing domain morphology observed in vitro versus in vivo.

Strengths:

The model is grounded in experimental binding affinities, reproduces key experimental observations in 3D and 2D contexts, and offers mechanistic insight into how geometry and molecular features drive phase behavior.

Weaknesses:

The model omits other synaptic components that may influence domain organization and does not extensively explore parameter sensitivity or broader physiological variability.

We thank the reviewer for his/her time and effort to our manuscript. We agree with the point that the contribution of other synaptic components should be addressed. We have included a discussion of the effects of environmental factors such as protein and ion concentrations, as well as other omitted postsynaptic components (SAPAP, Shank, and Homer) on phase morphology. In the middle of the 2^nd paragraph of Discussion, we added: 

“While these in vivo results contain additional scaffold and cytoskeletal elements omitted in our model, such as SAPAP, Shank and Homer, nearly all proteins in the middle and lower layers of the PSD associate directly or indirectly with PSD-95 in the upper PSD layer. Consequently, it is probable that other scaffold proteins contribute to the mobility of AMPAR-containing and NMDAR-containing nanodomains indistinguishably. They may increase the stability of the AMPAR and NMDAR clusters but are unlikely to have a distinct effect to reverse the phase-separation phenomenon.”

Also, as the reviewer pointed out, we agree with that physiological factors such as ion concentration may influence the phase. However, conditions such as ion concentration are implicitly implemented as the specific and nonspecific interactions in this model, which makes it difficult to estimate the effect of each physiological condition individually. We added the variability potential of physiological conditions to the discussion section as a limitation of this model. To investigate parameter sensitivity in more detail, we performed additional MD simulations with weakened membrane constraints to account for the behavior between 3D and 2D. We added:

“First, our results did not provide direct insights to physiological conditions, such as ion concentrations. Since such factors are implicitly implemented in our model, it is difficult to estimate these effects individually. This suggests the need for future implementation of environmental factors and validation under a broader range of in vivo-like settings.”

Reviewer #2 (Public review):

This is a timely and insightful study aiming to explore the general physical principles for the sub-compartmentalization--or lack thereof--in the phase separation processes underlying the assembly of postsynaptic densities (PSDs), especially the markedly different organizations in three-dimensional (3D) droplets on one hand and the twodimensional (2D) condensates associated with a cellular membrane on the other. Simulation of a highly simplified model (one bead per protein domain) is carefully executed. Based on a thorough consideration of various control cases, the main conclusion regarding the trade-off between repulsive excluded volume interactions and attractive interactions among protein domains in determining the structures of 3D vs 2D model PSD condensates is quite convincing. The results in this manuscript are novel; however, as it stands, there is substantial room for improvement in the presentation of the background and the findings of this work. In particular,

(i) conceptual connections with prior works should be better discussed 

(ii) essential details of the model should be clarified, and

(iii) the generality and limitations of the authors' approach should be better delineated.

We appreciate the reviewer for his/her time and effort on our manuscript and for encouraging comments and helpful suggestions. We answered every technical comment the reviewer mentioned below.

Specifically, the following items should be addressed (with the additional references mentioned below cited and discussed):

(1) Excluded volume effects are referred to throughout the text by various terms and descriptions such as "repulsive force according to the volume" (e.g., in the Introduction), "nonspecific volume interaction", and "volume effects" in this manuscript. This is somewhat curious and not conducive to clarity, because these terms have alternate or connotations of alternate meanings (e.g., in biomolecular modeling, repulsive interactions usually refer to those with longer spatial ranges, such as that between like charges). It will be much clearer if the authors simply refer to excluded volume interactions as excluded volume interactions (or effects).  

Thank you for this comment. We have substituted the words “excluded volume interactions” for words of similar meaning. However, we have left the expression of “non-specific interactions” as they are referring to explicit interactions that are given as force fields in the model, rather than in the general meaning of excluded volume effect.

(2) In as much as the impact of excluded volume effects on subcompartmentalization of condensates ("multiple phases" in the authors' terminology), it has been demonstrated by both coarse-grained molecular dynamics and field-theoretic simulations that excluded volume is conducive to demixing of molecular species in condensates [Pal et al., Phys Rev E 103:042406 (2021); see especially Figures 4-5 of this reference]. This prior work bears directly on the authors' observation. Its relationship with the present work should be discussed.  

We appreciate the reviewer’s insightful comment. We have now included a more detailed discussion on excluded volume effect in the revised manuscript, which provides important context for our findings. Furthermore, we have cited the references to support and enrich the discussion, as recommended.

(3)  In the present model setup, activation of the CaMKII kinase affects only its binding to GluN2Bc. This approach is reasonable and leads to model predictions that are essentially consistent with the experiment. More broadly, however, do the authors expect activation of the CaMKII kinase to lead to phosphorylation of some of the molecular species involved with PSDs? This may be of interest since biomolecular condensates are known to be modulated by phosphorylation [Kim et al., Science 365:825-829 (2019); Lin et al, eLife 13:RP100284 (2025)].  

We agree that phosphorylation effect on phase separation is an important and interesting aspect to consider. Some experimental results have shown that activation of CaMKII can lead to phosphorylation of various proteins and make PSD condensate more stable by altering their interactions. We included the sentence below in limitations:

“In this context, we also do not explicitly account for downstream phosphorylation events. Although such proteins are not included in the current components, they will regulate PSD-95, affecting its binding valency, or diffusion coefficient. This is a subject worthy of future research.”

(4) The forcefield for confinement of AMPAR/TARP and NMDAR/GluN2Bc to 2D should be specified in the main text. Have the authors explored the sensitivity of their 2D findings on the strength of this confinement?

We thank the reviewer for the helpful recommendation. We have revised the manuscript to include membrane-mimicking potential on main text. Furthermore, we also think that exploring the shape of the 3D/2D condensate phase due to the sensitivity of confinement is a very interesting point. We have additionally performed MD simulations with smaller/larger membrane constraints and included the results in supporting information as Figure S5. The following parts are added:

“We further attempted to mimic intermediate conditions between 3D and 2D systems in two different manners. First, we applied a weaker membrane constraint in 2D system. Even when the strength of membrane constraints is reduced by a factor of 1000, NMDARs are located on the inner side when the CaMKII was active, as well as the result in 2D system (Fig.S5ABC). Second, to weaken further the effect of membrane constraints, we artificially altered the membrane thickness from 5 nm to 50 nm, in addition to reducing the membrane constraints by 1000. As a result, NMDAR clusters move to the bottom and surround AMPAR (Fig.S5DEF). In this artificial intermediate condition, both states in which the NMDARs are outside (corresponding to 3D) and in which the NMDARs are inside (corresponding to 2D) are observed, depending on the strength of the membrane constraint.”

(5)  Some of the labels in Figure 1 are confusing. In Figure 1A, the structure labeled as AMPAR has the same shape as the structure labeled as TARP in Figure 1B, but TARP is labeled as one of the smaller structures (like small legs) in the lower part of AMPAR in Figure 1A. Does the TARP in Figure 1B correspond to the small structures in the lower part of AMPAR? If so, this should be specified (and better indicated graphically), and in that case, it would be better not to use the same structural drawing for the overall structure and a substructure. The same issue is seen for NMDAR in Figure 1A and GluN2Bc in Figure 1B. 

(6) In addition to clarifying Figure 1, the authors should clarify the usage of AMPAR vs TARP and NMDAR vs GluN2Bc in other parts of the text as well.

(7) The physics of the authors' model will be much clearer if they provide an easily accessible graphical description of the relative interaction strengths between different domain-representing spheres (beads) in their model. For this purpose, a representation similar to that given by Feric et al., Cell 165:1686-1697 (2016) (especially Figure 6B in this reference) of the pairwise interactions among the beads in the authors' model should be provided as an additional main-text figure. Different interaction schemes corresponding to inactive and activated CAMKII should be given. In this way, the general principles (beyond the PSD system) governing 3D vs 2D multiple-component condensate organization can be made much more apparent.  \

We sincerely appreciate the reviewer’s comments. According to the recommendation, we have changed the diagram in Figure 1B into interaction matrix with each mesoscale molecular representation and the expression in main text to be clearer about AMPAR and TARP, and about the relationship between NMDAR and GluN2Bc. Former diagram of the pairs of specific interaction is moved to supplementary figure. 

(8) Can the authors' rationalization of the observed difference between 3D and 2D model PSD condensates be captured by an intuitive appreciation of the restriction on favorable interactions by steric hindrance and the reduction in interaction cooperativity in 2D vs 3D?  

We thank the reviewer for the comment. As pointed out, the multiphase morphology change observed in this study can be attributed to a decrease in coordination number in 2D compared to 3D. We have included the physicochemical rationalization in the discussion.  

(9) In the authors' model, the propensity to form 2D condensates is quite weak. Is this prediction consistent with the experiment? Real PSDs do form 2D condensates around synapses.  

We are grateful to the reviewer for highlighting this important point. We agree with that the real PSD forms 3D condensates beneath the 2D membrane. Some lower PSD components under the membrane (i.e. SAPAP, Shank, and Homer) are omitted in our system, which may cause a weak condensation. To emphasize this, we have added the following sentence:

“While these in vivo results contain additional scaffold and cytoskeletal elements omitted in our model, such as SAPAP, Shank and Homer, nearly all proteins in the middle and lower layers of the PSD associate directly or indirectly with PSD-95 in the upper PSD layer. Consequently, it is probable that other scaffold proteins contribute to the mobility of AMPAR-containing and NMDAR-containing nanodomains indistinguishably. They may increase the stability of the AMPAR and NMDAR clusters but are unlikely to have a distinct effect to reverse the phase-separation phenomenon.”

However, we believe that the clusters formed on the 2D membrane are not a robust “phase” because they do not follow scaling law. In fact, in our previous study of PSD system with AMPAR(TARP)₄ and PSD-95, we have already reported that phase separation is less likely to occur in 2D than in 3D. The previous result suggests that phase separation on membrane may be difficult to achieve, which is consistent with the results of this study.

(10) More theoretical context should be provided in the Introduction and/or Discussion by drawing connections to pertinent prior works on physical determinants of co-mixing and de-mixing in multiple-component condensates (e.g., amino acid sequence), such as Lin et al., New J Phys 19:115003 (2017) and Lin et al., Biochemistry 57:2499-2508 (2018). 

(11) In the discussion of the physiological/neurological significance of PSD in the Introduction and/or Discussion, for general interest it is useful to point to a recently studied possible connection between the hydrostatic pressure-induced dissolution of model PSD and high-pressure neurological syndrome [Lin et al., Chem Eur J 26:11024-11031 (2020)].

We thank the reviewer for the helpful recommendation. We have added the recommended references in each relevant part in introduction, respectively.

(12) It is more accurate to use "perpendicular to the membrane" rather than "vertical" in the caption for Figure 3E and other such descriptions of the orientation of the CaMKII hexagonal plane in the text.

We thank you for your comment. We replaced the word “vertical” with “perpendicular" in the main text and caption.

Reviewer #3 (Public review):

Summary:

In this work, Yamada, Brandani, and Takada have developed a mesoscopic model of the interacting proteins in the postsynaptic density. They have performed simulations, based on this model and using the software ReaDDy, to study the phase separation in this system in 2D (on the membrane) and 3D (in the bulk). They have carefully investigated the reasons behind different morphologies observed in each case, and have looked at differences in valency, specific/non-specific interactions, and interfacial tension.

Strengths:

The simulation model is developed very carefully, with strong reliance on binding valency and geometry, experimentally measured affinities, and physical considerations like the hydrodynamic radii. The presented analyses are also thorough, and great effort has been put into investigating different scenarios that might explain the observed effects.

Weaknesses:

The biggest weakness of the study, in my opinion, has to do with a lack of more in-depth physical insight about phase separation. For example, the authors express surprise about similar interactions between components resulting in different phase separation in 2D and 3D. This is not surprising at all, as in 3D, higher coordination numbers and more available volume translate to lower free energy, which easily explains phase separation. The role of entropy is also significantly missing from the analyses. When interaction strengths are small, entropic effects play major roles. In the introduction, the authors present an oversimplified view of associative and segregative phase transitions based on the attractive and repulsive interactions, and I'm afraid that this view, in which all the observed morphologies should have clear pairwise enthalpic explanations, diffuses throughout the analysis. Meanwhile, I believe the authors correctly identify some relevant effects, where they consider specific/nonspecific interactions, or when they investigate the reduced valency of CaMKII in the 2D system.

We thank the reviewer for the insightful and constructive comments. Regarding the difference in phase behavior between 2D and 3D systems, we appreciate the reviewer’s clarification that differences in coordination number and entropy in higher dimensions can account for the observed morphology of the phases. While it may be clear that entropy decreases due to the decrease of coordination number, our objective was to uncover how such an isotropic entropy reduction regulates the behavior of each phase driven by different interactions, which remains largely unknown. To emphasize this, we modified the introduction and have now included a discussion of the entropic contributions to phase behavior in both 2D and 3D systems, and we have made this clearer in the revised manuscript by referencing relevant theoretical frameworks. In the Discussion, we added the sentence below:

“Generally, phase separation can be explained by the Flory-Huggins theory and its extensions: phase separation can be favored by the difference in the effective pairwise interactions in the same phase compared to those across different phases, and is disfavored by mixing entropy. The effective interactions contain various molecular interactions, including direct van der Waals and electrostatic interactions, hydrophobic interactions, and purely entropic macromolecular excluded volume interactions. For the latter, Asakura-Oosawa depletion force can drive the phase separation. Furthermore, the demixing effect was explicitly demonstrated in previous simulations and field theory (61). Importantly, we note that the effective pairwise interactions scale with the coordination number z. The coordination number is a clear and major difference between 3D and 2D systems. In 3D systems, large z allows both relatively strong few specific interactions and many weak non-specific interactions. While a single specific interaction is, by definition, stronger than a single non-specific interaction, contribution of the latter can have strong impact due to its large number. On the other hand, a smaller z in the membrane-bound 2D system limits the number of interactions. In case of limited competitive binding, specific interactions tend to be prioritized compared to non-specific ones. In fact, Fig. 3A clearly shows that number of specific interactions in 2D is similar to that in 3D, while that of non-specific interactions is dramatically reduced in 2D. In the current PSD system, CaMKII is characterized by large valency and large volume. In the 3D solution system, non-specific excluded volume interactions drive CaMKII to the outer phase, while this effect is largely reduced in 2D, resulting in the reversed multiphase.   

Also, I sense some haste in comparing the findings with experimental observations. For example, the authors mention that "For the current four component PSD system, the product of concentrations of each molecule in the dilute phase is in good agreement with that of the experimental concentrations (Table S2)." But the data used here is the dilute phase, which is the remnant of a system prepared at very high concentrations and allowed to phase separate. The errors reported in Table S2 already cast doubt on this comparison. 

We thank the reviewer for the insightful comment. In the validation process, we adjusted the parameters so that the number of molecules in dilute phase is consistent with the experimental lower limit of phase separation, based on the assumption that phase-separated dilute phase is the same concentration as the critical concentration. That is why we focus on comparing dilute phase concentration in Table S2. However, in our simulations, the number of protein molecules is relatively small since it is based on the average number per synapse spine. For example, there are only about 60 CaMKII molecules at most, and its presence in the dilute phase is highly sensitive to concentration, as the reviewer pointed out. This is one of the limitations, so we have added a description to the Limitations section. We added:

“Second, parameter calibration contains some uncertainty. Previous in vitro study results used for parameter validation are at relatively high concentrations for phase separation, which may shift critical thresholds compared to that in in vivo environments. Also, since the number of molecules included in the model is small, the difference of a single molecule could result in a large error during this validation process.”

Or while the 2D system is prepared via confining the particles to the vicinity of the membrane, the different diffusive behavior in the membrane, in contrast to the bulk (i.e., the Saffman-Delbrück model), is not considered. This would thus make it difficult to interpret the results of a coupled 2D/3D system and compare them to the actual system.

We appreciate the reviewer’s helpful comment. We agree with that there is a concern that the Einstein-Stokes equation does not adequately reproduce the diffusion of membrane-embedded particles. We recalculated the diffusion coefficients for every membrane particle used in this model using the Saffman-Delbrück model and found that diffusion coefficients for receptor cores (AMPAR and NMDAR) were approximately three times larger. These values are still about ~10 times smaller than that of molecules diffusing under the cytoplasm. Additionally, since this study focuses on the morphology of the phase/cluster at the thermodynamic equilibrium, we think that the magnitude of the diffusion coefficient has little influence on the final structure of the cluster. However, we will incorporate the membrane-embedded diffusion as a future improvement item for better modelling and implementation. We added:

“Third, we estimated all the diffusion coefficients from the Einstein-Stokes equation, which may oversimplify membrane-associated dynamics. Applying the Saffmann-Delbrück model to membrane-embedded particles would be desired although the resulting diffusion coefficients remain of the same order of magnitude. These limitations highlight the need for further research, yet they do not undermine the core significance of the present findings in advancing our understanding of multiphase morphologies.”

eLife Assessment

Kin selection and inclusive fitness have generated significant controversy. This paper reconsiders the general form of Hamilton's rule in which benefits and costs are defined as regression coefficients, with higher-order coefficients being added to accommodate non-linear interactions. The paper is a landmark contribution to the field with compelling, systematic analysis, giving clarity to long-standing debates.

Joint Public Review:

This manuscript reconsiders the "general form" of Hamilton's rule, in which "benefit" and "cost" are defined as regression coefficients. It points out that there is no reason to insist on Hamilton's rule of the form -c+br>0, and that, in fact, arbitrarily many terms (i.e. higher-order regression coefficients) can be added to Hamilton's rule to reflect nonlinear interactions. Furthermore, it argues that insisting on a rule of the form -c+br>0 can result in conditions that are true but meaningless and that statistical considerations should be employed to determine which form of Hamilton's rule is meaningful for a given dataset or model.

Comments on latest version:

The authors have provided a robust, valuable and detailed response to the previous reviews.

Comments from Reviewer #1: I have nothing further to add.

Comments from Reviewer #2: I appreciate the clarifications the author has made to the manuscript regarding (i) "sample covariance" terminology, (ii) the generality of the "generalized Price equation", and (iii) the distinction between the covariance and regression forms of the Price equation. I also appreciate that the ms now engages more deeply with some of the previous literature on regression-based Hamilton's rules (e.g. Smith et al., 2010; Rousset 2015). I feel these revisions make this contribution more valuable, and also more technically sound, since the term "sample covariance" is no longer used incorrectly.

I also add that I agree with the substance of the authors' response to Reviewer #3. That is, the original submission was very clear that the regression-based Hamilton's rule is already completely general in the range of situations to which it applies, and that the added "generality" in the present ms refers to the variety of regression models that can be applied to these situations. In this way, the original ms already anticipates and addresses the criticism that Reviewer #3 raises.

Reviewer #3 did not provide comments on the revised version.

Author response:

The following is the authors’ response to the original reviews

Reviewer #1 (Public review):

Summary:

There has been intense controversy over the generality of Hamilton's inclusive fitness rule for how evolution works on social behaviors. All generally agree that relatedness can be a game changer, for example allowing for otherwise unselectable altruistic behaviors when 𝑐 < 𝑟𝑏, where 𝑐 is the fitness cost to the altruism, 𝑏 is the fitness benefit to another, and 𝑟 their relatedness. Many complications have been successfully incorporated into the theory, including different reproductive values and viscous population structures.

I agree, especially if by incorporating viscous population structures, the reviewer means the discovery of the cancellation effect (Wilson, Pollock, and Dugatkin, 1992, Taylor, 1992).

The controversy has centered on another dimension; Hamilton's original model was for additive fitness, but how does his result hold when fitnesses are non-additive? One approach has been not to worry about a general result but just find results for particular cases. A consistent finding is that the results depend on the frequency of the social allele - nonadditivity causes frequency dependence that was absent in Hamilton's approach.

Just to be extra precise: Hamilton’s (1964) original model did not use the Price equation nor the regression approach to define costs and benefits, and it did indeed simply presuppose fixed, additive fitness effects.

Also for extra precision on terminology: many researchers will describe all fitnesses in social evolution as frequency dependent. The reason they do, is that with or without additivity, both the fitness of cooperators (with the social allele) and the fitness of defectors (without the social alle) typically increase in the frequency of cooperators in the population; the more cooperators there are, the more individuals run into them, which increases average fitness. The result depending on the frequency I take to mean that which of those two fitnesses is larger flips at a certain frequency, which automatically implies that the difference between them is depending on the frequency of the social allele. This is indeed the result of non-additivity. We will return to this in more detail in the response to Reviewer #3. Also at the end of Appendix B I have added a bit to be extra precise regarding frequency dependence.

Two other approaches derive from Queller via the Price equation. Queller 1 is to find forms like Hamilton's rule, but with additional terms that deal with non-additive interaction, each with an r-like population structure variable multiplied by a b-like fitness effect (Queller, 1985). Queller 2 redefines the fitness effects c and b as partial regressions of the actor's and recipient's genes on fitness. This leaves Hamilton's rule intact, just with new definitions of c and b that depend on frequency (Queller, 1992a).

Queller 2 is the version that has been most adopted by the inclusive fitness community along with assertions that Hamilton's rule in completely general. In this paper, van Veelen argues that Queller 1 is the correct approach. He derives a general form that Queller only hinted at. He does so within a more rigorous framework that puts both Price's equation and Hamilton's rule on firmer statistical ground. Within that framework, the Queller 2 approach is seen to be a statistical misspecification - it employs a model without interaction in cases that actually do have interaction. If we accept that this is a fatal flaw, the original version of Hamilton's rule is limited to linear fitness models, which might not be common.

I totally agree.

Strengths:

While the approach is not entirely new, this paper provides a more rigorous approach and a more general result. It shows that both Queller 1 and Queller 2 are identities and give accurate results, because both are derived from the Price equation, which is an identity. So why prefer Queller 1? It identifies the misspecification issue with the Queller 2 approach and points out its consequences. For example, it will not give the minimum squared differences between the model and data. It does not separate the behavioral effects of the individuals from the population state (𝑏 and 𝑐 become dependent on 𝑟 and the population frequency).

Just to be precise on a detail: in the data domain, as long as the number of parameters in a statistical model is lower than the number of data points, adding parameters typically (generically) lowers the sum of squared errors. That is to say, for an underspecified statistical model, the sum of squared errors goes down if a parameter is added, but for an already overspecified statistical model, the same is still true (although, typically, by how much the sum of squared errors is reduced will differ). The model specification task for a statistician includes knowing when to keep adding parameters, because the data suggest that the model is still underspecified, and when to stop adding parameters, because the model is well-specified, even if adding parameters still reduces the sum of squared errors.

In a modeling context, on the other hand, one can say that sum of squared differences will stop decreasing at the point where the statistical model is well-specified, that is: when it matches the model we are considering.

The paper also shows how the same problems can apply to non-social traits. Epistasis is the non-additivity of effects of two genes within the individual. (So one wonders why have we not had a similarly fierce controversy over how we should treat epistasis?)

The paper is clearly written. Though somewhat repetitive, particularly in the long supplement, most of that repetition has the purpose of underscoring how the same points apply equally to a variety of different models.

Finally, this may be a big step towards reconciliation in the inclusive fitness wars. Van Veelen has been one of the harshest critics of inclusive fitness, and now he is proposing a version of it.

I am very happy to hear this, because I am indeed hopeful for reconciliation. I would like to add a comment, though. The debate on Hamilton’s rule/inclusive fitness is regularly thought of as a battle between two partizan camps, where both sides care at least as much about winning as they do about getting things right. This is totally understandable, because to some degree that is true. Also, I agree that it is fair to position me in the camp that is critical of the inclusive fitness literature. However, I would like to think that I have not been taking random shots at Hamilton’s rule. I have pointed to problems with the typical use of the Price equation and Hamilton’s rule, and I think I did for very good reasons. I am obviously very happy that finding the Generalized Price equation, and the general version of Hamilton’s rule, allowed me to go beyond this, and (finally) offer a correct alternative, and I totally appreciate that this opens the door for reconciliation, as this reviewer points out. But I would not describe this as a road-toDamascus moment. In order to illustrate the continuity in my work, I would like to point to three papers.

In van Veelen (2007), I pointed to the missing link between the central result in Hamilton’s (1964) famous paper (which states that selection dynamics take the population to a state where mean inclusive fitness is maximized), and Hamilton’s actual rule (which states that selection will lead to individuals maximizing their individual inclusive fitness). My repair stated the additional assumptions that were necessary to make the latter follow from the former. I would say that this can hardly be characterized as an attack on Hamilton’s rule. Reading Hamilton (1964) with enough care to notice something is missing, and then repairing it, I think is a sign of respect, and not an attack.

Van Veelen (2011) is about the replicator dynamics for n-player games, with the possibility of assortment. This puts the paper in a domain that does not assume weak selection, and that is typically not much oriented towards inclusive fitness. I included a theorem that implies that, under the condition of linearity, inclusive fitness not only gets the direction of selection right, but 𝑟𝑏 − 𝑐 becomes a parameter that also determines the speed of selection. This I think is representative, in the sense that in many of my papers, I carefully stake out when the classic version of Hamilton’s rule does work.

In Akdeniz and van Veelen (2020), we moreover take a totally standard inclusive fitness approach in a model of the cancellation effect at the group level.

I would say that this does not line up with the image of a harsh critic that takes random shots at Hamilton’s rule or inclusive fitness.

Weaknesses:

van Veelen argues that the field essentially abandoned the Queller 1 approach after its publication. I think this is putting it too strongly - there have been a number of theoretical studies that incorporate extra terms with higher-order relatednesses. It is probably accurate to say that there has been relative neglect. But perhaps this is partly due to a perception that this approach is difficult to apply.

I can imagine that the perceived difficulty in application may have played a role in the neglect of the Queller 1 approach. What for sure has played a role, and I would think a much bigger one, is that the literature has been pretty outspoken that the Queller 1 approach is the wrong way to go. The main text cites a number of papers that hold this position very emphatically (The first one of those was a News and Views by Alan Grafen (1985) that accompanied the paper in which Queller presented his Queller 1 approach. I am very happy that Appendix B shows on how many levels this News and Views was wrong.). There is only a handful of papers that follow the Queller 1 example.

