Author response:
The following is the authors’ response to the original reviews.
The goal of the study was to demonstrate the role of the two thresholds in learning, i.e. the role of metaplasticity with a learning rule that is both as simple as possible, but also biologically-based (hence the use of the detailed SPN model, as well). The goal was not to solve the FBP and NFBP with a different rule. However, the text likely gives that impression. Therefore, in addition to addressing the reviewers’ comments, the text has been substantially revised to reflect the following:
Main results
(1) Metaplasticity enables synapses that undergo both LTP and LTD to ultimately express just one plasticity outcome (either LTP or LTD).
(2) Metaplasticity in the LTP threshold allows LTD to be expressed, and vice versa. (That is, the threshold regulating one plasticity process allows the expression of the opposite plasticity process.)
Reason for using the FBP and NFBP
The reason why the FBP and NFBP are particularly useful to demonstrate the thresholds’ roles is that the patterns in the tasks share features. (For example, in the FBP, the feature ‘strawberry’ is shared between both ‘red strawberry’ and ‘yellow strawberry’.) The synapses for these shared features experience precisely such competing LTP and LTD processes where the role of metaplasticity becomes evident. Specifically, the role of the LTD threshold is visible in shared synapses that need to be strengthened during learning (such as the shared ‘strawberry’ synapses in the FBP), while the LTP threshold’s role is visible in shared synapses that need to be weakened (there are no such synapses in the FBP, but there are in the NFBP, which is why it is needed in this article). In addition, feature binding is relevant for the striatum (now described in the introduction).
In the first version of the article there are sentences that are likely confusing and misleading regarding the goal of the study, and these have been removed (lines 98-100 in the tracked changes file).
The revised article now contains 4 new main figures and 15 new figure supplements prompted by the reviewers’ comments, thus expanding the scope of the study and hopefully clarifying its content, the mechanisms, and the conclusions.
Finally, the question whether this rule can solve the NFBP with excitatory synapses alone is being addressed in a new, ongoing study, as written at the end of the Discussion section in the first version of this article. The new study tests 100+ SPN models (71 dSPN and 34 iSPN models differing in ion channel composition, with two different morphologies), different locations of the synaptic clusters along the dendrites (from proximal to distal), and two different learning regimes (suprathreshold – where the neuron initially spikes for all patterns, and subthreshold – where the neuron is initially silent for all patterns, as in this study) containing both clustered and distributed synapses in the same setup. Where necessary, preliminary results from this study are attached in the responses.
Public Reviews:
Reviewer #1 (Public review):
Summary:
This computational modelling study addresses the important question of how neurons can learn non-linear functions using biologically realistic plasticity mechanisms. The study extends the previous related work on metaplasticity by Khodadadi et al. (2025), using the same detailed biophysical model and basic study design, while significantly simplifying the synaptic plasticity rule by removing non-linearities, reducing the number of free parameters, and limiting plasticity to only excitatory synapses. The rule itself is supervised by the presence or absence of a binary dopamine reward signal, and gated by separate calcium-sensitive thresholds for potentiation and depression. The author shows that, when paired with a strong form of dendritic non-linearity called a "plateau potential" and appropriate pre-existing dendritic clustering of features, this simpler learning mechanism can solve a non-linear classification task similar to the classic XOR logic operator, with equal or better performance than the previous publication. The primary claims of this publication are that metaplasticity is required for learning non-linear feature classification, and that simultaneous dynamics in two separate thresholds (for potentiation and depression) are critical in this process. By systematically studying the properties of a biophysically plausible supervised learning rule, this paper adds interesting insights into the mechanics of learning complex computations in single neurons.
