这项研究的核心突破在于利用3D打印技术制造出具有复杂微结构的声学超表面 (Acoustic Metasurface)，这种超表面能够精确地操控超声波，使其产生自弯曲的波束 (Self-Bending Acoustic Beam)，从而在特定区域形成难以被探测到的隐蔽声域 (Hidden Acoustic Zone)。下面我们来详细解释一下这个过程：

1. 声学超表面 (Acoustic Metasurface)

• 定义： 声学超表面是一种由亚波长（小于声波波长）的微结构单元组成的薄层材料。与传统的声学材料通过吸收或简单反射声波不同，超表面能够通过精心设计的微结构来调控声波的相位、振幅和极化等特性，实现对声波的灵活操控。
• 工作原理： 每个微结构单元（例如微小的柱状体、空腔、开孔等）与声波相互作用时，会引起局部的声波散射和延迟，从而改变声波的相位。通过精确排列和设计这些微结构单元的几何形状和尺寸，可以实现对整个声波前沿的任意调控，达到传统材料难以实现的效果。
• 3D打印的应用： 3D打印技术非常适合制造具有复杂三维几何结构的超表面。它可以精确地构建出所需的微结构单元，并允许设计更复杂的声学功能。

2. 自弯曲超声波束 (Self-Bending Ultrasonic Beam)

• 定义： 自弯曲波束是一种特殊的波束，与传统的直线传播的波束不同，它在传播过程中会沿着预定的曲线轨迹弯曲，而不需要任何外部的引导结构或力场。
• 原理： 产生自弯曲波束的关键在于对声波的初始相位分布进行精确的设计。通过在发射声波的源头上施加特定的相位梯度，可以使得波束在传播过程中发生弯曲。一种常见的自弯曲波束是艾里波束 (Airy Beam)，其横向强度分布呈现出主瓣和一系列逐渐衰减的旁瓣，并且主瓣在传播过程中会按照抛物线轨迹弯曲。
• 超声波的应用： 这项研究针对的是超声波，即频率高于人类听觉范围的声波。超声波具有波长短、方向性好等特点，在医学成像、工业检测、无线通信等领域有广泛应用。

3. 超表面如何生成自弯曲超声波束

研究团队利用 3D 打印技术制造的超表面，其微结构单元被设计成能够对入射的超声波产生特定的相位延迟。通过空间上精确地排列这些具有不同相位延迟的微结构单元，超表面可以对发射或透射的超声波施加一个特定的相位分布，这个相位分布正是生成自弯曲波束所需要的。

简单来说，超表面就像一个“声学透镜”，但它不是通过折射而是通过相位调制来改变声波的传播方向，使其按照预定的曲线弯曲。

4. 隐蔽声域的生成 (Generation of Hidden Acoustic Zones)

• 定义： 隐蔽声域指的是在空间中的某个特定区域内，声波的强度被显著降低，形成一个相对“安静”或难以被探测到的区域。
• 利用自弯曲波束实现隐蔽声域： 研究团队利用自弯曲超声波束的特性来实现隐蔽声域的生成。具体来说，他们设计的超表面能够产生一个或多个自弯曲的超声波束，这些波束在传播过程中会绕过目标区域，使得目标区域内的声波强度大大降低，从而形成一个“声学阴影”或“静音区”。

形象地理解：

想象一下，你想要在某个区域制造一个“声音盲区”。传统的做法可能是用吸声材料来吸收声音。但利用自弯曲超声波束，你可以像用一个无形的“声学屏障”一样，让声音波束从目标区域的周围弯曲通过，使得目标区域内部的声音强度很低，难以被外部的麦克风或其他声学传感器探测到。

5. 潜在的应用

这项技术在多个领域具有潜在的应用价值：

• 隐私和安全： 可以用于创建私密的谈话区域，防止声音被窃听。
• 定向声音传输： 可以将声音精确地引导到特定接收者，而不会干扰周围的人。
• 声学隐身/声学斗篷： 虽然这项研究侧重于生成隐蔽声域，但其原理也可能应用于更复杂的声学隐身技术，使得物体难以被声纳等设备探测到。
• 医学超声： 可以更精确地控制超声波束的聚焦位置和形状，提高医学成像和治疗的精度。
• 工业应用： 例如在工业检测中，可以利用自弯曲超声波束探测难以直接触及的区域。

6. 总结

这项研究的突破在于巧妙地结合了 3D 打印技术制造的 声学超表面和 自弯曲超声波束的概念。通过精确设计超表面的微结构，研究团队实现了对超声波的灵活操控，使其能够沿着弯曲的路径传播，从而在特定区域形成声音强度显著降低的隐蔽声域。这项技术为无线通信、雷达和传感器等领域的微型化和功能提升带来了新的可能性，尤其是在需要精确控制声波传播和实现隐蔽操作的场景中具有重要的应用潜力。

中国国防科技大学团队在声子激光（Saser，即“声激射器”）领域取得重要突破，通过注入锁定技术（Injection Locking）显著提升了声子激光的亮度和稳定性，亮度提升达3个量级（千倍），这一成果为声子激光在超高灵敏度传感、精密测量和量子技术等领域的应用开辟了新路径。以下是详细解析：

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1. 声子激光（Saser）的基本原理

声子激光是类比光子激光（Laser）的概念，其通过受激辐射放大机制产生相干声子束（即高频机械振动波）。核心原理包括： - 增益介质：如压电材料、半导体纳米结构或超晶格，通过外部能量泵浦（如光、电或热激励）产生声子激发。 - 谐振腔：利用声子晶体或纳米机械谐振器形成共振腔，筛选特定频率的声子模式并增强其相干性。 - 受激发射：当注入的声子与谐振腔内的声子模式相位同步时，触发链式放大，输出高亮度、窄线宽的声子束。

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2. 注入锁定技术的核心创新

国防科大团队通过注入锁定技术解决了传统声子激光亮度低、噪声高的瓶颈： - 技术原理：<br /> 向主声子激光谐振腔中注入一个弱但稳定的外部声子信号（种子信号），通过相位同步迫使主腔内的声子振荡锁定到种子信号的频率和相位上，从而抑制随机噪声并增强相干性。 - 关键突破：<br /> - 频率稳定性：注入锁定减少了声子模式的频率漂移，线宽显著变窄（提升频率纯度）。<br /> - 亮度提升：通过同步放大机制，声子束强度提高3个量级（从微瓦级到毫瓦级）。<br /> - 抗干扰能力：降低环境振动和热涨落对声子激光的影响，适用于复杂环境。

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3. 技术实现路径

• 材料与结构设计：<br /> 采用氮化铝（AlN）压电薄膜与纳米机械谐振器结合，利用其高机电耦合系数和低损耗特性构建高效声子腔。
• 注入信号生成：<br /> 通过外部微波源或光学泵浦产生高纯度种子声子信号，精准匹配主腔共振频率。
• 低温环境控制：<br /> 在低温（接近绝对零度）下操作，抑制热声子噪声，增强量子效应主导的相干性。

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4. 对传感领域的推动作用

声子激光亮度的提升直接转化为传感性能的飞跃，具体应用包括： - 超高灵敏度质量传感：<br /> 利用声子束与待测物的相互作用（如质量吸附导致的频率偏移），可检测亚飞克（10⁻¹⁵克）级质量变化，用于病毒颗粒、单分子检测。<br /> - 纳米尺度形变测量：<br /> 声子激光的短波长（纳米级）可分辨材料表面原子级形变，应用于半导体器件缺陷检测。<br /> - 生物医学成像：<br /> 高频声子束穿透细胞组织时，通过声子散射成像实现无损亚细胞结构观测，分辨率超越传统超声波。<br /> - 量子传感与信息处理：<br /> 高相干声子束可作为量子比特载体，用于构建混合量子系统（声子-光子-电子耦合），提升量子存储器与传感器的性能。

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5. 科学意义与未来展望

• 科学意义：<br /> 该成果首次将注入锁定技术成功应用于声子激光，验证了声子相干操控的可行性，为声子学与量子技术的深度融合奠定基础。
• 技术挑战：<br /> 当前仍需解决声子在传输中的损耗问题（如界面散射），以及大规模集成化制造的工艺难题。
• 未来方向：
• 多模式声子激光：实现太赫兹频段声子激光，拓展至通信与雷达领域。
• 片上集成系统：将声子激光器与光电芯片结合，开发全声子学传感与计算平台。
• 跨学科应用：结合人工智能算法，利用声子束进行实时高维数据处理。

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总结

国防科大的突破标志着声子激光从实验室走向实用化的关键一步。通过注入锁定技术实现亮度跃升，不仅推动了传感技术的极限，还为声子在量子信息、纳米制造和生物医学等领域的应用提供了全新工具。这一进展有望在未来十年内催生下一代超灵敏传感器和声子驱动的新型计算范式。

There could be a significant opportunity for a comprehensive study examining Trump's tweets. Despite experiencing multiple bans from social media platforms, he has consistently managed to regain access to his accounts. Furthermore, his actions frequently contravene Twitter's guidelines, yet he continues to secure reinstatement.

It was fascinating to learn from the Lonelygirl15 Wikipedia page because it gave more context as to how revolutionary this web show really was. Something I did notice particularly is how it is described as being one of the first "web series" attempts and an early example of interactive storytelling. I'm surprised by how something that began as seemingly just a vlog turned out to shape all of online video content. It makes me wonder—which would happen today, or have we become desensitized to blurred lines of fiction versus reality on TikTok and Instagram?

I think that this is very interesting because it exposes so much of Trump's mindset versus his staff's which is very contrasting when put side by side. Trump's staff is much more professional and informative. Trump himself appears to be much more emotional, and probably much more effective in creating a parasocial relationship as his tweets are less promotional and more emotionally evocative.

This article is how David Robinson, a director of engineering at contentsquare analyzed multiple tweets from Donald Trump where he discovered that Trump's account was being posted from two different devices. More promotional and general tweets most likely from staff being posted from an iPhone, while more emotional and not so nice tweets being posted from an Android, most likely from Trump himself.

This situation is very interesting as an example of these sock puppet accounts being used to push hateful rhetoric. Reading into the specifics of the issue it seems to me at least to be fairly obvious that Dean Browning just completely screwed up and had to do a lot of desperate back peddling and face saving that didn't hold up under scrutiny. It challenges the idea of what you can trust on the internet from just any person if even that account's personal opinion is valid for who they are saying they are.

I have read discussions regarding Dr. Bethany McLaughlin's leadership within the Me Too movement and its implications. but I also believe it is important to address individuals in positions of power, such as Mark Zuckerberg, particularly in relation to the creation of Facebook, which has ranked and publicly shamed women.

Due to the sample and how everything was weighed, this survey was probably a random survey.

This CBS Survey was done through YouGov. This is meaningful because they were able to gather a large survey size of 2175. They were able to accurately represent the opinions of most of the US.

This poll is meaningful because it provides a margin of error.

Что такое физика?: мистер Андерсен объясняет важность физики как науки. История и виртуальные примеры используются для того, чтобы представить дисциплину в контексте.

Shows a significant lead for the Republican party.

Political risk for the democratic party as swing voters lean closer to Republican views on this issue.

Clear national majority against taxpayer money for gender transition procedures.

The language of this question could potentially influence respondents' answers. Also, this question assumes the knowledge of the participants which may not reflect their actual knowledge. The context of this question is important to analyze as well because the responses can be bias based on how this question is framed and the specific details it highlights.

Fact statement that can be observed.

This could be a fact statement as it can be observed.

News value of conflict as it highlights an issue that divides public opinion and political parties.

News value of timeliness since it reports on recent polling data.

Opinion statement because it evokes a thought from an individual.

Opinion statement.

This statement raises questions on the reliability of the sample, but doesn't necessarily alter it entirely.

Good represenation of population with this sample size.

seeds = intercept + size + pollen type + size*pollen type + error seeds = intercept + size + pollen type + error

That it is independent to pollen type

Take averages

It increases type 1 error as it inflates the confidence interval and reduces variance artificially

50 independent replicants with two levels each so 25

total number is 250 as there are 50 plants and taking 5 measurements per plant

I thought there was something particularly interesting about lonelygirl15's story in that it illustrates how much responsibility there is to being authentic online. The fact that "humans don't like being fooled" really resonated with me—I have certainly felt that way when I discovered something I had considered to be true later turned out to have been staged or manufactured. And, I have to admit, I also think that something is sort of interesting in that despite the revelation of truth, the channel just kept growing. People may have been upset initially, but they also realized that the narrative being told really was good, and they still wanted to know what occurred. It makes me wonder if, even though we appreciate authenticity, we just sort of love a good story even if it isn't "real."

really strong comparison

!! What a great study

News value of conflict between the underlying tension of free speech and inclusivity.

This sample size is large which can pretty accurately represent the population.

News value of impact as it affects a large group of people.

comma after "sparkle"

This is a straight quote for some reason. Actually, as far as I can tell, I think they're all straight quotes in this one.

comma after "icon"

move period inside quotation marks

I think this "from" is the wrong font. Honestly, I think I missed this first sentence entirely when we had those issues with the character styles.

This word needs italics.

I could be crazy. Is this period bolded?

I might say "and has been recently . . ."

This also needs to be italicized.

I think for the stories this is italicized. I think this is how it is in the poetry template.

What a cool poem!!

I can't see this PDF in book format, so I'm going to assume this is an extra page before poetry.

I'd probably put a period after "shame" since it looks like we're ok with using periods throught the stanzas in the poem.

comma after "home"

comma after "cultures"

comma after "fantasies"

probably comma instead of a semicolon here

comma after "empire"

comma after "writing"

comma after cottagecore

Spacing here.

I don't think "for" should be capitalized. It could be the font though.

Spacing between periods in this ellipse.

Unfortunately, scaring your cat can have harmful effects on the cat. The cats could develop cat anxiety and develop distrust towards humans and their owners.

According to this article, it is a combination of the two reasons above why cats are scare of cucumbers.

Another reason why cats are surprised by the cucumbers. They pay close attention to their environments. If they owners put something down or something changed while they aren't looking, they will scare the cats. It doesn't have to be a cucumber but anything.

Cats jump high in the air when they are scare because it is their fear response. They do this to avoid being bitten and they can get away faster.

One reason why cats are afraid of cucumbers. They may think it looks like a snake. Not all cats are afraid of snakes. They may think snakes are prey. So this is just a possibility.

They pay more attention to their environment because they tend to be "independent creatures" causing them to have jump scares.

Torch song trilogy ed behavior, and the raism and gay promiscuity

This sounds like a class concept

I have many thoughts about this

Making the same argument as Tennesse Williams about how natural homosexuals are.

This section tells us they surveyed 1,000 registered voters, which we learned in class can be representative of 200 million people.

This shows how the poll was done and the margin of error.

Trump's support has risen from previous years when the same question has been asked. The poll suggests the popularity the president has accumulated in his base.

This information shows all of the statistical analysis that was used in this poll.

Although parasocial relationships are very common today, I haven't seen them be politely defined in such a way. I think that this clarification that their relationship is parasocial yet still being very kind and gracious is something that should be practiced more today. The clarification of their relationship is something we need more now that there are many intense parasocial relationships. However, people in parasocial relationships today are often made fun of and trolled online, which is not helpful and only calls attention to the problem without solving it, unlike Mr. Rodger's kind clarification of their relationship.

This is the sign of a good poll because of the amount of people that they polled and the fact that they were honest about their data and how they collected it.

These prices are important to show the fear that people have. A great majority say that prices are going up and are even worried about buying food.

Many Americans feel as if their income is not keeping up with the inflation that is rising. This gives residents the feeling that their purchasing power is decreasing. This is important because it sets up the reason for the poll.

It is interesting that the poll drew a difference between influencers and regular citizens. Do they believe (or answer) the same as they say on social media?

Both sample sizes are large enough to yield representative answers.

This poll being a random sample is a positive sign. It is much easier to do random polls using voter records because they can easily be contacted and the pool is exactly (for the most part) the same as the pool of people who have the ability to vote in the gubernatorial election.

This poll has a margin of error of +/- 5% which is not a great number and the results should definitely be taken with a grain of salt.

This is a relatively new development so people are still forming their opinions. Results of this poll will most likely not reflect what we see in the actual race if she does decide to run.

stated or appearing to be true, but not necessarily so.

a political system where international organizations and transnational actors, like non-governmental organizations, have the power to exercise authority over individual states, often beyond the level of government

something that is secondary, a by-product, or a consequence of another phenomenon, but doesn't have any causal influence itself

refers to the act of sacrificing something, often by burning, as an offering or a form of protest

I watched the video "Drunk History - John Adams and Thomas Jefferson Had Beef" in [e3] and thought it told real events in American history in a very humorous and creative way. Although the video presents history in the voice of a drunken narrator, it is based on actual historical sources, particularly the political and personal conflicts between Adams and Jefferson. This form of dissemination of knowledge in an entertaining way reminds me of the many content creators on social media today, who use jokes, clips or re-enactment to talk about history and science to reach a large audience of young people. In my opinion, this also reflects the diversification of information dissemination methods today, and echoes the "how blogs and other online platforms change the way information is transmitted" discussed in this chapter.

From my perspectives, Aza is the steppingstone of the evolutionary history of the social media platform. His technical design brings convenience and dependence to users to stick on receiving multiple scattered information quickly in a long duration, making us to be more addicative to internet and fall into the virtual world. It offers possibilities and exposure to content creators but on the humanity say it constrains people being actively thinking since they do not need to process their brain activity when scrolling the phone.

I think this section is really interesting to talk about the origins of blogging, but the earliest blogs were actually like people keeping diaries on the Internet. It reminds me that I used to use blogging platforms like Tumblr to record my mood and share photos, although I didn't think it was a "blog" at the time, but in fact, it did things very similar to the early blogs. Reading this part made me realize that, in fact, people have always had the need to share their lives and ideas through the Internet, but the platform has changed from the initial blog to the current micro blog, little red book, friend circle and so on. Tools are changing, but people's desire to express and communicate has always been there, which is really very touching.

inconsistency plays crucial role in judgments of improbability

• sentences can be: inconsistent, self-contradictory & inconsistent w/ presuppositions

• when given inconsistent info, you should reject SOME info

  • also want to find truth, ALWAYS reject info that is least well-supported/ most likely to be false

• cases where it isn't clear what to revise, need to SEARCH for info

when trying to access a belief, you should not cover up counterevidence & you should pay attention to strength/degree of certainty with which you should hold a belief

I would say antisocial posts and dark humors pervade across the internet. Personally, the reason why contents are created is because dark humor is the easiest blog content that can make audience laugh and like about it so that lots of content creators would treat it as a cheat sheet as their post when they are stuck for fresh ideas. Users and authors might not possess intentional means to be actual racists over the content, but if antisocial posts became popular, lots of people will overlook and got numb for the fact that dark humor is actually a serious stuff in reality and lots of people fail to separate themselves in reality from internet. My roommate is an example, always making fun of stereotypes of a group as a joke becomes a habit for himself but not for people in his surroundings.

Het betekent dat de kosten van het faillissement (zoals de kosten van de curator, de kosten van de boedel, etc.) worden verdeeld ("omgeslagen") over de schuldeisers proportioneel — dus iedereen "draagt" een stukje van die kosten.

Maar let op: dit gebeurt nádat de boedelschulden zijn betaald.

Er komt geld binnen in de boedel, bijvoorbeeld door verkoop van bezittingen. Uit dat geld wordt eerst het volgende betaald: Alle boedelschulden (bijv. loon curator, noodzakelijke kosten, bepaalde belastingvorderingen) Daarna blijft er een restbedrag over: dat heet de voor uitdeling beschikbare opbrengst. Over dat restbedrag worden de algemene faillissementskosten omgeslagen, oftewel: die kosten worden in mindering gebracht op wat de schuldeisers kunnen krijgen. Wat dan nog overblijft, wordt naar rato verdeeld onder de concurrente (en preferente) schuldeisers. Dit heet het uitkeringspercentage.

De algemene faillissementskosten worden omgeslagen over de voor uitdeling beschikbare opbrengst” betekent dat deze kosten worden afgetrokken van het bedrag dat nog beschikbaar is voor de schuldeisers, waarna het resterende bedrag evenredig wordt verdeeld over hun vorderingen.

De schuldeisers (indirect) “betalen mee” aan de algemene faillissementskosten, omdat die kosten worden afgetrokken van de opbrengst voordat er aan hen wordt uitgekeerd. Dus: hoe hoger de faillissementskosten, hoe minder zij uiteindelijk krijgen.

Een niet-verifieerbare vordering is een vordering die niet op de lijst van te verificeren schulden wordt geplaatst, en dus niet wordt meegenomen in de verdeling van het faillissementsvermogen.

Verificatie is het proces waarbij wordt vastgesteld welke schulden erkend worden in het faillissement — oftewel: welke schuldeisers hebben een geldige vordering, en hoeveel precies?

Voorbeeld: Loon van een werknemer ná faillissement Een werknemer is op het moment van faillietverklaring al in dienst bij de werkgever (de failliet verklaarde schuldenaar). De curator besluit de werknemer nog één week in dienst te houden, om bijv. te helpen met het afhandelen van administratie. Na die week ontslaat de curator de werknemer op grond van art. 40 Fw. De werknemer krijgt loon over die laatste week ná faillissement.

⚖️ Wat gebeurt er met dat loon? Normaal gesproken geldt: schulden die na faillietverklaring ontstaan, doen niet mee in het faillissement.

➡️ Maar hier geldt een uitzondering, omdat: De arbeidsrelatie al bestond vóór het faillissement (dus: een bestaande rechtsverhouding), én De curator houdt de werknemer expliciet nog even in dienst, dus hij kiest ervoor om prestaties te laten verrichten ten behoeve van de boedel.

➡️ In zo’n geval zegt men: deze schuld (het loon) is ontstaan ná faillissement, maar ze is zo nauw verbonden met een bestaande rechtsverhouding, én met de boedelafwikkeling, dat ze tóch meedoet in de vereffening — en dan meestal zelfs als boedelschuld, dus met voorrang.

should Kamala have ran sooner? or was it too late for the democratic party?

This rating also made his management look bad compared to others, which is not the case.

This could mean that the polls were not "rigged" as some may say

From the pole above, it is clear that the poll showed that biden got the lowest amount of rating of outgoing presidents

This could be because of his health that was declining which caused this.

the rating of Biden only went down over the last four years, which has been very rare according to CBS News.

STEM workers face more positive implications

Positive impact on high wage workers = upskilling of work force.

Who is impacted

AI related jobs increasing

Methods and sources of data

How AI affects different sectors.

How exactly does AI effect jobs. Decrease employment? Wipe it out completely? Big topic.

Lower income jobs face harder implications due to AI.

AI implementation will have an host of negative effects on employment.

Big question of my research topic

AI application increase in last two decades - time frame of much of this data/research

eorpijteopjewiopt

Yes, I very much believe that it matters whether or not a human typed a Tweet, especially if the Tweet is coming from a public figure. I believe that authenticity is the main factor here as its completely lost if a bot were to post a tweet instead of an actual person. For example if a public figure were to post something very controversial, theres a possibly that most people would feel a connection or get triggered by this comment. However, if a bot were to post the same tweet I don't think there would be much of a response from the public since the tweet lost its authenticity as it wasn't from a real person.

理解“系统基本规律具有对称性，但基态不具有”这个概念是理解自发对称性破缺的关键。我们用一些例子和类比来解释一下：

1. 什么是“系统基本规律具有对称性”？

这指的是描述系统行为的物理定律或方程，在某种变换下保持不变。想象一下：

• 旋转对称性： 如果你把一个系统旋转一定的角度，描述它的基本规律仍然是相同的。例如，一个孤立的原子，在真空中，其周围的空间是各向同性的，旋转它并不会改变描述电子运动的电磁定律。
• 平移对称性： 如果你把一个系统在空间中平移一定的距离，描述它的基本规律仍然是相同的。例如，在均匀的空间中，物理定律在任何位置都是一样的。
• 全局相位对称性： 在量子力学中，对波函数乘以一个相同的相位因子，系统的物理性质不会改变。

2. 什么是“基态”？

基态是指系统在最低能量状态下的配置或状态。这是系统最稳定的状态。

3. “但基态不具有这种对称性”是什么意思？

这意味着，尽管描述系统行为的基本规律是具有某种对称性的，但系统在能量最低的状态下所采取的具体形式或配置，却不再展现出那种对称性。系统“自发地”选择了一个不对称的基态。

类比解释：

例子一：墨西哥帽势能（Mexican Hat Potential）

想象一个形状像墨西哥帽底部的势能函数。中心有一个凸起，周围是一个圆形的谷底，谷底的能量是最低的。

• 基本规律的对称性： 这个势能函数本身是旋转对称的，绕着中心旋转任何角度，它的形状都一样。
• 基态的不对称性： 如果我们把一个小球放在帽子的顶部（一个不稳定的平衡点），它会自发地滚落到谷底的任何一个位置。一旦小球停在谷底的某一点，这个状态就失去了旋转对称性——小球现在指向了一个特定的方向。虽然所有谷底的点能量相同，但系统最终选择了一个特定的、不再具有旋转对称性的基态。

例子二：晚餐桌子（Dinner Table）

想象一个完美的圆形餐桌，周围放着完全相同的椅子。

• 基本规律的对称性： 桌子和椅子的配置具有完美的旋转对称性。
• 基态的不对称性： 当人们开始入座时，他们会选择坐到某个特定的椅子上。一旦大家都坐下，整个系统的配置就失去了旋转对称性——每个人的位置是固定的，不再具有任意旋转的对称性。然而，每个人选择哪个椅子是任意的，最终的座位安排是自发形成的，并且破坏了原始的对称性。

例子三：铁磁体（Ferromagnet）

想象一个由许多原子组成的铁磁材料，每个原子都带有一个微小的磁矩（就像一个小磁针）。

• 基本规律的对称性： 在高温下，这些磁矩是随机排列的，整个系统在宏观上是各向同性的，具有旋转对称性。描述原子之间相互作用的基本规律也是旋转对称的。
• 基态的不对称性： 当温度降低到居里温度以下时，原子之间的相互作用会导致所有的磁矩自发地沿着某个特定的方向排列（例如都指向北方）。这时，整个材料就具有了一个宏观的磁化方向，打破了原始的旋转对称性。虽然指向任何方向的磁化态能量都是相同的，但系统最终选择了一个特定的方向作为其基态。

关键点：

• 简并的基态： 自发对称性破缺通常伴随着多个能量相同的基态（例如墨西哥帽谷底的任何一点，晚餐桌子的任何一种座位安排，铁磁体的磁化方向可以是任意方向）。
• 自发选择： 系统在没有任何外部特定方向的干扰下，自发地选择其中一个基态，从而破坏了基本规律的对称性。
• 序参量： 通常会引入一个“序参量”来描述对称性破缺的程度和方向（例如墨西哥帽中小球的位置矢量，晚餐桌子上每个人的座位，铁磁体的宏观磁化方向）。序参量在对称的基态中为零，在破缺对称性的基态中不为零。

与南部-戈德斯通定理的联系：

当一个连续对称性被自发破缺时，系统会存在能量上连续简并的基态。在墨西哥帽势能的例子中，沿着谷底移动不需要额外的能量（在理想情况下）。这种能量上的平坦方向对应着无质量的激发，也就是戈德斯通玻色子。在铁磁体的例子中，缓慢地旋转整个磁化方向不需要额外的能量，对应的激发就是自旋波（在长波极限下是无质量的）。

希望这些例子能够帮助你更好地理解“系统基本规律具有对称性，但基态不具有”这个重要的概念。这是自发对称性破缺的核心思想。

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Reply to the reviewers

1 Summary of changes There were several points that were raised by multiple reviewers, which we respond to as follows. 1. The reviewers pointed to a lack of clear comparison with experimental data. Perhaps this was insufficiently clear in the first submission, but the analysis of ECT-2 localization during cytokinesis was intended as a validation of the model, parameterized based on polarization and applied without further modification to cytokinesis. These situations differ in numerous respects: centrosome number, centrosome size, and we used several experimental conditions to control centrosome positioning. To address this more extensively, in the revised submission we analyzed our data further (Longhini and Glotzer, 2022) to extract profiles of ECT-2 and myosin. We used these profiles both to constrain model parameters (Appendix B.3) and to compare with model predictions for both polarization and cytokinesis (Figs. 3 and 5).