The model in this paper is quite elegant and helps clarify conceptual issues, but I wonder how practical it will turn out to be. In terms of modeling complicated cases, I suspect most practitioners will continue doing what they have been doing, for example using population genetics or adaptive dynamics, without worrying about neatly separating out a series of terms multiplying fitness coefficients and population structure coefficients.

I am not sure if I see what the reviewer envisions practitioners that use population genetics will keep on doing. I would think that the Generalized Price equation in regression form is a description of population genetic dynamics, and therefore, if practitioners will not make an effort to “neatly separate out a series of terms multiplying fitness coefficients and population structure coefficients”, then all I can say is that they should. I cannot do more than explain why, if they do not, they are at risk of mischaracterizing what gets selected and why.

Regarding those that use adaptive dynamics, I would say that this is a whole different approach. Within this approach, one can also apply inclusive fitness; see Section 6 and Appendix D of van Veelen et al. (2017). Appendix D is full of deep technical results and was done by Benjamin Allen.

For empirical studies, it is going to be hard to even try to estimate all those additional parameters. In reality, even the standard Hamilton's rule is rarely tested by trying to estimate all its parameters. Instead, it is commonly tested more indirectly, for example by comparative tests of the importance of relatedness. That of course would not distinguish between additive and non-additive models that both depend on relatedness, but it does test the core idea of kin selection. It will be interesting to see if van Veelen's approach stimulates new ways of exploring the real world.

Regarding the impact on empirical studies, there are a few things that I would like to say. The first is that I would just like to repeat, maybe a bit more elaborately, what I wrote at the end of the main text. Given that the generalized version of Hamilton’s rule produces a host of Hamilton-like rules, and given the fact that all of them by construction indicate the direction of selection accurately, the question whether or not Hamilton’s rule holds turns out to be illposed. That means that we can stop doing empirical tests of Hamilton’s rule, which are predicated on the idea that Hamilton’s rule, with benefits and costs being determined by the regression method, could be violated – which it cannot (Side note: it is possible to violate Hamilton’s rule, if costs and benefits are defined according to the counterfactual method; see van Veelen et al. (2017) and van Veelen (2018). This way of defining costs and benefits is less common, although there are authors that find this definition natural enough to assume that this is the way in which everybody defines costs and benefits (Karlin and Matessi, 1983, Matessi and Karlin, 1984).). Instead, we should do empirical studies to find out which version of Hamilton’s rule applies to which behaviour in which species.

would like to not understate what a step forward this is. The size of the step forwards is of course also due to the dismal point of departure. As theorists, we have failed our empiricists, because all 12 studies included in the review by Bourke (2014) of papers that explicitly test Hamilton’s rule are based on the misguided idea that the traditional Hamilton’s rule, with costs and benefits defined according to the regression method, can be violated. While the field does sometimes have disdain for mathematical nit-picking, this is a point where a little more attention to detail would have really helped. If the hypothesis is that Hamilton’s rule holds, and the null is that it does not, then trying to specify how the empirical quantity that reflects inclusive fitness would be distributed under the null hypothesis (in order to do the right statistical tests) would have forced researchers to do something with the information that this quantity is not distributed at all, because Hamilton’s rule is general (in the sense that it holds for any way in which the world works). If one would prefer to reverse the null and the alternative hypothesis, one would run into similar problems. Understanding that the question is ill-posed therefore is a big step forwards from the terrible state of statistics and the waste of research time, attention and money on the empirical side of this field (see also Section 8 of van Veelen et al., 2017).

I would agree that doing comparative statics may not be much affected by this. Section 5 of van Veelen et al. (2017) indicates that there can be a large set of circumstances under which the general idea “relatedness up → cooperation up” still applies. But that may be a bit unambitious, and Section 8 of van Veelen et al. (2017), and the final section of van Veelen (2018) contain some reflections on empirical testing that may allow us to go beyond that. As long as there is change happening in the Generalized Price equation, the population is not in equilibrium. For empirical tests, one can either aim to capture selection as it happens, or assume that what we observe reflects properties of an equilibrium. This leads to interesting reflections on how to do empirics, which may differ between traits that are continuous and traits that are discrete (again: see van Veelen et al. (2017), and van Veelen (2018).

Reviewer #2 (Public review):

Summary:

This manuscript reconsiders the "general form" of Hamilton's rule, in which "benefit" and "cost" are defined as regression coefficients. It points out that there is no reason to insist on Hamilton's rule of the form −𝑐 + 𝑏𝑟 > 0, and that, in fact, arbitrarily many terms (i.e. higherorder regression coefficients) can be added to Hamilton's rule to reflect nonlinear interactions. Furthermore, it argues that insisting on a rule of the form −𝑐 + 𝑏𝑟 > 0 can result in conditions that are true but meaningless and that statistical considerations should be employed to determine which form of Hamilton's rule is meaningful for a given dataset or model.

Totally right. I cannot help to want to be extra precise, though, by distinguishing between the data domain and the modelling domain. In the data domain, statistical considerations apply in order to avoid misspecification. In this domain, avoiding misspecification can be complicated, because we do not know the underlying data generating process, and we depend on noisy data to make a best guess. In the modeling domain, however, there is no excuse for misspecification, as the model is postulated by the modeler. I therefore would think that in this domain, it does not really require “statistical considerations” to minimize the probability of misspecification; we can get the probability of misspecification all the way down to 0 by just choosing not to do it.

Strengths:

The point is an important one. While it is not entirely novel-the idea of adding extra terms to Hamilton's rule has arisen sporadically (Queller, 1985, 2011; Fletcher et al., 2006; van Veelen et al., 2017)--it is very useful to have a systematic treatment of this point. I think the manuscript can make an important contribution by helping to clarify a number of debates in the literature. I particularly appreciate the heterozygote advantage example in the SI.

Me too, and I really hope the readers make it this far! I have thought of putting it in the main text, but did not know where that would fit.

Weaknesses:

Although the mathematical analysis is rigorously done and I largely agree with the conclusions, I feel there are some issues regarding terminology, some regarding the state of the field, and the practice of statistics that need to be clarified if the manuscript is truly to resolve the outstanding issues of the field. Otherwise, I worry that it will in some ways add to the confusion.

(1) The "generalized" Price equation: I agree that the equations labeled (PE.C) and (GPE.C) are different in a subtle yet meaningful way. But I do not see any way in which (GPE.C) is more general than (PE.C). That is, I cannot envision any circumstance in which (GPE.C) applies but (PE.C) does not. A term other than "generalized" should be used.

This is a great point! Just to make sure that those that read the reports online understand this point, let me add some detail. The equation labeled (PE.C) – which is short for Price equation in covariance form – is

The derivation in Appendix A then assumes that we have a statistical model that includes a constant and a linear term for the p-score. It then defines the model-estimated fitness of individual 𝑖 as , where 𝑤_𝑖 is the realized number of offspring of individual 𝑖, and 𝜀_𝑖 is the error term – and it is the sum over all individuals of this error term-squared that is minimized. The vector of model-estimated fitnesses will typically be different for different choices of the statistical model. Appendix A then goes on to show that, whatever the statistical model is that is used, for all of them , as long as the statistical model includes a constant and a linear term for the p-score. That means that we can rewrite (PE.C) as

The point that the reviewer is making, is that this is not really a generalization. For a given dataset (or, more generally, for a given population transition, whether empirical or in a model), is just a number, and it happens to be the case that 𝐶𝑜𝑣(𝑤:, 𝑝) returns the same number, whatever statistical model we use for determining what the model-estimated fitnesses 𝑤_𝑖 are (as long as the statistical model includes a constant and a linear term for the p-score). In other words, (PE.C) is not really nested in (GPE.C), so (GPE.C) is not a proper generalization of (PE.C).

This is a totally correct point, and I had actually struggled a bit with the question what terminology to use here. Equation (GPE.C) is definitely general, in the sense that we can change the statistical model, and thereby change the vector of model-estimated fitnesses , but as long as we keep the constant and the linear term in the statistical model, the equation still applies. But it is not a generalization of (PE.C).

I do however have a hard time coming up with a better label. The General Price equation may be a bit better, but it still suggests generalization. The Statistical Model-based Price equation does not suggest or imply generalization, but it does not convey how general it is, and it suggests that it could be an alternative to the normal Price equation that one may or may not choose to use – while this version really is the one we should use. It may moreover create the impression that this is only for doing statistics, and one might use the traditional Price equation for anything that is not statistics. I cannot really think of other good alternatives, but I am of course open to suggestions.

So, by lack of a better label, I called this the Generalized Price equation in covariance form. Though clearly imperfect, there are still a few good things about this label. The first is that, as mentioned above, this equation is general, in the sense that it holds, regardless of the statistical model. The second reason is that this is Step 1 in a sequence of three steps., the other two of which do produce proper generalizations. Step 2 goes from this equation in covariance form to the Generalized Price Equation in regression form, which is a proper generalization of the traditional Price equation in regression form. Step 3 goes from the Generalized Price Equation in regression form to the general version of Hamilton’s rule, which is also a proper generalization of the classical Hamilton’s rule. Since I would suggest that Step 1 on its own is kind of useless, and therefore Step 1 and Step 2 will typically come as a package, I would be tempted to think that this justifies the abuse of terminology for the Price Equation in covariance form. I did however add the observation made by the reviewer at the point where the Generalized Price equation (in both forms) is derived, so I hope this at least partly addresses this concern.

(2) Regression vs covariance forms of the Price equation: I think the author uses "generalized" in reference to what Price called the "regression form" of his equation. But to almost everyone in the field, the "Price Equation" refers to the covariance form. For this reason, it is very confusing when the manuscript refers to the regression form as simply "the Price Equation".

As an example, in the box on p. 15, the manuscript states "The Price equation can be generalized, in the sense that one can write a variety of Price-like equations for a variety of possible true models, that may have generated the data." But it is not the Price equation (covariance form) that is being generalized here. It is only the regression that Price used that is being generalized.

To be consistent with the field, I suggest the term "Price Equation" be used only to refer to the covariance form unless it is otherwise specified as in "regression form of the Price equation".

I am not sure about the level of confusion induced here, but I totally see that it can be helpful to avoid all ambiguity. I therefore went over everything, and whenever I wrote “Price equation”, I tried to make sure it comes either with “in covariance form” or with “in regression form”. At some places, it is a bit over the top to keep repeating “in regression form”, when it is abundantly clear which form is being discussed. Also, I added no qualifiers if a statement is true for both forms of the Price equation, or if the claim refers to the whole package of going through Step 1 and Step 2 mentioned above.

(3) Sample covariance: The author refers to the covariance in the Price equation as “sample covariance”. This is not correct, since sample covariance has a denominator of N-1 rather than N (Bessel’s correction). The correct term, when summing over an entire population, is “population covariance”. Price (1972) was clear about this: “In this paper we will be concerned with population functions and make no use of sample functions”. This point is elaborated on by Frank (2012), in the subsection “Interpretation of Covariance”.

I totally agree. On page 418 of van Veelen (2005), I wrote:

“Another possibility is that we think of 𝑧_i and 𝑞_i, 𝑖 = 1,…,𝑁 as realizations of a jointly distributed random variable. […] In that case the expression between square brackets is a good approximation for what statisticians […] call a sample covariance. A sample covariance is defined as but in large samples it is OK to replace 𝑁 − 1 by 𝑁, and then this formula reduces to Price’s 𝐶𝑜𝑣(𝑧, 𝑞).”

In van Veelen et al. (2012), I slid a little, because in Box 1 on page 66, I wrote that is the sample covariance, and only in footnote 1 on the same page did I include Bessel’s correction, when I wrote:

“To be perfectly precise, the sample covariance is defined as ”

In this manuscript, I slid a little further, and left Bessel’s correction out altogether. I am happy that the reviewer pointed this out, so I can make this maximally precise again.

The reviewer also quotes Price (1972), page 485:

“In this paper we will be concerned with population functions and make no use of sample functions”.

Below, the reviewer will return to the issue of distinguishing between the sample covariance with Bessel’s correction, and the sample covariance without Bessel’s correction, where the latter is regularly also referred to as the population covariance. A natural interpretation of the quote from Price (1972), if we read a bit around this quote in the paper, is that the difference between his “population functions” and his “sample functions” is indeed Bessel’s correction.

The reviewer also states that Frank (2012) elaborates on this in the subsection “Interpretation of Covariance”. What is interesting, though, is that, when Frank (2012) writes, on page 1017 “It is important to distinguish between population measures and sample measures”, the difference between those is not that one does, and the other does not include Bessel’s correction. The difference between “population measures” and “sample measures” in Frank (2012), page 1017

“It is important to distinguish between population measures and sample measures”,

the difference between those is not that one does, and the other does not include Bessel’s correction. The difference between “population measures” and “sample measures” in Frank (2012), page 1017, is that

“In many statistical applications, one only has data on a subset of the full population, that subset forming a sample.”

The distinction between a population covariance and a sample covariance in Frank (2012) therefore is that they are “covariances” of different things (where the word covariances is in quotation marks, because, again, they are not really covariances). Besides just making sure that Price (1972) and Frank (2012) are not using these terms in the same way, this also perfectly illustrates the mix-up between statistical populations (or data generating processes) and biological populations that I discuss on pages 8 and 9 of Appendix A. I will return to this below, when I explain why I want to avoid using the word “population covariance” for the sample covariance without Bessel’s correction.

Of course, the difference is negligible when the population is large. However, the author applies the covariance formula to populations as small as 𝑁 = 2, for which the correction factor is significant.

Absolutely right.

The author objects to using the term "population covariance" (SI, pp. 8-9) on the grounds that it might be misleading if the covariance, regression coefficients, etc. are used for inference because in this case, what is being inferred is not a population statistic but an underlying relationship. However, I am not convinced that statistical inference is or should be the primary use of the Price equation (see next point). At any rate, avoiding potential confusion is not a sufficient reason to use incorrect terminology.

There are a few related, but separate issues. One is what to call the 𝐶𝑜𝑣(𝑤, 𝑝)-term. Another, somewhat broader, is to avoid mixing up statistical populations and biological populations. A third is what the primary use of the Price equation is. The third issue I will respond to below, where it reappears. Here I will focus on the first two, which can be discussed without addressing the third.

In a data context, I now call the 𝐶𝑜𝑣(𝑤, 𝑝)-term “’" times the sample covariance, or, in other words, the sample covariance without Bessel’s correction”. This should be unambiguous. In a modeling context I refer to 𝐶𝑜𝑣(𝑤, 𝑝)-term as “the 𝐶𝑜𝑣(𝑤, 𝑝)-term” and describe it as a summary statistic or a notational convention. There are two reasons for this choice.

The first is that neither of these use the word “population”. I like this, because there is a persistent scope for confusion between statistical populations and biological populations (as exemplified by Frank, 2012). This leads to an incorrect, but widespread intuition that if we “know the entire (biological) population” in a data context, there is nothing that can be estimated. This is what pages 8 and 9 of Appendix A are all about.

The second reason is that by using two labels, I also differentiate between the data context and the modeling context. This is important for reasons I will return to later.

Relatedly, I suggest avoiding using 𝐸 for the second term in the Price equation, since (as the ms points out), it is not the expectation of any random variable. It is a population mean. There is no reason not to use something like Avg or bar notation to indicate population mean. Price (1972) uses "ave" for average.

I totally agree that the second term in the Price equation is not an expectation. I made this point in van Veelen (2005), and I repeated this in the manuscript. This remark by the reviewer prompted me to spell this out a bit more emphatically in Appendix A. That still leaves me with the choice what notation to use.

I therefore looked up all contributions to the Theme issue “Fifty years of the Price equation” in the Philosophical Transactions of the Royal Society B, and found that almost all contributions use 𝐸, sometimes saying that this refers to an expectation or an average. Of course, this is wrong. However (and this is another argument), it is equally wrong as using 𝐶𝑜𝑣 or 𝑉𝑎𝑟. The terms abbreviated as 𝐶𝑜𝑣 and 𝑉𝑎𝑟 are equally much not a covariance and a variance as the term abbreviated as 𝐸 is not an expectation. So I would think that there are a few reasons for sticking with 𝐸 here; 1) consistency with the literature; 2) consistency with the treatment of other terms; and 3) the fact that this term is not really of any importance in this manuscript. I do however totally understand the reviewer’s reasons, which I suppose include that for using 𝐸, there are relatively unproblematic alternatives (ave or upper bar) that are not available for the other terms. I hope therefore that being a bit more emphatic in the manuscript about 𝐸 not being an expectation at least partly addresses this concern.

I should add, however, that the distinction between population statistics vs sample statistics goes away for regression coefficients (e.g. b, c, and r in Hamilton's rule) since in this case, Bessel's correction cancels out.

Totally correct.

(4) Descriptive vs. inferential statistics: When discussing the statistical quantities in the Price Equation, the author appears to treat them all as inferential statistics. That is, he takes the position that the population data are all generated by some probabilistic model and that the goal of computing the statistical quantities in the Price Equation is to correctly infer this model.

Before I respond to this, I would like to point out that this literature has started going off the rails right from the very beginning. One of the initial construction errors was to use the ungeneralized Price equation in regression form. The other one is that the paper in which Price (1970) presented his equation is inconsistent, and suggests that the equation can be used for constructing hypotheses and for testing them at the same time (see van Veelen (2005), page 416). That, of course, is not possible; the first happens in the theory/modeling domain, and the second in the empirical testing/statistics domain, and they are separate exercises.

These construction errors have warped the literature based on it, and have resulted in a lot of mental gymnastics and esoteric statements, which are needed if we are not willing to consider the possibility that there could be anything amiss with the original paper by Price (1970).

In this paper, I undo both of these construction errors. Undoing the second one means exploring both domains separately. In Sections 2-4 of Appendix A I explore the possibility that the Price equation is applied to data. In Section 5 of Appendix A I explore the possibility that it is used in a modelling context. The primary effort here is just to do it right, and I have not read anything to suggest that I did not succeed in doing this. Secondarily, of course, I also want to contrast this to what happens in the existing literature. That is what this point by the reviewer is about. It is therefore important to be aware that seeing the contrast accurately is complicated by the apologetic warp in the existing literature.

As a first effort to unwarp, I would like to point to the fact that I am not taking any position on what the Price equation should be used for. All I do here is explore (and find) possibilities, both in the statistical inference domain and in the modeling domain. I also find that there is scope for misspecification in both, and that, in both domains, we should want to avoid misspecification. The thing that I criticize in the existing literature therefore is not the choice of domain. The thing that I criticize is the insistence on, and celebrating of what is most accurately described as misspecification. This typically happens in the modeling domain.

It is worth pointing out that those who argue in favor of the Price Equation do not see it this way: "it is a mistake to assume that it must be the evolutionary theorist, writing out covariances, who is performing the equivalent of a statistical analysis." (Gardner, West, and Wild, 2011); "Neither data nor inferences are considered here" (Rousset, 2015). From what I can tell, to the supporters of the Price equation and the regression form of Hamilton's rule, the statistical quantities involved are either population-level *descriptive* statistics (in an empirical context), or else are statistics of random variables (in a stochastic modeling context).

Again, this description of the friction between my paper and the existing literature is predicated on the suggestion that I have only one domain in mind where the Price equation can be applied. That is not the case; I consider both.

In the previous paragraph, the reviewer states that I “treat statistical quantities as inferential statistics”, and in this paragraph the reviewer contrasts that with the supporters of the (ungeneralized) Price equation that supposedly treat the same quantities as “descriptive statistics”. This is also beside the point, but it will take some effort to sort out the spaghetti of entangled arguments (where the spaghetti is the result of the history in this field, as indicated earlier).

First of all, it is not unimportant to point out that the way most people use the terms “inferential statistics” and “descriptive statistics” is that the first refers to an activity, and the second to a function of a bunch of numbers, typically data. Inferential statistics is a combination of parameter estimation and model specification (those are activities). Descriptive statistics are for instance the average values of variables of interest (which makes them a function of a set of numbers). When doing inferential statistics (or statistical inference), looking at the descriptive statistics of the dataset is just a routine before the real work begins. It is important to remember that.

Now I suppose that this reviewer uses these words a little differently. When he or she writes that I “treat statistical quantities as inferential statistics”, I assume that the reviewer means that I want to use a term like for doing statistical inference, or that, when I want to interpret such a term, I include considerations typical of statistical inference. Within the data domain, that is totally correct. In the paper I argue that there are very good reasons for this. We would like to know what the data can tell us about the actual fitness function, and if we do our statistical inference right, and choose our Price-like equation accordingly, then that means that we would be able to give a meaningful interpretation to a term like . It also means that we then have an equation that describes the genetic population dynamics accurately.

When the reviewer states that other papers treat them as “population level descriptive statistics” in an empirical context, I have a hard time coming up with papers for which that is the case. Most papers apply the Price equation in the modeling domain (That is to say: this is true in evolution. In ecology the Price equation is often applied to data; see Pillai and Gouhier (2019) and Bourrat et al. (2023)). But even if there are researchers that apply the Price equation to data, then considering these statistical quantities as “descriptive statistics” would not make sense. Looking at the descriptive statistics alone is not an empirical exercise; it is just a routine that happens before the actual statistical inference starts. In a data context, saying that considerations that are standard in statistical inference do not apply, because one is just not doing statistical inference, is the equivalent of an admission of guilt. If you do not consider statistical significance, and never mention that sample size could matter, because you are using these terms as “descriptive statistics, not inferential statistics”, then you’re basically admitting to not doing a serious empirical study.

Besides treating statistical quantities as descriptive statistics in a data context, the reviewer also states that, in a stochastic modeling context, other researchers treat the same statistical quantities as “statistics of random variables”. This is first of all very generous to the existing literature. I imagine that the reviewer is imagining a modeling exercise where for instance the covariance between two variables is postulated. A theory exercise would then take that as a starting point for the derivation of some theoretical result. This, however, is not what happens in most of the literature.

There are two things that I would like to point out. First of all, postulating covariances and deriving results from assumptions regarding those covariances is not an activity that requires using the Price equation. There are many stochastic models that function perfectly fine without the Price equation. This is maybe a detail, but it is important to realize that what the reviewer probably thinks of as a legitimate theoretical exercise may be something that can very well be done without the Price equation.

Secondly, I would like to repeat something that I have pointed out before, which is that the Price equation can be written for any transition, whether this transition is likely or unlikely, given a model, and even for transitions that are impossible. For all of those transitions, one can write the (ungeneralized) Price equation, and for all of those, the Price equation will be an identity, and it will contain the things that the reviewer refers to as “statistical quantities”. It is important to realize that these “statistical quantities”, therefore, are properties of a transition, and that every transition comes with its own ”statistical quantity”. That implies that they are not properties of random variables; they reflect something regarding one transition. What one could imagine, though, is the following. To fix ideas, let’s take the Price equation in regression form, and focus on . A meaningful modeling exercise starts with assumptions about the likelihood of all different transitions, and therefore the likelihood of different values of 𝛽 materializing – or it starts with assumptions that imply those probabilities. In a theoretical exercise, one could then derive statements about the expectation and variance of those “statistical quantities”. For instance, one can calculate the expected value 𝐸[𝛽] =𝐸, and the variance 𝑉𝑎𝑟[𝛽] = 𝑉𝑎𝑟 , where this expectation is a proper expectation (taken over the probabilities with which these transitions materialize) and this variance is a proper variance, for the same reason.

This is what I do on page 416 of van Veelen (2005) and in Section 5 of Appendix A. I think something like this is what the reviewer may have in mind, but it is worth pointing out that this still does not mean that the from the Price equation for any given transition is now a property of a random variable. Much of the literature, however, is not at the level of sophistication that I imagine the reviewer has in mind – although there are papers that are; see the discussion below of Rousset and Billiard (2000) and Van Cleve (2015).

In the appendix to this reply, I will address the quotes from Gardner, West, and Wild (2011) and Rousset (2015). This takes up some space, so that is why it is at the end of this reply.

In short, the manuscript seems to argue that Price equation users are performing statistical inference incorrectly, whereas the users insist that they are not doing statistical inference at all.

That is not what the manuscript argues, but I am happy to clarify. The manuscript explores both the use of the Price equation when applied to data (and therefore for statistical inference) and when applied to transitions in a model. The criticism on the existing literature is not that it performs statistical inference incorrectly. The criticism is that the literature insists on misspecification, which typically happens in a modelling context.

The problem (and here I think the author would agree with me) arises when users of the Price equation go on to make predictive or causal claims that would require the kind of statistical analysis they claim not to be doing. Claims of the form "Hamilton's rule predicts.." or use of terms like "benefit" and "cost" suggest that one has inferred a predictive or causal relationship in the given data, while somehow bypassing the entire theory of statistical inference.

I do not really know how to interpret this paragraph. The use of the word “data” suggests that this pertains to a data context, but I do not know what would qualify as a “predictive claim” in that domain, or how any study would go from data to a claim of the form “Hamilton’s rule predicts …”. Again, I do not really know papers that apply the Price equation to data. None of the empirical papers reviewed in Bourke (2014) for instance do. I would however agree that it is close to obvious that an approach that does indeed bypass the entire theory of statistical inference cannot identify causal relations in datasets. I think the examples in Section 2 of Appendix A also clearly illustrate that a literature in which the word “sample size” is absent, cannot be doing statistical inference.

There is also a third way to use the Price equation which is entirely unobjectionable: as a way to express the relationship between individual-level fitness and population-level gene frequency change in a form that is convenient for further algebraic manipulation. I suspect that this is actually the most common use of the Price equation in practice.

I am not sure if I understand what it means for the Price equation to “express the relationship between individual-level fitness and population-level gene frequency change”. That is a bit reminiscent of how John Maynard Smith saw the Price equation (Okasha, 2005), but he also emphasized that he was unable to follow George Price and his equation. For sure, it cannot be that one side of the Price equation reflects something at the individual level and the other something at the population level, because both sides of the Price equation are equally aggregated over the population. Just to be safe, and to avoid unwarranted associative thinking, I would therefore choose to be minimalistic, and say that the Price equation is an identity for a transition between a parent population and an offspring population.