As mentioned in the introductory response above, the goal of the article was not to solve the NFBP, but to study the role of metaplasticity. The text has now been substantially revised to reflect that. One of the primary claims that “metaplasticity is required for learning non-linear feature classification, and that simultaneous dynamics in two separate thresholds (for potentiation and depression) are critical in this process” is now removed from the abstract. Instead, the abstract now focuses on the main results regarding the role of metaplasticity, as well as the results which arose from addressing the reviewers’ comments. However, I guess I should note that to be able to study the role of metaplasticity using the FBP and the NFBP, it was first necessary to have a rule that solves these tasks – that allows to later observe the effects of systematically fixing or modifying parameters in the rule. Another aspect which may have added to the confusion about the study’s goal may be due to the NFBP being a complex task requiring supralinear dendritic integration. Because of this, plateaus have received significant attention in the article, possibly diverting from the main focus. This is also now clarified in the article.
Strengths:
The simplified form of the learning rule makes it easier to understand and study than previous metaplasticity rules, and makes the conclusions more generalizable, while preserving biological realism. Since similar biophysical mechanisms and dynamics exist in many different cell types across the whole brain, the proposed rule could easily be integrated into a wide range of computational models specializing in brain regions beyond the striatum (which is the focus of this study), making it of broad interest to computational neuroscientists. The general approach of systematically fixing or modifying each variable while observing the effects and interactions with other variables is sound and brings great clarity to understanding the dynamic properties and mechanics of the proposed learning rule.
It would indeed be great if this rule facilitates similar studies in other neuron types. The rule requires at least qualitatively accurate calcium dynamics, which at the moment are not widely available for other neuron types (but will likely appear in the future).
Weaknesses:
General notes
(1) The credibility of the main claims is mainly limited by the very narrow range of model parameters that was explored, including several seemingly arbitrary choices that were not adequately justified or explored.
The parameter range has now been expanded to address all comments below.
(2) The choice to use a morphologically detailed biophysical model, rather than a simpler multicompartment model, adds a great deal of complexity that further increases uncertainty as to whether the conclusions can generalize beyond the specific choices of model and morphology studied in this paper.
Regarding the plasticity rule and the role of metaplasticity, the conclusions should hold if the calcium dynamics of other (simpler or detailed) neuron models is qualitatively similar (i.e. shows the same monotonicity of “stronger synaptic input – stronger calcium”, and not something like Figs. 12A, B for which the rule was not tested).
As to whether the NFBP can be solved, that is being addressed in the new study with 100+ neuron models (71 dSPN models and 34 iSPN models, and two morphologies: one for the dSPNs and another for the iSPNs). So far, the results show that the important ingredient is the threshold nonlinearity provided by the plateau potential (both dSPNs and iSPNs exhibit this nonlinearity, irrespectively of where the synaptic cluster is located, see Author response image 1).
Also, plateaus can be evoked in passive SPN dendrites (as stated in the methods in lines 916-919, by “turning off” ion channels in the computational model as in Fig. S7 of Du et al. (2017) (see list of references provided)). Although plateaus are somewhat modified by active conductances, the main behavior important for the NFBP is given by NMDARs. The most striking contributions of the other ion channels in SPNs are the low resting potential around -85 mV, delayed first spike under current injection and strong inward rectification. Basically, SPNs require more input to be stimulated compared to other neurons that lack these properties. So, other neurons with NMDAR-dependent nonlinearities should in principle be able to solve the same task, but perhaps needing less inputs (provided dendritic integration is sufficiently supralinear – see response to comment (2) under Reviewer #2 (Recommendations for the authors)).
(3) The requirement for pre-existing synaptic clustering, while not implausible, greatly limits the flexibility of this rule to solve non-linear problems more generally.
In my view, the limitation of this rule is that there is no mechanism for structural plasticity with which clusters could be “grown”. For example, Hedrick et al. 2022 demonstrate that during learning in the motor cortex, existing functional clusters are “enlarged” by growing new spines. Devising a biologically realistic rule for structural plasticity is a separate research project, which would be very interesting to do.