1. All of the reviewers pointed to our assumption that myosin indirectly recruits ECT-2. We apologize for a lack of clarity in the original draft about this. We had intended to convey the hypothesis that ECT-2 is recruited by a species that is advected with myosin, but for the sake of the minimal model we do not introduce any extra equations for this species and instead assume it colocalizes with myosin. In the revised manuscript, we address this by clearly listing the assumption (#2 on p. 7), and by comparing to an alternative model (Eq. (S4) and Fig. S7) that accounts directly for a third advected species. We also document specifically (second panel from left in Fig. 4) why the short residence time of ECT-2 makes patterning by pure advection impossible. That said, we still do not know the identity of this factor.

2. The reviewers pointed out that our use of the M4 term to limit contractility was dubious. This was a (probably misguided) attempt to use previously-published models to constrain our model. In the revised submission, we replaced this term with a more general nonlinear term Mk, where we first demonstrate that k = 1 is insufficient to match the data (p. 32), then consider k = 2,3. We present results in the main text for k = 2, while Fig. S5 shows that the corresponding results for k = 3 are not very different. Put another way, we empirically demonstrate that the specific form of this nonlinear term is not important, as long as it prevents contractile instabilities (as pointed out by one of the reviewers).

3. Apparently, our extension of the model to cytokinesis, and the evidence for validation of the model, was not clear in the original draft. Because of this, we reformulated the section (3.4) and figure (5) on cytokinesis. We identified four representative examples of centrosome positions, then compared the experimental profile of ECT-2 accumulation to the model result. For simplicity, we also eliminated the simulations of the non-phosphorylatable inactive copy of ECT-2 (“ECT-2 6A”). A more detailed analysis of that data revealed that the pattern of accumulation of ECT-2 6A at cleavage furrowing was more similar to the end of polarization, indicating that this copy of ECT-2 appears to have much slower turnover than the endogenous copy (as would expected from phosphorylation-dependent membrane displacement).

4. Fundamentally, our study addresses a similar question to (Illukkumbura et al., 2023), in the sense that we seek to understand how cortical flows could pattern ECT-2 and myosin, even though the residence time of ECT-2 is very low. Despite the similarities, it differs from the cited study in that ECT-2 is not an inert component that is asymmetrically distributed, but rather a component which regulates myosin levels and cortical flows, ultimately feeding back on its own accumulation. Due to these similarities and differences, we added an expository section in the discussion (p. 18) comparing our results to those of that study.

Point-by-point description of the revisions Reviewer 1 In this article, Maxian et al. propose a model combining 1-d simulations of ECT-2 and Myosin concentration at the cortex through binding/unbinding and advection at the cortex, with an input for AIR-1 cortical concentration based on the spatial localisation of the centrosomes in the cytoplasm. The objective of the authors is to recapitulate the role of (1) AIR-1, (2) its effector ECT-2 and (3) the downstream effector, driver of cortical flows, the molecular motors Myosin, in two key physiological processes, polarization and cell division. This is important as work over the last 10 years have emphasized the role of AIR-1 in embryo polarization. Previous biochemical-mechanical models have focused on RhoA/Myosin interactions (Nishikawa et al, 2017), the importance of a negative feedback and excitable RhoA dynamics (Michaux et al, 2018), or anterior PARs/posterior PARs/Myosin (Gross et al, 2019). The authors thus attempt to provide a new descriptive model in which RhoA is implicit, instead focusing on the role of centrosome localization on AIR-1 localization, and providing a framework to explore polarity establishment and cell division based on these 3 simple players. The first part of the model is very reminiscent of previously published models, while the second instead provides a link between the initial polarizing cue AIR-1 and polarization. Based on this description, the model is precisely tuned to achieve polarization while matching experimental observations of flow speed and ECT-2 A/P enrichment shape. The results are therefore certainly new and interesting.

Thank you for the positive assessment!

Major comments: 1. The authors use the position of the centrosomes as a static entry, resulting in a static AIR-1 input. Is this true, or are the positions of the centrosomes dynamically modulated over the course of the different processes simulated here (for example as a consequence of cortical flows?), and if so, is the assumption of immobile position?

We assume that the centrosomes are fixed on the timescale of the cortical dynamics, and study how the cortex responds to a static AIR-1 signal (see clarifying comment on p. 4). In Fig. S4, we show that the cortex responds rapidly to changes in the existence or position of the AIR-1 signal. As such, slower dynamics might be the result of slowly moving centrosomes, as we show in supplementary simulations (Fig. S8).

1. While in its principle the model is quite simple and elegant, the detailed form of the equations describing the interactions between the players is more complex. Are all these required? If they are crucially important for the behavior of the model, these should be described more thoroughly, and if possible rooted more directly in experimental results:

Thank you for this comment. We agree that there were several non-trivial terms in our “minimal” model. Our guiding principle for the revision was to reduce complexity and better justify the terms that are included.

(a) kMEMEc (Linear enhancement term): why would myosin impact E concentration? The authors state, p.7, ”There is a modest increase in the recruitment rate of ECT-2 due to cortical myosin (directly or indirectly), in a myosin concentration-dependent manner (Longhini and Glotzer, 2022).” I could not find the data supporting this assumption Longhini and Glotzer apparently rather point to a modulation of cortical flows. (”During anaphase, asymmetric ECT-2 accumulation is also myosin-dependent, presumably due to its role in generating cortical flows.”). Embedding this effect in the recruitment rate instead of expecting it from the model thus appears awkward. Could the authors specify how they came to this conclusion, which the authors might have derived from observations made in their previous work, but maybe did not fully document there?

This is an important issue. Since it was raised by all of the reviewers, we addressed it on page 1 above. Throughout the manuscript (Figs. 4 and S4), we tried to highlight that cortical flows are insufficient to localize ECT-2, while the recruitment hypothesis provides a better match to the experimental data. The recruitment by an advected species was speculated upon in Longhini and Glotzer: ”Rather, we favor a model in which the association of ECT-2 with the cortex involves interactions with cortical component(s) that are concentrated by cortical flows.”

(b) kEME2Mc (ECT-2 non-linear impact on Myosin): does the specific form of the value to convey the enhancement (square form) have an impact on the results?

The specific form does not have an impact. In fact, in the revised version, our experimental data shows an asymmetry in myosin that is actually lower than ECT-2. As such, a nonlinear term here lacks justification, and we switched to a linear term of the form kEMEMc (see model equations on p. 6).

(c) KfbM4 ”The form of this term is a coarse-grained version of previously-published work (Michaux et al., 2018).” Myosin feedback on myosin localization proportionally to M4 does not seem to directly derive from Michaux et al. Please detail this points more extensively and detail the derivation, in the supplements if not in the main text.

Based on this comment and that of reviewer 2, we decided to switch to a more general term for nonlinear negative feedback, as discussed in point 3 on page 1.

(d) P23. Parameter values: ”This is 1.5 times longer than the estimate for single molecules (Nishikawa et al., 2017; Gross et al., 2019) to reflect the more long-lived nature of myosin foci during establishment phase (Munro et al., 2004).” Not sure what the authors mean by more long-lived duration of foci during establishment phase. Seems rather arbitrary.

This was a misstatement on our part. A closer look at Gross et al. revealed that, under conditions similar to those we simulate (initial polarity establishment), the residence time of myosin is about 15 s (off rate 0.06 s−1). We modified our justification (p. 30) to include this. We also looked at the effect of longer myosin residence time on polarity establishment (Fig. S8).

1. It would be very helpful (and indeed more convincing) to include a direct comparison between modeling results and experimental counterpart whenever possible. This might not be possible for some data (e.g. Fig. 3d from Cowan et al), but should be possible for other, in particular Fig. 3c and Fig. 5b, for the flow speed and ECT-2 profiles. In Fig. 5b in particular, previously published experimental data could be produced to give the reader to compare model with experiments (possibly provided as an inset, at least for the wild type conditions).

We tried to bring in more data based on what was available from previous work (Longhini and Glotzer, 2022). Frame intervals of 10 s prohibited a PIV analysis for flow speeds, and punctate myosin profiles often made it difficult to measure myosin concentration. We were, however, able to extract the ECT-2 concentration from our previous movies and compare it to the model results. We included these comparisons in Figs. 3 and 5, with accompanying discussion in the text.

Minor comments: 1. Fig. 5b: ECT-2 C 6A(dhc-1) do not seem to be referenced or discussed in the main text. Also, why present the results for the flow for 2 conditions and the ECT-2 localisation for 4? Or does the variation of ECT-2 not impact the flow profile?

As discussed above on p. 2 (#4), we decided to reformulate the cytokinesis figure to incorporate more experimental data. Since we have detailed data on ECT-2 localization, we presented these in Fig. 5 for four experimental conditions, comparing each to the model.

1. p.6: Given that the non-normalized data is used in the main text, and the normalized only appears in the supplemental, maybe star the dimensionless and remove all hats from the main for greater legibility?

We changed the notation to make the main text variables (dimensional) unadorned, while the dimensionless variables in the SI now have hats.

1. p.6: Eqn 1a: carrot missing on 3rd E? This is now a moot point because of the previous comment.

2. p.14: replace “embryo treatment” with ”experimental conditions”? We changed “embryo treatment” to “experimental conditions” globally.

3. p.21, S4a: add ˆA=A/A(Tot) We added it in the last display on p. 28.

4. p.22: ”L = 134.6 µm” - please write 134 µm to retain the precision of original measurements We made this change.

5. p.22: Please provide formula for all dimensionless values as a table at the end of the supplemental for the eager but less-mathematically proficient reader. We added Table 1 to list the relationship between dimensional and dimensionless parameters.

Reviewer 2 The manuscript by Maxian, Longhini and Glotzer presents purely modeling work performed by the first author in conjunction with the already published experimental work by Longhini and Glotzer (eLife, 2022). The aim of the manuscript is to provide a mathematical model that connects the actomyosin contractility of the cell cortex in C. elegans zygote with the activity of the centrosomal kinase AurA (AIR-1 in C. elegans). The major claim of the authors is that their model, fitted to the experimental data pertaining to the zygote polarization, also describes dynamics during the zygote cytokinesis. In the model, the authors provide a heuristic approach to the biochemical dynamics, reducing their treatment to two variables: myosin and Ect2 Rho GEF. The biochemical model is integrated with a simple 1D active gel-type model for the cortical flow. The model uses static diffusive field of activity of AurA kinase in the cytoplasm as an input to their chemo-mechanical model. Major concerns: 1. The biochemical model is highly heuristic and several major assumptions are poorly justified. Thus, the authors explicitly introduce recruitment of Ect2 by myosin, something apparently based on the experimental observations by Longhini and Glotzer in 2022, which had not been biochemically confirmed since with a clear molecular mechanism. This is an important issue, and we appreciate your concern which was shared by the other reviewers. As discussed above on p. 1, we tried to justify this assumption better by (a) clearly stating it on p. 7, and (b) demonstrating that the dynamics we observe in live embryos are impossible without it. The model confirms what was pointed out by Longhini and Glotzer, that the short residence time of ECT-2, combined with in vivo flow speeds on the order of 10 µm/min, make it impossible for cortical flows alone to redistribute ECT-2. 2. The contribution of AurA is introduced highly schematically as a term based on enzyme inhibition biochemistry that increases the off rate of Ect2. The major assumption of the model is that AurA phosphorylates Ect2 strictly on the membrane (cortex) of the cell. Why? No molecular justification is given. If the authors cannot provide clear justification, this major assumption has to be clearly declared as such. The phosphorylation/dephosphorylation dynamics of Ect2 is not considered at all.

We clarified that the species we consider in the model (E) is unphosphorylated ECT-2, so that the negative flux comes from either unbinding or phosphorylation. Of course, AIR-1 phosphorylates ECT-2 in the cytoplasm as well, but our model only tracks the binding of unphosphorylated ECT-2 to the cortex. We clarified this on p. 6.

1. In the equation for myosin, the authors introduce disassembly/ inactivation term proportional to the fourth order of concentration of myosin. Why? This is a major assumption, which appears to be derived from the work by Michaux et al. 2018. There the authors (Michaux et al.) postulated that the rate of inactivation of RhoA GTPase was somehow proportional to the fourth power of RhoA concentration. It appears that Maxian et al. further assume that the myosin concentration is fast variable enslaved by Rho, so that M∼ [RhoA]. They then presumably assume that if the rate of degradation/ inactivation of Rho is proportional to the fourth power of Rho concentration, so is true for myosin (M). This is a logical error and is not justified. An important question, why do the current authors need this unusual assumption with such a high power of M disassembly/inactivation? Perhaps, this is because without this rather dubious term the cortex flow produces a blow-up of myosin concentration? This would be expected in their mechanical model - the continuous flow of actomyosin not compensated by cortex disassembly generally causes blow-up of biochemical concentrations transported by the flow, this is a known problem of the “simple” active gel model used by the authors. Maxian et al. have to provide clear derivation of the term−KfbM4 and also demonstrate why they need this exotic assumption.

As mentioned above on p. 1, this was a misguided attempt on our part to use previous literature to directly assign values to model parameters. In the revised manuscript, we considered a more general term for the nonlinear feedback. The fitting occurs in Fig. S3, where we impose the ECT-2 profile during pseudo-cleavage and try to fit the myosin profile. k = 1 is eliminated because the ECT-2 and myosin have different asymmetries. Higher order nonlinearities (k= 2,3) are successful in fitting the experimental data. In the main text, we present results from k= 2, then use Fig. S5 to present results on the k= 3 case.

1. The equation for myosin M has a membrane-binding term, which is second order in concentration of Ect2∼ E2, without which the model will not show the instability that the authors need. The only justification given is that ”some nonlinearity is required”. A proper derivation should be given here.

Our experimental data shows an asymmetry in myosin that is actually lower than ECT-2. As such, a nonlinear term in the binding rate lacks justification, and we switched to a linear term of the form kEMEMc (see model equations on p. 6).

1. The diffusion coefficients for Ect2 and myosin are chosen to be the same. Why? Clearly these molecules so different in size myosin being a gigantic cluster monster of∼ 300nm believed to be bound to actin, should have a much smaller diffusion coefficient?

Thank you for raising this point. We used the same diffusion coefficient for simplicity; because its dimensionless value is less than 10−4, diffusion is relatively unimportant in shaping the concentration fields. If we assume instead, for instance, that myosin cannot diffuse in the membrane, while ECT-2 has a ten-fold larger diffusion coefficient, the steady state profiles of ECT-2 and myosin are changed by at most 5% (see Fig. S6).

1. There are confusing statements regarding the role of actomyosin flows. In the beginning of the manuscript, the authors seem to state that since Ect2 has a high off rate, the effect of the flow on Ect2 localization is negligible in comparison with direct binding to myosin. Later, the authors state that flows are absolutely essential for the patterning. The authors need to clearly explain where and how the flows are important or not.

Thank you for pointing out this confusion. In the revised manuscript, we tried to be explicit that the combination of recruitment and flows is essential for patterning ECT-2. We did this in Figs. 4 and 5 by showing the results of simulations without recruitment (Fig. 4) and without recruitment and flows (Fig. 5).

Minor points: 1. page 9. Why is the rate of dephosphorylation of AurA is named Koff? We changed the notation to ¯kinac to reflect inactivation.

1. page 10. “Note that the model is calibrated to predict... which matches experimental observations” - this sentence needs changing. You want to say that you fit the model to experiments in the Longhini and Glotzer paper. There is no prediction here. We removed this sentence.

2. page 14. “A plot of Ect-2 accumulation as a function of distance from the nearest cortex...” - clearly the word ”centrosome” is meant here instead of ”cortex”. What was meant by this sentence was the distance from the centrosome to the nearest cortex pole (anterior or posterior). We modified it to make this more clear (p. 15).

3. page 16. ”Inactive, non-phosphorylatable version of Ect-2...” - non-phosphorylatable is clear, but why inactive? As discussed on p. 2 (#4), we decided to simplify the cytokinesis figure and remove the simulations with non-phosphorylatable ECT-2. While it is not relevant, the ECT-2 6A variant represents a fragment of the protein that lacks the catalytic domain. Our original goal was to use these data to track the ECT-2 localization without perturbing the system biochemistry, but the data gave the hint of longer exchange kinetics, which confounded our analysis.

Reviewer 3 Maxian et al. developed a mathematical model to explain the essential elements and interactions necessary and sufficient for the polarisation of the C. elegans zygote. The initiation of zygote polarisation has been extensively studied in recent years, highlighting the role of the centrosomal kinase Aurora-A (AIR-1) in controlling the cortical distribution of RhoGEF (ECT-2) and actomyosin contractility during polarisation. Although genetic experiments have demonstrated their function in this process, it remains to be tested whether these factors and their interactions are sufficient to induce polarisation. This work has provided a theoretical framework to predict the activity of AIR-1 in the cytoplasm and at the cell cortex, and the cortical distribution of ECT-2 and myosin-II (NMY-2). This framework can recapitulate the dynamic rearrangement of ECT-2 and myosin-II during polarisation, with centrosomes positioned at the posterior pole of the zygote. This model can explain, at least in part, the asymmetric distribution of ECT-2 and myosin-II in the zygote undergoing cytokinesis, suggesting that the mechanism of AIR-1-mediated control of ECT-2 and myosin-II would regulate patterning during polarisation and cytokinesis. This theoretical framework is developed with reasonable assumptions based on previous genetic experiments (except for the myosin-dependent regulation of ECT-2; see comments below).

Thank you for the positive assessment!

Major issues: 1. The authors insist that this model correctly predicts the spatio-temporal dynamics of ECT-2 and myosin-II during polarisation and cytokinesis. However, the predicted results do not reproduce the in vivo pattern of ECT-2 in both phases. ECT-2 is cleared from the posterior cortex and establishes a graded pattern across the antero-posterior axis during polarisation (see their previous publication in eLife 2022, 11, e83992, Fig1A -480s) and cytokinesis (see eLife 2022, 11, e83992, Fig1C 60s and 120s). During both stages, ECT-2 does not show local enrichment at the boundary between the anterior and posterior cortical domains in vivo. In fact, when comparing the predicted results with the in vivo pattern of ECT-2 and cortical flow, the authors used non-quantitative descriptions such as ’in good agreement’, ’a realistic magnitude’, ’resemble’. These vague descriptions should be revised and a quantitative assessment of ECT-2 distribution between in silico and in vivo should be included in a revised manuscript.

As mentioned on p. 1, in the revised manuscript we interacted with the data in a much stronger way. We first used data during pseudo-cleavage to infer the ECT-2/myosin relationship. We then examined (Fig. 3) quantitatively how the ECT-2 accumulation during polarization matches the experimental data (it matches early but not later stages). We repeated this for cytokinesis in Fig. 5, where we compared the ECT-2 profile across four experimental conditions to the model prediction.

1. I assume that the strange local enrichment of ECT-2 at the anteroposterior boundary is due to their assumption that the binding rate of ECT-2 is increased by a linear increase via cortical myosin-II (page 6). This assumption is not directly supported by experimental evidence. A previous study by the same group (eLife 2022, 11, e83992) showed that a progressive increase in ECT-2 concentration at the anterior cortex is partially accompanied by an increase in cortical flow and transport of myosin-II from the posterior pole to the anterior cortex. This observation supports the idea that ECT-2 may associate with cortical components transported by myosin-II based cortical flow. This unrealistic assumption makes the predicted distribution pattern of ECT-2 almost identical to that of cortical myosin-II, resulting in an increase in the concentration of ECT-2 at the anteroposterior boundary where myosin-II forms pseudocleavages and cleavage furrows. The authors should clarify why their mathematical model used this assumption and provide a comprehensive analysis and evaluation of the parameter value for an ECT-2-myosin-II interaction.

In the revised manuscript, we outlined the justification for this assumption after presenting the model equations. In Appendix B.3, we were able to constrain all parameters except the recruitment term. Then, in Appendix B.3.3, we provided an analysis of how polarization changes when the recruitment term is increased. We show that the ECT-2 asymmetries with myosin flows are the same as those simply due to AIR-1 inhibition (since the lifetime of ECT-2 is small). Adding indirect recruitment gives asymmetries that resemble experimental data from early establishment of polarity. We showed this both by assuming “myosin” (a species which colocalizes with myosin) recruits ECT-2 (Fig. S4) and by simulating an alternative model (Eq. (S4)) where an explicit species that is advected with cortical flows recruits myosin (Fig. S7).

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Referee #3

Evidence, reproducibility and clarity

Maxian et al. developed a mathematical model to explain the essential elements and interactions necessary and sufficient for the polarisation of the C. elegans zygote. The initiation of zygote polarisation has been extensively studied in recent years, highlighting the role of the centrosomal kinase Aurora-A (AIR-1) in controlling the cortical distribution of RhoGEF (ECT-2) and actomyosin contractility during polarisation. Although genetic experiments have demonstrated their function in this process, it remains to be tested whether these factors and their interactions are sufficient to induce polarisation.

This work has provided a theoretical framework to predict the activity of AIR-1 in the cytoplasm and at the cell cortex, and the cortical distribution of ECT-2 and myosin-II (NMY-2). This framework can recapitulate the dynamic rearrangement of ECT-2 and myosin-II during polarisation, with centrosomes positioned at the posterior pole of the zygote. This model can explain, at least in part, the asymmetric distribution of ECT-2 and myosin-II in the zygote undergoing cytokinesis, suggesting that the mechanism of AIR-1-mediated control of ECT-2 and myosin-II would regulate patterning during polarisation and cytokinesis. This theoretical framework is developed with reasonable assumptions based on previous genetic experiments (except for the myosin-dependent regulation of ECT-2; see comments below).

Issue #1

The authors insist that this model correctly predicts the spatio-temporal dynamics of ECT-2 and myosin-II during polarisation and cytokinesis. However, the predicted results do not reproduce the in vivo pattern of ECT-2 in both phases. ECT-2 is cleared from the posterior cortex and establishes a graded pattern across the antero-posterior axis during polarisation (see their previous publication in eLife 2022, 11, e83992, Fig1A -480s) and cytokinesis (see eLife 2022, 11, e83992, Fig1C 60s and 120s). During both stages, ECT-2 does not show local enrichment at the boundary between the anterior and posterior cortical domains in vivo. In fact, when comparing the predicted results with the in vivo pattern of ECT-2 and cortical flow, the authors used non-quantitative descriptions such as 'in good agreement', 'a realistic magnitude', 'resemble'. These vague descriptions should be revised and a quantitative assessment of ECT-2 distribution between in silico and in vivo should be included in a revised manuscript.

Issue #2

I assume that the strange local enrichment of ECT-2 at the anteroposterior boundary is due to their assumption that the binding rate of ECT-2 is increased by a linear increase via cortical myosin-II (page 6). This assumption is not directly supported by experimental evidence. A previous study by the same group (eLife 2022, 11, e83992) showed that a progressive increase in ECT-2 concentration at the anterior cortex is partially accompanied by an increase in cortical flow and transport of myosin-II from the posterior pole to the anterior cortex. This observation supports the idea that ECT-2 may associate with cortical components transported by myosin-II based cortical flow. This unrealistic assumption makes the predicted distribution pattern of ECT-2 almost identical to that of cortical myosin-II, resulting in an increase in the concentration of ECT-2 at the anteroposterior boundary where myosin-II forms pheudo-cleavages and cleavage furrows. The authors should clarify why their mathematical model used this assumption and provide a comprehensive analysis and evaluation of the parameter value for an ECT-2-myosin-II interaction.

Significance

This work includes a valuable tool that can be used to explain other actomyosin-mediated polarisation processes. Although the paper provides useful insights in principle, the weakness of this work is that the model is designed with parameter sets that only recapitulate previously published phenotypes. Therefore, this paper confirms previous findings and provides less/no new mechanistic insights into cell polarisation. As such, this work would be of interest to specialised cell biologists and biophysicists working on the cytoskeleton and cell division, but will not be of general interest to biologists and biochemists.

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Referee #2

Evidence, reproducibility and clarity

The manuscript by Maxian, Longhini and Glotzer presents purely modeling work performed by the first author in conjunction with the already published experimental work by Longhini and Glotzer (eLife, 2022). The aim of the manuscript is to provide a mathematical model that connects the actomyosin contractility of the cell cortex in C. elegans zygote with the activity of the centrosomal kinase AurA (AIR-1 in C. elegans). The major claim of the authors is that their model, fitted to the experimental data pertaining to the zygote polarization, also describes dynamics during the zygote cytokinesis. In the model, the authors provide a heuristic approach to the biochemical dynamics, reducing their treatment to two variables: myosin and Ect2 Rho GEF. The biochemical model is integrated with a simple 1D active gel-type model for the cortical flow. The model uses static diffusive field of activity of AurA kinase in the cytoplasm as an input to their chemo-mechanical model. Major concerns: 1. The biochemical model is highly heuristic and several major assumptions are poorly justified. Thus, the authors explicitly introduce recruitment of Ect2 by myosin, something apparently based on the experimental observations by Longhini and Glotzer in 2022, which had not been biochemically confirmed since with a clear molecular mechanism. 2. The contribution of AurA is introduced highly schematically as a term based on enzyme inhibition biochemistry that increases the off rate of Ect2. The major assumption of the model is that AurA phosphorylates Ect2 strictly on the membrane (cortex) of the cell. Why? No molecular justification is given. If the authors cannot provide clear justification, this major assumption has to be clearly declared as such. The phosphorylation/dephosphorylation dynamics of Ect2 is not considered at all. 3. In the equation for myosin, the authors introduce disassembly/ inactivation term proportional to the fourth order of concentration of myosin. Why? This is a major assumption, which appears to be derived from the work by Michaux et al. 2018. There the authors (Michaux et al.) postulated that the rate of inactivation of RhoA GTPase was somehow proportional to the fourth power of RhoA concentration. It appears that Maxian et al. further assume that the myosin concentration is fast variable enslaved by Rho, so that M ~ [RhoA]. They then presumably assume that if the rate of degradation/ inactivation of Rho is proportional to the forth power of Rho concentration, so is true for myosin (M). This is a logical error and is not justified. An important question, why do the current authors need this unusual assumption with such a high power of M disassembly/inactivation? Perhaps, this is because without this rather dubious term the cortex flow produces a blow-up of myosin concentration? This would be expected in their mechanical model - the continuous flow of actomyosin not compensated by cortex disassembly generally causes blow-up of biochemical concentrations transported by the flow, this is a known problem of the "simple" active gel model used by the authors. Maxian et al. have to provide clear derivation of the term -kfb*M^4 and also demonstrate why they need this exotic assumption. 4. The equation for myosin M has a membrane-binding term, which is second order in concentration of Ect2 ~E^2, without which the model will not show the instability that the authors need. The only justification given is that "some nonlinearity is required". A proper derivation should be given here. 5. The diffusion coefficients for Ect2 and myosin are chosen to be the same. Why? Clearly these molecules so different in size - myosin being a gigantic cluster monster of ~300 nm believed to be bound to actin, should have a much smaller diffusion coefficient? 6. There are confusing statements regarding the role of actomyosin flows. In the beginning of the manuscript, the authors seem to state that since Ect2 has a high off rate, the effect of the flow on Ect2 localization is negligible in comparison with direct binding to myosin. Later, the authors state that flows are absolutely essential for the patterning. The authors need to clearly explain where and how the flows are important or not. Minor points: 1. page 9. Why is the rate of dephosphorylation of AurA is named Koff? 2. page 10. "Note that the model is calibrated to predict... which matches experimental observations" - this sentence needs changing. You want to say that you fit the model to experiments in the Longhini and Glotzer paper. There is no prediction here. 3. page 14. "A plot of Ect-2 accumulation as a function of distance from the nearest cortex..." - clearly the word "centrosome" is meant here instead of "cortex". 4. page 16. "Inactive, non-phosphorylatable version of Ect-2..." - non-phosphorylatable is clear, but why inactive?