Regardless of the words we choose, however, the question how harmless or objectionable the use of the Price equation is in the literature is absolutely relevant. In earlier papers I have tried to cover a spectrum of examples of different ways to use (or misuse) the Price equation. In van Veelen (2005) I cover Grafen (1985a), Taylor (1989), Price (1972), and Sober and Wilson (2007). The main paper that is discussed in van Veelen et al. (2012) is Queller (1992b), but Section 7 of that paper also discusses the way the Price equation is used in Rousset and Billiard (2000), Taylor (1989), Queller (1985), and Page and Nowak (2002). These discussions also come with a description of how much it takes to repair them, and this varies all the way from nothing, or a bit of minor rewording, to being beyond repair.

What is good to observe, is that the papers in which the use of the Price equation is the least problematic, are also the papers in which, if the reference to the Price equation would be taken out, nothing really changes. These are papers that start with a model, or a collection of models, and that, at some point in the derivation of their results, point to a step that can, but does not have to be described as using the Price equation. An example of this is Rousset and Billiard (2000); see the detailed description in Section 7 of van Veelen et al. (2012).

I am happy to point to a few more papers on the no harm, no foul end of the spectrum here.

Allen and Tarnita (2012) discuss properties of the dynamics in a well-defined set of models.

Towards the end of the paper, a version of the Price equation more or less naturally appears. This is more of an interesting aside, though, and does not really play a role in derivation of the core results of the paper. Van Cleve (2015) is similar to Rousset and Billiard (2000), in that the “application of the Price equation” there is a minor ingredient of the derivation of the results. (A detail that this reviewer may find worth mentioning, given earlier comments, is that Van Cleve (2015) writes the left-hand side of the Price equation as 𝐸(𝑤Δ𝑝|𝐩), instead of . First two very unimportant things. Van Cleve (2015) uses 𝑤 for mean fitness, for which is a more common symbol. Another detail of lesser importance is that it includes the vector of parent p-scores in the notation, which in their notation is 𝐩. More importantly, however, is that Van Cleve (2015) writes 𝐸(Δ𝑝) for , which extends the (mis)use of the symbol 𝐸 for what really is just an average. This is consistent within the Price equation, in the sense that it now denotes the average with 𝐸, both on the right-hand side and on the left-hand side of the Price equation. It can however be a little bit confusing, because when Rousset and Billiard (2000) write , then this is a proper expectation. In their case, this summarizes all possible transitions out of a given state, and weighs them by their probabilities of happening, given a state summarized by 𝑝.). I am also happy to extend the spectrum a bit here. Some papers on inclusive fitness do not use the Price equation at all, even though one could imagine places where it could be inserted. A nice example of such a paper is Taylor et al. (2007).

In this paper, I hope I can be excused from taking a complete inventory of this literature, and I hope that I do not have to count how many papers fall into the different categories. This would help assess the veracity of the suspicion the reviewer has, which is that the most common use of the Price equation is entirely unobjectionable, but I just do not have the time. I would however not want to underestimate the aggregate damage done in this field. The spectrum spanned in my earlier papers does include a fair amount of nonsense results. This typically happens in papers that do not study a specific model or set of models, but that take the Price equation as their point of departure for their theorizing. Also there seems to be a positive correlation between how exalted and venerating the language is that is used when describing the wonders and depths of the Price equation, and how little sense the claims make that are “derived” with it.

We also should not set the bar too low. This is a literature that, at the starting point, has a few construction errors in it, as described in the paper. That is reason for concern. Moreover, one of the main end products of this literature is what we send our empiricists to the field with. As Section 8 of van Veelen et al. (2017) indicates, what we have supplied to our empiricists to work with is nothing short of terrible. I would therefore want to maintain that the damage done is enormous, and if there are also a few papers around that may use the ungeneralized Price equation in an innocuous way, then that is not enough redemption for my taste. We are still facing a literature in which, at every instance where the Price equation is used, we still need to check in which category it falls.

For a paper that aims to clarify these thorny concepts in the literature, I think it is worth pointing out these different interpretations of statistical quantities in the Price equation (descriptive statistics vs inferential statistics vs algebraic manipulation). One can then critique the conclusions that are inappropriately drawn from the Price equation, which would require rigorous statistical inference to draw. Without these clarifications, supporters of the Price equation will again argue that this manuscript has misunderstood the purpose of the equation and that they never claimed to do inference in the first place.

I would like to return to the point that I made at the beginning of my response to point (4), which is that the “thorniness” of these concepts is the result of the warp in the literature, resulting from the construction errors in Price (1970). If people want to understand how to apply the Price equation right, I think that reading Appendix A and B would work just fine. Again, I have not read anything that suggests that there is anything incorrect in there, so if the literature contains “thorny” concepts, it might just be that this is the result of the mental gymnastics necessitated by the unwillingness to accept that there might be something not completely right with Price (1970). Moreover, given my experiences in the field, I am not sure that there is anything that I could say that would convince the supporters of the ungeneralized Price equation.

(5) "True" models: Even if one accepts that the statistical quantities in the Price equation are inferential in nature, the author appears to go a step further by asserting that, even in empirical populations, there is a specific "true" model which it is our goal to infer. This assumption manifests at many points in the SI when the author refers to the "true model" or "true, underlying population structure" in the context of an empirical population.

Again, in Appendix A I explore both a data context and a modeling context. In the modeling context none of this applies, because in such a context, there is only the model that we postulate. In the part in which I explore what the Price equation can do in a data context, I do indeed use words like “true model” or "true underlying population structure".  

I do not think it is necessary or appropriate, in empirical contexts, to posit the existence of a Platonic "true" model that is generating the data. Real populations are not governed by mathematical models. Moreover, the goal of statistical inference is not to determine the "true model" for given data but to say whether a given statistical model is justified based on this data. Fitting a linear model, for example, does not rule out the possibility there may be higher-order interactions - it just means we do not have a statistical basis to infer these higher-order interactions from the data (say, because their p-scores are insignificant), and so we leave them out.

This remark suggests that the statistical approach in Sections 2-4 of Appendix A is more naïve than it should be, and that I would overlook the possibility of, for instance, interaction effects that are really nonzero, but that are statistically not significant. Now first of all, at a superficial level, I would like to say that this strikes me as somewhat inconsistent. In the remarks further back, the reviewer seems to excuse those that use the Price equation on data without any statistical considerations whatsoever. The reason why the reviewer is giving them a pass, is that they are “just not doing statistical inference”. Instead, they are doing this whole other thing with, you know, descriptive statistics. As I indicated above, that is just a fancy way of saying that they are not doing serious statistics – or serious empirics, for that matter.

In this comment, on the other hand, the reviewer also suggests that the statistics that I use to replace the total absence of any statistical considerations with, is not quite up to snuff. Below, I will indicate why that is not the case at all, but I think it is also worth registering a touch of irony there.

In order to address this issue, it is worth first observing that the whole of classical statistics is based on probability theory in the following sense. We are always asking ourselves the question: if the data generating process works like this, what would the likelihood be of certain outcomes (datasets); and if the data generating process works some other way (sometimes: the complement of whatever “this” is), what would the likelihood then be of the same outcomes. By comparing those, we draw inferences about the underlying data generating process (which is a word suggestive of a “Platonic” world view that the reviewer seems to reject). Therefore, if one would impose a ban on using Platonic words like “true data generating process”; “actual fitness function”; or “the population structure that is out there”, it would be impossible to teach any course in statistics, basic or advanced. Also it would be impossible to practice, and talk about, applied statistics.

Now the reviewer claims that “Real populations are not governed by mathematical models”. I do not really know if I agree or disagree with that statement, but the example that the reviewer gives does not fit that claim. The reviewer suggests that if we find a higher order term not to be statistically significant (and therefore we reject the hypothesis that it is nonzero), then that would not necessarily mean that it is not there. That is totally true, and statisticians tend to be fully aware of that. But that does not imply that there is no true data-generating process; the whole premise of this example is that there is, but that the sample size is not large enough to determine it in a detailed enough way so as to include this interaction effect, that apparently is small relative to the sample size.

The third thing to reflect on here, is that the reviewer seems to suggest that the Generalized Price equation in regression form, as presented in my paper, comes with a specific statistical approach, that he or she classifies as philosophically naïve or unsophisticated. That, however, is not the case, and I am very grateful that this remark by this reviewer allows me to make a point that I think shines a light on how the Generalized Price equation puts the train that started going off the rails in 1970 back on track, and reconnects it with the statistics it borrows its terminology from. To see that, it is good to be aware that statistics never gives certainty. The whole discipline is built around the awareness that it is possible to draw the wrong inference, and the aim is to determine, minimize, and balance, the likelihoods of making different wrong inferences. So, statistics produces statements about the confidence with which one can say that something works one way or the other. In some instances, the data are not enough to say anything with any confidence. In other cases, the data are rich enough so that it is really unlikely that we incorrectly infer that for instance a certain gene matters for fitness.

The nice thing about the setup with the Generalized Price equation, is that those statistical considerations translate one-to-one to considerations regarding which Price-like equation to choose. If the data do not allow us to pick any model with confidence, then we should be equally agnostic about which Price-like equation describes the population genetic dynamics accurately. If the statistics gives us high confidence that a certain model matches the data, then we should pick the matching Price-like equation with the same confidence. This also carries over to higher level statistical considerations.

If we think about terms that, if we would gather a gargantuan amount of data, might be statistically significant, but very small, then economists call those statistically significant, but economically insignificant. When rejecting the statistical significance on the basis of a not gargantuan dataset, statisticians are aware that terms that really have a zero effect, as well as terms, the effect of which is really small, are rejected with the same statistical test – and that we should be fine with that. All such considerations carry over to what we think of regarding the choice of a Price-like equation to describe the population genetic dynamics. Even if people disagree about whether or not to include a term that is statistically significant, but relatively small, such a disagreement can still happen within this setup, and just translates to a disagreement on which Price-like equation to choose.

Similarly, people could also disagree about whether it is justified to use polynomials to characterize a fitness function. If we decide that we can, because of Taylor expansions, then the core result of the paper implies that the population genetic dynamics can be summarized by a generalized Hamilton’s rule (as long as the fitness function includes a constant and a linear term regarding the p-score). On the other hand, if we do not believe this is justified, and prefer to use an altogether different family of fitness functions, then we can no longer do this. All of this leaves space for all kinds of statistical considerations and disagreements, that just carry over to the choice for one or the other Price-like equation as an accurate description of the population genetic dynamics. Or, if one does not believe polynomials should be used, then this leads to not picking any Price-like equation at all.

So, this is a long way of saying that the Generalized Price equation creates space for all statistical considerations to regain their place, and does not hinge on one approach to statistics or another.

What we can say is that if we apply the statistical model to data generated by a probabilistic model, and if these models match, then as the number of observations grows to infinity, the estimators in the statistical model converge to the parameters of the data-generating one.

But this is a mathematical statement, not a statement about real-world populations.

Again, I do not know if I agree or disagree with the last sentence. However, that does not really matter, because either option only has implications for how we are to think of the relation between a Price-like equation describing a population genetic dynamics and real-world populations. It is not relevant for the question which Price-like equation to pick, or whether to pick one at all.

A resolution I suggest to points 3, 4, and 5 above is:

*A priori, the statistical quantities in the Price Equation are descriptive statistics, pertaining only to the specific population data given.

*If one wishes to impute any predictive power, generalizability, or causal meaning to these statistics, all the standard considerations of inferential statistics apply. In particular, one must choose a statistical model that is justified based on the given data. In this case, one is not guaranteed to obtain the standard (linear) Hamilton's rule and may obtain any of an infinite family of rules.

*If one uses a model that is not justified based on the given data, the results will still be correct for the given population data but will lack any meaning or generalizability beyond that.

*In particular, if one considers data generated by a probabilistic model, and applies a statistical model that does not match the data-generating one, the results will be misleading, and will not generalize beyond the randomly generated realization one uses.

Of course, the author may propose a different resolution to points 3-5, but they should be resolved somehow. Otherwise, the terminology in the manuscript will be incorrect and the ms will not resolve confusion in the field.

I have outlined my solutions extensively above. I really appreciate that Reviewers #1 and #2 have spent time and attention on the manuscript and on the long appendices.  

Appendix to the response to reviewer #2: Some remarks on Gardner, West & Wild (2011), Frank (2012), and Rousset (2015)

An accurate response to the quote from Gardner, West, and Wild (2011) in the review report takes up space. I therefore wanted to put that in an appendix to the response to reviewer #2. I also include a few paragraphs regarding Frank (2012) and Rousset (2015), both of which are also mentioned by reviewer #2. All of this might also be of interest to people that are curious about how what I find in my paper relates to the existing literature.

Gardner, West & Wild (2011) The quote I am responding to is “it is a mistake to assume that it must be the evolutionary theorist, writing out covariances, who is performing the equivalent of a statistical analysis” I want to put that into context, so I will go over the whole paragraph that surrounds the quote. The paragraph is called Statistics and Evolutionary Theory and can be found on page 1038 of the paper. I think that it is worth pointing out that it is not easy to respond to their somewhat impressionistic collages of words and formulas. I will therefore cut the paragraph up in a few smaller bits and try to make sense of it bit by bit. The paragraph begins with:

“Our account of the general theory of kin selection has been framed in statistical terms.” Based on what they write two sentences down, the best match between those words and what they do in the paper would be: “our account uses words like “covariance”, “variance” and “expectation” for things that are not what “covariance”, “variance” and “expectation” mean in probability theory and statistics.” I would be totally open to an argument why that is nonetheless OK to do, but the way Gardner, West, and Wild (2011) phrase it obscures the fact that this needs any justification or reflection at all. “Framing something in statistical terms” is unspecific enough to sound completely harmless.

“The use of statistical methods in the mathematical development of Darwinian theory has itself been subjected to recent criticism (van Veelen, 2005; Nowak et al., 2010b), so we address this criticism here.

Also here, specifics would be helpful. The “use of statistical methods” sounds like it is more than just using terms from statistics, so this might refer to the minimizing of the sum of squared differences, which is also mentioned a sentence down in Gardner, West, and Wild (2011). If it does, then it is worth observing that in statistics, the minimizing of the sum of squared differences (or residuals, or errors) comes with theorems that point very clearly to what is being achieved by doing this. The Gauss–Markov theorem states that the ordinary least squares (OLS) estimator has the lowest variance within the class of linear unbiased estimators. This implies that minimizing the sum of squared errors helps answering a well-defined question in statistics; under certain conditions, an OLS estimator is our best shot at uncovering an unknown relation between variables. To also minimize a sum of squared differences, but now in the modeling domain, qualifies as “use of statistical methods” only in a very shallow way. It means that a similar minimization is performed. Without an equivalent of the Gauss-Markov theorem that would shine a light on what it is that is being achieved by doing so, that does not carry the same weight as it does in the statistics domain – in that it does not carry any weight at all.

“The concern is that statistical terms – such as covariances and least-squares regressions – should properly be reserved for conventional statistical analyses, where hypotheses are tested against explicit data, and that they are out of place in the foundations of evolutionary theory (van Veelen, 2005; Nowak et al., 2010b).”

Again, a few things are a bit vague. What are “explicit data”? Are there data that are not explicit? Why the generic “foundations of evolutionary theory”, instead of a more specific description of what these statistical terms are used for? But either way, this is a misrepresentation of what I wrote in van Veelen (2005). I did not suggest to “reserve statistical terms for conventional statistical analysis” just because. As I do here in the current paper, what I did there was explore the possibilities for the Price equation to help with what I then called Type I and Type II questions. Type I questions find themselves in the modeling domain and Type II questions find themselves in the statistical domain. I was not arguing for a ban on applying statistical concepts outside of the domain of statistical inference. All that I said is that in its current practice, it does not really help answering questions of either type.  

“However, this concern is misplaced. First, natural selection is a statistical process, and it is therefore natural that this should be defined in terms of aggregate statistics, even if only strictly by analogy (Frank, 1997a, 1998).”

This is a vague non-argument. Almost nothing is well-defined here. What does it mean for natural selection to be a statistical process? Is that just an unusual term for a random process? If so, then I suppose I agree, but that has nothing to do with what I state or claim. And what does it mean to be defined in terms of aggregate statistics? What is the alternative? I have no idea how any of this relates to anything that I claim or state in my papers.

“Second, Fisher (1930, p198) coined the term ‘covariance’ in the context of his exposition of the genetical theory of natural selection, so the evolutionary usage of this term has precedent over the way the term is used in other fields.”

This is what I would call a “historic fallacy”. The fact that Fisher coined the term “covariance” in a book on genetics and natural selection does not mean that any “evolutionary usage” of the term “covariance”, however nonsensical, now has precedent over the way the term is used in other fields. Irrespective of the path that the history of science, genetics, or statistics took, right now we are in a place where about every student at every university anywhere in the world that takes a course in probability theory and/or statistics, learns that covariance is a property of a random variable (see also Wikipedia). And they do for a very good reason; it is essential in recognizing the relation between probability theory on the one hand and statistics on the other. Being curious how this “evolutionary usage” of the term covariance works, if covariance turns out not to be a property of a random variable, is therefore perfectly justified, and “Fisher coined the term” is not a safe word that exempts it from scrutiny. 

Third, it is a mistake to assume that it must be the evolutionary theorist, writing out covariances, who is performing the equivalent of a statistical analysis.

Again, that is just not what anyone is saying. Nobody is suggesting that an evolutionary theorist should perform the equivalent of statistical analysis. All I did was point to how little is being achieved by transferring formulas from statistics to a modeling context.

A better analogy is to regard Mother Nature in the role of statistician, analysing fitness effects of genes by the method of least-squares, and driving genetic change according to the results of her analyses (cf. Crow, 2008).

I have no idea what any of this means. Mother Nature is a personification of something that is not a person, and that does not have cognition. Without sentience, “Mother Nature” cannot assume the role of statistician, and cannot analyse fitness effects.

More generally, analogy is the basis of all understanding, so when isomorphisms arise unexpectedly between different branches of mathematics (in this case, theoretical population genetics and statistical least-squares analysis) this represents an opportunity for advancing scientific progress and not an anomaly that is to be avoided.

This is a strawman argument, puffed up with platitudes. Nobody is arguing against analogies. But what is the analogy supposed to be here? Just taking least squares from statistical inference and performing it in a modeling context does not make it an analogy. The GaussMarkov theorem, which is the basis for why least squares helps answering questions in statistics, just does not mean anything in a modeling context. OLS in modeling is just willful misspecification, and nothing that it does in statistics translates to anything meaningful in modeling. Again, declaring it an analogy, or an isomorphism, does not make it one.

Frank (2012) Because the reviewer also mentions Frank (2012), I would like to include a small remark on this paper too. “Natural Selection. IV. The Price equation” by Frank (2012) is partly a response to my earlier criticism of the use of the Price equation. Much like Gardner, West, and Wild (2011), I would describe this paper as what is called a ”flight forwards” in Dutch. While the questions I ask are relatively prosaic (such as: how does the Price equation help derive a prediction from model assumptions?), Frank (2012) pivots to suggesting that there is a profound philosophy-of-science disagreement that I am on the wrong side of. It is close to impossible to respond to Frank (2012), because it is a labyrinth of arguments that sound deep and impressive, but that are just not specific enough to know how they relate to points that I made – or even just what they mean in general. Just to pick a random paragraph:

“Is there some reorientation for the expression of natural selection that may provide subtle perspective, from which we can understand our subject more deeply and analyse our problems with greater ease and greater insight? My answer is, as I have mentioned, that the Price equation provides that sort of reorientation. To argue the point, I will have to keep at the distinction between the concrete and the abstract, and the relative roles of those two endpoints in mature theoretical understanding.”

For many of those terms, I have no real idea what they mean, and also reading the rest of the paper does not help understanding what this has to do with the more prosaic questions that are waiting for an answer. What is “reorientation”? What does “concrete” versus “abstract” have to do with the question what is being achieved by doing least squares regressions in modeling? What would be an example of a mature and an immature theoretical understanding?

Rousset (2015) is also mentioned by the reviewer. This paper is not esoteric. It states, as reviewer #2 points out, that "neither data nor inferences are considered". This paper therefore finds itself in the modeling domain, and not in the data domain. It does however still dodge the question what the benefits are of misspecification in the modeling domain. As a matter of fact, it denies that there is misspecification at all.

“In the presence of synergies, the residuals have zero mean and are uncorrelated to the predictors. No further assumption is made about the distribution of the residuals. Thus, there is no sense in which the regression is misspecified.”

This is a remarkable quote, and testament to the lasting impact of the construction errors in Price (1970). Misspecification is literally defined as getting the model wrong. In statistics, avoiding misspecification can be complicated, because of the noise in the data. The real datagenerating process is unknown, and because of the noise, there is always the possibility that data that are generated by one model look like they could also have been generated by another. The challenge is to reduce the odds of getting the model wrong to acceptable proportions, which is what statistical tests are for. But in modeling, we know what the model is; it is postulated by the modeler. Therefore, misspecification can be avoided by just not replacing it with a different model.

What is being discussed in this part of Rousset (2015) is replacing what in this manuscript is called Model 3 (𝑤_𝑖 = 𝛼 + 𝛽_1,0𝑝_𝑖 + 𝛽_1,1𝑝_𝑖 + 𝛽_1,1𝑝_𝑖𝑞_𝑖 + 𝜀_𝑖) with Model 2 (𝑤_𝑖 = 𝛼 + 𝛽_1,0𝑝_𝑖+ 𝛽_1,0𝑝_𝑖𝑞_𝑖 + 𝜀_𝑖), and choosing the parameters in Model 2 so that it is as close as it can be to Model

(3) This is just the definition of misspecification. That is to say: the misspecification part is the choosing of Model 2 as a reference model. The minimizing of the sum of squared residuals one could consider as minimizing the damage.

While Rousset (2015) finds itself in the modeling domain, it does nonetheless point to the field of statistics here, by stating that “the residuals have zero mean and are uncorrelated to the predictors”. From this, the paper concludes that “there is no sense in which the regression is misspecified”. That is just plain wrong. Minimizing the sum of the squared residuals guarantees that the residuals are uncorrelated with the variables that are included in the reference model, with respect to which the squared sum of residuals is minimized. The criterion that Rousset (2015) uses is that the model is well-specified if there is no correlation between the residuals (here: ) and the variables included in the reference model (here: 𝑝_𝑖 and 𝑞_𝑖). But according to this criterion, all models would always be well-specified, and no model could ever be misspecified. The correct criterion, however, also requires that the residuals are not correlated with variables not included in the reference model. And here, the residuals are in fact correlated with 𝑝_𝑖𝑞_𝑖, which is the variable that is included in Model 3, but not in Model 2. Therefore, according to the correct version of this criterion, this model is in fact misspecified – as it should be, because getting the model wrong is the definition of misspecification.

In order to make sure that there can be no misunderstanding, I have added subsections at the end of Section 2 and Section 4 of Appendix A, and at the end of Section 2 of Appendix B. These subsections show that the algebra of minimizing the sum of squared errors implies that there is no correlation between the errors, or the residuals, and the variables that are included in the model. This is by no means something new; it is the reason why we do OLS to begin with. For additional details about misspecification, I would refer to Section 1b (viii) in van Veelen (2020).

Finally, there is a detail worth noticing. In the main text, as well as in Appendix B, I use an analogy (and, unlike what Gardner, West, and Wild, 2011, refer to as an analogy, this actually is one). This is an analogy between two choices. On the one hand, there is the choice between Price-like equation 1 (based on Model 1 as a reference model) and Price-like equation 2 (based on Model 2 as a reference model) both applied to Model 2. On the other hand, there is the choice between Price-like equation 2 (based on Model 2 as a reference model) and Price-like equation 3 (based on Model 3 as a reference model) both applied to Model 3. Model 1 is the non-social model, Model 2 is the social model without interaction term, and Model 3 is the social model with interaction term. That makes the first choice a choice between treating a social model as a social model, or as a non-social model. The second choice is between treating a social model with interaction term as a social model with interaction term, or as a social model without interaction term. The power of this analogy is that every argument against treating the social model as if it is a non-social model is also an argument against treating the social model with interaction term as if it is a social model without interaction term.

This ties in with the incorrect criterion for when a model is well-specified from Rousset (2015) as follows. His criterion (that there should be no correlation between the residuals and the variables in the model) declares the social model without interaction term well-specified as a reference model, when we are considering a social model with interaction term. According to the same criterion, however, the non-social model would also have to be declared to be wellspecified as a reference model, when the model we are considering is a social model. The reason is that also here, there is no correlation between the residuals and the variables that are included in this model. This is clearly not what anyone is advocating for, and for good reasons. The residuals here would, after all, be correlated with the p-score of the partner, which is a variable that is not included in the non-social model. This is a good indication that we should not use the non-social model for a social trait.

Reviewer #3 (Public review):

Before responding to this review, I would like to express that I appreciate the fact that the reviews and the responses are public at eLife. Besides just being useful in general, this also allows readers to get a behind the scenes glimpse into the state of the field, and the level of the reviewing. While the reports by Reviewers #1 and #2 show openness and an interest in getting things right, the report by Reviewer #3 is representative of the many review reports that I have received from the inclusive fitness community in the past. These reports tend to be rhetorically strong, and to those who do not have the time to dig deeper in the details, these reports are probably also convincing. I will therefore go through this review line by line to show how little there is behind the confident off-hand dismissal.

There is an interesting mathematical connection - an "isomorphism"-between Price's equation and least-squares linear regression.

This is esoteric and needlessly vague. Why is the word “isomorphism” used? In mathematics, an isomorphism is a structure-preserving mapping. The Price equation is an equation, or an identity, which makes it a bit difficult to imagine what the set of objects is on one end of the mapping. Least-squares linear regression can perhaps be seen as a function of a dataset, which would make it a single object (one function). This complicates things at the other end of the mapping too, if that set is a singleton set. The only isomorphism that I can think of is a trivial isomorphism where one equation is mapped onto one function and vice versa. It seems unlikely that this is what the reviewer means. The word isomorphism moreover is in quotes, so maybe this is supposed to be figurative. But what would it be that is being suggested here by this figure of speech? Just saying that there is, as the reviewer puts it, an “interesting mathematical connection”, does not make it so. It would already be a start to just specify what the mathematical connection is, because I have a hard time seeing what that would be. Is it just that, if you divide the Cov(𝑤, 𝑝)-term by the Var(𝑝)-term, then you get a regression coefficient? If that is what the reviewer has in mind, that would be a rather shallow observation.