In any case, to solve the NFBP with excitatory synapses alone, supralinear voltage elevations are necesssary (Tran-van-Minh et al. 2015). When it comes to NMDAR-dependent supralinear integration, clustering is basically necessary, within a smaller, e.g. 20 micron dendritic stretch, or more loosely, within a single dendritic branch (Losonczy and Magee, 2006; Branco et al. 2010). Also, synaptic clustering is quite present across different brain regions (such as the sensory and motor cortices, pallium, striatum, hippocampus, brainstem, the developing cortex, and across species, e. g. see the introduction of Kirchner and Gjorgjieva, 2021), so I suppose it is not that implausible. Inputs from motor cortex to striatum are also clustered (Hwang et al. 2022).
(4) In order to claim that two thresholds are truly necessary, the author would have to show that other well-known rules with a single threshold (e.g., BCM) cannot solve this problem. No such direct head-to-head comparisons are made, raising the question of whether the same task could be achieved without having two separate plasticity thresholds.
Although the goal of the study was not to solve the NFBP, this is a very interesting question related to the question “what is the use of having two separate thresholds for plasticity”? I have added simulations in which the rule is modified to use a single calcium threshold instead, showing that the FBP, NFBP, and reversal learning are solved just as well (Fig. 12 and Figure 12 – figure supplements 1 – 4). The results show that two calcium thresholds allow for separate control over the LTP and LTD processes (lines 687-706).
Specific notes
(1) Regarding the limited hyperparameter search:
(a) On page 5, the author introduces the upper LTP threshold Theta_LTP. It is not clear why this upper threshold is necessary when the weights are already bounded by w_max. Since w_max is just another hyperparameter, why not set it to a lower value if the goal is to avoid excessively strong synapses? The values of w_max and Theta_LTP appear to have been chosen arbitrarily, but this question could be resolved by doing a proper hyperparameter search over w_max in the absence of an upper Theta_LTP.
Thank you for raising this question – it is closely related to the very important question of when to stop updating the weights. Before providing the response, I should clear up any confusion made due to an error in notation. In this study,
, and
, meaning that during learning the weights can increase up to twice (up to 100% of) the initial value, and can decrease down to 1% of the initial value. Currently, it says w<sub>max</sub> = 2, and w<sub>min</sub> = 0.01, which is a mistake, and possibly a reason why the chosen values seem arbitrary.
The reason for introducing the upper threshold θ<sub>LTP</sub> is most easily seen in the parameter scan for w<sub>max</sub> done in the absence of θ<sub>LTP</sub> (Figure 4 – figure supplement 4) – it is very difficult to choose a value for w<sub>max</sub> with which all three tasks will be solved (FBP with linear integration, i.e. distributed synapses, the FBP with supralinear integration, i.e. clustered synapses, and the NFBP). Put differently, if there is a range of w<sub>max</sub> values which solves all three tasks, it is very narrow. So, θ<sub>LTP</sub> is introduced to solve all three cases without specially tuning w<sub>max</sub>.
The following is a description of the results in Figure 4 – figure supplement 4, which is also present in the article in lines 383-396. The reason why a single preset value for w<sub>max</sub> does not work is that distributed synapses sum only linearly at the soma, while clustered synapses sum supralinearly. This means that to trigger somatic spiking, the distributed synapses need to be strengthened more compared to clustered synapses. Concretely, this means that a
is needed to solve the FBP with linear integration (distributed synapses), but it is already too strong to solve the NFBP (Figure 4 – figure supplement 4, column four: top panel shows that FBP with linear integration is solved, while the bottom panel shows the average performance for the NFBP is right at the border – pink line aligns with the dashed line). On the other hand,
is enough in the FBP with clustered synapses and the NFBP to trigger glutamate spillover and a plateau potential, which drives somatic spiking (Figure 4 – figure supplement 4, column two). However, it is not enough to solve the FBP with linear integration. Larger values for w<sub>max</sub> increase the performance on the FBP with linear integration, but lower the performance on the NFBP due to spiking for the irrelevant patterns (especially visible once
). As said, in this parameter scan, only the value
solves all three tasks, with borderline performance on the NFBP (it is arguable whether the borderline performance means the NFBP is solved). This suggests that if a range of values for w<sub>max</sub> exists which solves all three tasks, it is very narrow.