Significance

This reviewer sees limited significance of this manuscript to the field in general. The modeling approach is hardly novel as it is based on a variety of published models, all cited by the authors, to be precise. The model, being very simplistic and heuristic, is not predictive. The main novelty of the current manuscript is the introduction of the effect of Aurora A on the activity of the actomyosin cortex. Since this is taken to be very schematic, simply via the effective increase in the off rate of Ect2, the model is showing that it is consistent with the earlier published experimental results by Longhini and Glotzer. This is to be expected. The main claim of the authors, that the model fitted to the polarization data also qualitatively describes the cytokinesis (there are no quantitative data to compare to) is probably valid, but the result is not surprising either. At best, the model can be labeled as fitted to the data and confirming the experimental results. Since it contains several postulated heuristic terms not properly justified on the mechanistic level, this is also not surprising.

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Referee #1

Evidence, reproducibility and clarity

Summary:

In this article, Maxian et al. propose a model combining 1-d simulations of ECT-2 and Myosin concentration at the cortex through binding/unbinding and advection at the cortex, with an input for AIR-1 cortical concentration based on the spatial localisation of the centrosomes in the cytoplasm. The objective of the authors is to recapitulate the role of (1) AIR-1, (2) its effector ECT-2 and (3) the downstream effector, driver of cortical flows, the molecular motors Myosin, in two key physiological processes, polarization and cell division. This is important as work over the last 10 years have emphasized the role of AIR-1 in embryo polarization. Previous biochemical-mechanical models have focused on RhoA/Myosin interactions (Nishikawa et al, 2017), the importance of a negative feedback and excitable RhoA dynamics (Michaux et al, 2018), or anterior PARs/posterior PARs/Myosin (Gross et al, 2019). The authors thus attempt to provide a new descriptive model in which RhoA is implicit, instead focusing on the role of centrosome localization on AIR-1 localization, and providing a framework to explore polarity establishment and cell division based on these 3 simple players. The first part of the model is very reminiscent of previously published models, while the second instead provides a link between the initial polarizing cue AIR-1 and polarization. Based on this description, the model is precisely tuned to achieve polarization while matching experimental observations of flow speed and ECT-2 A/P enrichment shape. The results are therefore certainly new and interesting.

Major comments:

1. The authors use the position of the centrosomes as a static entry, resulting in a static AIR-1 input. Is this true, or are the positions of the centrosomes dynamically modulated over the course of the different processes simulated here (for example as a consequence of cortical flows?), and if so, is the assumption of immobile position?
2. While in its principle the model is quite simple and elegant, the detailed form of the equations describing the interactions between the players is more complex. Are all these required? If they are crucially important for the behavior of the model, these should be described more thoroughly, and if possible rooted more directly in experimental results, in particular:
   • k(ME)MEc (Linear enhancement term): why would myosin impact E concentration? The authors state, p.7, "There is a modest increase in the recruitment rate of ECT-2 due to cortical myosin (directly or indirectly), in a myosin concentration-dependent manner (Longhini and Glotzer, 2022)." I could not find the data supporting this assumption - Longhini and Glotzer apparently rather point to a modulation of cortical flows. ("During anaphase, asymmetric ECT-2 accumulation is also myosin-dependent, presumably due to its role in generating cortical flows."). Embedding this effect in the recruitment rate instead of expecting it from the model thus appears awkward. Could the authors specify how they came to this conclusion, which the authors might have derived from observations made in their previous work, but maybe did not fully document there?
   • k(EM)E^2Mc (ECT-2 non-linear impact on Myosin): does the specific of the value to convey the enhancement (square form) have an impact on the results?
   • k(fb)*M^4 "The form of this term is a coarse-grained version of previously-published work (Michaux et al., 2018)." Myosin feedback on myosin localization proportionally to M^4 does not seem to directly derive from Michaux et al... Please detail this points more extensively and detail the derivation, in the supplements if not in the main text. P23. Parameter values: "This is 1.5 times longer than the estimate for single molecules (Nishikawa et al., 2017; Gross et al., 2019) to reflect the more long-lived nature of myosin foci during establishment phase (Munro et al., 2004)." Not sure what the authors mean by more long-lived duration of foci during establishment phase. Seems rather arbitrary.
3. It would be very helpful (and indeed more convincing) to include a direct comparison between modeling results and experimental counterpart whenever possible. This might not be possible for some data (e.g. Fig. 3d from Cowan et al), but should be possible for other, in particular Fig. 3c and Fig. 5b, for the flow speed and ECT-2 profiles. In Fig. 5b in particular, previously published experimental data could be produced to give the reader to compare model with experiments (possibly provided as an inset, at least for the wild type conditions).

Minor comments

Fig. 5b: ECT-2 C 6A(dhc-1) do not seem to be referenced or discussed in the main text. Also, why present the results for the flow for 2 conditions and the ECT-2 localisation for 4? Or does the variation of ECT-2 not impact the flow profile?

p.6: Eqn 1a: ^ missing on 3rd E?

p.6: Given that the non-normalized data is used in the main text, and the normalized only appears in the supplemental, maybe star the dimensionless and remove all hats from the main for greater legibility?

p.14: replace "embryo treatment" with "experimental conditions"?

p.21, S4a: add A=Â/Atot

p.22: "L = 134.6 μm" - please write 134µm to retain the precision of original measurements

p.22: Please provide formula for all dimensionless values as a table at the end of the supplemental for the eager but less-mathematically proficient reader.

The authors' attention to providing specific citations including figure number corresponding to the specific point they reference in the papers they cite is appreciated.

Significance

General assessment:

This modeling paper interestingly leverages existing experimental data to develop a new mathematical model of embryo polarization and cell division focusing on the role of AIR-1/Aurora Kinase. It combines classical 1-d advection/diffusion-reaction scheme with an upstream cue, AIR-1/Aurora Kinase, the profile of which is defined by the localization of the two centrosomes, and use the model as a framework to explore cortical flows and ECT-2 and Myosin cortical localization. Calibrated using information from polarization phase, the model recapitulates without any further tuning, in a variety of mutants, key localisation hallmarks of Ect-2 during cell division, simply based on the localization of the centrosomes. Finally, it provides strong, experimentally testable predictions of the validity of the proposed model.

Advance:

In particular, this study provide compelling evidence showing that their model, based on dynamics during polarization, is sufficient to explain the ultra-sensitivity of cortical ECT-2 accumulation to centrosome distance during cell division. Their model further predicts that short ECT-2 cortical residence time is required to prevent advection-mediated counter-flows of ECT-2 that would otherwise prevent polarization, a prediction testable experimentally by engineering modifications of ECT-2 cortical residence time.

Audience:

This is primarily a modeling paper. Although the bulk of the article is written to capture the interest of cellular biologists with a sound backgrounds in mathematics and an interest in minimal models of cell division and polarization, the overall conclusions and prediction are further-reaching and would be of interest to a larger audience with an interest in cell division, polarization, and the role of Aurora Kinase in these processes.

Expertise:

Developmental biology / Cell biology / Biological physics

eLife Assessment

The findings are important and intriguing, with theoretical or practical implications beyond a single subfield. The computational methods employed are clever and sophisticated and the strength of evidence is convincing. Many of the methodological concerns raised after the first round of review were addressed in the revised version, although all three reviewers also highlighted that the exploratory nature of the paper and the lack of clarity regarding the hypotheses make it hard to assess the impact of the results on existing theories.

Reviewer #1 (Public review):

Summary:

The authors use a sophisticated task design and Bayesian computational modeling to test their hypothesis that information generalization (operationalized as a combination of self-insertion and social contagion) in social situations is disrupted in Borderline Personality Disorder. Their main finding relates to the observation that two different models best fit the two tested groups: While the model assuming both self-insertion and social contagion to be present when estimating others' social value preferences fit the control group best, a model assuming neither of these processes provided the best fit to BPD participants.

Strengths:

The revisions have substantially strengthened the paper and the manuscript is much clearer and easier to follow now. The strengths of the presented work lie in the sophisticated task design and the thorough investigation of their theory by use of mechanistic computational models to elucidate social decision-making and learning processes in BPD.

Weaknesses:

Some critical concerns remain after the first revision, particularly regarding the use of causal language and the clarity of the hypotheses and results, specified in the points below.

(1) The authors frequently refer to their predictions and theory as being causal, both in the manuscript and in their response to reviewers. However, causal inference requires careful experimental design, not just statistical prediction. For example, the claim that "algorithmic differences between those with BPD and matched healthy controls" are "causal" in my opinion is not warranted by the data, as the study does not employ experimental manipulations or interventions which might predictably affect parameter values. Even if model parameters can be seen as valid proxies to latent mechanisms, this does not automatically mean that such mechanisms cause the clinical distinction between BPD and CON, they could plausibly also refer to the effects of therapy or medication. I recommend that such causal language, also implicit to expressions like "parameter influences on explicit intentional attributions", is toned down throughout the manuscript.

(2) Although the authors have now much clearer outlined the stuy's aims, there still is a lack of clarity with respect to the authors' specific hypotheses. I understand that their primary predictions about disruptions to self-other generalisation processes underlying BPD are embedded in the four main models that are tested, but it is still unclear what specific hypotheses the authors had about group differences with respect to the tested models. I recommend the authors specify this in the introduction rather than refering to prior work where the same hypotheses may have been mentioned.

(3) Caveats should also be added about the exploratory nature of the many parameter group comparisons. If there are any predictions about group differences that can be made based on prior literature, the authors should make such links clear.

(4) I'm not sure I understand why the authors, after adding multiple comparison correction, now list two kinds of p-values. To me, this is misleading and precludes the point of multiple comparison corrections, I therefore recommend they report the FDR-adjusted p-values only. Likewise, if a corrected p-value is greater than 0.05 this should not be interpreted as a result.

(5) Can the authors please elaborate why the algorithm proposed to be employed by BPD is more 'entropic', especially given both their self-priors and posteriors about partners' preferences tended to be more precise than the ones used by CON? As far as I understand, there's nothing in the data to suggest BPD predictions should be more uncertain. In fact, this leads me to wonder, similarly to what another reviewer has already suggested, whether BPD participants generate self-referential priors over others in the same way CON participants do, they are just less favourable (i.e., in relation to oneself, but always less prosocial) - I think there is currently no model that would incorporate this possibility? It should at least be possible to explore this by checking if there is any statistical relationship between the estimated θ_ppt^m and 〖p(θ〗_par |D^0).

"To note, social contagion under M3 was highly correlated with contagion under M1 (see Fig S11). This provides some preliminary evidence that trauma impacts beliefs about individualism directly, whereas trauma and persecutory beliefs impact beliefs about prosociality through impaired trait mentalising" - I don't understand what the authors mean by this, can they please elaborate and add some explanation to the main text?

Reviewer #2 (Public review):

Summary:

The paper investigates social-decision making, and how this changes after observing the behaviour of other people, in borderline personality disorder. The paper employs a task including three phases, the first where participants make decision on how to allocate rewards to oneself and to a virtual partner, the second where they observe the same task performed by someone else, and a third phase equivalent to phase one, but with a new partner. Using sophisticated computational modelling to analyse choice data, the study reports that borderline participants (versus controls) are more certain about their preferences in phase one, used more neutral priors and are less flexible during phase two, and are less influenced by partners in phase three.

Strengths:

The topic is interesting and important, and the findings are potentially intriguing. The computational methods employed is clever and sophisticated, at the cutting edge of research in the field.

Weaknesses:

The paper is not based on specific empirical hypotheses formulated at the outset, but, rather, it uses an exploratory approach. Indeed, the task is not chosen in order to tackle specific empirical hypotheses. This, in my view, is a limitation since the introduction reads a bit vague and it is not always clear which gaps in the literature the paper aims to fill. As a further consequence, it is not always clear how the findings speak to previous theories on the topic.

Reviewer #3 (Public review):

In this paper, the authors use a three-phase economic game to examine the tendency to engage in prosocial versus competitive exchanges with three anonymous partners. In particular, they consider individual differences in the tendency to infer about others' tendencies based on one's preferences and to update one's preferences based on observations of others' behavior. The study includes a sample of individuals diagnosed with borderline personality disorder and a matched sample of psychiatrically healthy control participants.

On the whole, the experimental design is well-suited to the questions and the computational model analyses are thorough, including modern model-fitting procedures. I particularly appreciated the clear exposition regarding model parameterization and the descriptive Table 2 for qualitative model comparison. In the revised manuscript, the authors now provide a more thorough treatment of examining group differences in computational parameters given that the best-fitting model differed by group. They also examine the connection of their task and findings to related research focusing on self-other representation and mentalization (e.g., Story et al., 2024).

The authors note that the task does not encourage competition and instead captures individual differences in the motivation to allocate rewards to oneself and others in an interdependent setting. The paper could have been strengthened by clarifying how the Social Value Orientation framework can be used to interpret the motivations and behavior of BPD versus CON participants on the task. Although the authors note that their approach makes "clear and transparent a priori predictions," the paper could be improved by providing a clear and consolidated statement of these predictions so that the results could be interpreted vis-a-vis any a priori hypotheses.

Finally, the authors have amended their individual difference analyses to examine psychometric measures such as the CTQ alongside computational model parameter estimate differences. I appreciate that these analyses are described as exploratory. The approach of using a partial correlation network with bootstrapping (and permutation) was interesting, but the logic of the analysis was not clearly stated. In particular, there are large group (Table 1: CON vs. BPD) differences in the measures introduced into this network. As a result, it is hard to understand whether any partial correlations are driven primarily by mean differences in severity (correlations tend to be inflated in extreme groups designs due to the absence of observation in middle of scales forming each bivariate distribution). I would have found these exploratory analyses more revealing if group membership was controlled for.

Author response:

The following is the authors’ response to the original reviews

Response to the Editors’ Comments

Thankyou for this summary of the reviews and recommendations for corrections. We respond to each in turn, and have documented each correction with specific examples contained within our response to reviewers below.

‘They all recommend to clarify the link between hypotheses and analyses, ground them more clearly in, and conduct critical comparisons with existing literature, and address a potential multiple comparison problem.’

We have restructured our introduction to include the relevant literature outlined by the reviewers, and to be more clearly ground the goals of our model and broader analysis. We have additionally corrected for multiple comparisons within our exploratory associative analyses. We have additionaly sign posted exploratory tests more clearly.

‘Furthermore, R1 also recommends to include a formal external validation of how the model parameters relate to participant behaviour, to correct an unjustified claim of causality between childhood adversity and separation of self, and to clarify role of therapy received by patients.’

We have now tempered our language in the abstract which unintentionally implied causality in the associative analysis between childhood trauma and other-to-self generalisation. To note, in the sense that our models provide causal explanations for behaviour across all three phases of the task, we argue that our model comparison provides some causal evidence for algorithmic biases within the BPD phenotype. We have included further details of the exclusion and inclusion criteria of the BPD participants within the methods.

R2 specifically recommends to clarify, in the introduction, the specific aim of the paper, what is known already, and the approach to addressing it.’

We have more thoroughly outlined the current state of the art concerning behavioural and computational approaches to self insertion and social contagion, in health and within BPD. We have linked these more clearly to the aims of the work.

‘R2 also makes various additional recommendations regarding clarification of missing information about model comparison, fit statistics and group comparison of parameters from different models.’

Our model comparison approach and algorithm are outlined within the original paper for Hierarchical Bayesian Model comparison (Piray et al., 2019). We have outlined the concepts of this approach in the methods. We have now additionally improved clarity by placing descriptions of this approach more obviously in the results, and added points of greater detail in the methods, such as which statistics for comparison we extracted on the group and individual level.

In addition, in response to the need for greater comparison of parameters from different models, we have also hierarchically force-fitted the full suite of models (M1-M4) to all participants. We report all group differences from each model individually – assuming their explanation of the data - in Table S2. We have also demonstrated strong associations between parameters of equivalent meaning from different models to support our claims in Fig S11. Finally, we show minimal distortion to parameter estimates in between-group analysis when models are either fitted hierarchically to the entire population, or group wise (Figure S10).

‘R3 additionally recommends to clarify the clinical and cognitive process relevance of the experiment, and to consider the importance of the Phase 2 findings.’

We have now included greater reference to the assumptions in the social value orientation paradigm we use in the introduction. We have also responded to the specific point about the shift in central tendencies in phase 2 from the BPD group, noting that, while BPD participants do indeed get more relatively competitive vs. CON participants, they remain strikingly neutral with respect to the overall statespace. Importantly, model M4 does not preclude more competitive distributions existing.

‘Critically, they also share a concern about analyzing parameter estimates fit separately to two groups, when the best-fitting model is not shared. They propose to resolve this by considering a model that can encompass the full dynamics of the entire sample.’

We have hierarchically force-fitted the full suite of models (M1-M4) to all participants to allow for comparison between parameters within each model assumption. We report all group differences from each model individually – assuming their explanation of the data - in Table S2 and Table S3. We have also demonstrated strong associations between parameters of equivalent meaning from different models to support our claims in Fig S11. We also show minimal distortion to parameter estimates in between-group analysis when models are either fitted hierarchically to the entire population, or group wise (Figure S10).

Within model M1 and M2, the parameters quantify the degree to which participants believe their partner to be different from themselves. Under M1 and M2 model assumptions, BPD participants have meaningfully larger versus CON (Fig S10), which supports the notion that a new central tendency may be more parsimonious in phase 2 (as in the case of the optimal model for BPD, M4). We also show strong correlations across models between under M1 and M2, and the shift in central tendenices of beliefs between phase 1 and 2 under M3 and M4. This supports our primary comparison, and shows that even under non-dominant model assumptions, parameters demonstrate that BPD participants expect their partner’s relative reward preferences to be vastly different from themselves versus CON.

‘A final important point concerns the psychometric individual difference analyses which seem to be conducted on the full sample without considering the group structure.’

We have now more clearly focused our psychometric analysis. We control for multiple comparisons, and compare parameters across the same model (M3) when assessing the relationship between paranoia, trauma, trait mentalising, and social contagion. We have relegated all other exploratory analyses to the supplementary material and noted where p values survive correction using False Discovery Rate.

Reviewer 1:

‘The manuscript's primary weakness relates to the number of comparisons conducted and a lack of clarity in how those comparisons relate to the authors' hypotheses. The authors specify a primary prediction about disruption to information generalization in social decision making & learning processes, and it is clear from the text how their 4 main models are supposed to test this hypothesis. With regards to any further analyses however (such as the correlations between multiple clinical scales and eight different model parameters, but also individual parameter comparisons between groups), this is less clear. I recommend the authors clearly link each test to a hypothesis by specifying, for each analysis, what their specific expectations for conducted comparisons are, so a reader can assess whether the results are/aren't in line with predictions. The number of conducted tests relating to a specific hypothesis also determines whether multiple comparison corrections are warranted or not. If comparisons are exploratory in nature, this should be explicitly stated.’

We have now corrected for multiple comparisons when examining the relationship between psychometric findings and parameters, using partial correlations and bootstrapping for robustness. These latter analyses were indeed not preregistered, and so we have more clearly signposted that these tests were exploratory. We chose to focus on the influence of psychometrics of interest on social contagion under model M3 given that this model explained a reasonable minority of behaviour in each group. We have now fully edited this section in the main text in response, and relegated all other correlations to the supplementary materials.

‘Furthermore, the authors present some measures for external validation of the models, including comparison between reaction times and belief shifts, and correlations between model predicted accuracy and behavioural accuracy/total scores. However it would be great to see some more formal external validation of how the model parameters relate to participant behaviour, e.g., the correlation between the number of pro-social choices and ß-values, or the correlation between the change in absolute number of pro-social choices and the change in ß. From comparing the behavioural and computational results it looks like they would correlate highly, but it would be nice to see this formally confirmed.’

We have included this further examination within the Generative Accuracy and Recovery section:

‘We also assessed the relationship (Pearson rs) between modelled participant preference parameters in phase 1 and actual choice behaviour: was negatively correlated with prosocial versus competitive choices (r=-0.77, p<0.001) and individualistic versus competitive choices (r=-0.59, p<0.001); was positively correlated with individualistic versus competitive choices (r=0.53, p<0.001) and negatively correlated with prosocial versus individualistic choices (r=-0.69, p<0.001).’

‘The statement in the abstract that 'Overall, the findings provide a clear explanation of how self-other generalisation constrains and assists learning, how childhood adversity disrupts this through separation of internalised beliefs' makes an unjustified claim of causality between childhood adversity and separation of self - and other beliefs, although the authors only present correlations. I recommend this should be rephrased to reflect the correlational nature of the results.’

Sorry – this was unfortunate wording: we did not intend to imply causation with our second clause in the sentence mentioned. We have amended the language to make it clear this relationship is associative:

‘Overall, the findings provide a clear explanation of how self-other generalisation constrains and assists learning, how childhood adversity is associated with separation of internalised beliefs, and makes clear causal predictions about the mechanisms of social information generalisation under uncertainty.’

‘Currently, from the discussion the findings seem relevant in explaining certain aberrant social learning and -decision making processes in BPD. However, I would like to see a more thorough discussion about the practical relevance of their findings in light of their observation of comparable prediction accuracy between the two groups.’

We have included a new paragraph in the discussion to address this:

‘Notably, despite differing strategies, those with BPD achieved similar accuracy to CON participants in predicting their partners. All participants were more concerned with relative versus absolute reward; only those with BPD changed their strategy based on this focus. Practically this difference in BPD is captured either through disintegrated priors with a new median (M4) or very noisy, but integrated priors over partners (M1) if we assume M1 can account for the full population. In either case, the algorithm underlying the computational goal for BPD participants is far higher in entropy and emphasises a less stable or reliable process of inference. In future work, it would be important to assess this mechanism alongside momentary assessments of mood to understand whether more entropic learning processes contribute to distressing mood fluctuation.’

‘Relatedly, the authors mention that a primary focus of mentalization based therapy for BPD is 'restoring a stable sense of self' and 'differentiating the self from the other'. These goals are very reminiscent of the findings of the current study that individuals with BPD show lower uncertainty over their own and relative reward preferences, and that they are less susceptible to social contagion. Could the observed group differences therefore be a result of therapy rather than adverse early life experiences?’

This is something that we wish to explore in further work. While verbal and model descriptions appear parsimonious, this is not straight forward. As we see, clinical observation and phenomenological dynamics may not necessarily match in an intuitive way to parameters of interest. It may be that compartmentalisation of self and other – as we see in BPD participants within our data – may counter-intuitively express as a less stable self. The evolutionary mechanisms that make social insertion and contagion enduring may also be the same that foster trust and learning.

‘Regarding partner similarity: It was unclear to me why the authors chose partners that were 50% similar when it would be at least equally interesting to investigate self-insertion and social contagion with those that are more than 50% different to ourselves? Do the authors have any assumptions or even data that shows the results still hold for situations with lower than 50% similarity?’

While our task algorithm had a high probability to match individuals who were approximately 50% different with respect to their observed behaviour, there was variation either side of this value. The value of 50% median difference was chosen for two reasons: 1. We wanted to ensure participants had to learn about their partner to some degree relative to their own preferences and 2. we did not want to induce extreme over or under familiarity given the (now replicated) relationship between participant-partner similarity and intentional attributions (see below). Nevertheless, we did have some variation around the 50% median. Figure 3A in the top left panel demonstrates this fluctuation in participant-partner similarity and the figure legend further described this distribution (mean = 49%, sd = 12%). In future work we want to more closely manipulate the median similarity between participants and partners to understand how this facilitates or inhibits learning and generalisation.

There is some analysis of the relationship between degrees of similiarity and behaviour. In the third paragraph of page 15 we report the influence of participant-partner similarity on reaction times. In prior work (Barnby et al., 2022; Cognition) we had shown that similarity was associated with reduced attributions of harm about a partner, irrespective of their true parameters (e.g. whether they were prosocial/competitive). We replicate this previous finding with a double dissociation illustrated in Figure 4, showing that greater discrepancies in participant-partner prosociality increases explicit harmful intent attributions (but not self-interest), and discrepancies in participant-partner individualism reduces explicit self-interest attributions (but not harmful intent). We have made these clearer in our results structure, and included FDR correction values for multiple comparisons.

The methods section is rather dense and at least I found it difficult to keep track of the many different findings. I recommend the authors reduce the density by moving some of the secondary analyses in the supplementary materials, or alternatively, to provide an overall summary of all presented findings at the end of the Results section.

We have now moved several of our exploratory findings into the supplementary materials, noteably the analysis of participant-partner similarity on reaction times (Fig S9), as well as the uncorrected correlation between parameters (Fig S7).

Fig 2C) and Discussion p. 21: What do the authors mean by 'more sensitive updates'? more sensitive to what?

We have now edited the wording to specify ‘more belief updating’ rather than ‘sensitive’ to be clearer in our language.

P14 bottom: please specify what is meant by axial differences.

We have changed this to ‘preference type’ rather than using the term ‘axial’.

It may be helpful to have Supplementary Figure 1 in the main text.

Thank you for this suggestion. Given the volume of information in the main text we hope that it is acceptable for Figure S1 to remain in the supplementary materials.

Figure 3D bottom panel: what is the difference between left and right plots? Should one of them be alpha not beta?

The left and right plots are of the change in standard deviation (left) and central tendency (right) of participant preference change between phase 1 and 3. This is currently noted in the figure legend, but we had added some text to be clearer that this is over prosocial-competitive beliefs specifically. We chose to use this belief as an example given the centrality of prosocial-comeptitive beliefs in the learning process in Figure 2. We also noticed a small labelling error in the bottom panels of 3D which should have noted that each plot was either with respect to the precision or mean-shift in beliefs during phase 3.

‘The relationship between uncertainty over the self and uncertainty over the other with respect to the change in the precision (left) and median-shift (right) in phase 3 prosocial-competitive beliefs .’

Supplementary Figure 4: The prior presented does not look neutral to me, but rather right-leaning, so competitive, and therefore does indeed look like it was influenced by the self-model? If I am mistaken please could the authors explain why.

This example distribution is taken from a single BPD participant. In this case, indeed, the prior is somewhat right-shifted. However, on a group level, priors over the partner were closely centred around 0 (see reported statistics in paragraph 2 under the heading ‘Phase 2 – BPD Participants Use Disintegrated and Neutral Priors). However, we understand how this may come across as misleading. For clarity we have expanded upon Figure S4 to include the phase 1 and prior phase 2 distributions for the entire BPD population for both prosocial and individualistic beliefs. This further demonstrates that those with BPD held surprisingly neutral beliefs over the expectations about their partners’ prosociality, but had minor shifts between their own individualistic preferences and the expected individualistic preferences of their partners. This is also visible in Figure S2.

Reviewer 2:

‘There are two major weaknesses. First, the paper lacks focus and clarity. The introduction is rather vague and, after reading it, I remained confused about the paper's aims. Rather than relying on specific predictions, the analysis is exploratory. This implies that it is hard to keep track, and to understand the significance, of the many findings that are reported.’

Thank you for this opportunity to be clearer in our framing of the paper. While the model makes specific causal predictions with respect to behavioural dynamics conditional on algorithmic differences, our other analyses were indeed exploratory. We did not preregister this work but now given the intriguing findings we intent to preregister our future analyses.

We have made our introduction clearer with respect to the aims of the paper:

‘Our present work sought to achieve two primary goals: 1. Extend prior causal computational theories to formalise the interrelation between self-insertion and social contagion within an economic paradigm, the Intentions Game and 2., Test how a diagnosis of BPD may relate to deficits in these forms of generalisation. We propose a computational theory with testable predictions to begin addressing this question. To foreshadow our results, we found that healthy participants employ a mixed process of self-insertion and contagion to predict and align with the beliefs of their partners. In contrast, individuals with BPD exhibit distinct, disintegrated representations of self and other, despite showing similar average accuracy in their learning about partners. Our model and data suggest that the previously observed computational characteristics in BPD, such as reduced self-anchoring during ambiguous learning and a relative impermeability of the self, arise from the failure of information about others to transfer to and inform the self. By integrating separate computational findings, we provide a foundational model and a concise, dynamic paradigm to investigate uncertainty, generalization, and regulation in social interactions.’