Some people have misinterpreted this connection as meaning that there is a generalitylimiting assumption of linearity within Price's equation, and hence that Hamilton's rule-which is derived from Price's equation-provides only an approximation of the action of natural selection.

Here, the reviewer pulls a switcheroo. The use of the word “general”, or “generality”, here refers to the fact that the classical Price equation is an identity for all possible transitions between a parent and an offspring population. This is the sense in which the inclusive fitness literature uses the word general, and so do I in the relevant places in the manuscript. When I do, I make sure to add phrases like “in the sense that whatever the true model is, it always gets the direction of selection right”. As a consequence, the classical Hamilton’s rule is also totally general, in the same sense.

One of the core points of the paper is that this is not unique to the classical Price equation. As a matter of fact, there is a large set of Price-like equations and Hamilton-like rules that are equally much identities, and equally much general (in the sense that they get the direction of selection right for all possible transitions). The being an identity and being completely general (in this sense) therefore cannot be a decisive criterion in favour of the classical Price equation and the classical Hamilton’s rule.

On the other hand, the way in which my Generalized Price equation and my generalized version of Hamilton’s rule are general, is that they do not restrict the statistical model with respect to which errors are squared, summed and minimized to one linear statistical model. This generalization generates the variety of Price-like equations and Hamilton-like rules mentioned above (all of which are general in the sense of always getting the direction of selection right) and it gives us the flexibility to pick one that separates terms that reflect the fitness function from terms that reflect the population state.

In response to my generalizing the Price equation and Hamilton’s rule in this second sense, the criticism of the reviewer comes down to saying that the Price equation and Hamilton’s rule do not need generalizing, because they already are general – the switcheroo being that this refers to generality in the first sense. That makes it sound like this could be an honest mistake, confusing one way in which these can be described as general with another. However, I really hammered this point home in the manuscript. Even a cursory reading of the manuscript reveals that I am fully aware that the classical Price equation and the classical Hamilton’s rule are general in the first sense.

It is also not helpful that, as a description of what I supposedly claim, this is impressionistic, and lacks specificity. The Price equation is an equation, or an identity. What does it mean for there to be an “assumption of linearity” within it? For the classical Price equation in covariance form (which Reviewer #2 argues is what most people think of as “the Price equation”) there is no way in which one can transform this into a meaningful statement. There is just nothing in there to which the adjective “linear” can be applied. Linearity only becomes a thing when we ask ourselves how we can interpret the regression coefficient in the classical Price equation in regression form. That would be the linearity of the statistical model the differences with which are squared, summed and minimized in the regression.

This is in contrast to the majority view that Hamilton's rule is a fully general and exact result.

Again, in this manuscript, I write, time and again, that the classical Hamilton’s rule is fully general (in the sense that it is applies to any transition), and exact (if that means that it always gets the direction of selection right). So, this is clearly not where the contrast with the majority view lies. The contrast with the majority view is that the majority insist on misspecification, and I suggest not to do that.

To briefly give some mathematical details: Price's equation defines the action of natural selection in relation to a trait of interest as the covariance between fitness 𝑤 and the genetic breeding value 𝑔 for the trait, i.e. Cov(𝑤, 𝑔);

The Price equation is an identity, not a definition. When deciding on a definition, there is some freedom. We can choose to define ⊂ so that 𝐴 ⊂ 𝐵 means that 𝐴 is a strict subset of 𝐵; or we can choose to define ⊂ so that 𝐴 ⊂ 𝐵 means that 𝐴 is a (not necessarily strict) subset of 𝐵. The Price equation does not “define the action of natural selection”, because it is an identity. There is no freedom to “define” any other way.

The more serious reason why this is conceptually also a little dangerous, is the following. Imagine a locus with two alleles. Both of them are non-coding bits of DNA. Selection therefore does not act on either of them. Now imagine a parent population with an average p-score of 0.5, or, in other words, the frequency of these alleles in the parent population is 50-50. That makes the expected value of the p-score in the offspring population 0.5 too. In finite populations, however, randomness can make the p-score grow a bit larger or a bit smaller than 0.5. If the parent population is small, the variance (the expected squared deviation from 0.5) can actually be sizeable. If the p-score in the offspring population lands above 0.5, then the Price equation has a > 0 and a 𝐶𝑜𝑣(𝑤, 𝑝) > 0. Describing the Price equation as “defining the action of natural selection” now suggests that higher p-scores have been selected for (or, in other words, that “the action of natural selection in relation to a trait of interest” is positive). With equal probability, however, < 0 and therefore also 𝐶𝑜𝑣(𝑤, 𝑝) < 0, and this would then make us draw the opposite conclusion, that natural selection has acted to lower the p-scores in the population. Both of those would be wrong, because in this situation, it would have been randomness that changed the average p-score. 

this is a fully general result that applies exactly to any arbitrary set of (𝑔, 𝑤) data; without any loss of generality this covariance can be expressed as the product of genetic variance Var(𝑝) and a coefficient 𝑏(𝑔, 𝑤), the coefficient simply being defined as 𝑏(𝑔, 𝑤) = for all Var(𝑝) > 0; it happens that if one fits a straight line to the same (𝑔, 𝑤) data by means of least-squares regression then the slope of that line is equal to 𝑏(𝑔, 𝑤).

Why this needs to be explained is a bit of a mystery. These “mathematical details” are in almost all Price equation papers, and they are the point of departure of my Appendix A (it is on page 7 of a more than 90 page long set of appendices). Seeing the need to explain this suggests that the reviewer thinks that there is a chance that I or anyone reading this paper would have missed this. I have not, and, more importantly, none of this invalidates the point I make in the paper.   

All of this has already been discussed, repeatedly, in the literature.

All of this has already been discussed, repeatedly, in the literature indeed. It is just that it does not engage with anything I write in the manuscript, or that I wrote in my other papers.

Now turn to the present paper: the first sentence of the Abstract says "The generality of Hamilton's rule is much debated", and then the next sentence says "In this paper, I show that this debate can be resolved by constructing a general version of Hamilton's rule".

This is correct.

But immediately it's clear that this isn't really resolving the debate, what this paper is actually doing is asserting the correctness of the minority view (i.e. that Hamilton's rule as it currently stands is not a general result)

It seems to me that the reason why this is “immediately clear” to this reviewer is that the reviewer has not processed the contents of the paper. I am not sure if I have to repeat this, but I am not saying that “Hamilton’s rule as it currently stands” is not general (in the sense that it always gets the direction of selection right). It is, and I say that it is a bunch of times. But so are other rules.

and then attempting to build a more general form of Hamilton's rule upon that shaky foundation.

I am not just “attempting to build a more general form of Hamilton's rule”. I did in fact build a more general form of Hamilton’s rule (where the generality refers to the richer set of reference statistical models).

Predictably, the paper erroneously interprets the standard formulation of Hamilton's rule as a linear approximation and develops non-linear extensions to improve the goodness of fit for a result that is already exactly correct.

Nowhere in the paper or the appendices do I describe the standard formulation of Hamilton’s rule (or, for that matter, any formulation of Hamilton’s rule) as an “approximation”. It is just not a word that has anything to do with this. If we are doing statistical inference, and the sum of squared errors that is minimized decreases by adding a variable in the statistical model with regard to which the sum of squared errors is minimized, then that will typically improve the goodness of fit. In statistics this is not described that as an improvement in how well the statistical model “approximates” the data, or whatever it is that the reviewer would suggest is being approximated here.

This is not a convincing contribution. It will not change minds or improve understanding of the topic.

There is indeed plenty of scope for this not to change minds or improve understanding of the topic. It will not change the minds or improve the understanding of those that are not really interested in getting this right. Obviously, it will also not convince those that do not read it.

Nor is it particularly novel. Smith et al (2010, "A generalisation of Hamilton's rule for the evolution of microbial cooperation" Science 328, 1700-1703) similarly interpreted Hamilton's rule as a linear model and provided a corresponding polynomial expansion - usefully fitting the model to microbial data so as to learn something about the costs and benefits of cooperation in an empirical setting. it's odd that this paper isn't cited here.

Let me begin by pointing to what I agree with. Given that smith et al. (2010) and my manuscript are both in the business of generalizing Hamilton’s rule, it would be helpful to the reader if my paper includes more information about how the two efforts relate. I will discuss the relation below, and I will also include that in Appendix B, and point to it in the main text. Before I do, however, I would like to point to two details in the review report that fit a pattern.

The first is that the reviewer describes what smith et al. (2010) do as “useful”, and seems to think of fitting polynomial expansions as a legitimate way to “learn something about the costs and benefits of cooperation in an empirical setting”. That sounds quite positive. My paper, in which I supposedly repeat this, however, is characterized as misguided. This fits a pattern; all of the reviews I received from the inclusive fitness community include a “done before”, and regularly the done before is described approvingly, while my paper is described as fundamentally flawed.

Also customary is the lack of detail. What would be really useful here, is something like “equation A.14 in this manuscript is the same as equation 6 in smith et al. (2010) if we choose . This kind of statement would pin down the way in which what I do has been done before. That, however, would require going into detail, at the risk of finding out that what is done in my manuscript is actually quite different from what happens in smith et al. (2010). That is also a recurrent thing. When I look up the done before, I typically find something that is not quite the same.  

Now on to the paper. What smith et al. (2010) try to do is something that I wholeheartedly support. It is an empirical study that tries to capture non-linearity. A first point of order is that it is worth asking ourselves: linear or non-linear in what? For that, I would like to go back to the setup of my manuscript. Model 2 from the Main Text is

In this fitness function, 𝑝! is the p-score of individual 𝑖 and 𝑞! is the p-score of the partner that individual 𝑖 is matched with. This is a standard model of social behaviour if 𝛽_1,0 < 0 and 𝛽_0,1 > 0. Such choices for 𝛽_1,0 and 𝛽_0,1 indicate that having a higher p-score decreases the fitness of individual 𝑖 and increases the fitness of its partner. Here we assume that 𝛼 = 1, 𝛽_1,0 \= −1, and 𝛽_0,1 \= 2. We assume that p-scores can only be 0 or 1, or, in other words, we assume that there are only cooperators and defectors in the population (or, in terms of smith et al., 2010: cooperators and cheaters).

For a well-mixed population, where the likelihood of being matched with a cooperator is the same for cooperators and defectors (it is equal to the frequency of cooperators for both), we can now plot the fitnesses of cooperators (red) and defectors (blue) as a function of the frequency of cooperators (Appendix 1-figure 6 left).

We can do the same for a population with relatedness where the probability of being matched with a cooperator is + 𝑓_c for cooperators, and 𝑓_c for defectors, where 𝑓_c is the frequency of cooperators (Appendix 1-figure 6 right). For relatedness 𝑟 = 0 and 𝑟 = "7, cooperation is selected against at every frequency.

Increasing relatedness further, we would find that for 𝑟 = the lines coincide, which implies that at every frequency, cooperation is neither selected for nor against. For 𝑟 > ": cooperation will be selected for at every frequency. This pattern implies that, as we have seen in the manuscript, the classical Hamilton’s rule works perfectly fine for Model 2; with 𝑐 = −𝛽_1,0 = 1 and 𝑏 = 𝛽_0,1 \= 2, cooperation is selected for if and only if 𝑟𝑏 > 𝑐. The fitnesses of cooperators and defectors as functions of the frequency of cooperators, moreover, are always parallel lines, regardless of relatedness.

Model 3 in the main text extends Model 2 by adding an interaction term:

Now we choose 𝛼 = 1, 𝛽_1,0 = −1, 𝛽_1,0 = 1, and 𝛽_1,1  \= 1. We again draw the fitnesses of cooperators and defectors, both at relatedness 𝑟 = 0 (Appendix 1-figure 7 left) and at relatedness 𝑟 = (Appendix 1-figure 7 right). In the manuscript, I argue that the appropriate version of Hamilton’s rule here is Queller’s rule: 𝑟_0,1𝑏_0,1 + 𝑟_1,1𝑏_1,1 > 𝑐 with 𝑐 = −𝛽_1,0 = 1, 𝑏_0,1 = 𝛽_0,1 = 1, and 𝑏_1,1 = 𝛽_1,1 = 1. The fitnesses of cooperators and defectors as functions of the frequency of cooperators are still straight lines, but they are no longer parallel.

The first thing to observe, therefore, is that a model with synergy, in which the classic version of Hamilton’s rule would be misspecified, and Queller’s rule would be well-specified, does not require the fitnesses as functions of the frequencies of cooperators to be non-linear. All that changes with the addition of the interaction term, is that they stop being parallel.

The paper by smith et al. (2010) is an effort to capture non-linearities in the way fitnesses depend on the frequency of cooperators. That, therefore, goes beyond the step from Model 2 to Model 3. Whether it uses the right method to capture those non-linearities, we will come back to in a second, but it is important to realize that also without these non-linearities, the classic version of Hamilton’s rule can be too limiting to accurately describe selection. (Here, I should add that this implies that we were wrong in Wu et al. (2013), when we suggested that “for this experiment, it seems unnecessary to use the generalized Hamilton’s rule, if instead the Malthusian fitness is adopted. In other words, the Wrightian fitness approach calls for a generalization of Hamilton’s rule, whereas the Malthusian fitness approach does not (or at least not in a drastic way, as Malthusian fitnesses are almost linear in the frequency of cooperators).” Using Malthusian fitnesses, the functions were close to linear, but not close to parallel, and therefore also here, Hamilton’s rule needs generalizing - albeit in a different way than smith et al. (2010) did).

The cooperation that is observed in the Myxococcus xanthus studied by smith et al. (2010) is not a good match with a model where individuals are matched in pairs for an interaction that determines their fitnesses. These microbes cooperate in large groups, and a better match would therefore be the n-player public goods games studied in van Veelen (2018). There, we see that simple, straightforward ways to describe synergies (or anti-synergies) can easily lead to fitnesses not being linear in the frequency of cooperators.

The way smith et al. (2010) try to capture those non-linearities, however, is not free of complications. We addressed those in Wu et al. (2013), and I summarized them, shortly, in van Veelen (2018). One of the issues is that most of the non-linearity smith et al. (2010) pick up is the result of considering Wrightian fitness rather than Malthusian fitness. In a continuous time model with a constant growth rate, the population size at time 𝑡 is 𝑁(𝑡) = 𝑒^mt𝑁(0), where 𝑚 is the Malthusian fitness. In a discrete time model with a constant average number of offspring per individual, the population at time 𝑡 is 𝑁(𝑡) = 𝑤^t𝑁(0), where 𝑤 is the Wrightian fitness. If we take 𝑚 = ln 𝑤, these are the same, and if 𝑤 is close to 1, then 𝑚 can be approximated by 𝑤 − 1. That also implies that if 𝑤 is close to 1 (or, equivalently, if 𝑚 is close to 0) one is locally linear if the other is too. However, in the experiment by smith et al. (2010) the aggregate fitness effects are not small, and what is highly nonlinear in terms of Wrightian fitness is close to linear in Malthusian fitness.

Another complication is that the Taylor coefficients that smith et al. (2010) find are the result of a combination of the data and the choice of a functional form they choose to first apply to their data. That means that a different choice of a functional form would have given different Taylor coefficients, while the in-between transformation can also be skipped. Also, the number of Taylor coefficients is larger than the dimensionality of the data, which are based on averages for 6 frequencies. For more details on these complications, I would like to refer to Wu et al. (2013) and van Veelen (2018). A nice detail is that if we consider the way the fitnesses of cooperators and defectors compare when using Malthusian fitnesses, then a comparison of the slopes actually suggests anti-synergies, which leads to a stable mix of cooperators and cheaters, already in the absence of population structure. This matches what is suggested by Archetti and Scheuring, (2011, 2012) and Archetti (2018).

Besides these technical complications, smith et al. (2010) is also different, in the sense that it is an empirical paper. It does not contain the Generalized Price equation, it contains no insights regarding how to derive population genetic dynamics from the Generalized Price equation, or how to derive the appropriate rules from those, and it has a very different approach to separating fitness effects and population structure.

To end on a positive note, I would like to quote a bit out of Wu et al. (2013):

“While we criticise these mathematical issues, we are convinced that smith et al. (2010) aim into the right direction: to incorporate the nonlinearities characteristic of biology into social evolution, we may have to extend and generalize the approach of inclusive fitness. It would be beautiful if such a generalization would ultimately include Hamilton’s original rule as a special case […].”

I like to think that this is exactly what I have done in this paper.

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I thought that this statement, for any culture fighting for preservation, can relate to very well. Like mentioned "varying lands" all are unique and moreover, so creative. It is that creativity and drive that allows cultures to continue perpetuating what they love, as a way of survival. In this part they talk about media ad artists, but this can expand over the many practices within every single culture in the world.

This came off as a very powerful statement, and can shed light on how people, within spaces, can be quick to judge when certain descriptive words are added. Interesting how the initial descriptors like writer or artist often are overlooked, but the moment "aboriginal" is included, whole perspectives change. Could that be for the better? Or for the worse?

a person who thinks and acts in an independent way, often behaving differently from the expected or usual way

eLife Assessment

The ratio of nuclei to cell volume is a well-controlled parameter in eukaryotic cells. This study now reports important findings that expand our understanding of the regulatory relationship between cell size and number of nuclei. The evidence supporting the conclusions is convincing obtained by applying appropriate and validated methodology in line with current state-of-the-art. The paper will be of broad interest for cell biologists and fungal biotechnologists seeking to understand mechanisms determining cell size and number of nuclei and why this knowledge might also be of importance for the production of enzymes and thus production strains not only of Aspergillus oryzae but also other industrially used fungi.

Reviewer #1 (Public review):

Filamentous fungi are established work horses in biotechnology with Aspergillus oryzae as a prominent example with a thousand-year of history. Still the cell biology and biochemical properties of the production strains is not well understood. The paper of the Takeshita group describes the change in nuclear numbers and correlate it to different production capacities. They used microfluidic devices to really correlate the production with nuclear numbers. In addition, they used microdissection to understand expression profile changes and found an increase of ribosomes. The analysis of two genes involved in cell volume control in S. pombe did not reveal conclusive answers to explain the phenomenon. It appears that it is a multi-trait phenotype. Finally, they identified SNPs in many industrial strains and tried to correlate them to the capability of increasing their nuclear numbers.

The methods used in the paper range from high quality cell biology, Raman spectroscopy to atomic force and electron microscopy and from laser microdissection to the use of microfluidic devices to study individual hyphae.

This is a very interesting, biotechnologically relevant paper with the application of excellent cell biology.

Comments on revised version:

The authors addressed all suggestions satisfactorily.

Reviewer #2 (Public review):

Summary:

In the study presented by Itani and colleagues it is shown that some strains of Aspergillus oryzae - especially those used industrially for the production of sake and soy sauce - develop hyphae with a significantly increased number of nuclei and cell volume over time. These thick hyphae are formed by branching from normal hyphae and grow faster and therefore dominate the colonies. The number of nuclei positively correlates with the thicker hyphae and also the amount of secreted enzymes. The addition of nutrients such as yeast extract or certain amino acids enhanced this effect. Genome and transcriptome analyses identified genes, including rseA, that are associated with the increased number of nuclei and enzyme production. The authors conclude from their data involvement of glycosyltransferases, calcium channels and the tor regulatory cascade in regulation of cell volume and number of nuclei. Thicker hyphae and an increased number of nuclei was also observed in high-production strains of other industrially used fungi such as Trichoderma reesei and Penicillium chrysogenum, leading to the hypothesis that the mentioned phenotypes are characteristic of production strains which is of significant interest for fungal biotechnology.

Strengths:

The study is very comprehensive and involves application of divers state-of-the-art cell biological, biochemical and genetical methods. Overall, the data are properly controlled and analyzed, figures and movies are of excellent quality.<br /> The results are particularly interesting with regard to the elucidation of molecular mechanisms that regulate the size of fungal hyphae and their number of nuclei. For this, the authors have discovered a very good model: (regular) strains with a low number of nuclei and strains with high number of nuclei. Also, the results can be expected to be of interest for the further optimization of industrially relevant filamentous fungi.

In the revision the authors addressed all my comments and as a result produced an even stronger study.

Reviewer #3 (Public review):

Summary:

The authors seek to determine the underlying traits that support the exceptional capacity of Aspergillus oryzae to secrete enzymes and heterologous proteins. To do so, they leverage the availability of multiple domesticated isolates of A. oryzae along with other Aspergillus species to perform comparative imaging and genomic analysis.

Strengths:

The strength of this study lies in the use of multifaceted approaches to identify significant differences in hyphal morphology that correlate with enzyme secretion, which is then followed by the use of genomics to identify candidate functions that underlie these differences.

Weaknesses:

Although the image analysis and data interpretation is convincing, the genetic data supporting the author's model is somewhat more speculative and will likely require additional investigation.

Overall, the authors have achieved their aims in that they are able to clearly document the presence of two distinct hyphal forms in A. oryzae and other Aspergillus species, and to correlate the presence of the thicker rapidly growing form with enhanced enzyme secretion. The image analysis is convincing. The discovery that addition of yeast extract and specific amino acids can stimulate formation of the novel hyphal form is also notable. Although the conclusions are generally supported by the results, this is perhaps less so for the genetic analysis as it remains unclear how direct the role of RseA and the calcium transporters might be in supporting the formation of the thicker hyphae.

The results presented here will impact the field. The complexity of hyphal morphology and how it affects secretion are not well understood despite the importance of these processes for the fungal lifestyle. In addition, the description of approaches that can be used to facilitate the study of these different hyphal forms (i.e., stimulation using yeast extract or specific animo acids) will benefit future efforts to understand the molecular basis of their formation.

Author response:

The following is the authors’ response to the original reviews.

Reviewer #1 (Public review): 

Filamentous fungi are established workhorses in biotechnology, with Aspergillus oryzae as a prominent example with a thousand-year history. Still, the cell biology and biochemical properties of the production strains is not well understood. The paper of the Takeshita group describes the change in nuclear numbers and correlates it to different production capacities. They used microfluidic devices to really correlate the production with nuclear numbers. In addition, they used microdissection to understand expression profile changes and found an increase in ribosomes. The analysis of two genes involved in cell volume control in S. pombe did not reveal conclusive answers to explain the phenomenon. It appears that it is a multi-trait phenotype. Finally, they identified SNPs in many industrial strains and tried to correlate them to the capability of increasing their nuclear numbers. 

The methods used in the paper range from high-quality cell biology, Raman spectroscopy, to atomic force and electron microscopy, and from laser microdissection to the use of microfluidic devices to

study individual hyphae. 

This is a very interesting, biotechnologically relevant paper with the application of excellent cell biology. I have only minor suggestions for improvement. 

We sincerely appreciate your fair and positive evaluation of our work. Thank you for your suggestions for improvement. We respond to each of them appropriately.

Reviewer #2 (Public review): 

Summary: 

In the study presented by Itani and colleagues, it is shown that some strains of Aspergillus oryzae - especially those used industrially for the production of sake and soy sauce - develop hyphae with a significantly increased number of nuclei and cell volume over time. These thick hyphae are formed by branching from normal hyphae and grow faster and therefore dominate the colonies. The number of nuclei positively correlates with the thicker hyphae and also the amount of secreted enzymes. The addition of nutrients such as yeast extract or certain amino acids enhanced this effect. Genome and transcriptome analyses identified genes, including rseA, that are associated with the increased number of nuclei and enzyme production. The authors conclude from their data involvement of glycosyltransferases, calcium channels, and the tor regulatory cascade in the regulation of cell volume and number of nuclei. Thicker hyphae and an increased number of nuclei were also observed in high-production strains of other industrially used fungi such as Trichoderma reesei and Penicillium chrysogenum, leading to the hypothesis that the mentioned phenotypes are characteristic of production strains, which is of significant interest for fungal biotechnology. 

Strengths: 

The study is very comprehensive and involves the application of diverse state-of-the-art cell biological, biochemical, and genetic methods. Overall, the data are properly controlled and analyzed, figures and

movies are of excellent quality. 

The results are particularly interesting with regard to the elucidation of molecular mechanisms that regulate the size of fungal hyphae and their number of nuclei. For this, the authors have discovered a very good model: (regular) strains with a low number of nuclei and strains with a high number of nuclei. Also, the results can be expected to be of interest for the further optimization of industrially relevant filamentous

fungi. 

Weaknesses: 

There are only a few open questions concerning the activity of the many nuclei in production strains (active versus inactive), their number of chromosomes (haploid/diploid), and whether hyper-branching always leads to propagation of nuclei. 

We are very grateful for your recognition of our findings, the proposed model, and their significance for future applications. We are grateful for the questions, which contribute to a more accurate understanding. 

Our responses to each are provided below.  

Reviewer #3 (Public review): 

Summary: 

The authors seek to determine the underlying traits that support the exceptional capacity of Aspergillus oryzae to secrete enzymes and heterologous proteins. To do so, they leverage the availability of multiple domesticated isolates of A. oryzae along with other Aspergillus species to perform comparative imaging and genomic analysis. 

Strengths: 

The strength of this study lies in the use of multifaceted approaches to identify significant differences in hyphal morphology that correlate with enzyme secretion, which is then followed by the use of genomics to identify candidate functions that underlie these differences. 

Weaknesses: 

There are aspects of the methods that would benefit from the inclusion of more detail on how experiments were performed and data interpreted. 

Overall, the authors have achieved their aims in that they are able to clearly document the presence of two distinct hyphal forms in A. oryzae and other Aspergillus species, and to correlate the presence of the thicker, rapidly growing form with enhanced enzyme secretion. The image analysis is convincing. The discovery that the addition of yeast extract and specific amino acids can stimulate the formation of the novel hyphal form is also notable. Although the conclusions are generally supported by the results, this is perhaps less so for the genetic analysis as it remains unclear how direct the role of RseA and the calcium transporters might be in supporting the formation of the thicker hyphae. 

The results presented here will impact the field. The complexity of hyphal morphology and how it affects secretion is not well understood despite the importance of these processes for the fungal lifestyle. In addition, the description of approaches that can be used to facilitate the study of these different hyphal forms (i.e., stimulation using yeast extract or specific amino acids) will benefit future efforts to understand the molecular basis of their formation. 