With the settings used in the study, the w <sub>max</sub> threshold for triggering glutamate spillover is a number between 1.2 and 1.3 with many decimals – 1.230769231. A possibility could be to program spillover to always occur at
, but this is also not a general solution. For example, other dSPN models from the model library in Lindroos et al. (2021) have different excitability, and that would mean a different, specific value of w<sub>max</sub> would be needed for each neuron model.
θ<sub>LTP</sub> is thus a solution that prevents “over-excitation” in a dendrite. The logic is that synapses in a cluster do not need to be as strong as distributed synapses to be effective in exciting the neuron. θ<sub>LTP</sub> ensures that once plateaus appear, synapses are not strengthened further. This allows using the same value
across all scenarios, i.e. avoiding tuning of w<sub>max</sub> or tuning the number of synapses representing the features. (Also, preliminary results show this works well in the new study which tests all dSPN and iSPN models in the model library.) As for the value of θ<sub>LTP</sub>, it can be set anywhere in the “blank” region in Fig. 2C<sub>3</sub> where the supralinear jump in [Ca]<sub>NMDA</sub> occurs. What is important is that [Ca]<sub>NMDA</sub> evoked by a plateau should be above θ<sub>LTP</sub> – then no more strengthening will occur once plateaus can be evoked.
(b) The author does not explore the effect of having separate learning rates for theta_LTP and theta_LTD, which could also improve learning performance in the NFBP. A more comprehensive exploration of these parameters would make the inclusion of theta_max (and the specific value chosen) a lot less arbitrary.
I am not sure I have understood this comment properly, but hopefully this response addresses it adequately. In fact, the computer code does use separate variables for the learning rates for θ<sub>LTP</sub> and θ<sub>LTP</sub>, but for simplicity, they are set to the same value. In this response I have included some simulations in which they are set to different values (Author response image 2), but to understand their effect it is better to read the response to the comment under c) first. The metaplasticity rates determine how fast the synaptic weights are stabilized, i.e. how long the time window is where the synapses are “flexible”. When the thresholds reach the calcium amplitudes, the weights are “locked”.
If the metaplasticity rates are too low, the weights take a longer time to stabilize and solving the tasks takes a long time (Figure 4 – figure supplement 10 from the response to c). If they are too high, weights are quickly stabilized and, in the case of weakened synapses, prematurely so, leading to worse performance on the NFBP due to spiking for the irrelevant patterns. (Figure 4 – figure supplement 11).
One can use different values for the metaplasticity rates, as in the examples in Fig. 2 , and this affects the speed of learning. A large η<sub>θLTD</sub> = 20 quickly prevents the LTD process (Figs. 2D<sub>1</sub>, D<sub>2</sub>), causing faster synaptic strengthening, but also quickly limiting weakening (Figs. 2B<sub>1</sub>, B<sub>2</sub>) – as a result, after learning, the neuron spiked for an irrelevant pattern (Fig. 2A<sub>1</sub>). Conversely, a large η<sub>θLTD</sub> = 20 quickly prevents the LTP process (Figs. 2C<sub>3</sub>, C<sub>4</sub>), prolonging synaptic strengthening and allowing faster weakening (Figs. 2B<sub>3</sub>, B<sub>4</sub>) – as a result, the NFBP is solved, but takes a longer time. However, this does not remove the need for using an upper threshold θ<sub>LTP</sub>. If I have not understood the comment properly, please let me know so I can address it further.
(c) Figure 4 Supplements 3-4: The author shows results for a hyperparameter search of the learning rule parameters, which is important to see. However, the parameter search is very limited: only 3 parameter values were tried, and there is no explanation or rationale for choosing these specific parameters. In particular, the metaplasticity learning rates do not even span one order of magnitude. If the author wants to claim that the learning rule is insensitive to this parameter, it should be explored over a much broader range of values (e.g., something like the range [0.1-10]).