‘Second, although the computational approach employed is clever and sophisticated, there is important information missing about model comparison which ultimately makes some of the results hard to assess from the perspective of the reader.’

Our model comparison employed what is state of the art random-effects Bayesian model comparison (Piray et al., 2019; PLOS Comp. Biol.). It initially fits each individual to each model using Laplace approximation, and subsequently ‘races’ each model against each other on the group level and individual level through hierarchical constraints and random-effect considerations. We included this in the methods but have now expanded on the descrpition we used to compare models:

In the results -

‘All computational models were fitted using a Hierarchical Bayesian Inference (HBI) algorithm which allows hierarchical parameter estimation while assuming random effects for group and individual model responsibility (Piray et al., 2019; see Methods for more information). We report individual and group-level model responsibility, in addition to protected exceedance probabilities between-groups to assess model dominance.’

We added to our existing description in the methods –

‘All computational models were fitted using a Hierarchical Bayesian Inference (HBI) algorithm which allows hierarchical parameter estimation while assuming random effects for group and individual model responsibility (Piray et al., 2019). During fitting we added a small noise floor to distributions (2.22e^-16) before normalisation for numerical stability. Parameters were estimated using the HBI in untransformed space drawing from broad priors (μM\=0, σ²_M = 6.5; where M\={M1, M2, M3, M4}). This process was run independently for each group. Parameters were transformed into model-relevant space for analysis. All models and hierarchical fitting was implemented in Matlab (Version R2022B). All other analyses were conducted in R (version 4.3.3; arm64 build) running on Mac OS (Ventura 13.0). We extracted individual and group level responsibilities, as well as the protected exceedance probability to assess model dominance per group.’

(1) P3, third paragraph: please define self-insertion

We have now more clearly defined this in the prior paragraph when introducing concepts.

‘To reduce uncertainty about others, theories of the relational self (Anderson & Chen, 2002) suggest that people have availble to them an extensive and well-grounded representation of themselves, leading to a readily accessible initial belief (Allport, 1924; Kreuger & Clement, 1994) that can be projected or integrated when learning about others (self-insertion).’

(2) Introduction: the specific aim of the paper should be clarified - at the moment, it is rather vague. The authors write: "However, critical questions remain: How do humans adjudicate between self-insertion and contagion during interaction to manage interpersonal generalization? Does the uncertainty in self-other beliefs affect their generalizability? How can disruptions in interpersonal exchange during sensitive developmental periods (e.g., childhood maltreatment) inform models of psychiatric disorders?". Which of these questions is the focus of the paper? And how does the paper aim at addressing it?

(3) Relatedly, from the introduction it is not clear whether the goal is to develop a theory of self-insertion and social contagion and test it empirically, or whether it is to study these processes in BPD, or both (or something else). Clarifying which specific question(s) is addressed is important (also clarifying what we already know about that specific question, and how the paper aims at elucidating that specific question).

We have now included our specific aims of the paper. We note this in the above response to the reviwers general comments.

(4) "Computational models have probed social processes in BPD, linking the BPD phenotype to a potential over-reliance on social versus internal cues (Henco et al., 2020), 'splitting' of social latent states that encode beliefs about others (Story et al., 2023), negative appraisal of interpersonal experiences with heightened self-blame (Mancinelli et al., 2024), inaccurate inferences about others' irritability (Hula et al., 2018), and reduced belief adaptation in social learning contexts (Siegel et al., 2020). Previous studies have typically overlooked how self and other are represented in tandem, prompting further investigation into why any of these BPD phenotypes manifest." Not clear what the link between the first and second sentence is. Does it mean that previous computational models have focused exclusively on how other people are represented in BPD, and not on how the self is represented? Please spell this out.

Thank you for the opportunity to be clearer in our language. We have now spelled out our point more precisely, and included some extra relevant literature helpfully pointed out by another reviewer.

‘Computational models have probed social processes in BPD, although almost exclusively during observational learning. The BPD phenotype has been associated with a potential over-reliance on social versus internal cues (Henco et al., 2020), ‘splitting’ of social latent states that encode beliefs about others (Story et al., 2023), negative appraisal of interpersonal experiences with heightened self-blame (Mancinelli et al., 2024), inaccurate inferences about others’ irritability (Hula et al., 2018), and reduced belief adaptation in social learning contexts (Siegel et al., 2020). Associative models have also been adapted to characterize  ‘leaky’ self-other reinforcement learning (Ereira et al., 2018), finding that those with BPD overgeneralize (leak updates) about themselves to others (Story et al., 2024). Altogether, there is currently a gap in the direct causal link between insertion, contagion, and learning (in)stability.’

(5) P5, first paragraph. The description of the task used in phase 1 should be more detailed. The essential information for understanding the task is missing.

We have updated this section to point toward Figure 1 and the Methods where the details of the task are more clearly outlined. We hope that it is acceptable not to explain the full task at this point for brevity and to not interrupt the flow of the results.

“Detailed descriptions of the task can be found in the methods section and Figure 1.’

(6) P5, second paragraph: briefly state how the Psychometric data were acquired (e.g., self-report).

We have now clarified this in the text.

‘All participants also self-reported their trait paranoia, childhood trauma, trust beliefs, and trait mentalizing (see methods).’

(7) "For example, a participant could make prosocial (self=5; other=5) versus individualistic (self=10; other=5) choices, or prosocial (self=10; other=10) versus competitive (self=10; other=5) choices". Not sure what criteria are used for distinguishing between individualistic and competitive - they look the same?

Sorry. This paragraph was not clear that the issue is that the interpretation of the choice depends on both members of the pair of options. Here, in one pair {(self=5,other=5) vs (self=10,other=5)}, it is highly pro-social for the self to choose (5,5), sacrificing 5 points for the sake of equality. In the second pair {(self=10,other=10) vs (self=10,other=5)}, it is highly competitive to choose (10,5), denying the other 5 points at no benefit to the self. We have clarified this:

‘We analyzed the ‘types’ of choices participants made in each phase (Supplementary Table 1). The interpretation of a participant’s choice depends on both values in a choice. For example, a participant could make prosocial (self=5; other=5) versus individualistic (self=10; other=5) choices, or prosocial (self=10; other=10) versus competitive (self=10; other=5) choices. There were 12 of each pair in phases 1 and 3 (individualistic vs. prosocial; prosocial vs. competitive; individualistic vs. competitive).’  

(8) "In phase 1, both CON and BPD participants made prosocial choices over competitive choices with similar frequency (CON=9.67[3.62]; BPD=9.60[3.57])" please report t-test - the same applies also various times below.

We have now included the t test statistics with each instance.

‘In phase 3, both CON and BPD participants continued to make equally frequent prosocial versus competitive choices (CON=9.15[3.91]; BPD=9.38[3.31]; t=-0.54, p=0.59); CON participants continued to make significantly less prosocial versus individualistic choices (CON=2.03[3.45]; BPD=3.78 [4.16]; t=2.31, p=0.02). Both groups chose equally frequent individualistic versus competitive choices (CON=10.91[2.40]; BPD=10.18[2.72]; t=-0.49, p=0.62).’

(9) P 9: "Models M2 and M3 allow for either self-insertion or social contagion to occur independently" what's the difference between M2 and M3?

Model M2 hypothesises that participants use their own self representation as priors when learning about the other in phase 2, but are not influenced by their partner. M3 hypothesises that participants form an uncoupled prior (no self-insertion) about their partner in phase 2, and their choices in phase 3 are influenced by observing their partner in phase 2 (social contagion). In Figure 1 we illustrate the difference between M2 and M3. In Table 1 we specifically report the parameterisation differences between M2 and M3. We have also now included a correlational analysis of parameters between models to demonstrate the relationship between model parameters of equivalent value between models (Fig S11). We have also force fitted all models (M1-M4) to the data independently and reported group differences within each (see Table S2 and Table S3).

(10) P 9, last paragraph: I did not understand the description of the Beta model.

The beta model is outlined in detail in Table 1. We have also clarified the description of the beta model on page 9:

‘The ‘Beta model’ is equivalent to M1 in its causal architecture (both self-insertion and social contagion are hypothesized to occur) but differs in richness: it accommodates the possibility that participants might only consider a single dimension of relative reward allocation, which is typically emphasized in previous studies (e.g., Hula et al., 2018).’

(11) P 9: I wonder whether one could think about more intuitive labels for the models, rather than M1, M2 etc.. This is just a suggestion, as I am not sure a short label would be feasible here.

Thank you for this suggestion. We apologise that it is not very intitutive. The problem is that given the various terms we use to explain the different processes of generalisation that might occur between self and other, and given that each model is a different combination of each, we felt that numbering them was a lesser evil. We hope that the reader will be able to reference both Figure 1 and Table 1 to get a good feel for how the models and their causal implications differ.

(12) Model comparison: the information about what was done for model comparison is scant, and little about fit statistics is reported. At the moment, it is hard for a reader to assess the results of the model comparison analysis.

Model comparison and fitting was conducted using simultaneous hierarchical fitting and random-effects comparison. This is employed through the HBI package (Piray et al., 2019) where the assumptions and fitting proceedures are outlined in great detail. In short, our comparison allows for individual and group-level hierarchical fitting and comparison. This overcomes the issue of interdependence between and within model fitting within a population, which is often estimated separately.

We have outlined this in the methods, although appreciate we do not touch upon it until the reader reaches that point. We have added a clarification statement on page 9 to rectify this:

‘All computational models were fitted using a Hierarchical Bayesian Inference (HBI) algorithm which allows hierarchical parameter estimation while assuming random effects for group and individual model responsibility (Piray et al., 2019; see Methods for more information). We report individual and group-level model responsibility, in addition to protected exceedance probabilities between-groups to assess model dominance.’

(13) P 14, first paragraph: "BPD participants were also more certain about both types of preference" what are the two types of preferences?

The two types of preferences are relative (prosocial-competitive) and absolute (individualistic) reward utility. These are expressed as b and a respectively. We have expanded the sentence in question to make this clearer:

‘BPD participants were also more certain about both self-preferences for absolute and relative reward ( = -0.89, 95%HDI: -1.01, -0.75; = -0.32, 95%HDI: -0.60, -0.04) versus CON participants (Figure 2B).’

(14) "Parameter Associations with Reported Trauma, Paranoia, and Attributed Intent" the results reported here are intriguing, but not fully convincing as there is the problem of multiple comparisons. The combinations between parameters and scales are rather numerous. I suggest to correct for multiple comparisons and to flag only the findings that survive correction.

We have now corrected this and controlled for multiple comparisons through partial correlation analysis, bootstrapping assessment for robustness, permutation testing, and False Detection Rate correction. We only report those that survive bootstrapping and permutation testing, reporting both corrected (p[fdr]) and uncorrected (p) significance.

(15) Results page 14 and page 15. The authors compare the various parameters between groups. I would assume that these parameters come from M1 for controls and from M4 for BDP? Please clarify if this is indeed the case. If it is the case, I am not sure this is appropriate. To my knowledge, it is appropriate to compare parameters between groups only if the same model is fit to both groups. If two different models are fit to each group, then the parameters are not comparable, as the parameter have, so to speak, different "meaning" in two models. Now, I want to stress that my knowledge on this matter may be limited, and that the authors' approach may be sound. However, to be reassured that the approach is indeed sound, I would appreciate a clarification on this point and a reference to relevant sources about this approach.

This is an important point. First, we confirmed all our main conclusions about parameter differences using the maximal model M1 to fit all the participants. We added Supplementary Table 2 to report the outcome of this analysis. Second, we did the same for parameters across all models M1-M4, fitting each to participants without comparison. This is particularly relevant for M3, since at least a minority of participants of both groups were best explained by this model. We report these analyses in Fig S11:

Since the M4 is nested within M1, we argue that this comparison is still meaningful, and note explanations in the text for why the effects noted between groups may occur given the differences in their causal meaning, for example in the results under phase 2 analyses:

‘Belief updating in phase 2 was less flexible in BPD participants. Median change in beliefs (from priors to posteriors) about a partner’s preferences was lower versus. CON ( = -5.53, 95%HDI: -7.20, -4.00; = -10.02, 95%HDI: -12.81, -7.30). Posterior beliefs about partner were more precise in BPD versus CON ( = -0.94, 95%HDI: -1.50, -0.45;  = -0.70, 95%HDI: -1.20, -0.25).  This is unsurprising given the disintegrated priors of the BPD group in M4, meaning they need to ‘travel less’ in state space. Nevertheless, even under assumptions of M1 and M2 for both groups, BPD showed smaller posteriors median changes versus CON in phase 2 (see Table T2). These results converge to suggest those with BPD form rigid posterior beliefs.’

(16) "We built and tested a theory of interpersonal generalization in a population of matched participants" this sentence seems to be unwarranted, as there is no theory in the paper (actually, as it is now, the paper looks rather exploratory)

We thank the reviewer for their perspective. Formal models can be used as a theoretical statement on the casual algorithmic process underlying decision making and choice behaviour; the development of formal models are an essential theoretical tool for precision and falsification (Haslbeck et al., 2022). In this sense, we have built several competing formal theories that test, using casual architectures, whether the latent distribution(s) that generate one’s choices generalise into one’s predictions about another person, and simultaneously whether one’s latent distribution(s) that represent beliefs about another person are used to inform future choices.

Reviewer 3:

‘My broad question about the experiment (in terms of its clinical and cognitive process relevance): Does the task encourage competition or give participants a reason to take advantage of others? I don't think it does, so it would be useful to clarify the normative account for prosociality in the introduction (e.g., some of Robin Dunbar's work).’

We agree that our paradigm does not encourage competition. We use a reward structure that makes it contingent on participants to overcome a particular threshold before earning rewards, but there is no competitive element to this, in that points earned or not earned by partners have no bearing on the outcomes for the participant. This is important given the consideration of recursive properties that arise through mixed-motive games; we wanted to focus purely on observational learning in phase 2, and repercussion-free choices made by participants in phase 1 and 3, meaning the choices participants, and decisions of a partner, are theoretically in line with self-preferences irrespective of the judgement of others. We have included a clearer statement of the structure of this type of task, and more clearly cited the origin for its structure (Murphy & Ackerman, 2011):

‘Our present work sought to achieve two primary goals. 1. Extend prior causal computational theories to formalise and test the interrelation between self-insertion and social contagion on learning and behaviour to better probe interpersonal generalisation in health, and 2., Test whether previous computational findings of social learning changes in BPD can be explained by infractions to self-other generalisation. We accomplish these goals by using a dynamic, sequential social value economic paradigm, the Intentions Game, building upon a Social Value Orientation Framework (Murphy & Ackerman, 2011) that assumes motivational variation in joint reward allocation.’

Given the introductions structure as it stands, we felt providing another paragraph on the normative assumptions of such a game was outside the scope of this article.

‘The finding that individuals with BPD do not engage in self-other generalization on this task of social intentions is novel and potentially clinically relevant. The authors find that BPD participants' tendency to be prosocial when splitting points with a partner does not transfer into their expectations of how a partner will treat them in a task where they are the passive recipient of points chosen by the partner. In the discussion, the authors reasonably focus on model differences between groups (Bayesian model comparison), yet I thought this finding -- BPD participants not assuming prosocial tendencies in phase 2 while CON participant did -- merited greater attention. Although the BPD group was close to 0 on the \beta prior in Phase 2, their difference from CON is still in the direction of being more mistrustful (or at least not assuming prosociality). This may line up with broader clinical literature on mistrustfulness and attributions of malevolence in the BPD literature (e.g., a 1992 paper by Nigg et al. in Journal of Abnormal Psychology). My broad point is to consider further the Phase 2 findings in terms of the clinical interpretation of the shift in \beta relative to controls.’

This is an important point, that we contextualize within the parameterisation of our utility model. While the shift toward 0 in the BPD participants is indeed more competitive, as the reviewer notes, it is surprisingly centred closely around 0, with only a slight bias to be prosocial (mean = -0.47;  = -6.10, 95%HDI: -7.60, -4.60). Charitably we might argue that BPD participants are expecting more competitive preferences from their partner. However even so, given their variance around their priors in phase 2, they are uncertain or unconfident about this. We take a more conservative approach in the paper and say that given the tight proximity to 0 and the variance of their group priors, they are likely to be ‘hedging their bets’ on whether their partner is going to be prosocial or competitive. While the movement from phase 1 to 2 is indeed in the competitive direction it still lands in neutral territory. Model M4 does not preclude central tendancies at the start of Phase 2 being more in the competitive direction.

‘First, the authors note that they have "proposed a theory with testable predictions" (p. 4 but also elsewhere) but they do not state any clear predictions in the introduction, nor do they consider what sort of patterns will be observed in the BPD group in view of extant clinical and computational literature. Rather, the paper seems to be somewhat exploratory, largely looking at group differences (BPD vs. CON) on all of the shared computational parameters and additional indices such as belief updating and reaction times. Given this, I would suggest that the authors make stronger connections between extant research on intention representation in BPD and their framework (model and paradigm). In particular, the authors do not address related findings from Ereira (2020) and Story (2024) finding that in a false belief task that BPD participants *overgeneralize* from self to other. A critical comparison of this work to the present study, including an examination of the two tasks differ in the processes they measure, is important.’

Thank you for this opportunity to include more of the important work that has preceded the present manuscript. Prior work has tended to focus on either descriptive explanations of self-other generalisation (e.g. through the use of RW type models) or has focused on observational learning instability in absence of a causal model from where initial self-other beliefs may arise. While the prior work cited by the reviewer [Ereira (2020; Nat. Comms.) and Story (2024; Trans. Psych.)] does examine the inter-trial updating between self-other, it does not integrate a self model into a self’s belief about an other prior to observation. Rather, it focuses almost exclusively on prediction error ‘leakage’ generated during learning about individual reward (i.e. one sided reward). These findings are important, but lie in a slightly different domain. They also do not cut against ours, and in fact, we argue in the discussion that the sort of learning instability described above and splitting (as we cite from Story ea. 2024; Psych. Rev.) may result from a lack of self anchoring typical of CON participants. Nevertheless we agree these works provide an important premise to contrast and set the groundwork for our present analysis and have included them in the framing of our introduction, as well as contrasting them to our data in the discussion.

In the introduction:

‘The BPD phenotype has been associated with a potential over-reliance on social versus internal cues (Henco et al., 2020), ‘splitting’ of social latent states that encode beliefs about others (Story et al., 2023), negative appraisal of interpersonal experiences with heightened self-blame (Mancinelli et al., 2024), inaccurate inferences about others’ irritability (Hula et al., 2018), and reduced belief adaptation in social learning contexts (Siegel et al., 2020). Associative models have also been adapted to characterize  ‘leaky’ self-other reinforcement learning (Ereira et al., 2018), finding that those with BPD overgeneralize (leak updates) about themselves to others (Story et al., 2024). Altogether, there is currently a gap in the direct causal link between insertion, contagion, and learning (in)stability.’

In the discussion:

‘Disruptions in self-to-other generalization provide an explanation for previous computational findings related to task-based mentalizing in BPD. Studies tracking observational mentalizing reveal that individuals with BPD, compared to those without, place greater emphasis on social over internal reward cues when learning (Henco et al., 2020; Fineberg et al., 2018). Those with BPD have been shown to exhibit reduced belief adaptation (Siegel et al., 2020) along with ‘splitting’ of latent social representations (Story et al., 2024a). BPD is also shown to be associated with overgeneralisation in self-to-other belief updates about individual outcomes when using a one-sided reward structure (where participant responses had no bearing on outcomes for the partner; Story et al., 2024b). Our analyses show that those with BPD are equal to controls in their generalisation of absolute reward (outcomes that only affect one player) but disintegrate beliefs about relative reward (outcomes that affect both players) through adoption of a new, neutral belief. We interpret this together in two ways: 1. There is a strong concern about social relativity when those with BPD form beliefs about others, 2. The absence of constrained self-insertion about relative outcomes may predispose to brittle or ‘split’ beliefs. In other words, those with BPD assume ambiguity about the social relativity preferences of another (i.e. how prosocial or punitive) and are quicker to settle on an explanation to resolve this. Although self-insertion may be counter-intuitive to rational belief formation, it has important implications for sustaining adaptive, trusting social bonds via information moderation.’

In addition, perhaps it is fairer to note more explicitly the exploratory nature of this work. Although the analyses are thorough, many of them are not argued for a priori (e.g., rate of belief updating in Figure 2C) and the reader amasses many individual findings that need to by synthesized.’

We have now noted the primary goals of our work in the introduction, and have included caveats about the exploratory nature of our analyses. We would note that our model is in effect a causal combination of prior work cited within the introduction (Barnby et al., 2022; Moutoussis et al., 2016). This renders our computational models in effect a causal theory to test, although we agree that our dissection of the results are exploratory. We have more clearly signposted this:

‘Our present work sought to achieve two primary goals. 1. Extend prior causal computational theories to formalise and test the interrelation between self-insertion and social contagion on learning and behaviour to better probe interpersonal generalisation in health, and 2., Test whether previous computational findings of social learning changes in BPD can be explained by infractions to self-other generalisation. We accomplish these goals by using a dynamic, sequential economic paradigm, the Intentions Game, building upon a Social Value Orientation Framework (Murphy & Ackerman, 2011) that assumes innate motivational variation in joint reward allocation.‘

‘Second, in the discussion, the authors are too quick to generalize to broad clinical phenomena in BPD that are not directly connected to the task at hand. For example, on p. 22: "Those with a diagnosis of BPD also show reduced permeability in generalising from other to self. While prior research has predominantly focused on how those with BPD use information to form impressions, it has not typically examined whether these impressions affect the self." Here, it's not self-representation per se (typically, identity or one's view of oneself), but instead cooperation and prosocial tendencies in an economic context. It is important to clarify what clinical phenomena may be closely related to the task and which are more distal and perhaps should not be approached here.’

Thank you for this important point. We agree that social value orientation, and particularly in this economically-assessed form, is but one aspect of the self, and we did not test any others. A version of the social contagion phenomena is also present in other aspects of the self in intertemporal (Moutoussis et al., 2016), economic (Suzuki et al., 2016) and moral preferences (Yu et al., 2021). It would be most interesting to attempt to correlate the degrees of insertion and contagion across the different tasks.

We take seriously the wider concern that behaviour in our tasks based on economic preferences may not have clinical validity. This issue is central in the whole field of computational psychiatry, much of which is based on generalizing from tasks like ours, and discussing correlations with psychometric measures. We hope that it is acceptable to leave such discussions to the many reviews on computational psychiatry (Montague et al., 2012; Hitchcock et al., 2022; Huys et al., 2016). Here, we have just put a caveat in the dicussion:

‘Finally, a limitation may be that behaviour in tasks based on economic preferences may not have clinical validity. This issue is central to the field of computational psychiatry, much of which is based on generalising from tasks like that within this paper and discussing correlations with psychometric measures. Extrapolating  economic tasks into the real world has been the topic of discussion for the many reviews on computational psychiatry (e.g. Montague et al., 2012; Hitchcock et al., 2022; Huys et al., 2016). We note a strength of this work is the use of model comparison to understand causal algorithmic differences between those with BPD and matched healthy controls. Nevertheless, we wish to further pursue how latent characteristics captured in our models may directly relate to real-world affective change.’

‘On a more technical level, I had two primary concerns. First, although the authors consider alternative models within a hierarchical Bayesian framework, some challenges arise when one analyzes parameter estimates fit separately to two groups, particularly when the best-fitting model is not shared. In particular, although the authors conduct a model confusion analysis, they do not as far I could tell (and apologies if I missed it) demonstrate that the dynamics of one model are nested within the other. Given that M4 has free parameters governing the expectations on the absolute and relative reward preferences in Phase 2, is it necessarily the case that the shared parameters between M1 and M4 can be interpreted on the same scale? Relatedly, group-specific model fitting has virtues when believes there to be two distinct populations, but there is also a risk of overfitting potentially irrelevant sample characteristics when parameters are fit group by group.

To resolve these issues, I saw one straightforward solution (though in modeling, my experience is that what seems straightforward on first glance may not be so upon further investigation). M1 assumes that participants' own preferences (posterior central tendency) in Phase 1 directly transfer to priors in Phase 2, but presumably the degree of transfer could vary somewhat without meriting an entirely new model (i.e., the authors currently place this question in terms of model selection, not within-model parameter variation). I would suggest that the authors consider a model parameterization fit to the full dataset (both groups) that contains free parameters capturing the *deviations* in the priors relative to the preceding phase's posterior. That is, the free parameters $\bar{\alpha}_{par}^m$ and $\bar{\beta}_{par}^m$ govern the central tendency of the Phase 2 prior parameter distributions directly, but could be reparametrized as deviations from Phase 1 $\theta^m_{ppt}$ parameters in an additive form. This allows for a single model to be fit all participants that encompasses the dynamics of interest such that between-group parameter comparisons are not biased by the strong assumptions imposed by M1 (that phase 1 preferences and phase 2 observations directly transfer to priors). In the case of controls, we would expect these deviation parameters to be centred on 0 insofar as the current M1 fit them best, whereas for BPD participants should have significant deviations from earlier-phase posteriors (e.g., the shift in \beta toward prior neutrality in phase 2 compared to one's own prosociality in phase 1). I think it's still valid for the authors to argue for stronger model constraints for Bayesian model comparison, as they do now, but inferences regarding parameter estimates should ideally be based on a model that can encompass the full dynamics of the entire sample, with simpler dynamics (like posterior -> prior transfer) being captured by near-zero parameter estimates.’

Thank you for the chance to be clearer in our modelling. In particular, the suggestion to include a model that can be fit to all participants with the equivalent of the likes of partial social insertion, to check if the results stand, can actually be accomplished through our existing models.  That is, the parameter that governs the flexibility over beliefs in phase 2 under models M1 (dominant for CON participant) and M2 parameterises the degree to which participants think their partner may be different from themselves. Thus, forcibly fitting M1 and M2 hierarchically to all participants, and then separately to BPD and CON participants, can quantify the issue raised: if BPD participants indeed distinguish partners as vastly different from themselves enough to warent a new central tendency, should be quantitively higher in BPD vs CON participants under M1 and M2.

We therefore tested this, reporting the distributional differences between for BPD and CON participants under M1, both when fitted together as a population and as separate groups. As is higher for BPD participants under both conditions for M1 and M2 it supports our claim and will add more context for the comparison - may be large enough in BPD that a new central tendency to anchor beliefs is a more parsimonious explanation.

We cross checked this result by assessing the discrepancy between the participant’s and assumed partner’s central tendencies for both prosocial and individualistic preferences via best-fitting model M4 for the BPD group. We thereby examined whether belief disintegration is uniform across preferences (relative vs abolsute reward) or whether one tendency was shifted dramatically more than another.  We found that beliefs over prosocial-competitive preferences were dramatically shifted, whereas those over individualistic preferences were not.

We have added the following to the main text results to explain this:

Model Comparison:

‘We found that CON participants were best fit at the group level by M1 (Frequency = 0.59, Protected Exceedance Probability = 0.98), whereas BPD participants were best fit by M4 (Frequency = 0.54, Protected Exceedance Probability = 0.86; Figure 2A). We first analyse the results of these separate fits. Later, in order to assuage concerns about drawing inferences from different models, we examined the relationships between the relevant parameters when we forced all participants to be fit to each of the models (in a hierarchical manner, separated by group). In sum, our model comparison is supported by convergence in parameter values when comparisons are meaningful. We refer to both types of analysis below.’

Phase 1:

‘These differences were replicated when considering parameters between groups when we fit all participants to the same models (M1-M4; see Table S2).’

Phase 2:

‘To check that these conclusions about self-insertion did not depend on the different models, we found that only under M1 and M2 were consistently larger in BPD versus CON. This supports the notion that new central tendencies for BPD participants in phase 2 were required, driven by expectations about a partner’s relative reward. (see Fig S10 & Table S2). and parameters under assumptions of M1 and M2 were strongly correlated with median change in belief between phase 1 and 2 under M3 and M4, suggesting convergence in outcome (Fig S11).’