We are very grateful for your fair and thoughtful evaluation of our work. We agree that the genetic analysis in the latter part is relatively weaker compared to the imaging analysis in the first half. Rather than a single mutation causing a dramatic phenotypic change, we believe that the accumulation of various mutations through breeding leads to the observed phenotype, making it difficult to clearly demonstrate causality. Since transcriptome and SNP analyses have revealed key pathways and phenotypes, it would be gratifying if these insights could contribute to future applications utilizing filamentous fungi.

Reviewer #1 (Recommendations for the authors): 

I was wondering what happens if thick hyphae were taken as inoculum for a new colony or thin hyphae. Is it possible to enrich for one or the other type of hyphae? Perhaps in the presence of yeast extract or certain amino acids. 

Added an explanation in the discussion.

L304-306. When thick hyphae were cultured on fresh medium, thin hyphae initially emerged, suggesting that sustained metabolic activity is required for the formation of thick hyphae with a high number of nuclei.    

L120-121. In some cases, thick hyphae emerged by branching from thick hyphae (Fig. 2D, left), while in other cases, thin hyphae emerged from thick hyphae (Fig. 2D, right). Thin hyphae emerge in the early stage of cultivation even in the presence of yeast extract or certain amino acids.

In the Discussion, they hypothesize that the primary effect could be on cell wall rigidity. I am wondering if that hypothesis could be tested by adding, for instance, sublethal concentrations of cytochalasin to hyphae of A. nidulans to weaken the cell wall. 

The question is reasonable. To ensure accurate understanding, we moved Fig. S6 to Fig. 6 and revised the discussion as follows. 

L294-295. In our model, cell wall loosening at a branching site and regulation of cell volume by turgor pressure constitute necessary conditions for increasing cell volume and maintaining thick hyphae. L306-309. Weakening the cell wall by treatment with a low concentration of calcofluor white did not lead to hyphal thickening or an increase in nuclear number. On the contrary, thick hyphae have thicker cell walls (Fig. 2H-K), which are necessary to maintain the increased cell volume.

I recommend including some older literature. It was described already 20 years ago that A. nigerdifferentiates hyphae with different capacities to secrete proteins (PMID: 16238620). In addition, there are old reports in A. nidulans reporting high numbers of nuclei (https://doi.org/10.1099/00221287-60-1-133). Perhaps it is worth trying to reproduce those cultural conditions. At least this should be discussed. In the same line, the number of nuclei increases a lot in the stalk of conidiophores in A. nidulans. These observations could be used as examples that the phenomenon observed in A. oryzae may be of general importance. 

Thank you for the suggestion. It is a very interesting proposal. We checked the nuclei distribution of A. nidulans on the media and added the following discussion.

L328-334. A previous study reported an increase in the number of nuclei in A. nidulans (62, 63). Here, we examined the nuclear distribution of A. nidulans grown on the culture media, however, did not find class III hyphae as observed in A. oryzae. Even in A. nidulans, conidiophore stalks contain a high number of nuclei. It has been shown that A. oryzae has a taller conidiophore stalk (64). In the thick hyphae of A. oryzae, the expression level of flbA, an early regulator of conidiophore development (65), was elevated. This suggests that differentiation to aerial hyphae may be involved in the increase of hyphal volume and nuclear number. 

(62) Clutterbuck A.J. Synchronous Nuclear Division and Septation in Aspergillus nidulans. J Gen Microbiol 60, 133-135 (1970).

(63) Vinck, A., Terlou, M., Pestman, W.R., Martens, E.P., Ram, A.F., van den Hondel, C.A., Wösten, H.A. Hyphal differentiation in the exploring mycelium of Aspergillus niger. Mol Microbiol 58, 693-9 (2005).

(64) Wada R, Maruyama J, Yamaguchi H, Yamamoto N, Wagu Y, Paoletti M, Archer DB, Dyer PS, Kitamoto K. Presence and functionality of mating type genes in the supposedly asexual filamentous fungus Aspergillus oryzae. Appl Environ Microbiol 78, 2819-29 (2012).

(65) Lee, B.N., Adams, T.H. Overexpression of flbA, an early regulator of Aspergillus asexual sporulation, leads to activation of brlA and premature initiation of development. Mol Microbiol 14, 323-34 (1994).

Reviewer #2 (Recommendations for the authors): 

I suggest addressing the following questions to strengthen the manuscript: 

(1) Do the authors have an explanation for their result that with an increase in the number of nuclei the individual nucleus is smaller? Have the authors checked whether all the nuclei are haploid or diploid?

Thank you for the very important question. We added new results to Fig. S5D and S5E and the following discussion.

L335-340. We investigated whether the reduction in nuclear size observed in thick hyphae was due to a change from diploid to haploid status. However, no difference in GFP-histone fluorescence intensity was detected between thick and thin hyphae (Fig. S5D). In both RIB40 and RIB915 strains, no significant difference in conidial spore size was observed despite the large difference in the number of nuclei within the hyphae (Fig. S5E). These results suggest that both thick and thin hyphae remain haploid, and that the smaller nuclear size observed in thick hyphae is likely due to a higher nuclear density.

(2) In this context, the biological relevance of the increase in the number of nuclei should also be discussed in more detail. It remains to be clarified whether in hyphae with a high number of nuclei all nuclei are functionally active or whether many nuclei are possibly "inactive". Studies on the transcriptional activity of individual nuclei or on DNA replication (e.g., by EdU labeling) could clarify this. 

Added the explanation below.

L102-105. The transcriptional activity of each nucleus is unknown. However, a previous study (Yasui et al., FBB 2020) demonstrated that nuclear division is synchronized even when there are more than 200 nuclei. This suggests that DNA replication occurs similarly in most nuclei. Furthermore, since the germination rate of conidia and the colonies formed from individual conidia show no significant abnormalities, it is suggested that nearly all nuclei possess normal genomes and chromosomes.

(3) It becomes not entirely clear what the underlying signal is that causes a thin hypha to branch into a thick multinucleated cell. This needs to be discussed in more detail. 

Thanks for the suggestion. We clarified the signal to increase nuclear number and cell volume.

L294-309. Although it is speculative, we propose a model to aid interpretation in the discussion. We have clarified that both genetic potential and environmental signals such as nutrients are important.

(4) Is increased branching always correlated with an increased number of nuclei? 

It is not an increase in branching, but rather the thickening of hyphae and an increase in cell volume that is consistently associated with an increase in nuclear number. Approximately 40 hours after inoculation, within 400 μm from the tip, the number of branches was 3.4 (SD=2.4) in thin hyphae and 2.6 (SD=0.5) in thick hyphae, suggesting that branching does not increase (n=4). Since thick hyphae elongate faster, it seems that fewer branches are present near the tip, even if the branching frequency itself remains unchanged.

(5) The abstract does not summarize the many findings of the manuscript in an adequate way. 

abstract change

Minor: 

(1) Lines 49-50: Why italics? 

corrected.

(2) Line 179: process. 

corrected.

(3) Lines 313-314: Do not forget (and discuss) in this context mycorrhiza fungi with up to thousands of nuclei that were apparently selected during evolution for this high number of nuclei. 

Thank you for the very interesting suggestion. We have added the following discussion.

L339-351. The regulation of nuclear number and its ecological strategy are intriguing in other fungi such as N. crassa, which rapidly spreads after wildfires (68), and arbuscular mycorrhiza fungi that form symbiotic relationships with plants and contain thousands of nuclei within hyphae lacking septa (69).

(68) Jacobson, D. J. et al. Neurospora in temperate forests of western North America. Mycologia 96, 66–74 (2004).

(69) Kokkoris V, Stefani F, Dalpé Y, Dettman J, Corradi N. Nuclear Dynamics in the Arbuscular Mycorrhizal Fungi. Trends Plant Sci. 25, 765-778 (2020).

(4) Lines 356-358: many typos.

corrected.

Reviewer #3 (Recommendations for the authors): 

Specific suggestions or clarifications for the authors include: 

(1) Lines 49-50: Is this sentence italicized for a reason? 

It was a mistake, so we have corrected it.

(2) Line 83: More detail on the specific characteristics of the different classes of hyphae would be helpful. Perhaps include a schematic drawing that emphasizes the differences between class I,II, and III hyphae. 

L398-400. The classification is described in the Methods section: Class I – nuclei are distributed at regular intervals without overlapping; Class II – nuclei are aligned but occasionally overlap; Class III – nuclei are scattered throughout the hyphae without alignment. Representative images are shown in a previous study (Yasui et al., FBB 2020). 

L82-84. We have added this information to clarify the classification.

(3) Lines 102-103: It was not very clear how this experiment was done. Are you counting nuclei within 100 um of the tip? Are these all in one hyphal compartment? These details could be provided in a drawing that would make it easier for the reader to understand how this was done. 

L109. Due to variation in the distance from the hyphal tip to the septum, we counted the number of nuclei within 100 μm from the hyphal tip. When septa were present, nuclei were counted in the same manner, so multiple compartments may be included. Changed the explanation.

(4) Lines 134-140: Is there a way to calibrate levels of secreted protein or amylase activity per nucleus? That is, if the ratio of cytoplasmic volume per nucleus is constant, does the same apply to the secreted product? Knowing this would help to clarify whether the key feature in enhanced secretion is nuclear (e.g., gene expression) versus a cytoplasmic trait (e.g., vesicle trafficking). 

Enzyme activity was measured across the entire mycelium, which includes a mixture of hyphae with high and low numbers of nuclei. Therefore, it is difficult to assess the correlation between enzyme activity and nuclear number. Enzyme activity was normalized by fungal biomass. The size of each colony is shown in Fig. 1B. Additionally, the correlation between the proportion of hyphae with increased nuclear number and enzyme activity is shown in Fig. 3H. In the experiment where enzyme activity was measured in a single hypha, we attempted to measure the number of nuclei; however, we could not use the nuclear GFP strain because the substrate exhibits green fluorescence. DAPI staining also failed due to limited dye access to the microfluidic channel. Changed the section title, ‘Increase in nuclear number and enzyme secretion’ from ‘Correlation between nuclear number and enzyme secretion’.

(5) Line 151 and Figure 3F: YE also triggered a ~5-fold enhancement of secretion in A. nidulans without a concomitant increase in hyphal width. This merits some comment in the text.  

Added an explanation, L156-157.

In A. nidulans, the addition of yeast extract did not cause a dramatic increase in nuclear number, but hyphal width increased by 1.4-times and protein secretion increased by 5.1-times.

(6) Line 252: Were nimE levels detected or altered in thick hyphae? The levels of this cycling might play a more important role in a shortened cell cycle than the authors have considered, especially as NimE functions during both G1 and G2. 

Added an explanation below, L260-262.

The expression level of nimE (AO090003000993) was low in both thick and thin hyphae, with no significant difference observed. As known in other organisms, its function is likely regulated through phosphorylation and the protein degradation.

(7) Line 254: Please provide a citation for the statement that branches emerge as a result of cell wall loosening. 

rephrased and added citation, L263.

Branching is thought to occur through the degradation and reconstruction of the cell wall at the branching site (54).

Harris SD. Branching of fungal hyphae: regulation, mechanisms and comparison with other branching systems. Mycologia 100, 823-32 (2008).   

(8) Lines 275-277: It would be interesting to know whether the addition of rapamycin also suppressed the ability of amino acids to trigger greater numbers of class III hyphae. 

We added new results at Fig. S2G.

L168. Rapamycin decreased the ratio of hyphae with increased nuclei even in the medium with yeast extract (Fig. S2G).

(9) Lines 282-289: My sense is that this model is too speculative at this time. The role of RseA seems very broad based on the strong deletion phenotype. How would the removal of RseA be regulated to limit its effect to the branch site? Also, the msyA deletion phenotype isn't entirely consistent with what you would expect if it were necessary to maintain thick hyphae. Lastly, the authors do not show that translational capacity is enhanced in thick hyphae. I would suggest that these statements be tempered to some degree. 

Thank you for your comment. We agree that it was too speculative, whereas we believe that some explanatory interpretation is necessary. Therefore, we have revised the text as follows, L294-300. In our model, cell wall loosening during branching and regulation of cell volume by turgor pressure constitute necessary conditions for increasing cell volume and maintaining thick hyphae. RseA and MsyA may be involved in these processes. At the same time, enhanced translational capacity by increased expression of ribosomal genes, possibly due to associated with TOR activation by specific amino acids, and mechanisms that accelerate the cell cycle represent another essential condition that enables an increase in nuclear number.

(10) General: how do the authors reconcile the observation that YE and amino acids stimulate the formation of thicker hyphae, yet the time lapse imaging (Figure 2E) suggests that these hyphae arise at a later time during colony development when these resources might be limiting? The authors should consider providing some insight into this in the Discussion. 

L300-305. Added a discussion below.

Both genetic potential and nutritional environmental signals are likely required for the formation of thick hyphae with a high number of nuclei. When thick hyphae were cultured on fresh medium, thin hyphae initially emerged, suggesting the necessity of sustained high metabolic activity.

eLife Assessment

This important study reports that an oncogenic population in an epithelium can either be repressed or spread, depending on the tissues. This is explained based on the differential interfacial tension hypothesis, and supported by pharmacological perturbations and numerical simulations using the vertex model. The study conveys a key message, but, as it stands, the strength of evidence is incomplete, and a more detailed analysis of the mechanistic origin of the different tensions and better comparison between experiments and simulations would strongly strengthen the message.

Reviewer #1 (Public review):

Summary:

The behaviour of cells expressing constitutively active HRas is examined in mosaic monolayers, both in MCF10a breast epithelial and Beas2b bronchial epithelial cell lines, mimicking the potential initial phase of development of carcinoma. Single HRas-positive cells are excluded from MCF10a but not Beas2b monolayers. Most interestingly, however, when in groups, these cells are not excluded, but rather sharply segregated within a MCF10a monolayer. In contrast, they freely mix with wt Beas2b cells. Biophysical analysis identifies high tension at heterotypic interfaces between HRas and wild-type cells as the likely reason for segregation of MCF10a cells. The hypothesis is supported experimentally, as myosin inhibition abolishes segregation. The probable reason for the lack of segregation in the bronchial epithelium is to be found in the different intrinsic properties of these cells, which form a looser tissue with lower basal actomyosin activity. The behaviour of single cells and groups is recapitulated in a vortex model based on the principle of differential interfacial tension, under the condition of high heterotypic interfacial tension.

Strengths:

Despite being long recognized as a crucial event during cancer development, segregation of oncogenic cells has been a largely understudied question. This nice work addresses the mechanics of this phenomenon through a straightforward experimental design, applying the biophysical analytical approaches established in the field of morphogenesis. Comparison between two cell types provides some preliminary clues on the diversity of effects in various cancers.

Weaknesses:

Although not calling into question the main message of this study, there are a few issues that one may want to address:

(1) One may be careful in interpreting the comparison between MCF10a and Beas2b cells as used in this study. The conditions may not necessarily be representative of the actual properties of breast and bronchial epithelia. How much of the epithelial organization is reconstituted under these experimental conditions remains to be established. This is particularly obvious for bronchial cells, which would need quite specific culture conditions to build a proper bronchial layer. In this study, they seemed to be on the verge of a mesenchymal phenotype (large gaps, huge protrusions, cells growing on top of each other, as mentioned in the manuscript).

As an alternative to Beas2b, comparison of MCF10a with another cell line capable of more robust in vitro epithelial organization, but ideally with different adhesive and/or tensile properties, would be highly interesting, as it may narrow down the parameters involved in segregation of oncogenic cells.

(2) While the seminal description of tissue properties based on interfacial tensions (Brodland 2002) is clearly key to interpreting these data, the actual "Differential Interfacial Tension Hypothesis" poses that segregation results from global differences, i.e., juxtaposition of two tissues displaying different intrinsic tensions. On the contrary, the results of the present work support a different scenario, where what counts is the actual difference in tension ALONG the tissue boundary, in other words, that segregation is driven by high HETEROTYPIC interfacial tension. This is an important distinction that should be clarified.

(3) Related: The fact that actomyosin accumulates at the heterotypic interface is key here. It would be quite informative to better document the pattern of this accumulation, which is not clear enough from the images of the current manuscript: Are we talking about the actual interface between mutant and wt cells (membrane/cortex of heterotypic contacts)? Or is it more globally overactivated in the whole cell layer along the border? Some better images and some quantification would help.

(4) In the case of Beas2b cells, mutant cells show higher actin than wt cells, while actin is, on the contrary, lower in mutant MCF10a cells (Figure 2b). Has this been taken into account in the model? It may be in line with the idea that HRas may have a different action on the two cell types, a possibility that would certainly be worth considering and discussing.

In conclusion, the study conveys an important message, but, as it stands, the strength of evidence is incomplete. It would greatly benefit from a more detailed and complete analysis of the experimental data, a better fit between this analysis and the corresponding vertex model, and a more in-depth discussion of biological and biophysical aspects. These revisions should be rather easily done, and would then make the evidence much more solid.

Reviewer #2 (Public review):

Summary:

The authors investigate the behavior of oncogenic cells in mammary and bronchial epithelia. They observe that individual oncogenic cells are preferentially excluded from the mammary epithelium, but they remain integrated in the bronchial epithelium. They also observe that clusters of oncogenic cells form a compact cluster in the mammary epithelium, but they disperse in the bronchial epithelium. The authors demonstrate experimentally and in the vertex model simulations that the difference in observed behavior is due to the differential tension between the mutant and wild-type cells due to a differential expression of actin and myosin.

Strengths:

(1) Very detailed analysis of experiments to systematically characterize and quantify differences between mammary and bronchial epithelia.

(2) Detailed comparison between the experiments and vertex model simulations to identify the differential cell line tension between the oncogenic and wild-type cells as one of the key parameters that are responsible for the different behavior of oncogenic cells in mammary and bronchial epithelia

Weaknesses:

(1) It is unclear what the mechanistic origin of the shape-tension coupling is, which is used in the vertex model, and how important that coupling is for the presented results. The authors claim that the shape-tension coupling is due to the anisotropic distribution of stress fibers when cells are under external stress. It is unclear why the stress fibers should affect an effective line tension on the cell boundaries and why the stress fibers should be sensitive to the magnitude of the internal isotropic cell pressure. In experiments, it makes sense that stress fibers form when cells are stretched. Similar stress fibers form when the cytoskeleton or polymer networks are stretched. It is unclear why the stress fibers should be sensitive to the magnitude of internal isotropic cell pressure. If all the surrounding cells have the same internal pressure, then the cell would not be significantly deformed due to that pressure, and stress fibers would not form. The authors should better justify the use of the shape-tension coupling in the model and also present simulation results without that coupling. I expect that most of the observed behavior is already captured by the differential tension, even if there is no shape-tension coupling.

(2) The observed difference of shape indices between the interfacial and bulk cells in simulations in the absence of differential line tension is concerning. This suggests that either there are not enough statistics from the simulations or that something is wrong with the simulations. For all presented simulation results, the authors should repeat multiple simulations and then present both averages and standard deviations. This way, it would be easier to determine whether the observed differences in simulations are statistically significant.

(3) The authors should also analyze the cell line tension data in simulations and make a comparison with experiments.

Author response:

Reviewer #1 (Public review):

Summary:

The behavior of cells expressing constitutively active HRas is examined in mosaic monolayers, both in MCF10a breast epithelial and Beas2b bronchial epithelial cell lines, mimicking the potential initial phase of development of carcinoma. Single HRas-positive cells are excluded from MCF10a but not Beas2b monolayers. Most interestingly, however, when in groups, these cells are not excluded, but rather sharply segregated within a MCF10a monolayer. In contrast, they freely mix with wt Beas2b cells. Biophysical analysis identifies high tension at heterotypic interfaces between HRas and wild-type cells as the likely reason for segregation of MCF10a cells. The hypothesis is supported experimentally, as myosin inhibition abolishes segregation. The probable reason for the lack of segregation in the bronchial epithelium is to be found in the different intrinsic properties of these cells, which form a looser tissue with lower basal actomyosin activity. The behaviour of single cells and groups is recapitulated in a vortex model based on the principle of differential interfacial tension, under the condition of high heterotypic interfacial tension.

Strengths:

Despite being long recognized as a crucial event during cancer development, segregation of oncogenic cells has been a largely understudied question. This nice work addresses the mechanics of this phenomenon through a straightforward experimental design, applying the biophysical analytical approaches established in the field of morphogenesis. Comparison between two cell types provides some preliminary clues on the diversity of effects in various cancers.

Weaknesses:

Although not calling into question the main message of this study, there are a few issues that one may want to address:

(1) One may be careful in interpreting the comparison between MCF10a and Beas2b cells as used in this study. The conditions may not necessarily be representative of the actual properties of breast and bronchial epithelia. How much of the epithelial organization is reconstituted under these experimental conditions remains to be established. This is particularly obvious for bronchial cells, which would need quite specific culture conditions to build a proper bronchial layer. In this study, they seemed to be on the verge of a mesenchymal phenotype (large gaps, huge protrusions, cells growing on top of each other, as mentioned in the manuscript).

We thank the reviewer for this important point. We agree that our experimental conditions do not fully recapitulate the in vivo architecture of either breast or bronchial epithelia. However, here, our intention is to compare two well-established epithelial lines with distinct intrinsic mechanical and organizational properties, rather than to reproduce in-vivo microenvironment. Nevertheless, to address this, we have now strengthened our quantitative analysis of epithelial integrity in Beas2b monolayers, by including ZO-1 immunofluorescence along with E-cadherin immunofluorescence. These measurements confirm that Beas2b monolayers under our culture conditions retain junctional organization, albeit with larger gaps and protrusions compared to MCF10a. We will revise the text to make this distinction explicit.

As an alternative to Beas2b, comparison of MCF10a with another cell line capable of more robust in vitro epithelial organization, but ideally with different adhesive and/or tensile properties, would be highly interesting, as it may narrow down the parameters involved in segregation of oncogenic cells.

We agree with the reviewer that the inclusion of an additional epithelial model system with distinct adhesive and organizational properties would provide valuable insights. In line with this suggestion, we are currently repeating the key experiments using Madin-Darby Canine Kidney (MDCK) cells, a well-established model epithelial cell line. We believe this complementary system will allow us to further dissect the behaviour of HRasV12-expressing cells.

(2) While the seminal description of tissue properties based on interfacial tensions (Brodland 2002) is clearly key to interpreting these data, the actual "Differential Interfacial Tension Hypothesis" poses that segregation results from global differences, i.e., juxtaposition of two tissues displaying different intrinsic tensions. On the contrary, the results of the present work support a different scenario, where what counts is the actual difference in tension ALONG the tissue boundary, in other words, that segregation is driven by high HETEROTYPIC interfacial tension. This is an important distinction that should be clarified.

We thank the reviewer for this insightful comment. As correctly noted, Brodland’s 2002 work provided a seminal formulation of the Differential Interfacial Tension Hypothesis (DITH), which frames tissue organization in terms of effective interfacial tensions. In its original form, DITH emphasized segregation as a consequence of global differences in the intrinsic (bulk) tensions of juxtaposed tissues.

While our results specifically show that segregation is determined by local interfacial mechanics between transformed- and host cells, from our experiments with blebbistatin, where we observed lost in segregation upon reducing global contractility, we believe that the differences in local interfacial mechanics also stem from global differences which belong intrinsically to the tissues in discussion here.

To directly map global interfacial tension, in the revised manuscript, we aim to perform staining with E-cadherin, and actin in the two tissues, and measure cortical actin, stress fibers, and E-cadherin levels at the cell-cell junctions. Once the global tissue mechanics are mapped, we can be more confident about our claim on DITH. Nevertheless, we will also clarify this distinction, more clearly in the text and explicitly state that while DITH provided the foundation for conceptualizing tissue mechanics, our findings on transformed cell- healthy cell interactions specifically demonstrate that segregation is driven by high heterotypic interfacial tension at the tissue boundary.

(3) Related: The fact that actomyosin accumulates at the heterotypic interface is key here. It would be quite informative to better document the pattern of this accumulation, which is not clear enough from the images of the current manuscript: Are we talking about the actual interface between mutant and wt cells (membrane/cortex of heterotypic contacts)? Or is it more globally overactivated in the whole cell layer along the border? Some better images and some quantification would help.

We agree that more detailed visualization of actomyosin distribution would strengthen our conclusion. We are currently working on re-imaging the heterotypic interfaces at higher magnification and are quantifying fluorescence intensity of actin and myosin-II along cell–cell boundaries. All of this will be integrated in the next version of the manuscript.

(4) In the case of Beas2b cells, mutant cells show higher actin than wt cells, while actin is, on the contrary, lower in mutant MCF10a cells (Author response image 2). Has this been taken into account in the model? It may be in line with the idea that HRas may have a different action on the two cell types, a possibility that would certainly be worth considering and discussing.

Our current vertex model does not explicitly incorporate actin levels; rather, it captures their functional consequences indirectly through effective mechanical parameters such as cortical tension and adhesion strength. Nonetheless, we agree that the opposite trends in actin enrichment between Beas2b and MCF10a HRasV12 mutants raise the important possibility that HRas signaling may act through distinct mechanisms in the two cell types.

To further investigate this, we are currently culturing MCF10a and Beas2b HRasV12 mutant populations separately (i.e., without wild-type cells) to assess their intrinsic organization and behavior in isolation. These experiments will help us disentangle how HRas activation differentially impacts epithelial architecture in these two cellular contexts, and we will discuss these ongoing efforts in the revised manuscript.

From the modelling perspective, the model currently does not account for the different actin levels of mutants with respect to wt cells in the two tissues. This can be accounted for by having different  and  for mutants and wt in the two cases in simulation.

In conclusion, the study conveys an important message, but, as it stands, the strength of evidence is incomplete. It would greatly benefit from a more detailed and complete analysis of the experimental data, a better fit between this analysis and the corresponding vertex model, and a more in-depth discussion of biological and biophysical aspects. These revisions should be rather easily done, and would then make the evidence much more solid.

Reviewer #2 (Public review):

Summary:

The authors investigate the behavior of oncogenic cells in mammary and bronchial epithelia. They observe that individual oncogenic cells are preferentially excluded from the mammary epithelium, but they remain integrated in the bronchial epithelium. They also observe that clusters of oncogenic cells form a compact cluster in the mammary epithelium, but they disperse in the bronchial epithelium. The authors demonstrate experimentally and in the vertex model simulations that the difference in observed behavior is due to the differential tension between the mutant and wild-type cells due to a differential expression of actin and myosin.