Thank you for bringing this up! I have expanded the parameter scan for both the learning rate η (Figure 4 – figure supplements 7 and 8) and the metaplasticity rate η<sub>θ</sub> (Figure 4 – figure supplements 10 and 11) to cover three orders of magnitude (when taken together with the results already present in the article in Figure 4 – figure supplements 6 and 9).
Figure 4 – figure supplements 7 and 8: The learning rate η was was tested with the values 0.1 and 20. This shows a known result in other plasticity rules, which is that if the learning rate is too fast or too slow, learning is not successful or is too slow. For η = 0.1, learning takes very long (around 2000 patterns for FBP with linear integration), and for the NFBP is at the borderline score (Figure 4 – figure supplement 7E). As the LTD thresholds rise, they will prevent the slowly decreasing synaptic weights from decreasing sufficiently. For η = 20, the weight updates are too large and no pattern is stored because calcium quickly falls below the thresholds as a result of such large weight updates (Figure 4 – figure supplement 8E). This leaves some intermediate range of learning rates that “works”. (The three values {0.4, 0.85, 1.7} that were tested in Figure 4 – figure supplement 6 are roughly a factor of 2 apart.) Results are described in more detail in lines 409-414 of the revised article.
Figure 4 – figure supplements 10 and 11: The metaplasticity rate η<sub>θ</sub> was tested with the values 0.2 and 20. This further demonstrates the role of metaplasticity as a “lock” on the learning process. η<sub>θ</sub> determines how fast the weights stabilize (i.e. how long they remain flexible for learning). With the value η<sub>θ</sub> = 0.2 the weights take a longer time to stabilize, because it takes a long time for the thresholds to reach the calcium amplitudes (Figure 4 – figure supplement 10). This affects the learning time on the NFBP only. In contrast, with the value η<sub>θ</sub> = 20, the thresholds quickly reach the calcium amplitudes, and quickly stabilize the weights. While the neuron does learn to evoke plateaus, the weakened synapses are stabilized too early, resulting in spikes for the irrelevant patterns and lowering the performance on the NFBP. (Figure 4 – figure supplement 11). Results are described in more detail in lines 415-429 of the revised article.
(2) Regarding the similarity to BCM, the author would ideally directly implement the BCM learning rule in their model, but at the least the author could have shown whether a slight variant of their rule presented here can be effective: for example having a single (plastic, not fixed) Cadependent threshold that applies to both LTP and LTD, with a single learning rate parameter.
- As mentioned above, this is also a very interesting question, related to the important question of “what is the use of having two separate calcium thresholds?”. I have added simulations according to your second suggestion – using a single calcium threshold that applies to both LTP and LTD. A single threshold can solve the FBP, NFBP, and reversal learning equally well (Fig. 12 and Figure 12
- Figure Supplements 1, 2). This indeed raises the question what are two separate thresholds useful for? Figure 12 – figure supplement 3 shows that when keeping the single calcium threshold fixed, none of the shared synapses stabilize. Comparing this to Figs. 5 and 6, where the LTP and LTD threshold are kept fixed one at a time, it shows that having two separate thresholds allows separate control over the LTP and LTD processes.
I also tried an implementation of the BCM rule using a nonlinear (quadratic) function in the metaplasticity rule for updating the threshold:


where c<sub>norm</sub> is a normalization constant set to 80 μM for [Ca]<sub>NMDA</sub> and 20 μM for [Ca]<sub>L-type</sub> (close to the maximal concentrations achieved throughout the article). In the BCM rule, a nonlinear function is necessary to prevent runaway growth (or collapse) of the weights. So, in principle, w<sub>max</sub> and θ<sub>LTP</sub> should be unnecessary with this quadratic metaplasticity rule. However, even though the weights seem to stabilize (around a high value), they are too strong and plateaus are triggered for all patterns (see Author response image 3). It is possible that only a narrow range of parameters in the quadratic function will allow weights to stabilize at appropriate values, similarly to the narrow range in w<sub>max</sub> in the absence of θ<sub>LTP</sub> (as described for comment 1a) above).