‘Furthermore, even under assumptions of M1-M4 for both groups, BPD showed smaller posterior median changes versus CON in phase 2 (see Table T2). These results converge to suggest those with BPD form rigid posterior beliefs.’

‘Assessing this same relationship under M1- and M2-only assumptions reveals a replication of this group effect for absolute reward, but the effect is reversed for relative reward (see Table S3). This accords with the context of each model, where under M1 and M2, BPD participants had larger phase 2 prior flexibility over relative reward (leading to larger initial surprise), which was better accounted for by a new central tendency under M4 during model comparison. When comparing both groups under M1-M4 informational surprise over absolute reward was consistently restricted in BPD (Table S3), suggesting a diminished weight of this preference when forming beliefs about an other.’

Phase 3

‘In the dominant model for the BPD group—M4—participants are not influenced in their phase 3 choices following exposure to their partner in phase 2. To further confirm this we also analysed absolute change in median participant beliefs between phase 1 and 3 under the assumption that M1 and M3 was the dominant model for both groups (that allow for contagion to occur). This analysis aligns with our primary model comparison using M1 for CON and M4 for BPD  (Figure 2C). CON participants altered their median beliefs between phase 1 and 3 more than BPD participants (M1: linear estimate = 0.67, 95%CI: 0.16, 1.19; t = 2.57, p = 0.011; M3: linear estimate = 1.75, 95%CI: 0.73, 2.79; t = 3.36, p < 0.001). Relative reward was overall more susceptible to contagion versus absolute reward (M1: linear estimate = 1.40, 95%CI: 0.88, 1.92; t = 5.34, p<0.001; M3: linear estimate = 2.60, 95%CI: 1.57, 3.63; t = 4.98, p < 0.001). There was an interaction between group and belief type under M3 but not M1 (M3: linear estimate = 2.13, 95%CI: 0.09, 4.18, t = 2.06, p=0.041). There was only a main effect of belief type on precision under M3 (linear estimate = 0.47, 95%CI: 0.07, 0.87, t = 2.34, p = 0.02); relative reward preferences became more precise across the board. Derived model estimates of preference change between phase 1 and 3 strongly correlated between M1 and M3 along both belief types (see Table S2 and Fig S11).’

‘My second concern pertains to the psychometric individual difference analyses. These were not clearly justified in the introduction, though I agree that they could offer potentially meaningful insight into which scales may be most related to model parameters of interest. So, perhaps these should be earmarked as exploratory and/or more clearly argued for. Crucially, however, these analyses appear to have been conducted on the full sample without considering the group structure. Indeed, many of the scales on which there are sizable group differences are also those that show correlations with psychometric scales. So, in essence, it is unclear whether most of these analyses are simply recapitulating the between-group tests reported earlier in the paper or offer additional insights. I think it's hard to have one's cake and eat it, too, in this regard and would suggest the authors review Preacher et al. 2005, Psychological Methods for additional detail. One solution might be to always include group as a binary covariate in the symptom dimension-parameter analyses, essentially partialing the correlations for group status. I remain skeptical regarding whether there is additional signal in these analyses, but such controls could convince the reader. Nevertheless, without such adjustments, I would caution against any transdiagnostic interpretations such as this one in the Highlights: "Higher reported childhood trauma, paranoia, and poorer trait mentalizing all diminish other-to-self information transfer irrespective of diagnosis." Since many of these analyses relate to scales on which the groups differ, the transdiagnostic relevance remains to be demonstrated.’

We have restructured the psychometric section to ensure transparency and clarity in our analysis. Namely, in response to these comments and those of the other reviewers, we have opted to remove the parameter analyses that aimed to cross-correlate psychometric scores with latent parameters from different models: as the reviewer points out, we do not have parity between dominant models for each group to warrant this, and fitting the same model to both groups artificially makes the parameters qualitatively different. Instead we have opted to focus on social contagion, or rather restrictions on , between phases 1 and 3 explained by M3. This provides us with an opportunity to examine social contagion on the whole population level isolated from self-insertion biases. We performed bootstrapping (1000 reps) and permutation testing (1000 reps) to assess the stability and significance of each edge in the partial correlation network, and then applied FDR correction (p[fdr]), thus controlling for multiple comparisons. We note that while we focused on M3 to isolate the effect across the population, social contagion across both relative and absolute reward under M3 strongly correlated with social contagion under M1 (see Fig S11).

‘We explored whether social contagion may be restricted as a result of trauma, paranoia, and less effective trait mentalizing under the assumption of M3 for all participants (where everyone is able to be influenced by their partner). To note, social contagion under M3 was highly correlated with contagion under M1 (see Fig S11). We conducted partial correlation analysis to estimate relationships conditional on all other associations and retained all that survived bootstrapping (1000 reps), permutation testing (1000 reps), and subsequent FDR correction. Persecution and CTQ scores were both moderately associated with MZQ scores (RGPTSB r = 0.41, 95%CI: 0.23, 0.60, p = 0.004, p[fdr]=0.043; CTQ r = 0.354 95%CI: 0.13, 0.56, p=0.019, p[fdr]=0.02). MZQ scores were in turn moderately and negatively associated with shifts in prosocial-competitive preferences () between phase 1 and 3 (r = -0.26, 95%CI: -0.46, -0.06, p=0.026, p[fdr]=0.043). CTQ scores were also directly and negatively associated with shifts in individualistic preferences (; r = -0.24, 95%CI: -0.44, -0.13, p=0.052, p[fdr]=0.065). This provides some preliminary evidence that trauma impacts beliefs about individualism directly, whereas trauma and persecutory beliefs impact beliefs about prosociality through impaired mentalising (Figure 4A).’

(1) As far as I could tell, the authors didn't provide an explanation of this finding on page 5: "However, CON participants made significantly fewer prosocial choices when individualistic choices were available" While one shouldn't be forced to interpret every finding, the paper is already in that direction and I found this finding to be potentially relevant to the BPD-control comparison.

Thank you for this observation. This sentance reports the fact that CON participants were effectively more selfish than BPD participants. This is captured by the lower value of reported in Figure 2, and suggests that CON participants were more focused on absolute value – acting in a more ‘economically rational’ manner – versus BPD participants. This fits in with our fourth paragraph of the discussion where we discuss prior work that demonstrates a heightened social focus in those with BPD. Indeed, the finding the reviewer highlights further emphasises the point that those with BPD are much more sensitive, and motived to choose, options concerning relative reward than are CON participants. The text in the discussion reads:

‘We also observe this in self-generated participant choice behaviour, where CON participants were more concerned over absolute reward versus their BPD counterparts, suggesting a heighted focus on relative vs. absolute reward in those with BPD.’

(2) The adaptive algorithm for adjusting partner behavior in Phase 2 was clever and effective. Did the authors conduct a manipulation check to demonstrate that the matching resulted in approximately 50% difference between one's behavior in Phase 1 and the partner in Phase 2? Perhaps Supplementary Figure suffices, but I wondered about a simpler metric.

Thanks for this point. We highlight this in Figure 3B and within the same figure legend although appreciate the panel is quite small and may be missed.  We have now highlighted this manipulation check more clearly in behavioural analysis section of the main text:

‘Server matching between participant and partner in phase 2 was successful, with participants being approximately 50% different to their partners with respect to the choices each would have made on each trial in phase 2 (mean similarity=0.49, SD=0.12).’

(3) The resolution of point-range plots in Figure 4 was grainy. Perhaps it's not so in the separate figure file, but I'd suggest checking.

Apologies. We have now updated and reorganised the figure to improve clarity.

(4) p. 21: Suggest changing to "different" as opposed to "opposite" since the strategies are not truly opposing: "but employed opposite strategies."

We have amended this.

(5) p. 21: I found this sentence unclear, particularly the idea of "similar updating regime." I'd suggest clarifying: "In phase 2, CON participants exhibited greater belief sensitivity to new information during observational learning, eventually adopting a similar updating regime to those with BPD."

We have clarified this statement:

‘In observational learning in phase 2, CON participants initially updated their beliefs in response to new information more quickly than those with BPD, but eventually converged to a similar rate of updating.’

(6) p. 23: The content regarding psychosis seemed out of place, particularly as the concluding remark. I'd suggest keeping the focus on the clinical population under investigation. If you'd like to mention the paradigm's relevance to psychosis (which I think could be omitted), perhaps include this as a future direction when describing the paradigm's strengths above.

We agree the paragraph is somewhat speculative. We have omitted it in aid of keeping the messaging succinct and to the point.

(7) p. 24: Was BPD diagnosis assess using unstructured clinical interview? Although psychosis was exclusionary, what about recent manic or hypomanic episodes or Bipolar diagnosis? A bit more detail about BPD sample ascertainment would be useful, including any instruments used to make a diagnosis and information about whether you measured inter-rater agreement.

Participants diagnosed with BPD were recruited from specialist personality disorder services across various London NHS mental health trusts. The diagnosis of BPD was established by trained assessors at the clinical services and confirmed using the Structured Clinical Interview for DSM-IV (SCID-II) (First et al., 1997). Individuals with a history of psychotic episodes, severe learning disability or neurological illness/trauma were excluded. We have now included this extra detail within our methods in the paper:

‘The majority of BPD participants were recruited through referrals by psychiatrists, psychotherapists, and trainee clinical psychologists within personality disorder services across 9 NHS Foundation Trusts in the London, and 3 NHS Foundation Trusts across England (Devon, Merseyside, Cambridgeshire). Four BPD participants were also recruited by self-referral through the UCLH website, where the study was advertised. To be included in the study, all participants needed to have, or meet criteria for, a primary diagnosis of BPD (or emotionally-unstable personality disorder or complex emotional needs) based on a professional clinical assessment conducted by the referring NHS trust (for self-referrals, the presence of a recent diagnosis was ascertained through thorough discussion with the participant, whereby two of the four also provided clinical notes). The patient participants also had to be under the care of the referring trust or have a general practitioner whose details they were willing to provide. Individuals with psychotic or mood disorders, recent acute psychotic episodes, severe learning disability, or current or past neurological disorders were not eligible for participation and were therefore not referred by the clinical trusts.‘

Why chatGPT can't replace writing

Se pueden unir varias cadenas con una coma (,)

Las cadenas son unir o concatenar varios caracteres para formar una palabra o expresión ' Pharo Tutorial ' es una cadena de caracteres

Se pueden unir varias cadenas con una (,)

EJERCICIO CARACTER

RESULTADO FACTORIAL

65 CODIGO DEL CARACTER EN ASCII

INSPECCIONANDO NUMEROS

regional anti-trust!

dfgdfgdf

fgf

two-round system, bunch of candidates run, then if no one gets an absolute majority the top 2 run against each other

electoral system: set of laws that regulate electoral competition between candidates/parties/both

electoral district

different types of elections use different rules

想要作为 “礼物” 摆脱的，不只是家政工作本身，也有在购买过程中的准备精力和情绪价值。

Code switching and changing how you express yourself in different situations I feel is fully natural to a degree. As a white male I don't have to deal with code switching in the same way it's talked about for AAVE but I still speak a different way at work than I do when I'm hanging out with my close friends. Everyone interacts with different people differently, and though one could argue I am less authentic to myself at work, I still can express myself as who I am without the exact same vocabulary.

How does this novel address themes of plurality and diversity? How can you use it to teach the same?

Use of research--connect it to the question about research, ethics, and skills?

aaaaa

Just testing

Can't remember what of his I was reading that was pinging this vibe despite not being facially relevant

I am only sad he will never feature in a Knives Out movie

comments

equation not balanced

equation 6 and 7 should be in intro or methods

maybe move this above the statement of the goal of the experiment

this should be in your intro not methods

good title i think

missing many equations that need to be in the methods or intro

explain what some of these values are, for example, q represents heat flow

maybe add some subsection titles like enthalpy change and hess's law

Sigh. that I'm female My face isn't good enough for Facebook.

Is this text operating under the awareness that Facebook was a platform designed by priveleged white men at an elite ivy league college and then had the platform stolen by the present owner of Meta, Mark Zuckerburg? The platform was designed as a way for men to judge and vote on the faces of their elite, ivy league female counterparts.

Gross.

I don't wear ties.

The "media" is a propaganda property owned by individuals or investors who pay or buy words from individuals who are seen as loyal, trustworthy and authority figures to disseminate information in a palatable and digestable fashion that won't be rejected by the masses.

And again, why is this? Is it because those of who identify as biracial have faced bias and mistreatment from both sides. Too light to be a dark skinned person. Too dark to be white. Must be mixed, therefore rejected by both societies. Forced to create ones own identity.

I'm 100% theres a buttload of things that men are more likely to do than women because we couldn't vote, own a credit card or even get divorced at one point. Some of these within my lifetime. So, we should always remember how long ago it was that divorce was finally legalized and women could own a credit card. Tell me what year was ERA ratified? How long did that take? What was the result?

I think it is interesting to say that the church opposes IVF because it undermines traditional pregnancy by it taking control away from God. But this part of the text shows that doctors in Ecuador don't believe that IVF is going against God's work. They actually pray to God for IVF to work and think that the success of it is thanks to God. Since Ecuador doesn't have a lot of money to maintain IVF labs in the best way possible, people often feel like they fail. Still, it's interesting to see medical practitioners credit the success of IVF to God. It's interesting to see how catholic medical workers negotiate their faith in their practices, and I like how they integrate faith into their medical work.

Is there any way to get government funding for this?

Good idea

my guyyyyyy

this is a very funny angle

eLife Assessment

This manuscript makes important contributions to our understanding of cell polarization dynamics by demonstrating how compensatory regulatory and spatial mechanisms enhance the robustness of polarization patterns. By integrating a computational pipeline with comparisons to experimental data, the authors provide convincing evidence that stability and asymmetry in reaction-diffusion networks are crucial for polarization in C. elegans zygotes. Their findings offer novel insights into essential biological processes such as cell migration, division, and symmetry breaking. Future theoretical and experimental work could refine the model by addressing its acknowledged limitations.

Joint Public Reviews:

In this manuscript, the authors aim to evaluate the robustness of stable asymmetric polarization patterns by analyzing both a minimal 2-node network and a more biologically realistic 5-node network based on the C. elegans polarization system. They introduce a computational pipeline for systematically exploring reaction-diffusion network dynamics. Their study highlights the limitations of the widely used 2-node antagonistic network, demonstrating its susceptibility to simple modifications that disrupt polarization. However, they show that polarization stability can be restored by combining multiple regulatory mechanisms, and that spatially varying kinetic parameters can fine-tune the interface position. The authors further investigate the 5-node network of C. elegans, identifying key parameters that enhance its robustness against perturbations. Their findings provide novel insights into the mechanisms that ensure stable polarization in biological systems.

The major strengths of this work lie in its rigorous computational approach and the clarity of its findings. The authors demonstrate that the widely used 2-node antagonistic network is highly sensitive to parameter changes, requiring precise fine-tuning to maintain stable polarization. However, they show that stability can be restored through compensatory modifications, which expand the range of parameter sets supporting polarization. By further exploring spatial parameter variations, the authors reveal how compensatory adjustments can stabilize polarization patterns, offering insights into potential biological mechanisms regulating interface localization.

Extending their analysis to the C. elegans polarization network, the authors construct a 5-node model grounded in an extensive literature review. Their computational pipeline identifies key parameters that enhance robustness, and their model successfully replicates experimental observations, even in mutant conditions. Notably, among 34 possible network structures, only the naturally evolved 5-node network with mutual inhibition between specific components maintains stable polarization, highlighting its evolutionary optimization. This work significantly advances our understanding of polarization maintenance and provides a valuable framework for future in silico experiments.

Despite its strengths, the study has some limitations related to simplifying assumptions. The model neglects cortical flows and the role of actomyosin dynamics, which are known to be crucial during the establishment phase of polarization in the C. elegans zygote. While the authors focus on the maintenance phase, the absence of these biomechanical effects may limit the model's applicability to the full polarization process. Additionally, the assumption of infinitely fast cytoplasmic diffusion disregards potential effects of cytoplasmic flows on the stability of molecular distributions. Experimental measurements suggest that cytoplasmic diffusion coefficients are only an order of magnitude higher than membrane diffusion coefficients, meaning that finite diffusion combined with cytoplasmic flows could influence polarization stability. Although the authors acknowledge and discuss these limitations, incorporating these effects in future models could provide a more complete picture of the polarization dynamics in C. elegans embryos.

Author response:

The following is the authors’ response to the original reviews

eLife Assessment

This manuscript makes valuable contributions to our understanding of cell polarisation dynamics and its underlying mechanisms. Through the development of a computational pipeline, the authors provide solid evidence that compensatory actions, whether regulatory or spatial, are essential for the robustness of the polarisation pattern. However, a more comprehensive validation against experimental data and a proper estimation of model parameters are required for further characterization and predictions in natural systems, such as the C. elegans embryo.

We sincerely thank the editor(s) for their pertinent assessment. We have carefully considered the constructive recommendations and made the necessary revisions in the manuscript, which are also detailed in this response letter. We have implemented most of the revisions requested by the reviewers. For the few requests we did not fully accept, we have provided justifications. The corresponding revisions in both the Manuscript and Supplementary Information are highlighted with a yellow background. To provide a more comprehensive validation against experimental data and model parameters used for characterizing and predicting natural systems, we reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total (two acting on LGL-1 and three on CDC-42), comprising eight perturbed conditions and using wild-type as the reference. These results effectively demonstrate how comprehensively the network structure and parameters capture the characteristics of the C. elegans embryo. We have also acknowledged the limitations of the current cell polarization model and provided, in 2. Results and 3. Discussion and conclusion, a detailed outline of potential model improvements.

Joint Public Reviews:

The polarisation phenomenon describes how proteins within a signalling network segregate into different spatial domains. This phenomenon holds fundamental importance in biology, contributing to various cellular processes such as cell migration, cell division, and symmetry breaking in embryonic morphogenesis. In this manuscript, the authors assess the robustness of stable asymmetric patterns using both a previously proposed minimal model of a 2-node network and a more realistic 5-node network based on the C. elegans cell polarisation network, which exhibits anterior-posterior asymmetry. They introduce a computational pipeline for numerically exploring the dynamics of a given reaction-diffusion network and evaluate the stability of a polarisation pattern. Typically, the establishment of polarisation requires the mutual inhibition of two groups of proteins, forming a 2-node antagonistic network. Through a reaction-diffusion formulation, the authors initially demonstrate that the widely-used 2-node antagonistic network for creating polarised patterns fails to maintain the polarised pattern in the face of simple modifications. However, the collapsed polarisation can be restored by combining two or more opposing regulations. The position of the interface can be adjusted with spatially varied kinetic parameters. Furthermore, the authors show that the 5-node network utilised by C. elegans is the most stable for maintaining polarisation against parameter changes, identifying key parameters that impact the position of the interface.

We sincerely thank the editor(s) for the pertinent summary!

While the results offer novel and insightful perspectives on the network's robustness for cell polarisation, the manuscript lacks comprehensive validation against experimental data, justified node-node network interactions, and proper estimation of model parameters (based on quantitative measurements or molecular intensity distributions). These limitations significantly restrict the utility of the model in making meaningful predictions or advancing our understanding of cell polarisation and pattern formation in natural systems, such as the C. elegans embryo.

We sincerely thank the editor(s) for the comment!

To provide a more comprehensive validation against experimental data and model parameters, we reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total (two acting on LGL-1 and three on CDC-42), comprising eight perturbed conditions and using wild-type as the reference. These meaningful predictions effectively demonstrate the utility of our model’s network structure and parameters in advancing our understanding of cell polarisation and pattern formation in natural systems, exemplified by the C. elegans embryo.

We have also acknowledged the limitations of the current cell polarization model and provided, in 2. Results and 3. Discussion and conclusion, a detailed outline of potential model improvements. The limitations include, but are not limited to, issues involving “node-node network interactions” and the “proper estimation of model parameters (based on quantitative measurements or molecular intensity distributions)”, both of which rely on experimental measurements of biological information.   However, comprehensive experimental measurement data on every molecular species, their interactions, and each species’ intensity distribution in space and time were not fully available from prior research. Refinement is lacking for some of these interactions, potentially requiring years of additional experimentation. Moreover, for certain species at specific developmental stages, only relative (rather than absolute) intensity measurements are available. We agreed that such information is essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion. From a theoretical perspective, we adopted assumptions from the previous literature and constructed a minimal model for a specific cell polarization phase to investigate the network's robustness, supported by five experimental groups and eight perturbed conditions in the C. elegans embryo.

The study extends its significance by examining how cells maintain pattern stability amid spatial parameter variations, which are common in natural systems due to extracellular and intracellular fluctuations. The authors found that in the 2-node network, varying individual parameters spatially disrupt the pattern, but stability is restored with compensatory variations. Additionally, the polarisation interface stabilises around the step transition between parameter values, making its localisation tunable. This suggests a potential biological mechanism where localisation might be regulated through signalling perception.

We sincerely thank the editor(s) for the pertinent review!

Focusing on the C. elegans cell polarisation network, the authors propose a 5-node network based on an exhaustive literature review, summarised in a supplementary table. Using their computational pipeline, they identify several parameter sets capable of achieving stable polarisation and claim that their model replicates experimental behaviour, even when simulating mutants. They also found that among 34 possible network structures, the wild-type network with mutual inhibition is the only one that proves viable in the computational pipeline. Compared with previous studies, which typically considered only 2- or 3-node networks, this analysis provides a more complete and realistic picture of the signalling network behind polarisation in the C. elegans embryo. In particular, the model for C. elegans cell polarisation paves the way for further in silico experiments to investigate the role of the network structure over the polarisation dynamics. The authors suggest that the natural 5-node network of C. elegans is optimised for maintaining cell polarisation, demonstrating the elegance of evolution in finding the optimal network structure to achieve certain functions.

We sincerely thank the editor(s) for the pertinent review!

Noteworthy limitations are also found in this work. To simplify the model for numerical exploration, the authors assume several reactions have equivalent dynamics, reducing the parameter space to three independent dimensions. While the authors briefly acknowledge this limitation in the "Discussion and Conclusion" section, further analysis might be required to understand the implications. For instance, it is not clear how the results depend on the particular choice of parameters. The authors showed that adding additional regulation might disrupt the polarised pattern, with the conclusion apparently depending on the strength of the regulation. Even for the 5-node wild-type network, which is the most robust, adding a strong enough self-activation of [A], as done in the 2-node network, will probably cause the polarised pattern to collapse as well.

We sincerely thank the editor(s) for the comment!

Now we have thoroughly expanded our acknowledgment of the model’s limitations in in 2. Results and 3. Discussion and conclusion. To rule out the equivalent dynamics assumption undermines our conclusions, we have added simulations showing that the cell polarization pattern stability does not depend on the exact strength of each regulation, provided the regulations on both sides are initially balanced as a whole (Fig. S5). Specifically, we used a Monte Carlo method to sample a wide range of various parameter values ( i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c) for all nodes and regulations in simple 2-node network and C. elegans 5-node network, to achieve pattern stability. Under these conditions (i.e., without any reduction in the parameter space), single-sided self-regulation, single-sided additional regulation, and unequal system parameters still cause the stable polarized pattern to collapse, consistent with our conclusions in the simplified conditions with the parameter space reduced to three independent dimensions.

Additionally, the authors utilise parameter values that are unrealistic, fail to provide units for some of them, and assume unknown parameter values without justification. The model appears to have non-dimensionalised length but not time, resulting in a mix of dimensional and non-dimensional variables that can be confusing. Furthermore, they assume equal values for Hill coefficients and many parameters associated with activation and inhibition pathways, while setting inhibition intensity parameters to 1. These arbitrary choices raise concerns about the fidelity of the proposed model in representing the real system, as their selected values could potentially differ by many orders of magnitude from the actual parameters.

We sincerely thank the editor(s) for the comment!

We apologize for the confusion. The non-dimensionalised parameter values are adopted from previous theoretical research [Seirin-Lee et al., Cells, 2020], which originates from the experimental measurement in [Goehring et al., J. Cell Biol., 2011; Goehring et al., Science, 2011]. With the in silico time set as 2 sec per step, now we have added the Supplemental Text justifying how the units are removed during non-dimensionalization. This demonstrates that the derived non-dimensionalized parameter in this paper achieves realistic values on the same order of magnitude as those observed in reality, confirming the fidelity of the proposed model in representing the real system.

The assumption of “equal values for Hill coefficients and many parameters associated with activation and inhibition pathways” is to reduce the parameter space for affordable computational cost. It is a widely-used strategy to fix Hill coefficients [Seirin-Lee et al., J. Theor. Biol., 2015; Seirin-Lee, Bull. Math. Biol., 2021] and unify parameter values for different pathways in network research about both cell polarization [Marée et al., Bull. Math. Biol., 2006; Goehring et al., Science, 2011; Trong et al., New J. Phys., 2014] and other biological topics (e.g., plasmid transferring in the microbial community [Wang et al., Nat. Commun., 2020]), to control computational cost. Nevertheless, to rule out that the equivalent dynamics assumption undermines our conclusions, we have added simulations showing that the cell polarization pattern stability does not depend on the exact parameter values associated with activation and inhibition pathways, provided the regulations on both sides are initially balanced as a whole (Fig. S5). Specifically, we used a Monte Carlo method to sample a wide range of various parameter values (i.e_., _γ, α, k₁, k₂, q₁, q₂ and [X_c) for all nodes and regulations in simple 2-node network and C. elegans 5-node network, to achieve pattern stability. Under these conditions ( i.e., without any reduction in the parameter space), single-sided self-regulation, single-sided additional regulation, and unequal system parameters still cause the stable polarized pattern to collapse, consistent with our conclusions in the simplified conditions with the parameter space reduced to three independent dimensions.

To confirm the fidelity of the proposed model in representing the real system, we reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total (two acting on LGL-1 and three on CDC-42), comprising eight perturbed conditions and using wild-type as the reference. These results effectively demonstrate how comprehensively the network structure and parameters capture the characteristics of the C. elegans embryo. We have also acknowledged the limitations of the current cell polarization model and provided, in 2. Results and 3. Discussion and conclusion, a detailed outline of potential model improvements.

It is worth noting that, although a strict match between numerical and realistic parameter values with consistent units is always helpful, a lot of notable pure numerical studies successfully unveil principles that help interpret [Ma et al., Cell, 2009] and synthesize real biological systems [Chau et al., Cell, 2012]. These studies suggest that numerical analysis in biological systems remains powerful, even when comprehensive experimental data from prior research are not fully available.

The definition of stability and its evaluation in the proposed pipeline might also be too narrow. Throughout the paper, the authors discuss the stability of the polarised pattern, checked by an exhaustive search of the parameter space where the system reaches a steady state with a polarised pattern instead of a homogeneous pattern. It is not clear if the stability is related to the linear stability analysis of the reaction terms, as conducted in Goehring et al. (Science, 2011), which could indicate if a homogeneous state exists and whether it is stable or unstable. The stability test is performed through a pipeline procedure where they always start from a polarised pattern described by their model and observe how it evolves over time. It is unclear if the conclusions depend on the chosen initial conditions. Particularly, it is unclear what would happen if the initial distribution of posterior molecules is not exactly symmetric with respect to the anterior molecules, or if the initial polarisation is not strong.

We sincerely thank the editor(s) for the comment!

The definition of stability and its evaluation in the proposed pipeline consider two criteria: 1. The pattern is polarized; 2. The pattern is stable. Following simulations, figures, and videos (Fig. 1-6; Fig. S1-S5; Fig. S7-S9; Movie S1-S5) have sufficiently demonstrated that the parameters and networks set up capture the cell polarization dynamis regarding both the stable and unstable states very well.