Strengths:

(1) Very detailed analysis of experiments to systematically characterize and quantify differences between mammary and bronchial epithelia.

(2) Detailed comparison between the experiments and vertex model simulations to identify the differential cell line tension between the oncogenic and wild-type cells as one of the key parameters that are responsible for the different behavior of oncogenic cells in mammary and bronchial epithelia

Weaknesses:

(1) It is unclear what the mechanistic origin of the shape-tension coupling is, which is used in the vertex model, and how important that coupling is for the presented results. The authors claim that the shape-tension coupling is due to the anisotropic distribution of stress fibers when cells are under external stress. It is unclear why the stress fibers should affect an effective line tension on the cell boundaries and why the stress fibers should be sensitive to the magnitude of the internal isotropic cell pressure. In experiments, it makes sense that stress fibers form when cells are stretched. Similar stress fibers form when the cytoskeleton or polymer networks are stretched. It is unclear why the stress fibers should be sensitive to the magnitude of internal isotropic cell pressure. If all the surrounding cells have the same internal pressure, then the cell would not be significantly deformed due to that pressure, and stress fibers would not form. The authors should better justify the use of the shape-tension coupling in the model and also present simulation results without that coupling. I expect that most of the observed behavior is already captured by the differential tension, even if there is no shape-tension coupling. 

While the segregation behavior can be captured by the differential tension, without the shape-tension coupling, we noticed unjamming and aligned movement of wild type cells at the mutant-cell interface. This was only captured when we incorporated shape tension coupling in the model, suggesting changes in cell shapes due to differential interfacial tension is essential in driving the fate of the mutants.  Below, difference between shape indices of cells at the interface and away from the boundary is plotted versus the interfacial tension in the case of no shape-tension coupling [Author response image 1]. The red dashed line represents the experimental value of the shape index difference. The blue line is the shape index difference between two randomly chosen groups of cells (half of the total number of cells in each group is taken). At zero line-tension, the difference in shape index between interface cells and cells away from the interface is same as that between randomly chosen groups of cells, which is expected since there should be no interface at zero line-tension. The no shape-tension data presented here are averaged over 19 seeds. Although the results without shape-tension coupling reaches experimental values at high enough differential tension [Author response image 2], a closer inspection of the simulation results show that the cells are just squeezed and are aligned perpendicular to the interface, which is contrary to what is seen in experiments.

Author response image 1.

Shape indices versus the interfacial line tension<br />

Calculating the average of the absolute value of the dot product of the nematic director and the interface edge for simulations with and without shape-tension coupling clearly shows that with shape-tension coupling, the cells align and elongate along the interface as is seen in experiment, given by an interface dot product value > 0.5 at high enough line-tension values. Further, shape-tension coupling or biased edge tension has been used before to model for cell elongation during embryo elongation [1] and here we use it as an active line-tension force, which elongates cells along the interface, in addition to the differential tension which is passive. This additional quantification of the alignment and elongation of cells along the interface will be added to the Supplementary Information (SI).

[1] Dye, N. A., Popović, M., Iyer, K. V., Fuhrmann, J. F., Piscitello-Gómez, R., Eaton, S., & Jülicher, F. (2021). Self-organized patterning of cell morphology via mechanosensitive feedback. Elife, 10, e57964.

Author response image 2.

Change in interfacial tension with and without shape tension coupling<br />

(2) The observed difference of shape indices between the interfacial and bulk cells in simulations in the absence of differential line tension is concerning. This suggests that either there are not enough statistics from the simulations or that something is wrong with the simulations. For all presented simulation results, the authors should repeat multiple simulations and then present both averages and standard deviations. This way, it would be easier to determine whether the observed differences in simulations are statistically significant.

The reviewer is right in pointing out that statistics for the plots must be shown. The difference in shape indices between the interfacial and bulk cells in simulations has been calculated over 11 different seed values. The observed differences in simulations along with the standard deviations have been plotted below [Author response image 3]. This figure in the paper will be updated to include the standard deviations. The non-zero difference in shape index in the absence of differential line tension for low values of stress threshold is due to the shape-tension coupling acting even at low differential tension. Thus, a non-zero, sufficiently high value of the stress threshold is required in our model with shape-tension coupling, for the model to make sense. This has also been stated in section 4 of the paper. The importance of the stress-tension coupling has been stated in response to the previous point.

Author response image 3.<br />

(3) The authors should also analyze the cell line tension data in simulations and make a comparison with experiments.

We agree with the reviewer that cell line tension data should also be analyzed and compared with experiments. This will be added to the next version of the paper.

memory spatial vs temporal

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East West Memory

clearest exposition

explaining principles

eLife Assessment

In this important study, the authors use computational modeling to explore how fast learning can be reconciled with the accumulation of stable memories in the olfactory bulb, where adult neurogenesis is prominent. Their model demonstrates that changes in excitability, plasticity, and susceptibility to apoptosis during the maturation of adult-born granule cells can help resolve the flexibility-stability dilemma. These compelling results provide a coherent picture of a neurogenesis-dependent learning process that is consistent with diverse experimental observations and may serve as a foundation for further experimental and computational studies.

Reviewer #1 (Public review):

Summary:

Sakelaris and Riecke used computational modeling to explore how neurogenesis and sequential integration of new neurons into a network support memory formation and maintenance. They focus on the integration of granule cells in the olfactory bulb, a brain area where adult neurogenesis is prominent. Experimental results published during recent years provide an excellent basis to address the question at hand by biologically constrained models. The study extends previous computational models and provides a coherent picture of how multiple processes may act in concert to enable rapid learning, high stability of memories, and high memory capacity. This computational model generates experimentally testable predictions and is likely to be valuable to understand roles of neurogenesis and related phenomena in memory. One of the key findings is that important features of the memory system depend on transient properties of adult-born granule cells such as enhanced excitability and apoptosis during specific phases the development of individual neurons. The model can explain many experimental observations, and suggests specific functions for different processes (e.g., importance of apoptosis for continual learning). While this model is obviously a massive simplification of the biological system, it conceptualizes diverse experimental observations into a coherent picture, it generates testable predictions for experiments, and it and will likely inspire further modeling and experimental studies.

Strengths:

- The model can explain diverse experimental observations

- The model directly represents the biological network

Weaknesses:

- As many other models of biological networks, this model contains major simplifications.

Reviewer #2 (Public review):

Summary:

The authors propose a mechanism to provide flexibility to learn new information while preserving stability in neural networks by combining structural plasticity and synaptic plasticity.

Strengths:

An intriguing idea, well embedded in experimental data.

Authors have done a great job addressing reviewers' concerns

Weaknesses:

None

Reviewer #3 (Public review):

The manuscript is focused on local bulbar mechanisms to solve the flexibility-stability dilemma in contrast to long range interactions documented in other systems (hippocampus-cortex). The network performance is assessed in a perceptual learning task: the network is presented with alternating, similar artificial stimuli (defined as enrichment) and the authors assess its ability to discriminate between these stimuli by comparing the mitral cell representations quantified by Fisher discriminant analysis. The authors use enhancement in discriminability between stimuli as function of the degree of specificity of connectivity in the network to quantify the formation of an odor-specific network structure which as such has memory - they quantify memory as the specificity of that connectivity.

The focus on neurogenesis, excitability and synaptic connectivity of abGCs is topical, and the authors systematically built their model, clearly stating their assumptions and setting up the questions and answers. In my opinion, the combination of latent dendritic representations, excitability and apoptosis in an age-dependent manner is interesting and as the authors point out leads to experimentally testable hypotheses.

In the revised manuscript, the authors have systematically addressed my previous concerns. In particular, they now refer to previous work on granule cells-mitral cell interactions more generally, they explain the pros and cons for usage of specificity in connectivity as a proxy for memory capacity, and the biological plausibility of the model.

Author response:

The following is the authors’ response to the original reviews

Reviewer #1:

(1) Figure 2 and related text: it would be useful to explain more explicitly what is meant by "neurogenic" and "non-neurogenic" models. I presume that the total number of neurons in non-neurogenic models is lower than in neurogenic models because no new neurons are added. It would be useful to plot the number of GCs as a function of timesteps.

We have clarified the distinction between neurogenic and non-neurogenic models in the text (Lines 142-145), explicitly noting that in non-neurogenic models, no new GCs are added, resulting in a lower total neuron count over time. In response to the reviewer’s suggestion, we generated a plot showing the number of GCs over time (see below). Because the neurogenic model exhibits a simple linear increase, we found this plot not especially informative for inclusion in the manuscript. However, we agree with the reviewer’s later comments that similar plots are useful for interpreting specific results, and we have included those where appropriate.

Author response image 1.

Number of GCs over time for neurogenic (solid line) and non-neurogenic (dotted line) networks

(2) Figure 2F, G: memory declines dramatically when the number of GCs at enrichment onset increases beyond an optimum. Why?

We have explained the reasoning more thoroughly in the text (Lines 174-177) and added a new supplemental figure to support this reasoning (Figure S2). As the number of GCs increases, the network becomes overly inhibited and the response of abGCs to the stimuli decreases (Fig S2A). This leads to a smaller population of GCs being able to integrate with the stimulus (Fig S2B) which is expected given the activity-dependent plasticity rule. Moreover, it can be seen in Fig S2C that for networks with increasing size, the GCs that do learn only connect to MCs that are driven strongest by the stimuli until they struggle to connect to any MCs at all.

In principle, a homeostatic mechanism like synaptic scaling could reduce activity to restore balance, but such a mechanism would also likely disrupt existing memories. Alternatively, we suggest activity-dependent apoptosis as a superior homeostatic mechanism because it leads to a stable level of activity without substantially erasing existing memories.

(3) The paragraph describing synaptic connectivity of abGCs (related to Figure 2H) is confusing. What is the directionality of synapses considered here: mitral-to-granule, or granule-to-mitral? The text is opaque here. Connectivity matrix in Figure 2H: who is presynaptic, who is postsynaptic? If I understand correctly, these questions are actually irrelevant because all mitralgranule synapses in the network are reciprocal. This should be pointed out explicitly in the figure legend. Generally: the fact that the network is fully reciprocal (if I understand correctly) is very important but not stated with sufficient emphasis. It should be stated very explicitly in the text that connectivity matrices are fully reciprocal, and an equation clarifying this point should be included in Methods.

(6) Connectivity matrix: to what degree was connectivity between mitral and granule cells reciprocal (fraction of connections in either direction that were paired with a connection in the opposite direction between the same cell pair)? Was connectivity shaped by experience (enrichment) reciprocal?

(7) Directly related to the above: it would be useful to show the disynaptic connectivity matrix between mitral cells and analyze its symmetry. For the symmetric component, it should then be analyzed what fraction of this can be attributed to the reciprocal synapses, and what fraction is contributed by connectivity via different granule cells. This should then be compared to models with biologically realistic fractions of reciprocal connections. Is the model proposed here consistent with a biologically realistic fraction of reciprocal synapses between mitral-granule cell pairs?

We appreciate these insightful and detailed comments. We agree that the assumption that MC-GC synapses were fully reciprocal was not clearly stated. We now explicitly state this in the main text (lines 90-94, 369-370, Figure 2 caption) and methods (line 561), emphasize its importance. As the reviewer points out, this is a simplifying assumption and does not fully reflect the biology because not all synapses are reciprocal in the true system. We also note that our synaptic plasticity model does not break the reciprocity assumption: all connections added or pruned during learning remain reciprocal. As a result, the disynaptic connectivity matrix (Bottom panel below, MCs sorted by stimulus as shown in the top panel) is always symmetric.

We have now made these statements explicit in the main text and in the methods. Regarding functional consequences of this assumption, earlier work by our group has examined the impact of the degree of reciprocity of MC-GC synapses in a similar OB model (Chow, Wick & Riecke, Plos Comp Bio 2012). The study examined three different changes in reciprocity by (1) redirecting a fraction of the inhibitory connections of each GC to randomly chosen MCs instead of the MCs that drive that GC, (2) allowing heterogeneity in reciprocal weights so that there is no relationship between the strength of the MC -> GC synapse and the GC -> MC synapse, (3) reducing the level of self-inhibition a MC receives from the GCs that it excites. The model was found to be quite robust to each of these manipulations, suggesting that our present model likely remains functionally relevant even if biological reciprocity is partial. We reference this work now in the discussion, lines 490-492.

Author response image 2.

Disynaptic connectivity. Top: MC activity in response to the two stimuli, sorted by MC selectivity. Bottom: Disynaptic connectivity matrix (diagonal subtracted).

(4) How were mitral cells sorted in Figure 2H? This needs to be explained.

(5) Directly related to the point above: the text mentions that synaptic connectivity between GCs of the "learning cluster" and mitral cells (which direction?) is increased for mitral cells responding by enrichment odors, but this is not shown in the figure. This statement suggests that mitral cells sorted to the bottom of the y-axis respond more strongly to enrichment odors, but the information is not given directly. Please provide more information to back up your statements.

Indeed as the reviewer inferred, MCs in Figure 2H were sorted so that those that receive the strongest stimulation from the odor were at the bottom of the y-axis. We have clarified this in the Figure 2 caption and added a subplot to Figure 2H showing the average MC input to make this more explicit.

(8) Apoptosis (Figure 4 and related text): paragraph 231ff is somewhat difficult to comprehend because the "number" of enrichments should really be the "frequency" of enrichments. In Figure 4, it is not mentioned explicitly that each enrichment is with different random new odors.

We agree that the term “number” of enrichments was imprecise and have revised the text to refer instead to the frequency of enrichment events (Lines 255-267). We also clarified that in Figure 4, each enrichment corresponds to a different set of randomly sampled odors, and we now state this explicitly in both the Figure 4 legend and main text (Lines 260-261).

(9) Apoptosis: apoptosis improves memory but the underlying reason remains opaque. A simple prediction of the data in Figure 4D and 4E is that the number of GCs in 4E. It would be helpful to show this. Furthermore, an obvious question that arises is whether a higher frequency of enrichments improves memories because the total number of granule cells is kept low, or because granule cells are removed specifically based on their activity (or both). This could be addressed easily by artificially removing a random subset of granule cells in a simulation such as 4E to match granule cell numbers to the case in 4D.

Apoptosis improves learning is because it reduces the total inhibition in the network by removing GCs and thus prevents deficits in learning that occur in Fig. 2G as GCs accumulate in the network. As the reviewer inferred, the number of GCs in Figure 4D is lower than in 4E and this is now clarified in the text. This difference was shown implicitly in Supplementary Figure S4D (previously S3D), but we now explicitly reference this plot to support this point as well (Line 266).

As the reviewer notes, there is a question in whether increased enrichment frequency improves memory because it limits the total number of GCs, or because apoptosis selectively removes GCs based on their activity, or both. Our model supports both mechanisms. Importantly, simply reducing GC numbers through random deletion will degrade existing memories: random removal erodes memory representations encoded by those GCs. In contrast, our age and activity dependent apoptosis rule targets a specific cohort of adult-born GCs. This selective removal minimizes damage to existing memories encoded by GCs outside of this cohort while keeping GC numbers within a regime that supports robust learning (as shown in Figure 2G).

However, we note that if enrichment frequency becomes too high, even recent memories can be lost due to premature pruning of GCs that have not yet stabilized their synaptic connections. This tradeoff has been shown experimentally (Forest et al., Nat Comm 2019) which we reproduce in our model (Figure S4).

(10) Text related to Figure 5: "Learning flexibility...approached a steady state when the growth of the network started to saturate". Please show the growth (better: size) of the network (total number of GCs) for these simulations (and other panels in Figure 5). It would also be useful to show the total number of GCs in other figures (e.g. Figure 4; see above).

We have now added a supplementary figure (Figure S6) that shows the total number of GCs over time for the simulations presented. This confirms that the network size approaches a steady state around the same time that learning flexibility begins to plateau, as noted in the original text (now line 275), and highlights the large number of GCs without apoptosis as well as the slightly reduced number of GCs in the permanent encoding model (line 312).

(11) As much as I appreciate the comprehensive discussion of the results in a broader context, I feel that the discussion can be somewhat shortened. The section on lateral inhibition is not fully valid given that synaptic connectivity is reciprocal. I also feel that much of the final section (Model assumptions and outlook) can be dropped (except for the last paragraph), not because anything is irrelevant, but because these points have been made, onen repeatedly, in the text above.

We agree that the discussion could be streamlined and have revised the manuscript accordingly. Specifically, we have shortened the section on lateral inhibition and clarified that the OB relies predominantly on reciprocal connectivity (Line 370). We also agree that parts of the final section were repetitive and have removed these. However, to address comments by Reviewer 3, we also expanded on some of the model assumptions. We thank the reviewer for helping us improve the clarity and focus of the manuscript.

(12) Figure 5: bolding every 5th curve is confusing.

We have adjusted our figure accordingly.

(13) "...we biased the dendritic field...": it would be helpful to explain the idea of a "dendritic field" in a bit more detail prior to this sentence.

We have now noted that GC’s "dendritic field" refers to the subset of MCs with which it is capable of forming synaptic connections when we initially describe the model (Line 97).

Reviewer #3:

(1) The authors find that a network with age-dependent synaptic plasticity outperforms one with constant age-independent plasticity and that having more GC per se is not sufficient to explain this effect. In addition, having an initial higher excitability of GCs leads to increased performance. To what degree the increased excitability of abGCs is conceptually necessarily independent of them having higher synaptic plasticity rates / fast synapses?

We thank the reviewer for this question, as the difference between excitability and plasticity rate in memory formation is something we intended to highlight in this study. We have updated the (Lines 157-198) to clarify this.

At the cellular level, a neuron's excitability and its rate of synaptic plasticity are mechanistically distinct: excitability is governed by factors such as ion channel expression or membrane resistance, whereas plasticity rates are influenced by molecular pathways involved in synapse and dendritic spine formation and remodeling. While these are independent properties, they are functionally coupled: most synaptic plasticity rules are activity-dependent, so greater excitability can increase the likelihood of plasticity being induced but does not itself guarantee learning.

Our model reflects this distinction. Increased excitability biases which neurons become activated and thus eligible to undergo plasticity, but actual learning still depends on the plasticity rate itself. This can be seen by comparing the model constant plasticity and excitability (solid blue and green curves in Figure 2C) to the model with only transient excitability (solid blue and green lines in Figure 2E). In both cases, the strength and duration of the memory remain limited by the plasticity rate. We note additionally that, in this network, neurons compete to learn new stimuli: as GCs start to learn, they suppress MC activity through recurrent inhibition which suppresses learning in other GCs who otherwise would have been in position to learn the odor. As a result there is not a significant increase in the overall number of neurons recruited to learn (Figure 2J). In a different network architecture, such as a feedforward network, we would not expect this to be the case; greater excitability in a population of neurons would likely increase the memory by increasing the number of neurons recruited to learn. Transiently enhanced excitability biases which neurons join the memory engram (Figure 2J), but the extent and rate of learning still depend on the plasticity rates themselves. We did note in the original text (now lines 284-286) that this bias in recruitment subtly increases memory stability, but the extent is not great. In principle, a model can be engineered to rely on transiently increased excitability to encode memories in orthogonal subpopulations of neurons and that this could resolve the flexibility-stability dilemma. However, in that case, the number of memories that can be stored within a short time would be bounded by the size of this subpopulation such that even if a large number of odors are presented, mature GCs cannot become part of the engram and the network would likely fail to learn the stimuli. However, when this was tested experimentally (Forest et al. Cereb Cor. 2020), it was found that mature GCs participated in the engram when the number of odors was sufficiently high. Our results are consistent with these experiments: for complex odor environments, neonatal GCs, which are mature during odor exposure, and abGCs both participate in the engrams.

Author response image 3.

Simulating learning in more complex odor environments. Top: enrichment consisted of three odor pairs presented sequentially in a random order. Bottom: enrichment consisted of five odor pairs. Left: discriminability of the odor pairs over time. Middle: connectivity between MCs (sorted by odor selectivity) and GCs (sorted by age). In both cases AbGCs develop a clear connectivity structure. In more complex environments neonatal GCs also start to develop a clear connectivity structure. Right: combined engram membership across all stimuli by GC age.

In sum, transiently increased excitability alone will not make learning any faster, so a fast learning system must have a high plasticity rate. If this plasticity rate stays high, then memories stored in these neurons, even if no longer highly excitable, will be vulnerable as the neurons can still be driven above their plasticity threshold by moderately interfering stimuli and will thus be quickly forgotten. Conversely, if the reviewer is wondering if a greater increase in the plasticity rate of new neurons can compensate for a lack of excitability, this is not the case: if a newborn neuron is not sufficiently driven by the stimulus it will not learn regardless of how high its plasticity rate is.

(2) The authors do not mention previous theoretical work on the specificity of mitral to granule cell interactions from several groups (Koulakov & Rinberg - Neuron, 2011; Gilra & Bhalla, PLoSOne, 2015; Grabska-Bawinska...Mainen, Pouget, Latham, Nat. Neurosci. 2017; Tootoonian, Schaefer, Latham, PLoS Comput. Biol., 2022), nor work on the relevance of top-down feedback from the olfactory cortex on the abGC during odor discrimination tasks (Wu & Komiyama, Sci. Adv. 2020), or of top-down regulation from the olfactory cortex on regulating the activity of the mitral/tuned cells in task engaged mice (Lindeman et al., PLoS Comput. Biol., 2024), or in naïve mice that encounter odorants (in the absence of specific context; Boyd, et al., Cell Rep, 2015; Otazu et al., Neuron 2015, Chae et al., Neuron, 2022). In particular, the presence of rich topdown control of granule cell activity (including of abGCs) puts into question the plausibility of one of the opening statements of the authors with respect to relying solely on local circuit mechanisms to solve the flexibility-stability dilemma. I think the discussion of this work is important in order to put into context the idea of specific interactions between the abGCs and the mitral cells.

We thank the reviewer for these detailed and thorough comments, and whole-heartedly agree that it is important to discuss the listed studies in order to contextualize our work through the broader lens of how information is processed in the OB. We have expanded our discussion to further acknowledge and integrate insight from previous theoretical and experimental work cited by the reviewer. (Lines 361-366, 493-550)

Regarding the importance of top-down feedback, we of course recognize that in practice cortical inputs play a critical role in abGC survival and synaptic integration. However, its nature is not quite clear and is likely variable across behavioral seungs. In the paradigm that we study in the manuscript, there is likely no key reward value or contextual signal that is relayed to the OB. One plausible interpretation is that in this task, cortical feedback provides a random, variable baseline excitatory drive to GCs. This would likely be consistent with many of the listed studies, e.g.

(1) Glomerular layer targeting of feedback would be explicitly unrelated to glomerular odor specificity, as in Boyd et al.

(2) GC activity would decrease if these cortical inputs were silenced, resulting in stronger MC responses as in Otazu et al., Chae et al.

(3) Silencing PCx during learning would prevent GCs from reaching activity-dependent plasticity thresholds, resulting in decreased spine density as in Wu & Komiyama.

Likewise activating PCx would lead to increased spine density.

In this interpretation, the effect of top-down input could be captured implicitly by adjusting model parameters such as activity or plasticity thresholds. For the purposes of our study, we opted to neglect these inputs in favor of model simplicity.

Critically, even if top-down inputs play a substantially larger role, by perhaps even going as far as providing signals to abGCs to modulate their development, the core solution to the flexibility-stability dilemma that we describe stays local: we predict that the memory persists in the same network in which it was formed.

(3) To what the degree of specific connectivity reflects a specific stimulus configuration, and is a good proxy for determining the stimulus discriminability and memory capacity in terms of temporal activity patterns (difference in latency/phase with respect to the respiration cycle, etc.) which may account to a substantial fraction of ability to discriminate between stimuli? The authors mention in the discussion that this is, indeed, an upper bound and specific connectivity is necessary for different temporal activity patterns, but a further expansion on this topic would help in understanding the limitations of the model.

We thank the reviewer for raising this important point. Indeed, there have been several recent experimental studies indicating that much of the information needed for olfactory discrimination is encoded in the temporal activity patterns of mitral and tuned cells. Our model does not explicitly simulate these dynamics. It was for this reason that we defined memory in terms of the learned structure of the network rather than by firing rate activity. This is motivated by the idea that learned patterns of connectivity constrain the space of neural activity the network can support, and thus shape stimulus responses. We now make this limitation more explicit in the discussion and clarify that the specific MC–GC connectivity we analyze should be seen as a structural substrate that constrains the possible temporal transformations the network could support (Lines 492-506).

(4) Reward or reward prediction error signals are not considered in the model. They however are ubiquitous in nature and likely to be encountered and shape the connectivity and activity patterns of the abGC-mitral cell network. Including a discussion of how the model may be adjusted to incorporate reward/error signals would strengthen the manuscript.

We appreciate the reviewer’s suggestion and agree that reward and reward prediction error signals are critical components of many learning paradigms. We deliberately chose not to model associative learning, reward signals or top-down neuromodulation in this work. Our goal is to investigate the role of adult neurogenesis in a regime where its contribution has been shown to be experimentally necessary. Specifically, we focused on an unsupervised perceptual learning paradigm where adult neurogenesis is required for successful odor discrimination (Moreno et al. PNAS, 2008). In contrast, when the same odors are used in a rewarded learning paradigm, performance remains intact even when adult neurogenesis is ablated (Imayoshi et al., Nat. Neuro., 2008). This dissociation suggests that neurogenesis is dispensable in contexts where reward can guide learning. As such, we argue that isolating the contribution of local circuit dynamics in an unsupervised setting is critical to understanding what neurogenesis is uniquely enabling, especially given the evolutionary cost of maintaining it.

We agree that extending this work to incorporate reward-driven plasticity or neuromodulatory influences would be a valuable direction for future research. In particular, it could help clarify how different learning paradigms engage distinct abGC cohorts (e.g., Mandairon et al., eLife 2018; Wu & Komiyama, Sci. Adv. 2020), and how task structure shapes memory allocation and engram composition. We have incorporated this into the discussion regarding extending our model to include top down feedback (lines 539-553).