Below are some questions about how to “correctly translate” the BCM rule from its formulation for rate-coded inputs to a formulation for sparsely-coded inputs which are used in this article. I did not address these questions in detail. The following is meant for readers who might be interested in pursuing these questions.
Questions when translating the BCM rule for rate-coded inputs to a rule for sparsely-coded inputs:
The similarity of this study’s rule to BCM is only qualitative – a sliding threshold was added that follows an indicator of synaptic activity (in this study it is the amplitude of the calcium concentration). The original BCM rule is defined for rate-based synapses, and its threshold θ is a nonlinear function of the average (synaptic) activity:

where p and c<sub>0</sub> are positive constants, and c) is the average activity. The threshold θ is updated as the average activity c) changes (the averaging being done over a time interval) [1]. Changes in the rate-coded inputs drive changes in c) continuously, thus changing θ over time.
(1) What should be chosen as the average activity c̅ ?
In the BCM model, the average activity, and consequently the threshold θ, are global for the whole neuron (which is represented just by its firing rate), meaning that θ is the same for all synapses. In a morphologically realistic neuron model, what should be the average activity? Especially in the case of supralinear integration occuring in a dendrite, one could also consider average activities in dendrites. In the dSPN model, the calcium concentration decays by the time the next pattern arrives, so one probably needs another, low-pass filtered variable of the calcium concentration (or voltage), with a much longer time constant than that of the calcium decay. (I have chosen to slide the thresholds towards the amplitude of the calcium evoked by a pattern, which could be viewed as an approximation of such a long-lived variable. This is one possible “translation” of this aspect of the BCM rule.)
(2) How to update the chosen indicator of activity c̅?
Assuming an adequate indicator is chosen (different from the calcium amplitude that I have chosen), how should it be updated when using sparsely-coded inputs? Should it evolve continuously, or only when the sparsely-coded inputs are active? If updated continuously, it should not decay very fast when synapses are inactive (not activated by a pattern), while still change fast enough to detect changes in synaptic weight occuring due to learning. (I have chosen to slide the thresholds towards the evoked calcium amplitude only when synapses have been activated, so this is also one way of “translating” this second aspect.)
(1) which in the BCM article is replaced with the average over the input’s probability distribution
(3) What nonlinear function to use to update the threshold?
The BCM rule allows any function with p > 1, but how fast the synapses stabilize will likely depend on c<sub>0</sub>, the normalization constant in the nonlinear function, and the power p. The role of the nonlinear function is to ensure stability of the synaptic weights (prevent runaway growth), meaning no θ<sub>LTP</sub> nor w<sub>max</sub> should be needed. However, achieving high performance on all three tasks might still require a specific tuning of these parameters, as w<sub>max</sub> does if no θ<sub>LTP</sub> is used. That is, these parameters will need to be chosen such that the threshold quickly goes up once a plateau appears, so weights are not allowed to strengthen further. Having in mind that there is a very narrow range in w<sub>max</sub> where all three tasks are solved, there might similarly be only a narrow range in c<sub>0</sub> and p.
Since the goal of the article was to study the role of the two thresholds (not to optimize the rule’s parameters on the three tasks), I have only tried a quadratic function for the metaplasticity rule, and did not search for a region of parameters that could work.
(3) This paper is extremely similar (and essentially an extension) to the work of Khodadadi et al. (2025). Yet this paper is not mentioned at all in the introduction, and the relation between these papers is not made clear until the discussion, leaving me initially puzzled as to what problems this paper addresses that have not already been extensively solved. The introduction could be reworked to make this connection clearer while pointing out the main differences in approach (e.g., the important distinction between "boosting" nonlinearities and plateau potentials).
The last paragraph in the introduction now makes this comparison, highlighting the differences in approach, and mainly emphasizing that the goal of the two studies is different. The open question that this study addresses is to pinpoint the roles of the two calcium thresholds (present in dSPNs) in learning. Also see the response to the similar comment (1) from Reviewer #2 (Public review): Weaknesses.