Now we have added new simulation on alternative initial conditions. They demonstrating the necessity of a polarized initial pattern set up independently of the reaction-diffusion network during the establishment phase, probably through additional mechanisms such as the active actomyosin contractility and flow [Cuenca et al., Development, 2003; Gross et al., Nat. Phys., 2019]. Our conclusions ( i.e., single-sided self-regulation, single-sided additional regulation, and unequal system parameters cause the stable polarized pattern to collapse) have little dependence on the chosen initial conditions as long as the unsymmetric initial patterns can set up a stable polarized pattern. A part of the simulations institutively show our conclusions still hold if the initial distribution of posterior molecules is not exactly symmetric with respect to the anterior molecules, or if the initial polarisation is not strong (Fig. S4 and Fig. S9).

Regarding the biological interpretation and relevance of the model, it overlooks some important aspects of the C. elegans polarisation system. The authors focus solely on a reaction-diffusion formulation to reproduce the polarisation pattern. However, the polarisation of the C. elegans zygote consists of two distinct phases: establishment and maintenance, with actomyosin dynamics playing a crucial role in both phases (see Munro et al., Dev Cell 2004; Shivas & Skop, MBoC 2012; Liu et al., Dev Biol 2010; Wang et al., Nat Cell Biol 2017). Both myosin and actin are crucial to maintaining the localisation of PAR proteins during cell polarisation, yet the authors neglect cortical flows during the establishment phase and any effects driven by myosin and actin in their model, failing to capture the system's complexity. How this affects the proposed model and conclusions about the establishment of the polarisation pattern needs careful discussion. Additionally, they assume that diffusion in the cytoplasm is infinitely fast and that cytoplasmic flows do not play any role in cell polarity. Finite cytoplasmic diffusion combined with cytoplasmic flows could compromise the stability of the anterior-posterior molecular distributions. The authors claim that cytoplasmic diffusion coefficients are two orders of magnitude higher than membrane diffusion coefficients, but they seem to differ by only one order of magnitude (Petrášek et al., Biophys. J. 2008). The strength of cytoplasmic flows has been quantified by a few studies, including Cheeks et al., and Curr Biol 2004.

We sincerely thank the editor(s) for the comment!

Indeed, previous research highlighted the importance of convective cortical flow in orchestrating the localisation of PAR proteins during the establishment phase of polarisation formation [Goehring et al., J. Cell Biol., 2011; Rose et al., WormBook, 2014; Beatty et al., Development, 2013]. However, during the maintenance phase, the non-muscle myosin II (NMY-2) is regulated downstream by the PAR protein network rather than serving as the primary upstream factor controlling PAR protein localization [Goehring et al., J. Cell Biol., 2011; Rose et al., WormBook, 2014; Beatty et al., Development, 2013]. While some theoretical studies integrated both reaction-diffusion dynamics and the effects of myosin and actin [Tostevin, 2008; Goehring, Science, 2011], others focused exclusively on reaction-diffusion dynamics [Dawes et al., Biophys. J., 2011; Seirin-Lee et al., Cells, 2020]. We have now clarified the distinction between the establishment and maintenance phases in 1. Introduction, emphasized our research focus on the reaction-diffusion dynamics during the maintenance phase in 2. Results, and provided a discussion of the omitted actomyosin dynamics to foster a more comprehensive understanding in the future in 3. Discussion and conclusion. The effect of the establishment phase is studied as the initial condition for the cell polarization simulation solely governed by reaction-diffusion dynamics, with new simulations demonstrating the necessity of a polarized initial pattern set up independently of the reaction-diffusion network during the establishment phase, probably through additional mechanisms such as the active actomyosin contractility and flow [Cuenca et al., Development, 2003; Gross et al., Nat. Phys., 2019].

Cytoplasmic and membrane diffusion coefficients differ by two orders of magnitude according to previous experimental measurements on PAR-2 and PAR-6 [Goehring et al., J. Cell Biol., 2011; Lim et al., Cell Rep., 2021]. Many previous C. elegans cell polarization models have incorporated mass-conservation model combined with finite cytoplasmic diffusion, but this model description can lead to reverse spatial concentration distribution between the cell membrane and cytosol [Fig. 3 of Seirin-Lee et al., J. Theor. Biol., 2016; Fig. 2ab of Seirin-Lee et al., J. Math. Biol., 2020], disobeying experimental observation [Fig. 4A of Sailer et al., Dev. Cell, 2015; Fig. 1A of Lim et al., Cell Rep., 2021]. This implies that the infinite cytoplasmic diffusion, without precise experiment-based parameter assignment or accounting for other hidden biological processes ( e.g., protein production and degradation), may be inappropriate in modeling the real spatial concentration distributions distinguished between the cell membrane and cytosol. To address this issue, some theoretical research incorporated protein production and degradation into their model, to acquire the consistent spatial concentration distribution between the cell membrane and cytosol [Tostevin et al., Biophys. J., 2008]. More definitive experimental data on the spatiotemporal changes in protein diffusion, production, and degradation are essential for providing a more realistic representation of cellular dynamics and enhancing the model's predictive power.

Now we have acknowledged the possibly overlooked aspects of the C. elegans polarisation system in 3. Discussion and conclusion, a detailed outline of potential model improvements. Those aspects include, but are not limited to, issues involving “neglect cortical flows” and the “diffusion in the cytoplasm is infinitely fast”. From a theoretical perspective, we adopted assumptions from the previous literature and constructed a minimal model for a specific cell polarization phase to investigate the network's robustness. The meaningful predictions of five experimental groups and eight perturbed conditions in the C. elegans embryo faithfully supports the biological interpretation and relevance of the model.

Although the authors compare their model predictions to experimental observations, particularly in reproducing mutant behaviours, they do not explicitly show or discuss these comparisons in detail. Diffusion coefficients and off-rates for some PAR proteins have been measured (Goehring et al., JCB 2011), but the authors seem to use parameter values that differ by many orders of magnitude, perhaps due to applied scaling. To ensure meaningful predictions, whether their proposed model captures the extensive published data should be evaluated. Various cellular/genetic perturbations have been studied to understand their effects on anterior-posterior boundary positioning. Testing these perturbations' responses in the model would be important. For example, comparing the intensity distribution of PAR-6 and PAR-2 with measurements during the maintenance phase by Goehring et al., JCB 2011, or comparing the normalised intensity of PAR-3 and PKC-3 from the model with those measured by Wang et al., Nat Cell Biol 2017, during establishment and maintenance phases (in both wild-type and cdc-42 (RNAi) zygotes) could provide insightful validation. Additionally, in the presence of active CDC-42, it has been observed that PAR-6 extends further into the posterior side (Aceto et al., Dev Biol 2006). Conducting such validation tests is essential to convince readers that the model accurately represents the actual system and provides insights into pattern formation during cell polarisation.

We sincerely thank the editor(s) for the comment!

To provide more comprehensive validations and refinements to ensure the model accurately represents biological systems, we extensively reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total from published data, comprising eight perturbed conditions and using wild-type as the reference. We have also explicitly show the comparison between model predictions and experimental observations (including the mutant behaviors reproduction as well) in detail, by describing how “cell polarization pattern characteristics in simulation” responds to various cellular/genetic perturbations (Section 2.5; Fig. 5; Fig. S7 and S8). The original and new validation tests conducted can convince readers that the model accurately represents the actual system and provides insights into pattern formation during cell polarisation.

The diffusion coefficients for anterior and posterior molecular species were assigned according to previous experimental and theoretical research [Goehring et al., J. Cell Biol., 2011; Goehring et al., Science, 2011; Seirin-Lee et al., Cells, 2020]. The off-rates are assigned uniformly by searching viable parameter sets that can set up a network with cell polarization pattern stability. Now we have added simulations showing that the cell polarization pattern stability and response to network structure and parameter perturbation does not depend on the exact parameter values (incl., diffusion coefficients and off-rates), provided the parameter values on both sides are initially balanced as a whole (Fig. S5). Specifically, we used a Monte Carlo method to sample a wide range of various parameter values ( i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c) for all nodes and regulations in simple 2-node network and C. elegans 5-node network, to achieve pattern stability. Under these conditions ( i.e., without any reduction in the parameter space), single-sided self-regulation, single-sided additional regulation, and unequal system parameters still cause the stable polarized pattern to collapse, consistent with our conclusions in the simplified conditions with the parameter space reduced to three independent dimensions.

With the in silico time set as 2 sec per step, now we have added the Supplemental Text justifying how the units are removed during non-dimensionalization. This demonstrates that the derived non-dimensionalized parameter in this paper achieves realistic values on the same order of magnitude as those observed in reality, confirming the fidelity of the proposed model in representing the real system. We agreed that full experimental measurements of biological information are essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion.

A clear justification, with references, for each network interaction between nodes in the five-node model is needed. Some of the activatory/inhibitory signals proposed by the authors have not been demonstrated ( e.g. CDC-42 directly inhibiting CHIN-1). Table S2 provided by the authors is insufficient to justify each node-node interaction, requiring additional explanations. (See the review by Gubieda et al., Phil. Trans. R. Soc. B 2020, for a similar node network that differs from the authors' model.) Additionally, the intensity distributions of cortical PAR-3 and PKC-3 seem to vary significantly during both establishment and maintenance phases (Wang et al., Nat Cell Biol 2017), yet the authors consider the PAR-3/PAR-6/PKC-3 as a single complex. The choices in the model should be justified, as the presence or absence of clustering of these PAR proteins can be crucial during cell polarisation (Wang et al., Nat Cell Biol 2017; Dawes & Munro, Biophys J 2011).

We sincerely thank the editor(s) for the comment!

Now we have acknowledged the limitations of the current cell polarization model and provided, in 2. Results and 3. Discussion and conclusion, a detailed outline of potential model improvements. The limitations include, but are not limited to, issues involving “each network interaction between nodes” and the “consider the PAR-3/PAR-6/PKC-3 as a single complex”, in which the former one relies on experimental measurements of biological information. However, comprehensive experimental measurement data on every molecular species, their interactions, and each species’ intensity distribution in space and time were not fully available from prior research. Refinement is lacking for some of these interactions, potentially requiring years of additional experimentation. Moreover, for certain species at specific developmental stages, only relative (rather than absolute) intensity measurements are available. We agreed that such information is essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion.

In consistent with previous modeling efforts [Goehring et al., Science, 2011; Gross et al., Nat. Phys., 2019; Lim et al., Cell Rep., 2021], our model treats the PAR-3/PAR-6/PKC-3 complex as a single entity for simplification, thus neglecting the potentially distinct spatial distributions of each single molecular species. We agree that a more comprehensive model, capable of resolving the individual localization patterns of these anterior PAR proteins, would be a valuable future direction. From a theoretical perspective, we adopted assumptions from the previous literature and constructed a minimal model for a specific cell polarization phase to investigate the network's robustness, supported by five experimental groups and eight perturbed conditions in the C. elegans embryo.

In summary, the authors successfully demonstrate the importance of compensatory actions in maintaining polarisation robustness. Their computational pipeline offers valuable insights into the dynamics of reaction-diffusion networks. However, the lack of detailed experimental validation and realistic parameter estimation limits the model's applicability to real biological systems. While the study provides a solid foundation, further work is needed to fully characterise and validate the model in natural contexts. This work has the potential to significantly impact the field by providing a new perspective on the robustness of cell polarisation networks.

We sincerely thank the editor(s) for the pertinent summary!

To provide a more comprehensive validation against experimental data and model parameters, three more groups of the qualitative and semi-quantitative phenomenon regarding CDC-42 are reproduced based on previously published experiments (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total, comprising eight perturbed conditions and using wild-type as the reference.

With the in silico time set as 2 sec per step, now we have added the Supplemental Text justifying how the units are removed during non-dimensionalization. This demonstrates that the derived non-dimensionalized parameter in this paper achieves realistic values on the same order of magnitude as those observed in reality, confirming the fidelity of the proposed model in representing the real system. Together with the reproduction of five experimental groups (eight perturbed conditions with wild-type as the reference), the model’s applicability to real biological systems in natural contexts are are fully characterised and validated.

The computational pipeline developed could be a valuable tool for further in silico experiments, allowing researchers to explore the dynamics of more complex networks. To maximise its utility, the model needs comprehensive validation and refinement to ensure it accurately represents biological systems. Addressing these limitations, particularly the need for more detailed experimental validation and realistic parameter choices, will enhance the model's predictive power and its applicability to understanding cell polarisation in natural systems.

We sincerely thank the editor(s) for the comment!

To provide more comprehensive validations and refinements to ensure the model accurately represents biological systems, we extensively reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total from published data, comprising eight perturbed conditions and using wild-type as the reference. We have also explicitly show the comparison between model predictions and experimental observations (including the mutant behaviors reproduction as well) in detail, by describing how “cell polarization pattern characteristics in simulation” responds to various cellular/genetic perturbations (Section 2.5; Fig. 5; Fig. S7 and S8).

With the in silico time set as 2 sec per step, now we have added the Supplemental Text justifying how the units are removed during non-dimensionalization. This demonstrates that the derived non-dimensionalized parameter in this paper achieves realistic values on the same order of magnitude as those observed in reality, confirming the fidelity of the proposed model in representing the real system. Together with the reproduction of five experimental groups (eight perturbed conditions with wild-type as the reference), the model's predictive power and its applicability to understanding cell polarisation in natural systems are enhanced.

Now we have added simulations showing that the cell polarization pattern stability and response to network structure and parameter perturbation does not depend on the exact parameter values (incl., diffusion coefficients, basal off-rates and inhibition intensity), provided the parameter values on both sides are initially balanced as a whole (Fig. S5). Specifically, we used a Monte Carlo method to sample a wide range of various parameter values (i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c) for all nodes and regulations in simple 2-node network and C. elegans 5-node network, to achieve pattern stability. Under these conditions ( i.e., without any reduction in the parameter space), single-sided self-regulation, single-sided additional regulation, and unequal system parameters still cause the stable polarized pattern to collapse, consistent with our conclusions in the simplified conditions with the parameter space reduced to three independent dimensions.

Recommendations for the Authors:

(1) Parameterisation and Model Validation: The authors utilise parameter values that lack realism and fail to provide units for some of them, which can lead to confusion. For instance, the length of the cell is set to 0.5 without clear justification, raising questions about the scale used. Additionally, there's a mix of dimensional and non-dimensional variables, potentially complicating interpretation. Furthermore, arbitrary choices such as equal Hill coefficients and setting inhibition intensity parameters to 1 raise concerns about model fidelity. To ensure meaningful predictions, the authors should validate their model against extensive published data, including cellular/genetic perturbations. For example, comparing intensity distributions of PAR proteins measured during maintenance phases by Goehring et al., JCB 2011, and those obtained from the model could provide valuable validation. Similarly, comparisons with data from Wang et al., Nat Cell Biol 2017, on wild-type and cdc-42 (RNAi) zygotes, as well as observations from Aceto et al., Dev Biol 2006, on PAR-6 extension in the presence of active CDC-42, would strengthen the model's validity. Such validation tests are essential for convincing readers that the model accurately represents the actual system and can provide insights into pattern formation during cell polarisation.

We sincerely thank the editor(s) and referee(s) for the helpful suggestion!

Now we have added a new section, Parameter Nondimensionalization and Order of Magtitude Consistency, into Supplemental Text. In this section, we introduced how we adopted the parameter nondimensionalization and value assignments from previous works [Goehring et al., J. Cell Biol., 2011; Goehring et al., Science, 2011; Seirin-Lee et al., Cells, 2020]. We listed four examples (i.e., evolution time, membrane diffusion coefficient, basal off-rate, and inhibition intensity) to show the consistency in order of magtitude between numerical and realistic values.

The assumption of “equal Hill coefficients” is to reduce the parameter space for an affordable computational cost. It is a widely-used strategy to fix Hill coefficients [Seirin-Lee et al., J. Theor. Biol., 2015; Seirin-Lee, Bull. Math. Biol., 2021] in network research, to control computational cost. Besides, setting inhibition intensity parameters to 1 is for determining a numerical scale. Now we have added simulations showing that the cell polarization pattern stability does not depend on the exact parameter values associated with activation and inhibition pathways, provided the regulations on both sides are initially balanced as a whole (Fig. S5). Specifically, we used a Monte Carlo method to sample a wide range of various parameter values (i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c) for all nodes and regulations in simple 2-node network and C. elegans 5-node network, to achieve pattern stability. Under these conditions (i.e., without any reduction in the parameter space), single-sided self-regulation, single-sided additional regulation, and unequal system parameters still cause the stable polarized pattern to collapse, consistent with our conclusions in the simplified conditions with the parameter space reduced to three independent dimensions.

To confirm the fidelity of the proposed model in representing the real system, we reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total (two acting on LGL-1 and three on CDC-42), comprising eight perturbed conditions and using wild-type as the reference. These results effectively demonstrate how comprehensively the network structure and parameters capture the characteristics of the C. elegans embryo. We have also acknowledged the limitations of the current cell polarization model and provided, in 2. Results and 3. Discussion and conclusion, a detailed outline of potential model improvements.

It is worth noting that, although a strict match between numerical and realistic parameter values with consistent units is always helpful, a lot of notable pure numerical studies successfully unveil principles that help interpret [Ma et al., Cell, 2009] and synthesize real biological systems [Chau et al., Cell, 2012]. These studies suggest that numerical analysis in biological systems remains powerful, even when comprehensive experimental data from prior research are not fully available.

(2) Parameter Changes: It is not clear how the parameters change as more complicated networks are explored, and how this affects the comparison between the simple and complete model. Clarification on this point would be beneficial.

We sincerely thank the editor(s) and referee(s) for the helpful suggestion!

The computational pipeline in Section 2.1 is generalized for all reaction-diffusion networks, including the simple and complete ones studied in this paper. The parameter changes included two parts: 1. The mutual activation in the anterior (none for the simple 2-node network and q<sub2</sub> for the complete 5-node network); 2. The viable parameter sets (122 sets for the simple 2-node network and 602 sets for the complete 5-node network). Now we have explicitly clarified those differences:

Those differences don’t affect the comparison between the simple and complete models. Now we have added comprehensive comparisons between the simple and complete models about 1. How they respond to alternative initial conditions consistently (Fig. S2). 2. How they respond to alternative single modifications consistently (Fig. S4 and S9), even when the parameters (i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c) are assigned with various values concerning all nodes and regulations (Fig. S5).

(3) Exploration of Model Parameter Space: In the two-node dual antagonistic model, the authors observe that the cell polarisation pattern is unstable for different systems (Fig. 1). However, it remains uncertain whether this instability holds true for the entire model parameter space. Have the authors thoroughly screened the full model parameter space to support their statements? It would be beneficial for the authors to provide clarification on the extent of their exploration of the model parameter space to ensure the robustness of their conclusions.

We sincerely thank the editor(s) and referee(s) for the helpful suggestion!

The trade-off between considered parameter space and computational cost is a long-term challenge in network study as there are always numerous combinations of network nodes, edges, and parameters [Ma et al., Cell, 2009; Chau et al., Cell, 2012]. The computational pipeline in Section 2.1 generalized for all reaction-diffusion networks exerts two strategies to limit the computational cost and set up a basic network reference: 1. Dimension Reduction (Strategy 1) - Unifying the parameter values for different nodes and different edges within the same regulatory type to minimize the unidentical parameter numbers into 3; 2: Parameter Space Confinement (Strategy 2): Enumerating the dimensionless parameter set on a three-dimensional (3D) grid confined by γ∈ [0,0.05] in steps ∆γ = 0.001, k₁∈[0,5] in steps ∆k₁ = 0.05,  and  in steps .

In the early stage of our project, we tried to explore “the entire model parameter space” as indicated by the reviewer. We first tried to use the Monte Carlo method to find parameter solutions in an open parameter space and with all parameter values allowed to be different. However, such a process is full of randomness and is computationally expensive (taking months to search viable parameter sets but still unable to profile the continuous viable parameter space; the probability of finding a viable parameter set is no higher than 0.02%, making it very hard to profile a continuous viable parameter space). Now we clearly can see the viable parameter space is a thin curved surface where all parameters have to satisfy a critical balance (Fig. 3a, b, Fig. 5e, f). This is why we exert a typical strategy for dimension reduction in network research in both cell polarization [Marée et al., Bull. Math. Biol., 2006; Goehring et al., Science, 2011; Trong et al., New J. Phys., 2014] and other biological topics (e.g., plasmid transferring in the microbial community [Wang et al., Nat. Commun., 2020]), i.e., unifying the parameter values for different nodes and different edges within the same regulatory type.

Additionally, the curved surface for viable parameter space can be extended to infinite as long as the parameter balance is achieved (Fig. 3a, b, Fig. 5e, f), it is impossible or unnecessary to explore “the entire model parameter space”. Setting up a confined parameter region near the original point for parameter enumeration can help profile the continuous viable parameter space, which is sufficient for presenting the central conclusion of this paper – that is - the network structure and parameter need to satisfy a balance for stable cell polarization.

To support a comprehensive study considering all kinds of reference and perturbed networks, we have maximized the parameter domain size by exhausting all the computational research we can access, including 400-500 Intel(R) Core(TM) E5-2670v2 and Gold 6132 CPU on the server (High-Performance Computing Platform at Peking University) and 5 Intel(R) Core(TM) i9-14900HX CPU on personal computers.

To make it certain that instability holds true when the model parameter space is extended, we add a comprehensive comparison between the simple and complete models about how their instability occurs consistently even when the parameters (i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c) are assigned with various values concerning all nodes and regulations, searched by the Monte Carlo method (Fig. S5).

(4) Sensitivity of Numerical Solutions to Initial Conditions: Are the numerical solutions in both models sensitive to the chosen initial condition? What results do the models provide if uniform initial distributions were utilised instead?

We sincerely thank the editor(s) and referee(s) for the comments!

To investigate both the simple network and the realistic network consisting of various node numbers and regulatory pathways [Goehring et al., Science, 2011; Lang et al., Development, 2017], we propose a computational pipeline for numerical exploration of the dynamics of a given reaction-diffusion network's dynamics, specifically targeting the maintenance phase of stable cell polarization after its initial establishment [Motegi et al., Nat. Cell Biol., 2011; Goehring et al., Science, 2011; Seirin-Lee et al., Cells, 2020].

Now we have added new simulations and explanations for the sensitivity of numerical solutions to initial conditions. For both models, a uniform initial distribution leads to a homogeneous pattern while a Gaussian noise distribution leads to a multipolar pattern. In contrast, an initial polarized distribution (even with shifts in transition planes, weak polarization, or asymmetric curve shapes between the two molecular species) can maintain cell polarization reliably.

(5) Initial Conditions and Stability Tests: In Figure 1, the authors discuss the stability of the basic two-node network (a) upon modifications in (b-d). The stability test is performed through a pipeline procedure in which they always start from a polarised pattern described by Equation (4) and observe how the pattern evolves over time. It would be beneficial to explore whether the stability test depends on this specific initial condition. For instance, what would happen if the posterior molecules have an initial distribution of 1/(1+e^(-10x)), which is not exactly symmetric with respect to the anterior molecules' distribution of 1-1/(1+e^(-20x))? Additionally, if the initial polarisation is not as strong, for example, with the anterior molecules having a distribution of 10-1/(1+e^(-20x)) and the posterior molecules having a distribution of 9+1/(1+e^(-20x)), how would this affect the results?

We sincerely thank the editor(s) and referee(s) for the constructive advice!

Now we have added comprehensive comparisons between the simple and complete models about how they respond to alternative initial conditions consistently (Fig. S4, Fig. S9). The successful cell polarization pattern requests an initial polarized pattern, but its following stability and response to perturbation depend very little on the specific form of the initial polarized pattern. All the conditions mentioned by the reviewer have been included.

(6) Stability Analysis: Throughout the paper, the authors discuss the stability of the polarised pattern. The stability is checked by an exhaustive search of the parameter space, ensuring the system reaches a steady state with a polarised pattern instead of a homogeneous pattern. It would be beneficial to explore if this stability is related to a linear stability analysis of the model parameters, similar to what was conducted in Reference [18], which can determine if a homogeneous state exists and whether it is stable or unstable. Including such an analysis could provide deeper insights into the system's stability and validate its robustness.

We sincerely thank the editor(s) and referee(s) for the comments!

We agree that the linear stability analysis can potentially offer additional insights into polarized pattern behavior. However, this approach often requests the aid of numerical solutions and is therefore not entirely independent [Goehring et al., Science, 2011]. Over the past decade, numerical simulations have consistently proven to be a reliable and sufficient approach for studying network dynamics, spanning from C. elegans cell polarization [Tostevin et al., Biophys. J, 2008; Blanchoud et al., Biophys. J, 2015; Seirin-Lee, Dev. Growth Differ., 2020] to topics in metazoon [Chau et al., Cell, 2012; Qiao et al., eLife, 2022; Sokolowski et al., arXiv, 2023]. Numerous purely numerical studies have successfully unveiled principles that help interpret [Ma et al., Cell, 2009] and synthesized real biological systems [Chau et al., Cell, 2012], independent of additional mathematical analysis. Thus, we leverage our numerical framework to address the cell polarization problems cell polarization problems in this paper.

To confirm the reliability of stability checked by an exhaustive search of the parameter space, now we reproduce the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], we reproduce five experimental groups in total (two acting on LGL-1 and three acting on CDC-42), comprising eight perturbed conditions and using wild-type as the reference.

To confirm the robustness of our conclusions regarding the system's stability, now we add comprehensive comparisons between the simple and complete models about 1. How they respond to alternative initial conditions consistently (Fig. S4; Fig. S9). 2. How they respond to alternative single modifications consistently, even when the parameters (i.e., γ, α, k₁, k₂, q₁, q₂ and [X_c ) are assigned with various values concerning all nodes and regulations (Fig. S5).

(7) Interface Position Determination: In Figure 4, the authors demonstrate that by using a spatially varied parameter, the position of the interface can be tuned. Particularly, the interface is almost located at the step where the parameter has a sharp jump. However, in the case of a homogeneous parameter (e.g., Figure 4(a)), the system also reaches a stable polarised pattern with the interface located in the middle (x = 0), similar to Figure 4(b), even though the homogeneous parameter does not contain any positional information of the interface. It would be helpful to clarify the difference between Figure 4(a) and Figure 4(b) in terms of the interface position determination.

We sincerely thank the editor(s) and referee(s) for the comments!

The case of a homogeneous parameter (e.g., Fig. 4a), in which the system also reaches a stable polarised pattern with the interface located in the middle (x = 0), is just a reference adopted from Fig. 1a to show that the inhomogeneous positional information in Fig. 4b can achieve a similar stable polarised pattern.

Now we clarify the interface position determination to Section 2.4 to improve readability. Moreover, it is marked with grey dashed line in all the patterns in Fig. 4 and Fig. 6 to highlight the importance of inhomogeneous parameters on interface localization.

(8) Presented Comparison with Experimental Observations: The comparison with experimental observations lacks clarity. It isn't clear that the model "faithfully recapitulates" the experimental observations (lines 369-370). We recommend discussing and showing these comparisons more carefully, highlighting the expectations and similarities.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we remove the word “faithfully” and highlight the expectations and similarities of each experimental group by describing “cell polarization pattern characteristics in simulation: …”.

(9) Validation of Model with Experimental Data: Given the extensive number of model parameters and the uncertainty of their values, it is essential for the authors to validate their model by comparing their results with experimental data. While C. elegans polarisation has been extensively studied, the authors have yet to utilise existing data for parameter estimation and model validation. Doing so would considerably strengthen their study.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

To utilise existing data for parameter estimation, now we add a new section, Parameter Nondimensionalization and Order of Magtitude Consistency, into Supplemental Text. In this section, we introduced how we adopted the parameter nondimensionalization and value assignments from previous works [Goehring et al., J. Cell Biol., 2011; Goehring et al., Science, 2011; Seirin-Lee et al., Cells, 2020]. We listed four examples (i.e., evolution time, membrane diffusion coefficient, basal off-rate, and inhibition intensity) to show the consistency in order of magtitude between numerical and realistic values.

To utilise existing data for model validation, now we reproduce the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], we reproduce five experimental groups in total (two acting on LGL-1 and three acting on CDC-42), comprising eight perturbed conditions and using wild-type as the reference.