Specific comments

(1) Lines 84-86; 507-509; Eq(3): Sensory input is defined by a basal parameter of MCs spontaneous activity (Sspontaneus) and the odor stimuli input (Siodor) but is not clear from the main text or methods how sensory inputs (glomerular patterns) were modeled

We now clarify in the Methods section "Stimulus model" how the sensory inputs were modeled. Specifically, odor-evoked inputs to mitral cells (Siodor) were generated either as Gaussian profiles across the mitral cell population (Figs. 2,3) or as sparser random patterns (Figs. 4,5). In Figures 2 and 3, the denser Gaussian stimuli require more GCs to learn the odors, aiding in visualization of the connectivity matrix (Figure 2H) and abGC recruitment plots (Figure 2I,J; Figure 3C,E). However, real olfactory stimuli activate a sparse set of MCs, so in Figures 4 and 5 where we address learning of many stimuli, we utilize sparser, binary, stimuli delivered to only 10% of MCs, in range of experimental data (Wachowiak and Cohen, Neuron, 2001). The fact that the stimuli are binary, however, is not realistic and leads to denser representations. This leads to a worst-case scenario for the model as denser memory representations are easier to overwrite. These points has been added explicitly to the Methods section "Stimulus model" to improve clarity.

(2) Lines 118-122: The used perceptual learning task explanation is done only in the context of the discriminability of similar artificial stimuli using the Fisher discriminant and "Memory" metric. A detailed description of the logic of the perceptual learning task methods and objective, taking into account Comment 1, would help to better understand the model.

We thank the reviewer for pointing out had not adequately described the task and have updated the main text (lines 125-132) and included a new methods section "Perceptual learning task" to describe it more explicitly. The experiments that inspired the simulation followed an ecological model of discrimination learning (Moreno et al. PNAS 2009): For one hour a day over a ten day "enrichment period", two tea balls containing similar but distinct odors were suspended from the lid of each mouse's home cage. The mice engaged with the stimuli under self-directed conditions, therefore learning through natural experience. As a result the mice use olfactory information to discriminate between the similar stimuli, a skill potentially relevant for navigation or social behaviors.

In our simulations, we model these experiments as follows. During the enrichment period, the model is stimulated with a randomly selected stimulus chosen from a set of two similar stimuli, corresponding to a mouse choosing to sniff one of the tea balls. During enrichment, in between these bouts of "sniffing", the model only receives spontaneous activity, reflecting the temporal sparsity of sensory input even over the enrichment period. Outside of enrichment, the model again receives only spontaneous input.

(3) Rapid re-learning of forgotten odor pair is enabled by sensory-dependent dendritic elaboration of neurons that initially encoded the odors and the observed re-learning would occur even if neurogenesis was blocked following the first enrichment and even though the initial learning did require neurogenesis. When this would ever occur in nature? The re-learning of an odor period? Why is this highlighted in the study?

We believe that this sort of learning is certainly relevant in nature. To clarify: by “learning,” we do not refer to the memory of an entire “odor period”, but simply an altered mapping of specific stimuli. Therefore, forgeung could occur if these specific stimuli are absent from the environment for a period of time, and re-learning would occur when these stimuli are re-encountered. Natural odor environments are highly dynamic, as environmental conditions and social contexts change over time. The odors an animal encounters also depend strongly on its own behavior; as it explores different environments, it may be exposed to particular odors intermittently: it could encounter them in one location, then not return to that location for some time before returning again.

Such natural variability in odor exposure makes the ability to forget and re-learn especially valuable, allowing the animal to prioritize relevant information while maintaining flexibility. To this end, we show in Figure 5G that the synaptic forgetting of odors is beneficial to the performance of the model because it reduces interference in the network. Therefore we highlight that re-learning enabled by adult neurogenesis is a highly efficient strategy for memory storage and retrieval, which is why he emphasize it in this study.

(4) Figure 2A: I understand that the ages shown at the bottom of the colored boxes represent the GC age. If so, find a better way to express that to avoid confusing 'GC ages' from the days shown in the perceptual learning task description (Figure 2B).

We have updated the text in the figure to disambiguate the two and refer to the “days” shown in the perceptual learning task description now as “time relative to enrichment”

(5) Figure 2B: Clarify how the two-dimensional arrays are arranged to represent the patterns shown. Does each point of the array represent one neuron? If so, are these neurons re-arranged to help the readers visually differentiate patterns A and B? Are the patterns of activity of MCs in the model spatially and temporally sparse as observed in experimental work?

In Figure 2B, each point in the two-dimensional array represents the activity of a single mitral cell. The layout is purely for visualization—neurons are re-arranged to make the differences between odor patterns A and B visually apparent. This ordering does not reflect anatomical position or model architecture. We revised the Figure 2 caption to say this explicitly.

Regarding spatial sparseness, as we mentioned in the response to the reviewer’s comment (1), the activity of mitral cells in response to odors is spatially sparse in the model. Regarding temporal sparseness, while the model is not spiking and does not include temporal dynamics within the timescale of the breath, however, odor input is delivered in discrete, odorspecific epochs interleaved with periods of no input, which leads to temporally structured activity patterns. This information has been made explicit in the new methods sections "Stimulus model" and "Perceptual learning task"

(6) Figure 3C and Line 189: potential confusion between the color code mentioned in the legend for the enrichment and developing periods.

It appeared to be a confusion in the text and has been corrected (Lines 212-213).

(7) Figure 5F: For clarity, this would benefit from replacing the bold line with areas in the plot to depict the enrichment periods.

We agree that replacing the bolded line segments with shaded areas is more clear and have updated the figure accordingly, and appreciate the reviewer's suggestion to clarify the figure.

(8) Lines 380, 416: Potential role of cortical feedback and or neuromodulation depending on behavioral relevance or permanent exposure? Later mentioned in Lines 467 - 474.

We have updated the text to acknowledge the role of potential cortical feedback and neuromodulation, now in lines 403-407.

eLife Assessment

This important work sets out to identify the neural substrates of associative fear responses in adult zebrafish. Through a compelling and innovative paradigm and analysis, the authors suggest brain regions associated with individual differences in fear memory. While several findings are well supported, aspects of the interpretation and presentation are partially incomplete, and the manuscript would benefit from adjusting key claims or including additional experiments. Nonetheless, this study showcases the strength of zebrafish for systems-level neuroscience and will be of broad interest to the neuroscience community.

Reviewer #1 (Public review):

Summary:

This work provides a comprehensive analysis of how adult zebrafish show fear responses to conspecific alarm substances (CAS) and retain their associative memory. It shows that freezing is a more reliable measure of fear response and memory compared to evasive swimming, and that the reactivity and the type of responses depend on the zebrafish strain. It further suggests neuronal substrates of different fear responses based on c-Fos mapping.

Strengths:

The behavioral part is the most comprehensive and detailed yet in the zebrafish field, providing strong support for the authors' claim. The flow from Figure 1 to Figure 4 is very smooth. They provide extremely detailed, yet complementary and necessary, analyses of how different categories of behavior emerge over time during the CAS exposure and memory retrieval. I'm convinced that neuro researchers who study fear/stress responses will always refer to this paper to plan and interpret their future experiments.

Weaknesses:

The neural analysis part is very comprehensive. Figure 5 and Figure 6 are independent but complement each other very well. They together support that the cerebellar system is the key brain component for a freezing response. Their extreme focus on high-level analyses, however, came at the expense of biological intuitions. I suggest adding some figure panels and result/discussion paragraphs to help with that aspect.

Reviewer #2 (Public review):

In this study, Fontana et al. develop a paradigm for associative conditioning by pairing exposure to an alarm substance with a novel tank. Exposure to conspecific alarm substance (CAS) in the novel tank triggers freezing and what they characterize as evasive swimming behaviour, which is subsequently seen in a re-exposure to the novel tank without the CAS present. Importantly, these states are identified via automated processes, including postural tracking and a random forest classification process, which could be very useful tools for subsequent studies.

In their experiments, they focus on the differences in behaviour among strains of zebrafish (both males and females), and among individual zebrafish. For males and females of different strains, they find some differences, though the clearest message seems to be that the most robust measure of the behaviour in response to both the CAS and in the memory trials is the freezing behaviour, while evasive behaviour is more variable. and not always seen. This may relate to their observation of significant "evasiveness" in vehicle control experiments (discussed further below).

Moving on to individual variation from within this multi-strain male/female dataset, they first examine transition matrices between states and find tthat his is not dramatically altered by stimulus exposure. They then use clustering to identify 4 different "classes" of zebrafish that differ in their expression (or not) of two types of behaviour: freezing and/or evasive behaviour. They show that over the three exposure epochs of the experiment, this classification is somewhat stable in an individual fish, though many fish change their behaviour - e.g., evading + freezing -> only freezing.

In the final set of experiments, the authors move beyond behavioural analyses and perform whole-brain cFos mapping of these individual zebrafish. They perform analyses aimed at identifying correlations between individual behavioural expression and the number of cFos-positive cells in different brain regions. Using partial least squares analysis, they find areas associated with two types of behavioural contrasts, which differ in their weighting of different behavioural expression during the Memory trials. Covariation and network structure analysis within different classes of larvae also find some differences in covariation among brain areas, providing hypotheses as to underlying network effects that may govern the expression of freezing and/or evasive behavior in the memory trial phases.

Overall, I find this to be an interesting study that employs state of the are methods of behavioural analyses and whole-brain cFos analyses, but I am left a little bit confused as to what the take home message is and what can be concluded from this complex study that mixes in analyses of strain, sex, and individuality within a quite complex assay with multiple behavioural parameters.

My suggestions are as follows:

(1) My first concern relates to the claim in the abstract that "We found that fear memory behavior fell into four distinct groups: non-reactive, evaders, evading freezers, and freezers".

In my opinion, the "freezing" aspect is well supported as being both triggered by the CAS and for memory effect upon re-exposure to the tank, but I am less convinced about the "evasive" behaviour. In Figure 2, it appears that "evasiveness" is generally not increased in both the Exposure or Memory phases for many groups, and in Figure 5, it appears that "evasiveness" is expressed by nearly 50% of the fish in the pre-exposure condition before CAS addition and in all phases in the vehicle condition. Therefore, it appears that most of the expression of this behaviour is independent of any memory-based effect.

(2) My second concern relates to the claim in the abstract that "background strain and sex influenced how fish respond to CAS, with males more likely to increase evasive behaviors than females and the TU strain more likely to be non-reactive."

My understanding, based on the introduction and on the methods, is that it is likely important that the CAS be prepared from conspecifics of the same strain and sex, and for this reason, they prepared different CAS specific for each strain and each sex. Therefore, the "CAS" that is applied is necessarily different for each condition, and I am concerned about if the differences observed could relate more to variation in the quality, purity, concentration, etc. of the specific CAS samples for different groups, rather than their reactivity to the substance or their ability to form memories based on such experiences.

(3) My third concern relates to the interpretation of the cFos data.

As I mentioned above, I feel as though the behavioural analysis is perhaps more complex than is warranted via the inclusion of evasiveness, and I wonder if the conclusions from the experiments would be simpler if analyzed only from the perspective of freezing.

But considering the presented analyses: while I dont think there is anything wrong with the partial least squares approach and the network analyses, I am concerned that the simple messaging in the text does not reflect the complexity of this analysis combining different weightings of different behavioural characteristics in a behavioural contrast, or covariations among many regions and what such analyses mean at the level of brain function. For these reasons, I feel like statements along the lines of "Behavioral variation is driven by differences in the activity of brain regions outside the telencephalon, such as the cerebellum, preglomerular nuclei, preoptic area and hypothalamus" are not well supported.

Reviewer #3 (Public review):

Summary:

This manuscript by Fontana et al. sets out to fill a critical gap in our understanding of how individuality in fear responses corresponds to changes in brain activity. Previous work has shown in myriad species that fear behaviors are highly variable, and these variabilities correlate with sex and strain, with epigenetic modifications, and neural activity in specific regions of the brain, such as the amygdala. However, a whole-brain functional assessment of whether activity in different regions of the brain is associated with fear behavior has been difficult to assess, in part due to the large size and opacity of the brain. The Kenney group overcomes these limitations using the zebrafish, together with powerful behavioral and brain imaging approaches pioneered by their lab. To overcome the technical obstacles of delivering a reproducible unconditioned stimulus in water and quantifying nuanced behavioral responses, the authors developed a three-day conditioning paradigm in which fish were repeatedly exposed to CAS in one tank context and to control water in another. Leveraging automated cluster analysis across over 300 individuals from four inbred strains, they identified four distinct memory-recall phenotypes - non-reactive, evaders, evading freezers, and freezers - demonstrating both the robustness of their assay and the influence of genetic background and sex on fear learning. Finally, whole-brain imaging using the AZBA atlas (Kenney et al. eLife) and cfos mapping coupled with multivariate analysis revealed that although all fish reengaged telencephalic regions during recall, high-freezing phenotypes uniquely recruited cerebellar, preglomerular, and pretectal nuclei, whereas mixed evasion-freezing fish showed preferential activation of preoptic and hypothalamic areas - a finding that lays the groundwork for dissecting the distributed neural substrates of associative fear in zebrafish.

Strengths:

The strengths of the study lie in the use of zeberarish and the innovative behavioral, modeling, and brain imaging tools applied to address this question. The question of how brain-wide activity correlates with variations in fear behavior is fundamental, and arguably, this system is the only system that could be used to address this. The statistics are appropriate, and the study is well reasoned. Overall, I like this manuscript very much and think it adds invaluable information to the field of fear/anxiety.

Weaknesses:

I have a few questions and suggestions.

(1) The three-day contextual fear paradigm, as implemented - one CAS pairing on day 2 followed by a single recall test on day 3 - inevitably conflates acquisition and long-term memory, making it impossible to know whether strains like TU truly recall the association poorly or simply learn it more slowly. For example, given that TU fish extinguish fear faster than AB or TL strains in extended protocols, they may simply require additional or repeated CAS pairings to achieve the same asymptotic performance. To disentangle learning kinetics from recall strength, the assay could be revised to include multiple acquisition trials (e.g., conditioning on two or more consecutive days) with an immediate post-conditioning probe to assess acquisition independent of consolidation, and continuous measurement of freezing and evasive behaviors across each trial to fit learning curves for each strain. Such refinements - even if on a subset of the strains - would reveal whether "non-reactive" phenotypes reflect genuine recall deficits or merely delayed acquisition.

(2) My second major question is with respect to Figure 3 panel B. This is a complex figure, and I can understand the gist of what the authors are attempting to show, but it is difficult to understand as it is. Can this be represented in a way that is clearer and explained a bit more easily?

(3) The brain mapping is by far one of the most interesting aspects of this study, and the methods that the group used are interesting. The brain mapping, however, relies on generating "contrasting" groups (Figure 6A), and I was not clear as to how these two groups were formed. Could the authors elaborate a bit?

eLife Assessment

This valuable study focuses on defining how the HSP70 chaperone system utilizes J-domain proteins to regulate the heat shock response-associated transcription factor HSF1. Using a combination of orthogonal techniques in yeast, this manuscript provides compelling evidence that the J-domain protein Apj1 facilitates attenuation of HSF1 transcriptional activity through a mechanism involving its dissociation from heat shock gene promoter regions. This work generates new insight into the mechanism of HSF1 transcriptional regulation and is a significant contribution of broad interest to cell biologists interested in proteostasis, chaperone networks, and stress-responsive signaling.

Reviewer #1 (Public review):

Summary:

In this study, the authors present a thorough mechanistic study of the J-domain protein Apj1 in Saccharomyces cerevisiae, establishing it as a key repressor of Hsf1 during the attenuation phase of the heat shock response (HSR). The authors integrate genetic, transcriptomic (ribosome profiling), biochemical (ChIP, Western), and imaging data to dissect how Apj1, Ydj1 and Sis1 modulate Hsf1 activity under stress and non-stress conditions. The work proposes a model where Apj1 specifically promotes displacement of Hsf1 from DNA-bound heat shock elements, linking nuclear PQC to transcriptional control.

Strengths:

Overall, the work is highly novel-this is the first detailed functional dissection of Apj1 in Hsf1 attenuation. It fills an important gap in our understanding of how Hsf1 activity is fine-tuned after stress induction, with implications for broader eukaryotic systems. I really appreciate the use of innovative techniques including ribosome profiling and time-resolved localization of proteins (and tagged loci) to probe Hsf1 mechanism. The overall proposed mechanism is compelling and clear-the discussion proposes a phased control model for Hsf1 by distinct JDPs, with Apj1 acting post-activation, while Sis1 and Ydj1 suppress basal activity.

The manuscript is well-written and will be exciting for the proteostasis field and beyond.

Comments on revised version:

The authors have addressed all my concerns,

Reviewer #2 (Public review):

Summary:

Overall, the work is exceptionally well done and controlled and the results properly and appropriately interpreted. While several of the approaches, while powerful, are somewhat indirect (i.e., following gene expression via ribosomal profiling) additional experiments utilizing traditional gene expression assays added in revision combine to ultimately provide a compelling answer to the main questions being asked.

The key finding from this work is the discovery that Apj1 regulates Hsf1 attenuation in a manner that includes Hsp70. That finding is strongly supported by the experimental data. While it would be ideal to also demonstrate Apj1-controlled differential binding of Ssa1/2 to Hsf1 at either the N- or C-terminal binding sites during attenuation, the Hsp70-Hsf1 interactions are difficult to reproducibly assess in cell extracts and are likely beyond the scope of this study. However, this work paves the way in the future for potential biochemical reconstitution assays that could elucidate both Hsp70-Hsf1 interactions as well as the distinct JDP-Hsf1 interactions reported here.

This discovery raises additional new questions about JDP specificity in HSR regulation and the role of JDPs in navigating protein aggregation and sensing of proteostatic challenge in the nucleus, thus advancing the field and opening new, exciting avenues for exploration.

Reviewer #3 (Public review):

Summary:

The heat shock response (HSR) is an inducible transcriptional program that has provided paradigmatic insight into how stress cues feed information into the control of gene expression. The recent elucidation that the chaperone Hsp70 controls the DNA binding activity of the central HSR transcription factor Hsf1 by direct binding has spurred the question how such a general chaperone obtains specificity. This study has addressed the next logical question, how J-domain proteins execute this task in budding yeast, the leading cell model for studying the HSR. While an involvement and in part overlapping function of general class A and B J-domain proteins, Ydj1 and Sis1 are indicated by the genetic analysis a highly specific role for the class A Apj1 in displacing Hsf1 from the promoters is found unveiling specificity in the system.

Strengths

The central strong point of the paper is the identification of class A J-domain protein Apj1 as a specific regulator of the attenuation of the HSR by removing Hsf1 from HSEs at the promoters. The genetic evidence and the ChIP data strongly support this claim. This identification of a specific role for a lowly expressed nuclear J-domain protein changes how the wiring of the HSR should be viewed. It also raises important questions regarding the model of chaperone titration, the concept that a chaperone with limiting availability is involved in a thug of war involving competing interactions with misfolded protein substrates and regulatory interactions with Hsf1. Perhaps Apj1 with its low levels and interactions with misfolded and aggregated proteins in the nucleus is the titrated Hsp70 (co)chaperone that determines the extent of the HSR? This would mean that Apj1 is at the nexus of the chaperone titration mechanism. Although Apj1 is not a highly conserved J domain protein among eukaryotes the strength of the study is that is provides a conceptual framework for what may be required for chaperone titration in other eukaryotes: One or more nuclear J-domain proteins with low nuclear levels that has an affinity for Hsf1 and that can become limiting due to interactions with misfolded Hsp70 proteins. The provides a pathway for how these may be identified using for example ChIP-seq.

Weakness

A built-in challenge when studying the mechanism of the HSR is the general role of Hsp70 chaperone system and its J domain proteins. Indeed, a weakness of the study is that it is unclear what of the phenotypic effects have to do with directly recruiting Hsp70 to Hsf1 dependent on a J domain protein and what instead is an indirect effect of protein misfolding caused by the mutation. This interpretation problem is clearly and appropriately dealt with in the manuscript text and in experiments but is of such fundamental nature that it cannot easily be fully ruled out.

Author response:

The following is the authors’ response to the original reviews.

Reviewer #1 (Public review):

We thank the reviewer for his/her very positive comments.

Reviewer #2 (Public review):

We thank the reviewer for his/her positive evaluation. We plan to add RNAseq data of yeast wild-type and JDP mutant strains as more direct readout for the role of Apj1 in controlling Hsf1 activity. We agree with the reviewer that our study includes one major finding: the central role of Apj1 in controlling the attenuation phase of the heat shock response. In accordance with the reviewer we consider this finding highly relevant and interesting for a broad readership. We agree that additional studies are now necessary to mechanistically dissect how the diverse JDPs support Hsp70 in controlling Hsf1 activity. We believe that such analysis should be part of an independent study but we will indicate this aspect as part of an outlook in the discussion section of a revised manuscript.

Reviewer #3 (Public review):

We thank the reviewer for his/her suggestions. We agree that it is sometimes difficult to distinguish direct effects of JDP mutants on heat shock regulation from indirect ones, which can result from the accumulation of misfolded proteins that titrate Hsp70 capacity. We also agree that an in vitro reconstitution of Hsf1 displacement from DNA by Apj1/Hsp70 will be important, also to dissect Apj1 function mechanistically. We will add this point as outlook to the revised manuscript.

Reviewer #1 (Recommendations for the authors): 

(1) Can the authors submit the raw translatome data to a standard repository? Also, the data should be summarized in a supplemental Excel table. 

We submitted the raw translatome data to the NCBI Gene Expression Omnibus and added the analyzed data sets (shown in Figures 1 and 5) as Supplementary Tables S4/S5 (excel sheets). We additionally included RNAseq analysis of yeast WT and JDP mutants set grown at 25°C, complementing and confirming our former translatome analysis (new Figure 5, Figure Supplement 2). Respective transcriptome raw data were also deposited at the NCBI Gene Expression Omnibus and analyzed data are available as Supplementary Table S7.

(2) MW indicators need to be added to the Western Blot figures. 

We added molecular weight markers to the Western Blot figures.

(3) Can the authors please include the sequences of the primers used in all the RT-qPCR experiments? They mention they are in the supplemental information, but I couldn't locate them. 

We added the sequences of the RT-qPCR primers as Supplementary Table S4.

(4) Given the clear mechanism proposed, it would be nice if the authors could provide a nice summary figure. 

We followed the suggestion of the reviewer and illustrate our main finding as new Figure 7.

Reviewer #2 (Recommendations for the authors): 

(1) As mentioned above, a co-IP experiment between Hsf1 and Ssa1/2 in APJ1 and apj1∆ cells, utilizing Hsf1 alleles with and without the two known binding sites, would cement the assignment of Apj1 in the Hsf1 regulatory circuit. 

We agree with the reviewer that Hsf1-Ssa1/2 pulldown experiments, as done by Pincus and colleagues (1), will further specify the role of Apj1 in targeting Hsp70 to Hsf1 during the attenuation phase of the heat shock response. We have tried extensively such pulldown experiments to document dissociation of Ssa1/2 from Hsf1 upon heat shock in yeast wild-type cells. While we could specifically detect Ssa1/2 upon Hsf-HA1 pulldown, our results after heat shock were highly variable and inconclusive and did not allow us to probe for a role of Apj1 or the two known Ssa1/2 binding sites in the phase-specific targeting. We now discuss the potential roles of the two distinct Ssa1/2 binding sites for phase-specific regulation of Hsf1 activity in the revised manuscript (page 12, lanes 17-21).

(2) Experiments in Figure 3 nicely localize CHIP reactions with known HSEs. A final confirmatory experiment utilizing a mutated HSE (another classic experiment in the field) would cement this finding and validate the motif and reporter-based analysis. 

We thank the reviewer for this meaningful suggestions. We have done something like this by using the non-Hsf1 regulated gene BUD3, which lacks HSEs, as reference. We engineered a counterpart, termed “BUD3 HS-UAS”, which bears inserted HSEs, derived from the native UAS of HSP82, within the BUD3 UAS. We show that BUD3⁺ lacking HSEs is not occupied by Hsf1 and Apj1 under either non-stress or heat shock conditions while BUD3-HSE is clearly occupied under both, paralleling Hsf1 and Apj1 occupancy of HSP82 (Figure 3E). We have renamed the engineered allele to “BUD3-HSE” to clarify the experimental design and output.

(3) Page 8 - the ydj1-4xcga allele is introduced without explaining why it's needed, since ydj1∆ cells are viable. The authors should acknowledge the latter fact, then justify why the RQC depletion approach is preferred. Especially since the ydj1∆ mutant appears in Figure 5B. 

ydj1∆ cells are viable, yet they grow extremely slowly at 25°C and hardly at 30°C,  making them difficult to handle. The RQC-mediated depletion of Ydj1 in ydj1-4xcga cells allows for solid growth at 30°C, facilitating strain handling and analysis of Ydj1 function. Importantly, ydj1-4xcga cells are still temperature-sensitive and exhibit the same deregulation of the heat shock response upon combination with apj1D as observed for ydj1∆ cells. Thus ydj1 knockout and knockdown cells do not differ in the relevant phenotypes reported here and we performed most of the analysis with  ydj1-4xcga cells due to their growth advantage. We added a respective explanation to the text (page 8, lanes 13-14) .

(4) The authors raise the possibility that Sis1, Apj1, and Ydj1 may all be competing for access to Ssa1/2 at different phases of the HSR, and that access may be dictated by conformational changes in Hsf1. Given that there are at least two known Hsp70 binding sites that have negative regulatory activity in Hsf1, the possibility that domain-specific association governs the different roles should be considered. It is also unclear how the JDPs are associating with Hsf1 differentially if all binding is through Ssa1/2. 

We thank the reviewer for the comment and will add the possibility of specific roles of the identified Hsp70 binding sites in regulating Hsf1 activity at the different phases of the heat shock response to the discussion section. Binding of Ssa1/2 to substrates (including Hsf1) is dependent on J-domain proteins (JDPs), which differ in substrate specificity. It is tempting to speculate that the distinct JDPs recognize different sites in Hsf1 and are responsible for mediating the specific binding of Ssa1/2 to either N- or C-terminal sites in Hsf1. Thus, the specific binding of a JDP to Hsf1 might dictate the binding to Ssa1/2 to either binding site. We discuss this aspect in the revised manuscript (page 12, lanes 17-21).