(4) The introduction is missing some citations of other recent work that has addressed single-neuron non-linear computation and learning, such as Gidon et al (2020); Jones & Kording (2021).
Thank you for mentioning this. Since the first version of the article caused confusion regarding the goal of the study (which is to study metaplasticity), I avoided focusing on nonlinear computation in the introduction, and instead added these references to the Discussion (in line 850 the section regarding nonlinear computation).
(5) Figure 1: The figure prominently features mGluR next to the CaV channel, but there is no mention of mGluR in the introduction. The introduction should be updated to include this.
Thank you for noticing this. It is now included in the introduction in lines 50-53.
(6) Could the author explain why there is a non-monotonic increase/decrease in the [Ca]_L in Figure 2B_4? Perhaps my confusion comes from not understanding what a single line represents. Does each line represent the [Ca] in a single spine (and if so, which spine), or is each line an average of all the spines in a given stim condition?
Thank you for noticing this, that information was missing from the figure caption. The line is from a single spine which is placed at a random location on a randomly chosen dendrite. Because each line comes from a different trial with a different number of synapses, the spine it corresponds to is in a different location, resulting in different voltage and different calcium signals when using distributed synapses. (Clustered synapses are placed at approximately the same somatic distance, despite being on a randomly chosen dendrite, so this effect does not appear in Figs. 2C<sub>3</sub>, C<sub>4</sub>). The figure caption has been updated accordingly.
(7) Row 124 (page 4): L-type Ca microdomains (in which ions don't diffuse and therefore don't interact with Ca_NMDA) is a critical assumption of this model. The references for this appear only in the discussion, so when reading this paper, I found myself a bit confused about why the same ion is treated as two completely independent variables with separate dynamics. Highlighting the assumption (with citations) a bit more clearly in the results section when describing the rule would help with understanding.
Thank you for pointing this out! This assumption is now clearly stated with citations in lines 174176 when characterizing the plateaus in SPNs, and lines 205-207 when describing the rule (in addition to the existing description in the Methods).
(8) Row 149 (page 5): The current formulation of the update rule is not actually multiplicative. The fact that the update is weight-dependent alone does not make it a multiplicative rule, and judging by equation (1) it appears to simply be an additive rule with a weight regularization term that guarantees weight bounds. For example, a similar weight-dependent update is also a core component of BTSP (Milstein et al. 2021; Galloni et al. 2025), which is another well-known *additive* rule. An actual multiplicative rule implies that the update itself is applied via a multiplication, i.e. w_new = w_old * delta_w
For an example of a genuinely multiplicative rule, see: Cornford et al. 2024, "Brain-like learning with exponentiated gradients"). Multiplicative rules have very different properties to additive rules, since larger weights tend to grow quickly while small weights shrink towards 0.
Thank you for explaining the difference between “additive” and “multiplicative”. I have removed the word “multiplicative” from the description of the rule, as it is not necessary. (In the first version of the manuscript I followed the nomenclature by Gütig et al. (2003), which refers to the weight-dependent update as a multiplicative rule, while an additive rule has no weight dependence in the equation for Δw, which is Eq. 2 in Gütig et al. (2003).)
(9) Equation 1 (page 5): Shouldn't the depression term be written as: (w_min - w)? This term would be negative if w is larger than w_min, leading to LTD. As it is written now, a large w and small w_min would just cause further potentiation instead of depression.
Yes, a minus sign is missing in front of the depression term. Thank you for noticing this! It is now corrected.
(10) In the introduction, the teaching signal is described in binary terms (DA peak, or DA pause), but in Equation 1, it actually appears to take on 3 different values. Could the author clarify what the difference is between a "DA pause" and the "no DA" condition? The way I read it, pause = absence of DA = no DA
Yes, the “no DA” condition should say “baseline DA”. The DA signal does indeed take three different values. In the striatum, there is a baseline tone of dopamine. The DA peaks are transient increases from this tone, and the DA pauses are transient decreases. The basal dopamine level is now introduced in line 113 of the introduction, so that Eq. 1 should be clearer. In the computer code, DA is in effect a ternary signal, with three values, +1 for DA peak, -1 for DA pause, and 0 for baseline DA.