Also, we acknowledge the limitations of the current cell polarization model and provided, in 3. Discussion and conclusion, a detailed outline of potential model improvements. The limitations include, but are not limited to, issues involving “extensive number of model parameters” and “uncertainty of their values”, both of which rely on experimental measurements of biological information. However, comprehensive experimental measurement data on every molecular species, their interactions, and each species’ intensity distribution in space and time were not fully available from prior research. Refinement is lacking for some of these interactions, potentially requiring years of additional experimentation. Moreover, for certain species at specific developmental stages, only relative (rather than absolute) intensity measurements are available. We agreed that such information is essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion. From a theoretical perspective, we adopted assumptions from the previous literature and constructed a minimal model for a specific cell polarization phase to investigate the network's robustness, supported by five experimental groups and eight perturbed conditions with wild-type as a reference in the C. elegans embryo.

(10) Enhancing Model Accuracy by Considering Cortical Flows: The authors are encouraged to include cortical flows in their cell polarisation model, as these flows are known to be pivotal in the process. Although the current model successfully predicts cell polarisation without accounting for cortical flows, research has demonstrated their significant role in polarisation formation. By incorporating cortical flows, the model would provide a more thorough and precise representation of the biological process. Furthermore, previous studies, such as those by Goehring et al. (References 17 and 18), highlight the importance of convective actin flow in initiating polarisation. It would be valuable for the authors to address the contribution of convection with actin flow to the establishment of the polarisation pattern. The polarisation of the C. elegans zygote progresses through two distinct phases: establishment and maintenance, both heavily influenced by actomyosin dynamics. Works by Munro et al. (Dev Cell 2004), Shivas & Skop (MBoC 2012), Liu et al. (Dev. Biol. 2010), and Wang et al. (Nat Cell Biol 2017) underscore the critical roles of myosin and actin in orchestrating the localisation of PAR proteins during cell polarisation. To enhance the fidelity of their model, we recommend that the authors either integrate cortical flows and consider the effects driven by myosin and actin, or provide a discussion on the repercussions of omitting these dynamics.

We sincerely thank the editor(s) and referee(s) for the comment!

Indeed, previous research highlighted the importance of convective cortical flow in orchestrating the localisation of PAR proteins during the establishment phase of polarisation formation [Goehring et al., J. Cell Biol., 2011; Rose et al., WormBook, 2014; Beatty et al., Development, 2013]. However, during the maintenance phase, the non-muscle myosin II (NMY-2) is regulated downstream by the PAR protein network rather than serving as the primary upstream factor controlling PAR protein localization. While some theoretical studies integrated both reaction-diffusion dynamics and the effects of myosin and actin [Tostevin et al., Biophys J, 2008; Goehring et al, Science, 2011], others focused exclusively on reaction-diffusion dynamics [Dawes et al., Biophys. J., 2011; Seirin-Lee et al., Cells, 2020]. Now we clarify the distinction between the establishment and maintenance phases, emphasize our research focus on the reaction-diffusion dynamics during the maintenance phase, and provide a discussion of these omitted dynamics to foster a more comprehensive understanding in the future, as suggested.

(11) Further Justification of Network Interactions: The authors should provide additional explanations, supported by empirical evidence, for the network interactions assumed in their model. This includes both node-node interactions and the rationale behind protein complex formations. Some of the proposed interactions lack empirical validation, as noted in studies such as Gubieda et al., Phil. Trans. R. Soc. B 2020. Additionally, discrepancies in protein intensity distributions, as observed in Wang et al., Nat Cell Biol 2017, should be addressed, particularly concerning the consideration of the PAR-3/PAR-6/PKC-3 complex as a single entity. Justifying these choices is crucial for ensuring the model's credibility and alignment with experimental findings.

We sincerely thank the editor(s) and referee(s) for the helpful advice!

In consistency with previous modeling efforts [Goehring et al., Science, 2011; Gross et al., Nat. Phys., 2019; Lim et al., Cell Rep., 2021], our model treats the PAR-3/PAR-6/PKC-3 complex as a single entity for simplification, thus neglecting the potentially distinct spatial distributions of each single molecular species.

Now we acknowledge the limitations of the current cell polarization model and provided, in 3. Discussion and conclusion, a detailed outline of potential model improvements. The limitations include, but are not limited to, issues involving “node-node interactions” and “discrepancies in protein intensity distributions”, both of which rely on experimental measurements of biological information. However, comprehensive experimental measurement data on every molecular species, their interactions, and each species’ intensity distribution in space and time were not fully available from prior research. Refinement is lacking for some of these interactions, potentially requiring years of additional experimentation. Moreover, for certain species at specific developmental stages, only relative (rather than absolute) intensity measurements are available. We agreed that such information is essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion.

To ensure the model's credibility and alignment with experimental findings, now we reproduce the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total (two acting on LGL-1 and three on CDC-42), comprising eight perturbed conditions and using wild-type as the reference.

(12) Further Justification of Node-Node Network Interactions: The authors should provide further justification for the node-node network interactions assumed in their study. To the best of our knowledge, some of the node-node interactions proposed have not yet been empirically demonstrated. Providing additional explanations for these interactions would enhance the credibility of the model and ensure its alignment with empirical evidence.

We sincerely thank the editor(s) and referee(s) for the helpful advice!

Now we acknowledge the limitations of the current cell polarization model and provided, in 3. Discussion and conclusion, a detailed outline of potential model improvements. The limitations include, but are not limited to, issues involving “node-node network interactions”, which rely on experimental measurements of biological information. However, comprehensive experimental measurement data on every molecular species, their interactions, and each species’ intensity distribution in space and time were not fully available from prior research. Refinement is lacking for some of these interactions, potentially requiring years of additional experimentation. Moreover, for certain species at specific developmental stages, only relative (rather than absolute) intensity measurements are available. We agreed that such information is essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion.

To enhance the credibility of the model and ensure its alignment with empirical evidence, we reproduced the qualitative and semi-quantitative phenomenon in three more experimental groups previously published (Section 2.5; Fig. S8) [Gotta et al., Curr. Biol., 2001; Aceto et al., Dev. Biol., 2006]. Combined with the original experiments (Section 2.5; Fig. 5; Fig. S7) [Hoege et al., Curr. Biol., 2010; Beatty et al., Development, 2010; Beatty et al., Development, 2013], now we have reproduced five experimental groups in total (two acting on LGL-1 and three on CDC-42), comprising eight perturbed conditions and using wild-type as the reference.

(13) Justification for Network Interactions and Protein Complexes: The authors must provide clear justifications, supported by references, for each network interaction between nodes in the five-node model. Some of the activatory/inhibitory signals proposed lack empirical validation, such as CDC-42 directly inhibiting CHIN-1. The provided Table S2 is insufficient to justify these interactions, necessitating additional explanations. Reviewing relevant literature, such as the work by Gubieda et al., Phil. Trans. R. Soc. B 2020, may offer insights into similar node networks. Furthermore, the authors should address discrepancies in protein intensity distributions, as observed in studies like Wang et al., Nat Cell Biol 2017. Specifically, the authors consider the PAR-3/PAR-6/PKC-3 complex as a single entity despite potential differences in their distributions. Justification for this choice is essential, particularly considering the importance of clustering dynamics during cell polarisation, as demonstrated by Wang et al., Nat Cell Biol 2017, and Dawes & Munro, Biophys J 2011.

We sincerely thank the editor(s) and referee(s) for the helpful advice!

In consistent with previous modeling efforts [Goehring et al., Science, 2011; Gross et al., Nat. Phys., 2019; Lim et al., Cell Rep., 2021], our model treats the PAR-3/PAR-6/PKC-3 complex as a single entity for simplification, thus neglecting the potentially distinct spatial distributions of each single molecular species. Besides, the inhibition of CHIN-1 from CDC-42, which recruits cytoplasmic PAR-6/PKC-3 to form a complex, may act indirectly to restrict CHIN-1 localization through phosphorylation [Sailer et al., Dev. Cell, 2015; Lang et al., Development, 2017].

Now we acknowledge the limitations of the current cell polarization model and provided, in 3. Discussion and conclusion, a detailed outline of potential model improvements. The limitations include, but are not limited to, issues involving “each network interaction between nodes in the five-node model” and “discrepancies in protein intensity distributions”, both of which rely on experimental measurements of biological information. However, comprehensive experimental measurement data on every molecular species, their interactions, and each species’ intensity distribution in space and time were not fully available from prior research. Refinement is lacking for some of these interactions, potentially requiring years of additional experimentation. Moreover, for certain species at specific developmental stages, only relative (rather than absolute) intensity measurements are available. We agreed that such information is essential for establishing a more utilizable model and discussed it thoroughly in 3. Discussion and conclusion. From a theoretical perspective, we adopted assumptions from the previous literature and constructed a minimal model for a specific cell polarization phase to investigate the network's robustness, supported by five experimental groups and eight perturbed conditions with wild-type as a reference in the C. elegans embryo.

(14) Incorporating Cytoplasmic Dynamics into the Model: The authors assume infinite cytoplasmic diffusion and neglect the role of cytoplasmic flows in cell polarity, which may oversimplify the model. Finite cytoplasmic diffusion combined with flows could potentially compromise the stability of anterior-posterior molecular distributions, affecting the accuracy of the model's predictions. The authors claim a significant difference between cytoplasmic and membrane diffusion coefficients, but the actual disparity seems smaller based on data from Petrášek et al., Biophys. J. 2008. For example, cytosolic diffusion coefficients for NMY-2 and PAR-2 differ by less than one order of magnitude. Additionally, the strength of cytoplasmic flows, as quantified by studies such as Cheeks et al., and Curr Biol 2004, should be considered when assessing the impact of cytoplasmic dynamics on polarity stability. Incorporating finite cytoplasmic diffusion and cytoplasmic flows into the model could provide a more realistic representation of cellular dynamics and enhance the model's predictive power.

We sincerely thank the editor(s) and referee(s) for the comment!

Cytoplasmic and membrane diffusion coefficients differ by two orders of magnitude according to previous experimental measurements on PAR-2 and PAR-6 [Goehring et al., J. Cell Biol., 2011; Lim et al., Cell Rep., 2021]. Many previous C. elegans cell polarization models have incorporated mass-conservation model combined with finite cytoplasmic diffusion, but this model description can lead to reverse spatial concentration distribution between the cell membrane and cytosol [Fig. 3 of Seirin-Lee et al., J. Theor. Biol., 2016; Fig. 2ab of Seirin-Lee et al., J. Math. Biol., 2020], disobeying experimental observation [Fig. 4A of Sailer et al., Dev. Cell, 2015; Fig. 1A of Lim et al., Cell Rep., 2021]. This implies that the infinite cytoplasmic diffusion, without precise experiment-based parameter assignment or accounting for other hidden biological processes (e.g., protein production and degradation), may be inappropriate in modeling the real spatial concentration distributions distinguished between the cell membrane and cytosol. To address this issue, some theoretical research incorporated protein production and degradation into their model, to acquire the consistent spatial concentration distribution between the cell membrane and cytosol [Tostevin et al., Biophys. J., 2008]. More definitive experimental data on the spatiotemporal changes in protein diffusion, production, and degradation are essential for providing a more realistic representation of cellular dynamics and enhancing the model's predictive power.

Cytoplasmic flows indeed play an unneglectable role in cell polarity during the establishment phase [Kravtsova et al., Bull. Math. Biol., 2014], which creates a spatial gradient of actomyosin contractility and directs PAR-3/PKC-3/PAR-6 to the anterior membrane by cortical flow [Rose et al., WormBook, 2014; Lang et al., Development, 2017]. However, during the maintenance phase, the non-muscle myosin II (NMY-2) is regulated downstream by the PAR protein network rather than serving as the primary upstream factor controlling PAR protein localization [Goehring et al., J. Cell Biol., 2011; Rose et al., WormBook, 2014; Geβele et al., Nat. Commun., 2020]. While some theoretical studies integrated both reaction-diffusion dynamics and the effects of myosin and actin [Tostevin, 2008; Goehring, Science, 2011], others focused exclusively on reaction-diffusion dynamics [Dawes et al., Biophys. J., 2011; Seirin-Lee et al., Cells, 2020]. We now emphasize our research focus on the reaction-diffusion dynamics during the maintenance phase, so the dynamics between NMY-2 and PAR-2 are not included. We have also provided a discussion of the simplified cytoplasmic diffusion and omitted cytoplasmic flows to foster a more comprehensive understanding in the future.

(15) Explanation of Lethality References: On page 13, the authors mention lethality without adequately explaining why they are drawing connections with lethality experimental data.

We sincerely thank the editor(s) and referee(s) for the comment!

It is well-known that cell polarity loss in C. elegans zygote will lead to symmetric cell division, which brings out the more symmetric allocation of molecular-to-cellular contents in daughter cells; this will result in abnormal cell size, cell cycle length, and cell fate in daughter cells, followed by embryo lethality [Beatty et al., Development, 2010; Beatty et al., Development, 2013; Rodriguez et al., Dev. Cell, 2017; Jankele et al., eLife, 2021]. Now we explain why we are drawing connections with lethality experimental data in Section 2.5.

(16) Improved Abstract: "...However, polarity can be restored through a combination of two modifications that have opposing effects..." This sentence could be revised for better clarity. For example, the authors could consider rephrasing it as follows: "...However, polarity restoration can be achieved by combining two modifications with opposing effects...".

We sincerely thank the editor(s) and referee(s) for helpful advice!

Now we revise the abstract as follows:

“Abstract – However, polarity restoration can be achieved by combining two modifications with opposing effects.”

(17) Conservation of Mass in Network Models: Is conservation of mass satisfied in their network models?

We sincerely thank the editor (s) and referee(s) for the comment!

While previous experiments provide evidence for near-constant protein mass during the establishment phase [Goehring et al., Science, 2011], whether this is consistent until the end of maintenance is unclear.

Many previous C. elegans cell polarization models have assumed mass conservation on the cell membrane and in the cell cytosol, this model description can lead to reverse spatial concentration distribution between the cell membrane and cytosol [Fig. 3 of Seirin-Lee et al., J. Theor. Biol., 2016; Fig. 2ab of Seirin-Lee et al., J. Math. Biol., 2020], disobeying experimental observation [Fig. 4A of Sailer et al., Dev. Cell, 2015; Fig. 1A of Lim et al., Cell Rep., 2021]. This implies that mass conservation may be inappropriate in modeling the real spatial concentration distributions distinguished between the cell membrane and cytosol. To address this issue, some theoretical research incorporated protein production and degradation into their model, instead of assuming mass conservation [Tostevin et al., Biophys. J., 2008]. More definitive experimental data on the spatiotemporal changes in protein mass are essential for constructing a more accurate model.

Given the absence of a universally accepted model in agreement with experimental observation, we adopted the assumption that the concentration of molecules in the cytosol (not the total mass on the cell membrane and in the cell cytosol) is spatially inhomogeneous and temporally constant, which was also used before [Kravtsova et al., Bull. Math. Biol., 2014]. In the context of this well-mixed constant cytoplasmic concentration, our model successfully reproduced the cell polarization phenotype in wild-type and eight perturbed conditions (Section 2.5; Fig. S7; Fig. S8), supporting the validity of this simplified, yet effective, model. Now we have provided a discussion of protein mass assumption to foster a more comprehensive understanding in the future.

(18) Comparison of Network Structures: In Figure 1c, the authors demonstrate that the symmetric two-node network is susceptible to single-sided additional regulation. They considered four subtypes of modifications, depending on whether [L] is in the anterior or posterior and whether [A] and [L] are mutually activating or inhibiting. What is the difference between the structure where [L] is in the anterior and in the posterior? Upon comparing the time evolution of the left panel ([L] is sided with

) and the right panel ([L] is sided with [A]), the difference is so tiny that they are almost indistinguishable. It might be beneficial for the authors to provide a clearer explanation of the differences between these network structures to aid in understanding their implications.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

The difference between the structures where [L] is in the anterior and posterior is the initial spatial concentration distribution of [L], which is polarized to have a higher concentration in the anterior and posterior respectively. The time evolution of the left panel ([L] is sided with [P]) and the right panel [L] is sided with [P]) is almost indistinguishable because the perturbation from [L] is slight (less than over one order of magnitude) compared to the predominant [A]~[P] interaction ( for [A]~[P] mutual inhibition while for [A]~[L] mutual inhibition and for [A]~[L] mutual activation), highlighting the response of cell polarization pattern. To aid the readers in understanding their implications, we have added the [L] and plotted the spatial concentration distribution of all three molecular species at t=0,100, 200, 300, 400 and 500 in Fig. S3, where the difference between the [L] ones in the left and right panels are distinguishably shown.

(19) Figure Reference: In line 308, Fig. 4a is referenced when explaining the loss of pattern stability by modifying an individual parameter, but this is not shown in that panel. Please update the panel or adjust the reference in the main text.

We sincerely thank the editor(s) and referee(s) for pointing out this problem!

Fig. 4 focuses on the regulatable shift of the zero-velocity interface by modifying a pair of individual parameters, not on the loss (or recovery) of pattern stability, which has been analyzed as a focus in Fig. 1, Fig. 2, and Fig. 3. Fig. 4a is actually from the same simulation as the one in Fig. 1a, which has spatially uniform parameters used as a reference in Fig. 4. The individual parameter modification in other subfigures of Fig. 4 shows how the zero-velocity interface is shifted in a regulatable manner always in the context of pattern stability. Now we update the panel, adjust the reference, add one more paragraph, and improve the wording to clarify how the analyses in Fig. 4 are carried out on top of the pattern stability already studied.

(20) Viable Parameter Sets: In line 355, the number of viable parameter sets (602) is not very informative by itself. We suggest reporting the fraction or percentage of sets tested that resulted in viable results instead. This applies similarly to lines 411 and 468.

We sincerely thank the editor(s) and referee(s) for the constructive comment!

Now the fraction/percentage of parameter sets tested that resulted in viable results are added everywhere the number appears.

(21) Perturbation Experiments: In lines 358-359, "the perturbation experiments" implies that those considered are the only possible ones. Please rephrase to clarify.

We sincerely thank the editor(s) and referee(s) for the helpful advice!

Now we rephrase three paragraphs to clarify why the perturbation experiments involved with [L] and [C] are considered instead of other possible ones.

(22) Figure 2S: This figure is unclear. The caption states that panel (a) shows the "final concentration distribution," but only a line is shown. If "distribution" refers to spatial distribution, please clarify which parameters are shown.

We sincerely thank the editor(s) and referee(s) for pointing out this problem!

Now we clarify the “spatial concentration distribution” and which parameters are shown in the figure caption.

(23) Figure 5 and 6 Captions: The captions for Figures 5 and 6 could benefit from clarification for better understanding.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we clarify the details in the captions of Fig. 5 and Fig. 6 for better understanding.

(24) Figure 5 Legend: The legend on the bottom right corner of Figure 5 is unclear. Please specify to which panel it refers.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we clarify to which the legend on the bottom right corner of Fig. 5 refers.

(25) L and A~C Interactions: In paragraphs 405-418, please explain why the L and A~C interactions are removed for the comparison instead of others.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we add a separate paragraph and a supplemental figure to explain why the L and A~C interactions are removed for the comparison instead of others.

(26) Network Structures in Figure S3: From the "34 possible network structures" considered in Figure S3 (lines 440-441), why are the "null cases" (L disconnected from the network) relevant? Shouldn't only 32 networks be considered?

We sincerely thank the editor(s) and referee(s) for pointing out this problem!

Now the two “null cases” are removed:

(27) Figure S3 Caption: The caption must state that the position of the nodes (left or right) implies the polarisation pattern. Additionally, with the current size of the figure, the dashed lines are extremely hard to differentiate from the continuous lines.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we state that the position of the nodes (left or right) implies the polarization pattern. Additionally, we have modified the figure size and dashed lines so that the dash lines are adequately distinguishable from the continuous lines.

(28) Equation #7: It is confusing to use P as the number of independent simulations when P is also one of the variables/species in the network. Please consider using different notation.

We sincerely thank the editor(s) and refer(s) for the hhelpful advice!

Now we replace the P in current Equation #8 with Q and the P in current Equation #10 with W.

(29) Use of "Detailed Balance": The authors used the term "detailed balance" to describe the intricate balance between the two groups of proteins when forming a polarised pattern. However, "detailed balance" is a term with a specific meaning in thermodynamics. Breaking detailed balance is a feature of nonequilibrium systems, and the polarisation phenomenon is evidently a nonequilibrium process. Using the term "detailed balance" may cause confusion, especially for readers with a physics background. It might be advisable to reconsider the terminology to avoid potential confusion and ensure clarity for readers.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

To avoid potential confusion and ensure clarity for readers, now we replace “detailed balance” with “balance”, “required balance”, or “interplay” regarding different contexts.

(30) Terminology: The word "molecule" is used where "molecular species" would be more appropriate, e.g., lines 456 and 551. Please revise these instances.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we replace all the “molecule” by “molecular species” as suggested.

(31) Section 2.5: This section is confusing. It isn't clear where the "method outlined" (line 464) is nor what "span an iso-velocity surface at vanishing speed" means in line 470. The sentence in lines 486-488, "An expression similar to Eq. 8 enables quantitative prediction...", is too vague. Please clarify these points and specify what the "similar expression" is and where it can be found.

We sincerely thank the editor(s) and referee(s) for the constructive suggestion!

Now we clarify these points and specify the terms as suggested.

(32) Software Mention: The software is only mentioned in the abstract and conclusions. It should also be mentioned where the computational pipeline is described, and the instructions available in the supplementary information need to be referenced in the main text.

We sincerely thank the editor(s) and referee(s) for pointing out this problem!

Now we mention the software where the computational pipeline is described and reference the instructions available in the Supplemental Text.

(33) Supplementary Material References: Several parts of the supplementary material are never referenced in the main text, including Figure S1, Movies S3-S4, and the Instructions for PolarSim. Please reference these in the main text to clarify their relevance and how they fit with the manuscript's narrative.

We sincerely thank the editor(s) and referee(s) for pointing out this problem!

Now we add all the missing references for supplementary materials to the main text properly.

approaching

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Reply to the reviewers

Referee #1 Major concerns:

1) One major concern that I have about the sexual dimorphism in tolerance to nutrient deprivation is that the papers cited by the authors, and paradigms that are used broadly in the field, all use adult flies. The authors must show that in larvae, a completely different life stage from their citations, there is a sexual dimorphism in tolerance to nutrient deprivation.

In our descriptions of previous literature that describes tolerance to nutrient deprivation, we have added language that specifies that the results from nutrient deprivation mentioned therein were performed in adults (lines 82, 91, 96, highlighted in the preliminary revision).

In response to the concern from this reviewer that our data do not assay for nutrient deprivation in larvae, we would like to clarify that our “stress tolerance assay” more specifically demonstrates that developmental nutrient deprivation compromises male survival through pupariation to adulthood. While the effects of acute nutrient deprivation on developmental delay can be assayed in foraging or earlier larval stages, we have not tested whether ATF4 signaling is present and dimorphic in these stages and believe it to be beyond the scope of this study. In the revision, we will edit the text to be more precise in our conclusions with these data.

Interestingly, Diaz et al 2023 (Genetics) show that male larvae have greater fat stores than female larvae. Considering fat is the main determinant of tolerance to nutrient deprivation it's not clear that females will actually survive nutrient deprivation longer as larvae. This is an essential test of whether female larvae do have increased tolerance to nutrient deprivation, which is the basic foundation of the authors' model.

We thank the reviewer for making this clarifying point about the relationship between fat stores and nutrient deprivation. ____In response to the concern our data do not assay for nutrient deprivation in larvae (major point #1), we would like to clarify that our “stress tolerance assay” more specifically demonstrates that developmental nutrient deprivation compromises male survival through pupariation to adulthood. While the effects of acute nutrient deprivation on developmental delay can be assayed in foraging or earlier larval stages, we have not tested whether ATF4 signaling is present and dimorphic in these stages and believe it to be beyond the scope of this study. In the revision, we will edit the text to be more precise in our conclusions with these data.

2) Another concern is the way that the authors "genetically induce nutrient deprivation using methioninase overexpression". As they acknowledge in the discussion (Line 381-390), methioninase overexpression will have many cellular effects. While there is no doubt that methionine levels would be lower in their model, it is less certain whether this is the main driver of the male-specific lethality.

There are two potential solutions to this problem. First, the authors could change the text throughout the paper to more accurately describe their paradigm as "methioninase-induced lethality" rather than "nutrient deprivation". This would limit the scope of their scientific question and the conclusions they draw, but would eliminate the need for more experiments.

The second solution would be to complete experiments to establish the following points: i) methioninase overexpression causes all the classical features of nutrient deprivation (e.g. changes to canonical signaling pathways such as TOR); ii) using other genetic means of nutrient deprivation such as slimfast-RNAi to see if those manipulations phenocopies the male-specific lethality they see with methioninase overexpression; iii) testing a role for ATF4 in mediating sex differences (if any) in other contexts such as slimfast-RNAi. This will take 2-3 months but is essential to draw any conclusions about whether their paradigm is truly a model for nutrient deprivation.

We agree that methionine depletion is not the only cellular change effected by methioninase over-expression. For example, a molecular byproduct of methioninase metabolism via methioninase is the production of ammonia, which has recently been shown to indue ISR signaling in the context of____ alcohol-associated liver disease (Song et al. 2024, PMID 37995805). We believe our experimental controls and genetic rescues account for this and other possible effects in the interpretation of our data. ____To further establish the utility of methioninase overexpression as a genetic means of methionine deprivation (first described in Parkhitko et al. 2021, PMID 34588310), we will perform ____slimfastRNAi_ in the fat (another genetic means of reducing intracellular amino acid levels) per the reviewer’s suggestion. In these animals we will evaluate 1) ATF4 activity in L3 adipocytes using 4E-BPintron-GFP (1.5 months) , and 2) male vs. female lethality (as determined by counting eclosed adults) (2 months. If male lethality is observed with _UAS-slimfastRNAi _as with _methioninase ____expression, we will test the requirement for dimorphic ATF4 signaling in the fat for such male susceptibility to lethality/female resistance to lethality. (3 months)

3) Another important point is that the authors state that sexually dimorphic ATF4 activity in the fat body is instructed by sexual identity in a cell-autonomous manner. Despite a clear decrease in ATF4 reporter levels in tra mutants, the fat body-specific tra-RNAi effect on the ATF4 reporter was less convincing. Together with the fact that changes to tra in the fat body affect insulin secretion from the insulin-producing cells, it is possible that the effect on ATF4 is not cell-autonomous. To conclusively test if sexual identity regulates ATF4 in a cell-autonomous manner the authors should use the flp-out system to make Tra-expressing or tra-RNAi-expressing clones in the fat body. This would take approximately 1.5 months to make the strain and test this.

We thank the reviewer for making the astute observation that the effect of fat body-specific ____tra_ knockdown on female ATF4 reporter activity was more modest than whole-animal _tra_ mutants. We ascribe this to RNAi knockdown efficiency rather than non-autonomous effects of sexual identity on ATF4 expression in the fat. This is underscored by our data showing fat body knockdown of _spenito_ (_nito_), a sex determinant upstream of _tra____ that is shown to instruct female sexual identity in the larval fat (Diaz et al. 2023, PMID 36824729), does indeed reduce ATF4 levels in female fat to that of control male fat (Fig. 2K).

4) As the authors show for the UAS-methioninase, other UAS lines used in the paper such as UAS-traF, UAS-tra-RNAi, UAS-dsx-RNAi may have leaky effects on gene/reporter expression. The authors must include a UAS only control to establish that the tra-RNAi, UAS-traF, UAS-dsx-RNAi do not affect gene/reporter expression.