(5) Figure 6 - temperature sensitivity of hsf1 and ydj1 mutants has been linked to defects in the cell wall integrity pathway rather than general proteostasis collapse. This is easily tested via plating on osmotically supportive media (i.e., 1M sorbitol) and should be done throughout Figure 6 to properly interpret the results.

Our data indicate proteostasis breakdown in ydj1 cells by showing strongly altered localization of Sis1-GFP, pointing to massive protein aggregation (Figure 6 – Figure Supplement  1D).

We followed the suggestion of the reviewer and performed spot tests in presence of 1 M sorbitol (see figure below). The presence of sorbitol is improving growth of ydj1-4xcga mutant cells at increased temperatures, in agreement with the remark of the reviewer. We, however, do not think that growth rescue by sorbitol is pointing to specific defects of the ydj1 mutant in cell wall integrity. Sorbitol functions as a chemical chaperone and has been shown to have protective effects on cellular proteostasis and to rescue phenotypes of diverse point mutants in yeast cells by facilitating folding of the respective mutant proteins and suppressing their aggregation (2-4). Thus sorbitol can broadly restore proteostasis, which can also explain its effects on growth of ydj1 mutants at increased temperatures. Therefore the readout of the spot test with sorbitol is not unambiguous and we therefore prefer not showing it in the manuscript.

Author response image 1.

Serial dilutions of indicated yeast strains were spotted on YPD plates without and with 1 M sorbitol and incubated at indicated temperatures for 2 days.<br />

Reviewer #3 (Recommendations for the authors): 

(1) Line 154: Can the authors, by analysis, offer an explanation for why HSR attenuation varies between genes for the sis1-4xcga strain? Is it, for example, a consequence of that a hypomorph and not a knock is used, a mRNA turnover issue, or that Hsf1 has different affinities for the HSEs in the promoters? 

We used the sis1-4xcga knock-down strain because Sis1 is essential for yeast viability. The point raised by the reviewer is highly valid and we extensively thought about the diverse consequences of Sis1 depletion on levels of e.g. translated BTN2 (minor impact) and HSP104 (strong impact) mRNA. We meanwhile performed transcriptome analysis and confirmed the specific impact of Sis1 depletion on HSP104 mRNA levels, while BTN2 mRNA levels remained much less affected (new Figure 5 - Figure Supplement 2A/B). We compared numbers and spacings of HSEs in the respective target genes but could not identify obvious differences. Hsf1 occupancy within the UAS region of both BTN2 and HSP104 is very comparable at three different time points of a 39°C heat shock: 0, 5 and 120 min, arguing against different Hsf1 affinities to the respective HSEs (5). The molecular basis for the target-specific derepression upon Sis1 depletion thus remains to be explored. We added a respective comment to the revised version of the manuscript (page 12, lanes 3-8) .

(2) Line 194: The analysis of ChIP-seq is not very elaborated in its presentation. How specific is this interaction? Can it be ruled out by analysis that it is simply the highly expressed genes after the HS that lead to Apj1 appearing there? More generally: Can the data in the main figure be presented to give a more unbiased genome-wide view of the results?

We overall observed a low number of Apj1 binding events in the UAS of genes. The interaction of Apj1 with HSEs is specific as we do not observe Apj1 binding to the UAS of well-expressed non-heat shock genes. Similarly, Apj1 does not bind to ARS504 (Figure S3 – Figure Supplement 1). We extended the description of our ChIP-seq analysis procedures leading to the identification of HSEs as Apj1 target sites to make it easier to understand the data analysis. We additionally re-analysed the two Apj1 binding peaks that did not reveal an HSE in our original analysis. Using a modified setting we can identify a slightly degenerated HSE in the promoter region of the two genes (TMA10, RIE1) and changed Figure 3C accordingly. Notably, TMA10 is a known target gene of Hsf1. The expanded analysis is further documenting the specificity of the Apj1 binding peaks.

(3) Line 215. Figure 3. The clear anticorrelation is puzzling. Presumably, Apj1 binds Hsf1 as a substrate, and then a straight correlation is expected: When Hsf1 substrate levels decrease at the promoters, also Apj1 signal is predicted to decrease. What explanations could there be for this? Is it, for example, that Hsf1 is not always available as a substrate on every promoter, or is Apj1 tied up elsewhere in the cell/nucleus early after HS? 

We propose that Apj1 binds HSE-bound Hsf1 only after clearance of nuclear inclusions, which form upon heat stress. Apj1 thereby couples the restoration of nuclear proteostasis to the attenuation of the heat shock response. This explains the delayed binding of Apj1 to HSEs (via Hsf1), while Hsf1 shows highest binding upon activation of the heat shock response (early timepoints). Notably, the binding efficiency of Hsf1 and Apj1 (% input) largely differ, as we determine strong binding of Hsf1 five min post heat shock (30-40% of input), whereas maximal 3-4% of the input is pulled down with Apj1 (60 min post heat shock) (Figure 3D). Even at this late timepoint 10-20% of the input is pulled down with Hsf1. The diverse kinetics and pulldown efficiencies suggest that Apj1 displaces Hsf1 from HSEs and accordingly Hsf1 stays bound to HSEs in apj1D cells (Figure 4). This activity of Apj1 explains the anti-correlation: increased targeting of Apj1 to HSE-bound Hsf1 will lower the absolute levels of HSE-bound Hsf1. What we observe in the ChIP experiment at the individual timepoints is a snapshot of this reaction. Accordingly, at the last timepoint (120 min after heat shock ) analyzed, we observe low binding of both Hsf1 and Apj1 as the heat shock response has been shut down.

(4) Line 253: "Sis-depleted".  

We have corrected the mistake.

(5) Line 332: Fig. 6C SIS1 OE from pRS315. A YIP would have been better, 20% of the cells will typically not express a protein with a CEN/ARS of the pRS-series so the Sis1 overexpression phenotype may be underestimated and this may impact on the interpretation. 

We agree with the reviewer that Yeast Integrated Plasmids (YIP) represent the gold standard for complementation assays. We are not aware of a study showing that 20% of cells harboring pRS-plasmids do not express the encoded protein. The results shown in Fig. 8C/D demonstrate that even strong overproduction of Sis1 cannot restore Hsf1 activity control. This interpretation also will not be affected assuming that a certain percentage of these cells do not express Sis1. Nevertheless, we added a comment to the respective section pointing to the possibility that the Sis1 effect might be underestimated due to variations in Sis1 expression (page 11, lanes 15-19).

(6) Figure 1C. Since n=2, a more transparent way of showing the data is the individual data points. It is used elsewhere in the manuscript, and I recommend it. 

We agree that showing individual data points can enhance transparency, particularly with small sample sizes. However, the log2 fold change (log2FC) values presented in Figure 1C and other figures derived from ribosome profiling and RNAseq experiments were generated using the DESeq2 package. This DeSeq2 pipeline is widely used in analyzing differential gene expression and known for its statistical robustness. It performs differential expression analysis based on a model that incorporates normalization, dispersion estimation, and shrinkage of fold changes. The pipeline automatically accounts for biological, technical variability, and batch effects, thereby improving the reliability of results. These log2FC values are not directly calculated from log-transformed normalized counts of individual samples but are instead estimated from a fitted model comparing group means. Therefore, the individual values of replicates in DESeq2 log2FC cannot be shown.

(7) Figure 1D. Please add the number of minutes on the X-axis. Figure legend: "Cycloheximide" is capitalized.  

We revised the figure and figure legend as recommended.

(8) Several figure panels: Statistical tests and SD error bars for experiments performed in duplicates simply feel wrong for this reviewer. I do recognize that parts of the community are calculating, in essence, quasi-p-values using parametric methods for experiments with far too low sample numbers, but I recommend not doing so. In my opinion, better to show the two data points and interpret with caution.

We followed the advice of the reviewer and removed statistical tests for experiments based on duplicates.

References

(1) Krakowiak, J., Zheng, X., Patel, N., Feder, Z. A., Anandhakumar, J., Valerius, K. et al. (2018) Hsf1 and Hsp70 constitute a two-component feedback loop that regulates the yeast heat shock response eLife 7,

(2) Guiberson, N. G. L., Pineda, A., Abramov, D., Kharel, P., Carnazza, K. E., Wragg, R. T. et al. (2018) Mechanism-based rescue of Munc18-1 dysfunction in varied encephalopathies by chemical chaperones Nature communications 9, 3986

(3) Singh, L. R., Chen, X., Kozich, V., and Kruger, W. D. (2007) Chemical chaperone rescue of mutant human cystathionine beta-synthase Mol Genet Metab 91, 335-342

(4) Marathe, S., and Bose, T. (2024) Chemical chaperone - sorbitol corrects cohesion and translational defects in the Roberts mutant bioRxiv  10.1101/2024.09.04.6109452024.2009.2004.610945

(5) Pincus, D., Anandhakumar, J., Thiru, P., Guertin, M. J., Erkine, A. M., and Gross, D. S. (2018) Genetic and epigenetic determinants establish a continuum of Hsf1 occupancy and activity across the yeast genome Mol Biol Cell 29, 3168-3182

Same here. And it's really not that complicated to understand and execute.Once you have a RSS reader, the process is really straightforward even for non IT people.

eLife Assessment

This important study provides compelling evidence that fever-like temperatures enhance the export of Plasmodium falciparum transmembrane proteins, including the cytoadherence protein PfEMP1 and the nutrient channel PSAC, to the red blood cell surface, thereby increasing cytoadhesion. Using rigorous and well-controlled experiments, the authors convincingly demonstrate that this effect results from accelerated protein trafficking rather than changes in protein production or parasite development. These findings significantly advance our understanding of parasite virulence mechanisms and offer insights into how febrile episodes may exacerbate malaria severity.

Reviewer #1 (Public review):

Summary:

This manuscript from Jones and colleagues investigates a previously described phenomenon in which P. falciparum malaria parasites display increased trafficking of proteins displayed on the surface of infected RBCs, as well as increased cytoadherence in response to febrile temperatures. While this parasite response was previously described, it was not uniformly accepted, and conflicting reports can be found in the literature. This variability likely arises due to differences in the methods employed and the degree of temperature increase to which the parasites were exposed. Here, the authors are very careful to employ a temperature shift that likely reflects what is happening in infected humans and that they demonstrate is not detrimental to parasite viability or replication. In addition, they go on to investigate what steps in protein trafficking are affected by exposure to increased temperature and show that the effect is not specific to PfEMP1 but rather likely affects all transmembrane domain-containing proteins that are trafficked to the RBC. They also detect increased rates of phosphorylation of trafficked proteins, consistent with overall increased protein export.

Strengths:

The authors used a relatively mild increase in temperature (39 degrees), which they demonstrate is not detrimental to parasite viability or replication. This enabled them to avoid potential complications of a more severe heat shock that might have affected previously published studies. They employed a clever method of fractionation of RBCs infected with a var2csa-nanoluc fusion protein expressing parasite line to determine which step in the export pathway was likely accelerating in response to increased temperature. This enabled them to determine that export across the PVM is being affected. They also explored changes in phosphorylation of exported proteins and demonstrated that the effect is not limited to PfEMP1 but appears to affect numerous (or potentially all) exported transmembrane domain-containing proteins.

Weaknesses:

All the experiments investigating changes resulting from increased temperature were conducted after an increase in temperature from 16 to 24 hours, with sampling or assays conducted at the 24 hr mark. While this provided consistency throughout the study, this is a time point relatively early in the export of proteins to the RBC surface, as shown in Figure 1E. At 24 hrs, only approximately 50% of wildtype parasites are positive for PfEMP1, while at 32 hrs this approaches 80%. Since the authors only checked the effect of heat stress at 24 hrs, it is not possible to determine if the changes they observe reflect an overall increase in protein trafficking or instead a shift to earlier (or an accelerated) trafficking. In other words, if a second time point had been considered (for example, 32 hrs or later), would the parasites grown in the absence of heat stress catch up?

Reviewer #2 (Public review):

This manuscript describes experiments characterising how malaria parasites respond to physiologically relevant heat-shock conditions. The authors show, quite convincingly, that moderate heat-shock appears to increase cytoadherance, likely by increasing trafficking of surface proteins involved in this process.

While generally of a high quality and including a lot of data, I have a few small questions and comments, mainly regarding data interpretation.

(1) The authors use sorbitol lysis as a proxy for trafficking of PSAC components. This is a very roundabout way of doing things and does not, I think, really show what they claim. There could be a myriad of other reasons for this increased activity (indeed, the authors note potential PSAC activation under these conditions). One further reason could be a difference in the membrane stability following heat shock, which may affect sorbitol uptake, or the fragility of the erythrocytes to hypotonic shock. I really suggest that the authors stick to what they show (increased PSAC) without trying to use this as evidence for increased trafficking of a number of non-specified proteins that they cannot follow directly.

(2) Supplementary Figure 6C/D: The KAHRP signal does not look like it should. In fact, it doesn't look like anything specific. The HSP70-X signal is also blurry and overexposed. These pictures cannot be used to justify the authors' statements about a lack of colocalisation in any way.

(3) Figure 6: This experiment confuses me. The authors purport to fractionate proteins using differential lysis, but the proteins they detect are supposed to be transmembrane proteins and thus should always be found associated with the pellet, whether lysis is done using equinatoxin or saponin. Have they discovered a currently unknown trafficking pathway to tell us about? Whilst there is a lot of discussion about the trafficking pathways for TM proteins through the host cell, a number of studies have shown that these proteins are generally found in a membrane-bound state. The authors should elaborate, or choose an experiment that is capable of showing compartment-specific localisation of membrane-bound proteins (protease protection, for example).

(4) The red blood cell contains, in addition to HSP70-X, a number of human HSPs (HSP70 and HSP90 are significant in this current case). As the name suggests, these proteins non-specifically shield exposed hydrophobic domains revealed upon partial protein unfolding following thermal insult. I would thus have expected to find significantly more enrichment following heat shock, but this is not the case. Is it possible that the physiological heat shock conditions used in this current study are not high enough to cause a real heat shock?

Reviewer #3 (Public review):

Summary:

In this paper, it is established that high fever-like 39{degree sign}C temperatures cause parasite-infected red blood cells to become stickier. It is thought that high temperatures might help the spleen to destroy parasite-infected cells, and they become stickier in order to remain trapped in blood vessels, so they stop passing through the spleen.

Strengths:

The strength of this research is that it shows that fever-like temperatures can cause parasite-infected red blood cells to stick to surfaces designed to mimic the walls of small blood vessels. In a natural infection, this would cause parasite-infected red blood cells to stop circulating through the spleen, where the parasites would be destroyed by the immune system. It is thought that fevers could lead to infected red blood cells becoming stiffer and therefore more easily destroyed in the spleen. Parasites respond to fevers by making their red blood cells stickier, so they stop flowing around the body and into the spleen. The experiments here prove that fever temperatures increase the export of Velcro-like sticky proteins onto the surface of the infected red blood cells and are very thorough and convincing.

Weaknesses:

A minor weakness of the paper is that the effects of fever on the stiffness of infected red blood cells were not measured. This can be easily done in the laboratory by measuring how the passage of infected red blood cells through a bed of tiny metal balls is delayed under fever-like temperatures.

Author response:

Reviewer #1 (Public review):

Summary:

This manuscript from Jones and colleagues investigates a previously described phenomenon in which P. falciparum malaria parasites display increased trafficking of proteins displayed on the surface of infected RBCs, as well as increased cytoadherence in response to febrile temperatures. While this parasite response was previously described, it was not uniformly accepted, and conflicting reports can be found in the literature. This variability likely arises due to differences in the methods employed and the degree of temperature increase to which the parasites were exposed. Here, the authors are very careful to employ a temperature shift that likely reflects what is happening in infected humans and that they demonstrate is not detrimental to parasite viability or replication. In addition, they go on to investigate what steps in protein trafficking are affected by exposure to increased temperature and show that the effect is not specific to PfEMP1 but rather likely affects all transmembrane domain-containing proteins that are trafficked to the RBC. They also detect increased rates of phosphorylation of trafficked proteins, consistent with overall increased protein export.

Strengths:

The authors used a relatively mild increase in temperature (39 degrees), which they demonstrate is not detrimental to parasite viability or replication. This enabled them to avoid potential complications of a more severe heat shock that might have affected previously published studies. They employed a clever method of fractionation of RBCs infected with a var2csa-nanoluc fusion protein expressing parasite line to determine which step in the export pathway was likely accelerating in response to increased temperature. This enabled them to determine that export across the PVM is being affected. They also explored changes in phosphorylation of exported proteins and demonstrated that the effect is not limited to PfEMP1 but appears to affect numerous (or potentially all) exported transmembrane domain-containing proteins.

Weaknesses:

All the experiments investigating changes resulting from increased temperature were conducted after an increase in temperature from 16 to 24 hours, with sampling or assays conducted at the 24 hr mark. While this provided consistency throughout the study, this is a time point relatively early in the export of proteins to the RBC surface, as shown in Figure 1E. At 24 hrs, only approximately 50% of wildtype parasites are positive for PfEMP1, while at 32 hrs this approaches 80%. Since the authors only checked the effect of heat stress at 24 hrs, it is not possible to determine if the changes they observe reflect an overall increase in protein trafficking or instead a shift to earlier (or an accelerated) trafficking. In other words, if a second time point had been considered (for example, 32 hrs or later), would the parasites grown in the absence of heat stress catch up?

We did not assess cytoadhesion at later stages, but in the supplementary figures we show that at 40 hours post infection both heat stress and control conditions have comparable proportions of VAR2CSA-positive iRBCs, whilst they differ at 24h. This is true for the DMSO (control wildtype resembling) HA-tagged lines of HSP70x and PF3D7_072500 (Supplementary Figures 9 and 12 respectively). In the light that protein levels appear not changed, we conclude that trafficking is accelerated during these earlier timepoints, but remains comparable at later stages. This would still increase the overall bound parasite mass as parasites start to adhere earlier during or after a heat stress.

Reviewer #2 (Public review):

This manuscript describes experiments characterising how malaria parasites respond to physiologically relevant heat-shock conditions. The authors show, quite convincingly, that moderate heat-shock appears to increase cytoadherance, likely by increasing trafficking of surface proteins involved in this process.

While generally of a high quality and including a lot of data, I have a few small questions and comments, mainly regarding data interpretation.

(1) The authors use sorbitol lysis as a proxy for trafficking of PSAC components. This is a very roundabout way of doing things and does not, I think, really show what they claim. There could be a myriad of other reasons for this increased activity (indeed, the authors note potential PSAC activation under these conditions). One further reason could be a difference in the membrane stability following heat shock, which may affect sorbitol uptake, or the fragility of the erythrocytes to hypotonic shock. I really suggest that the authors stick to what they show (increased PSAC) without trying to use this as evidence for increased trafficking of a number of non-specified proteins that they cannot follow directly.

This is a valid point, however, uninfected RBCs do not lyse following heat stress, nor do much younger iRBCs, indicating that the observed effect is specific to infected RBCs at a defined stage. The sorbitol sensitivity assay is performed at 37°C under normal conditions after cells are returned to non–heat stress temperatures, so the effect is not due to transient changes in membrane permeability at elevated temperature. 

Planned experiment: However, to increase the strength of our conclusions and further test our hypothesis, we will perform sorbitol sensitivity assays on >20 hours post infection iRBCs following heat stress in the presence and absence of furosemide, a PSAC inhibitor. If iRBC lysis is abolished with furosemide present, this would confirm that the effect is PSAC-dependent. However, the effect could also possibly be due to altered PSAC activity during heat stress which is maintained at lower temperatures, as outlined in the discussion.

(2) Supplementary Figure 6C/D: The KAHRP signal does not look like it should. In fact, it doesn't look like anything specific. The HSP70-X signal is also blurry and overexposed. These pictures cannot be used to justify the authors' statements about a lack of colocalisation in any way.

Planned experiment: We agree that the IFAs are not the best as presented and will include better quality supplementary images in a revised version.

(3) Figure 6: This experiment confuses me. The authors purport to fractionate proteins using differential lysis, but the proteins they detect are supposed to be transmembrane proteins and thus should always be found associated with the pellet, whether lysis is done using equinatoxin or saponin. Have they discovered a currently unknown trafficking pathway to tell us about? Whilst there is a lot of discussion about the trafficking pathways for TM proteins through the host cell, a number of studies have shown that these proteins are generally found in a membrane-bound state. The authors should elaborate, or choose an experiment that is capable of showing compartment-specific localisation of membrane-bound proteins (protease protection, for example).

We do not believe we identified a novel trafficking pathway, but that we capture trafficking intermediates of PfEMP1 between the PVM and the RBC periphery, in either small vesicles, and/ or possibly Maurer’s clefts. These would still be membrane embedded, but because of their small size, not be pelleted using the centrifugation speeds in our study (we did not use ultracentrifugation). This explanation, we believe, is in line with the current hypothesis of PfEMP1 and other exported TMD protein trafficking to the periphery or the Maurer’s clefts.

(4) The red blood cell contains, in addition to HSP70-X, a number of human HSPs (HSP70 and HSP90 are significant in this current case). As the name suggests, these proteins non-specifically shield exposed hydrophobic domains revealed upon partial protein unfolding following thermal insult. I would thus have expected to find significantly more enrichment following heat shock, but this is not the case. Is it possible that the physiological heat shock conditions used in this current study are not high enough to cause a real heat shock?

As noted by the reviewer, we do not see enrichment of red blood cell heat shock proteins following heat stress, either with FIKK10.2-TurboID or in the phosphoproteome. We used a physiologically relevant heat stress that significantly modifies the iRBC, as shown by our functional assays. While a higher temperature might induce an association of red blood cell heat shock proteins, such conditions may not accurately reflect the most commonly found context of malaria infection.

Reviewer #3 (Public review):

Summary:

In this paper, it is established that high fever-like 39 C temperatures cause parasite-infected red blood cells to become stickier. It is thought that high temperatures might help the spleen to destroy parasite-infected cells, and they become stickier in order to remain trapped in blood vessels, so they stop passing through the spleen.

Strengths:

The strength of this research is that it shows that fever-like temperatures can cause parasite-infected red blood cells to stick to surfaces designed to mimic the walls of small blood vessels. In a natural infection, this would cause parasite-infected red blood cells to stop circulating through the spleen, where the parasites would be destroyed by the immune system. It is thought that fevers could lead to infected red blood cells becoming stiffer and therefore more easily destroyed in the spleen. Parasites respond to fevers by making their red blood cells stickier, so they stop flowing around the body and into the spleen. The experiments here prove that fever temperatures increase the export of Velcro-like sticky proteins onto the surface of the infected red blood cells and are very thorough and convincing.

Weaknesses:

A minor weakness of the paper is that the effects of fever on the stiffness of infected red blood cells were not measured. This can be easily done in the laboratory by measuring how the passage of infected red blood cells through a bed of tiny metal balls is delayed under fever-like temperatures.

Previous work by Marinkovic et al. (cited in this manuscript) reported that all RBCs, both infected and uninfected, increase in stiffness at 41 °C compared with 37 °C, with trophozoites and schizonts exhibiting a particularly pronounced increase. We agree that it would be interesting to determine whether similar changes occur at physiological fever-like temperatures, and whether this increase in stiffness coincides with the period of elevated protein trafficking. However, since we have already demonstrated enhanced protein export using multiple complementary approaches, we have chosen to address these questions in a follow-up study.

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I never knew the first best film was frankenstein i really like this because i love to watch horror movies.

i can relate this a lot to society today how big businesses use their profit for monopolizing.

this is crazy to me that people thought adding sound to films was not importants i think adding sound to films allows the watcher to get more indigh tinopt the charaters

this is interesting because now they have added emotional effects so they the viewers can feel what is going on throughout the film.

this is interesting to see how they took a 5 second film to recreating actors on the moon this shows me how much films have evolved in this short time period.

this is one of the first films created at i think it is funny that is is just a man sneezing and it was only 5 second long i was hoping for the first firm to be at least 10 minutes

This is interesting that the first motion picture was on a horse. Maybridge received a lot of money for this.

I believe that teach your student to take challenges and learn through mistakes and at the end of the road that is what make you smarter and full experience.

Stereotyped students are most likely to fail a career than the ones that have a cero stereotypes.

the "now" is totally different than the past. in the past we were building to be strong people and in the now a lot of people get to be fragile emotionally and psychological and for that is necessary to constantly work on the confidence.

I believe that things can happened naturally but not all people's way to learn is the same, and it shouldn't be compare one to another's ability as we all are different.

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They're open to welcome more groups of people within the Tree of Peace, therefore, making the figurative tree grow.

Repetition.

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This struck me as an obviously good idea the first time I came across something similar where Wikileaks published their recording of an interview of Julian Assange by some large news organization (who published their own copy that they owned the rights to).

I find this information interesting because this switch was so early in history. I also assume that many believed it was a part of philosophy due to its research on behavioral phenomenons.

Not to mention that recycling is considered economically inefficient, so it is not performed at the rate that people may expect.

So what can be done about that?

I wish more people had mindsets like this one.

I'm curious to learn more about sustainability-related economics. From what I'm seeing, there's no way for us to maintain such a high level of global economic growth while still being sustainable. Should the economy keep growing?

It's actually quite uplifting to see the decrease in carbon emissions in the later years. I'm curious to what the graph would look like if extended to 2025. I looked it up and per capita carbon emissions are decreasing in many countries but not in China or India and are increasing (very slightly) in the world as a whole.

I'd love to know more about the ways in which they are doing this. Love Zurich.

I am really hoping that we are able to improve environmental (and science in general) communication at a level that resonates with the public and is accessible to the poor and to those in developing countries.

If only there were consequences in place for this

I wonder how this research is impacted by the fact that there are many undefined groups (invertebrates especially) as projects involving those often aren't well-funded.

I actually didn't know much about the negative impacts of aquaculture, and I took an aquaculture class in high school! I am curious about how this compares with the impacts of fisheries.

I wish that more communication about the environment focuses on things like this. A lot of people disregard the importance of environmental issues because they don't think it applies to them.

There have been some recent changes in legislature in Brazil regarding deforestation that have been concerning me. Lula has been doing a mostly good job, but people are trying to undo the work that he has done.