We thank the reviewer for suggesting that we evaluate the “leakiness” of all UAS lines used in this study (major point #4). To do this, we will quantify ATF4 reporter activity in the fat (4E-BPintron-GFP) in the presence of UAS lines but in the absence of GAL4 for ____UAS-traRNAi_, _UAS-traF_, and _UAS-dsxRNAi____ (1.5 months)

5) I have concerns about the statistics used. In the methods and legends only t-tests are mentioned; however, when three groups are compared a one-way ANOVA with post-hoc tests must be used to correct for multiple comparisons. To compare differential responses to genetic/environmental manipulations between the sexes, a two-way ANOVA must be used. For example, to conclude that males and females have different responses in the two-way ANOVA, there must be a significant genotype:sex interaction. The p-values for comparisons between genotypes in either the one-way or two-way ANOVA must be derived from post-hoc tests within the ANOVA analysis.

__We thank the reviewer for carefully assessing our usage of statistical analyses to interpret the data in the study. To the best of our understanding, such ANOVA analyses are helpful in evaluating significance when comparing multiple sample groups simultaneously. However, in all our analyses we are only ever comparing two samples at a time, making a two-tailed Student’s t-test with Welch’s correction (assuming unequal variance) to be the best statistical method. __

Referee #1 Minor points

1) Please ensure to make the reader aware of which life stage was tested in the literature cited supporting sexually dimorphic tolerance to nutrient deprivation.

We thank the reviewer for pointing out this ambiguity in our description of previous and current work on nutrient deprivation tolerance. We address this minor point in tandem with major point #1 above ____by adding language that specifies that the results from nutrient deprivation mentioned therein were performed in adults (lines 82, 91, 96, highlighted in the preliminary revision).

2) Published data about sex-specific mechanisms of metabolic regulation mean that the introduction should be more fully cited than it is. Even in the introduction "the molecular basis of these differences and how they impact tolerance to nutrient deprivation is still under investigation" is inaccurate, as there are published studies identifying some mechanisms (work on gut hormones and sex-specific effects on starvation resistance and body fat, role of ecdysone on body fat and feeding, sex-specific roles for brummer and Akh in regulating body fat, intestinal transit and gut size and feeding). Please adjust the paper to acknowledge this growing body of knowledge.

We thank the reviewer for appropriately highlighting that there are other relevant studies in the context of sex-specific mechanisms of metabolic regulation in addition to those referenced in the original manuscript. Specifically, we will include additional citations and appropriate descriptions of previous work, such as those that report on sex-specific effects of starvation (i.e. Millington et al. 2022, PMID 35195254) and sex-specific roles for metabolic regulators such as Brummer/ATGL (Wat et al. 2020, PMID 31961851) and Adipokinetic hormone (Wat et al. 2021, PMID 34672260) in _Drosophila fat storage._ __

3) Please list the ingredients per L so that individuals can replicate the diet easily.

__We thank the reviewer for requesting additional details on the diet fed to animals in this study, which will improve the reproducibility of our findings. In the Methods section, we have now included additional details on the specific diet fed to animals used in this study (lines 465-468 in the preliminary revision).____ __

4) Please cite grant numbers for all the community resources (e.g. Bloomington, DSHB), and please acknowledge FlyBase and its grants as well. For example, here are the instructions for citing BDSC https://bdsc.indiana.edu/about/acknowledge.html and similar instructions are available for the other resources.

We thank the reviewer for underscoring the importance of citing grant numbers for all community resources used. We have added to the Acknowledgements section statements and grant numbers regarding use of community resources such as FlyBase, Bloomington Drosophila Stock Center, and DSHB (lines 533-538 in the preliminary revision).

Referee #2:

1. Figure 4 is an important part of this study, where the authors show a male-specific vulnerability to methioninase expression. They show that ATF4 RNAi confers vulnerability to methioninase expression even in females. An obvious question is whether ATF4 overexpression is sufficient to enhance resistance to methionine deprivation in males.

We thank the reviewer for pointing out that the ability of increased ATF4 in male fat to enhance resistance to methionine deprivation was not interrogated. To examine this, ____we will quantify survival rates of males and females following dual over-expression of methioninase and ATF4 (3 months). We would like to state here that experimental over-expression of ATF4 at the levels induced by GAL4 activity is sometimes lethal, so this experiment may be difficult to execute/interpret due to technical limitations.

Methioninase expression results (Figure 4) are interesting. Are the levels of methioninase expression similar between males and females?

We thank the reviewer for asking for clarification on whether methioninase induction is similar between males and females. Whether methioninase induction is sexually dimorphic is likely a function of whether there is sexual dimorphism in the strength of the GAL4 driver used. While the drivers employed in this study are widely used for fat body expression, to our knowledge relative expression of ____Dcg-GAL4_ in males versus females has never been reported. Thus, we will perform qPCR to compare GAL4 and methioninase transcript levels in _Dcg-GAL4; UAS-methioninase____ male and female fat bodies (1 month).

1. This manuscript focuses on ATF4, but there could be additional possible reasons for the sexually dimorphic ISR activity. For example, the degree of physiological stress that activates ISR could be different between males and females. I suggest comparing the levels of Phospho-eIF2alpha (or any other markers upstream of ATF4) in both sexes.

We thank the reviewer for suggesting additional checks for sexual dimorphism in ISR activity in the fat, such as degree of eIF2α phosphorylation, which is directly upstream of ATF4 induction. Per their suggestion, we will compare p-eIF2α staining in male and female larval adipocytes (1.5 months).

In Figures 1 to 3, the authors examine the intensity of ATF4 signaling after perturbing the sexual determination pathway. The methioninase experiments in Figure 4 are interesting, but there is nothing in this Figure linking male-specific vulnerability to sex determination genes. Examining the vulnerability to methioninase expression after perturbing the sexual determination genes would make Figure 4 integrate better with the rest of the manuscript.

We thank the reviewer for highlighting that the role of male sexual identity in vulnerability of males to methioninase expression was not interrogated. Similar to our genetic interaction study proposed in point #1 from this reviewer, we will test whether feminizing male fat bodies (using UAS-traF over-expression) will change survival rate of males in our methioninase-expression paradigm (3 months).

1. The authors write that they generated 4EBP intron-GFP because the 4EBP intron-DsRed signal was frequently observed in the cytoplasm (line 122). They seem to suggest that the DsRed reporter is less reliable than the GFP reporter. However, they continue to mix results using 4EBP intron-GFP (Fig. 4A) and 4EBP intron-DsRed (Fig. 4F). The two figures examine slightly different conditions (Fig 4A shows tra1 KO females, while Fig. 4F shows traF males). If the DsRed reporter is less reliable due to the signal from the cytoplasm, the authors should show results with the GFP reporter in traF males.

We thank the reviewer for raising the legitimate concern that the ____4EBPintron-DsRed_ reporter used for some of the included quantifications in Fig. 3 might be less reliable then _4EBPintron-GFP_ that was generated for this study. We have updated the manuscript text (in the Results section) to more accurately describe the justification for building the _4EBPintron-GFP____ line (lines 122-127 in the preliminary revision).

1. In Figure S1, the authors label 4EBP intron-GFP as Thor2p-GFP, which is confusing. There are other parts in the methods section referring to Thor2p. I suggest using consistent terminology throughout the manuscript.

We thank the reviewer for pointing out this typo. We have modified the text accordingly in Figure S1.

Referee #3 Major concerns:

1) Sexually dimorphic ATF4 activity (Figure 1 and associated supplemental figure) as evidenced by reporter expression is the basis of this study, yet a detailed description of the immunofluorescence quantification is lacking. The methods sections needs to include information on how a) images were acquired (Were the same acquisition settings used across all images?), b) the intensity measurements were taken (What software was used? Does each data point in the distribution represent a single nucleus (the assumption is yes)? Is nuclear size adjusted for? Panels A' and B' have obvious differences in nuclear size which would in turn affect total intensity measurements), c) the sample size (How many fat images taken per animal per sample/genotype? How many trials were performed?)

We thank the reviewer for requesting additional information describing the immunofluorescence quantification methods. ____We have now added an additional paragraph to the Methods section detailing image acquisition for quantifying reporter activity (lines 483-494 in the preliminary revision).

2) While the authors nicely address the lack in specificity for two of the Gal4 driver lines used in the study limitation section, the fact that the one driver that is fat body-specific, 3.1Lsp2-Gal4, shows a modest, not statistically significant decrease in Figure 4C still raises some concern. There is another Lsp2-Gal4 line described in Lazareva et al., 2007 (PLoS Genetics) that drives expression in larval fat, perhaps to combat the issue of 3.1Lsp2-Gal4 have low activity, as mentioned by the authors. Alternatively, this phenotype could be assessed using Gal4 lines that only drive expression in the other tissues (if available). Otherwise, the conclusion that ISR/ATF4 signaling specifically in the fat mediates the starvation response needs to be toned down.

We thank the reviewer for carefully analyzing our data showing survival during methioninase over-expression using different GAL4 drivers. ____The reviewer raises a valid concern that the GAL4 driver with highest specificity for the fat body (that is, with the least off-target tissue expression), ____3.1 Lsp2-GAL4_, induces the most modest methioninase-induced lethality (major point #2). We attribute this to the fact that _3.1 Lsp2-GAL4_ is reportedly (and in our hands) a weaker driver than _Dcg-GAL4_ in the larval fat body. We will demonstrate this experimentally by performing UAS-nucGFP expression using both _Dcg-GAL4_ and _3.1 Lsp2-GAL4____ side by side and quantifying nuclear GFP intensity in the larval fat (2 months).

The reviewer also mentions that the other drivers with more statistically significant effects on male lethality (____Dcg-GAL4_ and _r4-GAL4_, Fig. 4) are not restricted to the fat body. Importantly, both these drivers are also expressed in the blood lineage (hemocytes). To examine whether ISR activation in hemocytes contributes to the female stress tolerance (and/or male lethality) observed upon methioninase induction, we will quantify male and female survival rate following methioninase induction in the blood lineage using a blood-specific driver, _HHLT-GAL4____ (Mondal et al 2014, PMID 25201876). (2.5 months)

3) Several analyses rely on RNAi, and this is understandably important for tissue-specific knockdown of gene expression. At least one of the two following issues needs to be addressed: a) the efficiency of knockdown for each gene are not provided or reported on and b) only single RNAi lines were used for each gene targeted for knockdown.

We thank the reviewer for pointing out that the original manuscript does not report on knockdown efficiencies of the RNAi lines used in the study. The RNAi lines from the Harvard Transgenic RNAi Project (TRiP) collection (traRNAi, dsxRNAi, nitoRNAi) have been verified in Yan & Perrimon 2015 (PMID 26324914). The ATF4RNAi line was verified in Grmai et al. 2024 (PMID 38457339). We have included all citations for these validation studies in Table S1 in the preliminary revision.

Referee #3 Moderate concerns:

1) Lines 137-141: It would be nice to see a gel that confirms that these newly designed primers detect the expected isoforms (supplemental perhaps).

We thank the reviewer for requesting confirmation of isoform specificity of the primers used to detect ATF4 transcript in the fat body in Fig. 2B-C. Because these are qPCR primers, they were all designed to produce amplicons of nearly equal size. There is currently no reliable method to specifically deplete one ____ATF4_ isoform at a time, which would be the only way to experimentally demonstrate isoform specificity of each primer set. However, we have designed each primer pair to specifically detect isoform-specific regions of _ATF4_ mRNA and have verified specificity (and lack of off-target products in the _D. melanogaster_ genome) _in silico____ using Primer-BLAST (NCBI).

2) Lines 278-282 and Figure 4D: Shouldn't the second and fourth bars be compared? Based on the hypothesis and conclusion, second bar females can resist nutrient stress because they have ATF4, but fourth bar females can't because they don't have ATF4 - is this difference statistically significant?

We thank the reviewer for pointing out this missing statistical report that compares the second and fourth bars in Figure 4D ____(females expressing methioninase, with and without ATF4 knockdown). We have now performed this analysis and reported the p-value in text (lines 282-285 in the preliminary revision).

3) For all scatter plot graphs, figure legends should indicate what the horizontal line represents (is this the average?). Also, error bars and what they represent (SD or SEM) are not included or described.

We thank the reviewer for asking for additional details on our graph annotations. We have added language to explain that 1) horizontal lines on ATF4 reporter quantification graphs denote mean intensity (Fig. 1 legend, lines 567-568 in the preliminary revision) and 2) error bars on qPCR graphs represent SEM (Fig. 2 legend, line 583 in the preliminary revision).

Referee #3 Minor concerns:

1) Line 27: "counter parts" should be one word 2) Line 33: should the word "nutrient" be included before "stress" 3) Line 42: It would be nice to see a couple of examples of the "well documented across species" statement 4) Line 44-45: Add in the word "human" before population and use "women" instead of "females" 5) Line 53: There seems to be an issue with comma placement or word usage in the section of the sentence that reads "coincident with, or a comorbidity, for" 6) Lines 82-83: Mention of a couple examples would be nice 7) Line 104: Perhaps add the word "cellular" before "sexual" 8) Line 204: Delete the word "and" after "expression" 9) Line 234: Delete "a" before "significantly" 10) Line 276: Should "adult" be "adulthood" 11) For the discussion, a model schematic would nicely depict the findings as a whole 12) Line 330: May consider incorporating the following studies - Stobdan et al., 2019 and De Groef et al., 2021 13) Related to the point above: It would be great to see discussion/speculation of potential ATF4 targets that might be mediating this effect 14) Line 374: The placement of "yet unidentified" makes it seem like other ATF4 target genes aren't known, but really what is meant is that their sexually dimorphic expression is not known 15) Line 535: (beta-gal) "protein" instead of "gene"? 16) Figure S2: Please indicate what the two horizontal dotted lines are supposed to point out

We thank the reviewer for carefully pointing out these minor yet critical text concerns. ____We have addressed all minor concerns raised by the reviewer in text edits to the preliminary revision, which are each highlighted in yellow in lines 27, 33, 44, 53, 105, 204, 236, 279, 375,554, 624 in the preliminary revision. The exceptions are points 3, 6, 11, 13, which we will address in the subsequent revision as described in the previous section.

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Referee #3

Evidence, reproducibility and clarity

Summary: Using a combination of genetic and molecular tools, Grmai and colleagues present data showing the sexually dimorphic expression of ATF4, a transcription factor that mediates the integrated stress response, in larval fat tissue. Moreover, they find that higher basal ATF4 activity in female larvae supports the stronger resistance to nutrient deprivation that females exhibit compared to male larvae. The data are clearly described and nicely laid out in well-organized figures. Some major, moderate, and minor concerns, delineated below, regarding the approach and conclusions should be addressed prior to acceptance for publication.

Major concerns:

1. Sexually dimorphic ATF4 activity (Figure 1 and associated supplemental figure) as evidenced by reporter expression is the basis of this study, yet a detailed description of the immunofluorescence quantification is lacking. The methods sections needs to include information on how a) images were acquired (Were the same acquisition settings used across all images?), b) the intensity measurements were taken (What software was used? Does each data point in the distribution represent a single nucleus (the assumption is yes)? Is nuclear size adjusted for? Panels A' and B' have obvious differences in nuclear size which would in turn affect total intensity measurements), c) the sample size (How many fat images taken per animal per sample/genotype? How many trials were performed?)
2. While the authors nicely address the lack in specificity for two of the Gal4 driver lines used in the study limitation section, the fact that the one driver that is fat body-specific, 3.1Lsp2-Gal4, shows a modest, not statistically significant decrease in Figure 4C still raises some concern. There is another Lsp2-Gal4 line described in Lazareva et al., 2007 (PLoS Genetics) that drives expression in larval fat, perhaps to combat the issue of 3.1Lsp2-Gal4 have low activity, as mentioned by the authors. Alternatively, this phenotype could be assessed using Gal4 lines that only drive expression in the other tissues (if available). Otherwise, the conclusion that ISR/ATF4 signaling specifically in the fat mediates the starvation response needs to be toned down.
3. Several analyses rely on RNAi, and this is understandably important for tissue-specific knockdown of gene expression. At least one of the two following issues needs to be addressed: a) the efficiency of knockdown for each gene are not provided or reported on and b) only single RNAi lines were used for each gene targeted for knockdown.

Moderate concerns:

1. Lines 137-141: It would be nice to see a gel that confirms that these newly designed primers detect the expected isoforms (supplemental perhaps).
2. Lines 278-282 and Figure 4D: Shouldn't the second and fourth bars be compared? Based on the hypothesis and conclusion, second bar females can resist nutrient stress because they have ATF4, but fourth bar females can't because they don't have ATF4 - is this difference statistically significant?
3. For all scatter plot graphs, figure legends should indicate what the horizontal line represents (is this the average?). Also, error bars and what they represent (SD or SEM) are not included or described.

Minor concerns:

1. Line 27: "counter parts" should be one word
2. Line 33: should the word "nutrient" be included before "stress"
3. Line 42: It would be nice to see a couple of examples of the "well documented across species" statement
4. Line 44-45: Add in the word "human" before population and use "women" instead of "females"
5. Line 53: There seems to be an issue with comma placement or word usage in the section of the sentence that reads "coincident with, or a comorbidity, for"
6. Lines 82-83: Mention of a couple examples would be nice
7. Line 104: Perhaps add the word "cellular" before "sexual"
8. Line 204: Delete the word "and" after "expression"
9. Line 234: Delete "a" before "significantly"
10. Line 276: Should "adult" be "adulthood"
11. For the discussion, a model schematic would nicely depict the findings as a whole
12. Line 330: May consider incorporating the following studies - Stobdan et al., 2019 and De Groef et al., 2021
13. Related to the point above: It would be great to see discussion/speculation of potential ATF4 targets that might be mediating this effect
14. Line 374: The placement of "yet unidentified" makes it seem like other ATF4 target genes aren't known, but really what is meant is that their sexually dimorphic expression is not known
15. Line 535: (beta-gal) "protein" instead of "gene"?
16. Figure S2: Please indicate what the two horizontal dotted lines are supposed to point out

Significance

Study novelty: This work begins to shed light on the underlying molecular mechanisms that mediate differential responses to nutrient deprivation in male and female larvae. The knowledge gained from Drosophila studies will very likely have implications for human adipose physiology given the known sex differences in adipose associated physiology and pathophysiology in men and women.

General assessment: This study makes excellent use of the Drosophila melanogaster genetic toolkit to better understand the involvement of the ISR in mediating sexually dimorphic responses to nutrient deprivation. In addition, carefully thought-out figure layouts make the data easy to visualize. Limitations of the study include lack of specificity of fat body-specific driver lines and thus a potentially overstated conclusion.

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Referee #2

Evidence, reproducibility and clarity

It is now well-established that the Integrated Stress Response (ISR) mediated by ATF4 plays important roles in metabolism and proteostasis. This manuscript by Grmai and colleagues reports that the sex determination genes tra and dsx allow higher levels of ATF4 expression in Drosophila. They further show that female flies depend on ATF4 to survive under conditions of metabolic stress.

The presented data are technically sound, and the manuscript is generally very well written. It is a concise study with four Figures. The authors could have chosen to expand the scope: For example, they have shown the requirement, but not the sufficiency, of ATF4 in the sexually dimorphic nature of vulnerability to nutrient deprivation. They also demonstrate that ATF4 affects male-specific survival upon metabolic stress, which could be improved with additional experiments. These and other technical points are outlined below:

1. Figure 4 is an important part of this study, where the authors show a male-specific vulnerability to methioninase expression. They show that ATF4 RNAi confers vulnerability to methioninase expression even in females. An obvious question is whether ATF4 overexpression is sufficient to enhance resistance to methionine deprivation in males.
2. Methioninase expression results (Figure 4) are interesting. Are the levels of methioninase expression similar between males and females?
3. This manuscript focuses on ATF4, but there could be additional possible reasons for the sexually dimorphic ISR activity. For example, the degree of physiological stress that activates ISR could be different between males and females. I suggest comparing the levels of Phospho-eIF2alpha (or any other markers upstream of ATF4) in both sexes.
4. In Figures 1 to 3, the authors examine the intensity of ATF4 signaling after perturbing the sexual determination pathway. The methioninase experiments in Figure 4 are interesting, but there is nothing in this Figure linking male-specific vulnerability to sex determination genes. Examining the vulnerability to methioninase expression after perturbing the sexual determination genes would make Figure 4 integrate better with the rest of the manuscript.
5. The authors write that they generated 4EBP intron-GFP because the 4EBP intron-DsRed signal was frequently observed in the cytoplasm (line 122). They seem to suggest that the DsRed reporter is less reliable than the GFP reporter. However, they continue to mix results using 4EBP intron-GFP (Fig. 4A) and 4EBP intron-DsRed (Fig. 4F). The two figures examine slightly different conditions (Fig 4A shows tra1 KO females, while Fig. 4F shows traF males). If the DsRed reporter is less reliable due to the signal from the cytoplasm, the authors should show results with the GFP reporter in traF males.
6. In Figure S1, the authors label 4EBP intron-GFP as Thor2p-GFP, which is confusing. There are other parts in the methods section referring to Thor2p. I suggest using consistent terminology throughout the manuscript.

Significance

Overall, the authors report a novel and interesting observation because the sex determination pathway was not previously associated with ISR signaling. As many metabolic diseases show sex-specific outcomes, the main findings of this study will draw broad interest.

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Referee #1

Evidence, reproducibility and clarity

Summary

This study aims to explore sexual dimorphism in tolerance to nutrient deprivation using Drosophila larvae as a model. In particular the authors focus on sex differences in the larval fat body. They show that ATF4, an ISR transcription factor, has higher mRNA levels in female fat bodies. ATF4 transcriptional activity is also higher based on a reporter of ATF4 function, where this female bias in expression is influenced by sex determination factors. When the authors

Overall, this study is interesting, as it identifies previously unrecognized sex-specific regulation of ATF4, an important transcription factor that mediates cellular stress responses. The study also shows that sex determination genes regulate ATF4. However, I have concerns about the paradigms of nutrient deprivation used in the study, and about data interpretation and statistical analysis that should be addressed prior to publication to support the authors' conclusions.

Major concerns

1. One major concern that I have about the sexual dimorphism in tolerance to nutrient deprivation is that the papers cited by the authors, and paradigms that are used broadly in the field, all use adult flies. The authors must show that in larvae, a completely different life stage from their citations, there is a sexual dimorphism in tolerance to nutrient deprivation.

Interestingly, Diaz et al 2023 (Genetics) show that male larvae have greater fat stores than female larvae. Considering fat is the main determinant of tolerance to nutrient deprivation it's not clear that females will actually survive nutrient deprivation longer as larvae. This is an essential test of whether female larvae do have increased tolerance to nutrient deprivation, which is the basic foundation of the authors' model. 2. Another concern is the way that the authors "genetically induce nutrient deprivation using methioninase overexpression". As they acknowledge in the discussion (Line 381-390), methioninase overexpression will have many cellular effects. While there is no doubt that methionine levels would be lower in their model, it is less certain whether this is the main driver of the male-specific lethality.

There are two potential solutions to this problem. First, the authors could change the text throughout the paper to more accurately describe their paradigm as "methioninase-induced lethality" rather than "nutrient deprivation". This would limit the scope of their scientific question and the conclusions they draw, but would eliminate the need for more experiments.

The second solution would be to complete experiments to establish the following points: i) methioninase overexpression causes all the classical features of nutrient deprivation (e.g. changes to canonical signaling pathways such as TOR); ii) using other genetic means of nutrient deprivation such as slimfast-RNAi to see if those manipulations phenocopies the male-specific lethality they see with methioninase overexpression; iii) testing a role for ATF4 in mediating sex differences (if any) in other contexts such as slimfast-RNAi. This will take 2-3 months but is essential to draw any conclusions about whether their paradigm is truly a model for nutrient deprivation. 3. Another important point is that the authors state that sexually dimorphic ATF4 activity in the fat body is instructed by sexual identity in a cell-autonomous manner. Despite a clear decrease in ATF4 reporter levels in tra mutants, the fat body-specific tra-RNAi effect on the ATF4 reporter was less convincing. Together with the fact that changes to tra in the fat body affect insulin secretion from the insulin-producing cells, it is possible that the effect on ATF4 is not cell-autonomous. To conclusively test if sexual identity regulates ATF4 in a cell-autonomous manner the authors should use the flp-out system to make Tra-expressing or tra-RNAi-expressing clones in the fat body. This would take approximately 1.5 months to make the strain and test this. 4. As the authors show for the UAS-methioninase, other UAS lines used in the paper such as UAS-traF, UAS-tra-RNAi, UAS-dsx-RNAi may have leaky effects on gene/reporter expression. The authors must include a UAS only control to establish that the tra-RNAi, UAS-traF, UAS-dsx-RNAi do not affect gene/reporter expression. 5. I have concerns about the statistics used. In the methods and legends only t-tests are mentioned; however, when three groups are compared a one-way ANOVA with post-hoc tests must be used to correct for multiple comparisons. To compare differential responses to genetic/environmental manipulations between the sexes, a two-way ANOVA must be used. For example, to conclude that males and females have different responses in the two-way ANOVA, there must be a significant genotype:sex interaction. The p-values for comparisons between genotypes in either the one-way or two-way ANOVA must be derived from post-hoc tests within the ANOVA analysis.

Minor points

1. Please ensure to make the reader aware of which life stage was tested in the literature cited supporting sexually dimorphic tolerance to nutrient deprivation.
2. Published data about sex-specific mechanisms of metabolic regulation mean that the introduction should be more fully cited than it is. Even in the introduction "the molecular basis of these differences and how they impact tolerance to nutrient deprivation is still under investigation" is inaccurate, as there are published studies identifying some mechanisms (work on gut hormones and sex-specific effects on starvation resistance and body fat, role of ecdysone on body fat and feeding, sex-specific roles for brummer and Akh in regulating body fat, intestinal transit and gut size and feeding). Please adjust the paper to acknowledge this growing body of knowledge.
3. Please list the diet ingredients per L so that individuals can replicate the diet easily.
4. Please cite grant numbers for all the community resources (e.g. Bloomington, DSHB), and please acknowledge FlyBase and its grants as well. For example, here are the instructions for citing BDSC https://bdsc.indiana.edu/about/acknowledge.html and similar instructions are available for the other resources.

Significance

This study identifies for the first time the sex-specific regulation of ATF4, and reveals the sex determination genes that mediate this effect. A strength of the study is the characterization of sex-specific ATF4 regulation. Limitations of the study include the paradigm for nutrient deprivation, need for additional controls, and statistical analysis. If the concerns above are addressed, this study will be of interest to researchers studying organismal and cellular stress responses, stress signaling, and builds upon a growing body of knowledge of sex differences in stress responses (e.g. autophagy, infection responses).

This description of the creative process feels almost like how artificial intelligence works — taking massive amounts of data and producing something new. Could writing historical fiction be seen as a kind of human-powered algorithm?

This line struck me because it mirrors how science fiction or fantasy writers build believable worlds from scratch. It made me reflect on how storytelling—whether historical or imagined—relies on human emotion and detail to make us believe in it.

This draws a powerful parallel to today’s discussions on power dynamics and consent. Can authors responsibly write historical romance without romanticizing abuse?

This reflects a broader issue in historiography — how often the perspectives of colonized or oppressed peoples are erased from the narrative. Could this challenge how we teach or interpret empire in classrooms?

This raises a question: How much creative liberty is too much when historical facts are sparse? At what point does fiction risk distorting history instead of enhancing it?

It’s fascinating how these stories reveal that struggles like corruption, inequality, and violence are not modern issues—they’ve always been part of society. Could these common struggles be what make historical fiction so emotionally relatable?

indolanda is a Roman fort in northern England. The preserved writing tablets discovered there provide rare personal insights into Roman military and domestic life in Britain.

Aquae Sulis was a Roman spa town known for its healing hot springs and religious worship of the goddess Sulis Minerva — a unique hybrid of Roman and Celtic deities.

Sue Peabody is a historian who explores how historical fiction allows readers to visualize and emotionally connect to the past, functioning as a metaphorical and immersive experience of history.

Higher level of purpose

I really like this quote because it resonates so much in today's world. Everyday people post with social media to people who watch their videos all over the world who are absolute strangers. This also goes for radio and tv who has been broadcasting content decades before social media.