(11) Figure 3: In these experimental simulations, DA feedback comes in 400ms after the stimulus. The author could motivate this choice a bit better and explain the significance of this delay. Clearly, the equations have a delta_t term, but as far as the learning algorithm is concerned, it seems like learning would be more effective at delta_t=0. Is the choice of 400ms mainly motivated by experimental observations? On a related note, is it meaningful that the 200ms delta_t before the next stimulus is shorter than the 400ms pause from the first stimulus? Wouldn't the DA that arrives shortly before a stimulus also have an effect on the learning rule?
These time windows were chosen purely to keep the simulations as short as possible (since a computing cluster was used to run many trials). In reality, two patterns would probably arrive after a longer time window, as an animal should reach for the pattern (and in the case of these fruit patterns, eat it) which would last on the order of seconds. However, the calcium signals that trigger plasticity in these simulations are shorter than that (Figs. 2B<sub>3,4</sub>, 2C<sub>3,4</sub>), and only the amplitude of the signal is used to trigger plasticity. This gives an opportinity to not have to wait for several seconds between two patterns arrive (as might occur in reality), but shorten that interval and so shorten the simulation time. (This is now stated in lines 245-247 in the Results section where the rule is described, pointing to the Methods for more detials.)
Hence, the dopamine feedback is given at 400 ms after a pattern appears because the calcium amplitudes would have surely occurred by then (even if a plateau were evoked, see Figs. 2B<sub>3,4</sub>, 2C<sub>3,4</sub>). Similarly, the next pattern is given at 600 ms because the calcium signals would have decreased to baseline by then. (This is already explained in the Methods section in lines 1101-1117). The key implicit assumption here is that the calcium amplitude is somehow remembered by the synaptic circuitry. In experiments, dopamine feedback up to 2 seconds after synaptic stimulation can cause LTP, so it is OK to assume this (Yagishita et al., 2014). However, dopamine signaling before synaptic stimulation has no effect (Yagishita et al., 2014). (This assumption is now clearly stated in the Methods in lines 902-906.)
Lastly, in this rule, if the dopamine feedback coincides with the pattern, then whatever calcium levels were reached at that time would be used to check whether the thresholds are crossed, and these will most likely not be the maximal calcium levels (these are reached some time later, as seen in Figs. 2B<sub>3,4</sub>, 2C<sub>3,4</sub>).
One last note is that from your comment I got the impression that you may have understood Δt to be the time until dopamine feedback is provided. It is not, it is simply the time step in the simulation (already stated in line 211; now an additional explanation is added in lines 211-214, just in case).
(12) Figure 4C: How is it possible that the theta_LTP value goes higher than the upper threshold (dashed line)? Equation 3 implies that it should always be lower.
This is also just a choice of implementation: θ<sub>LTP</sub> evolves independently of θ<sub>LTP</sub>, reflecting an implicit assumption that different molecular machinery implements θ<sub>LTP</sub> and θ<sub>LTP</sub>. This assumption is similar to the findings in Figs. 4, 5 in Ngezahayo et al. 2000, where in weakened synapses the voltage threshold for LTD can increase (to -20 mV) above the voltage threshold for LTP (at -30 mV). (This assumption is now explicitly written out in lines 316-322.)
(13) Row 429 (page 11): The statement that "without metaplasticity the NFBP cannot be solved" is overly general and not supported by the evidence presented. There exist many papers in which people solve similar non-linear feature learning problems with Hebbian or other bio-plausible rules that don't have metaplasticity. A more accurate statement that can be made here is that the specific rule presented in this paper requires metaplasticity.
Yes, that is what is meant with that statement – that this specific rule requires metaplasticity. The text has been corrected. Thank you for noticing this.
(14) The methods section does not make any mention of publicly available code or a GitHub repository. The author should add a link to the code and put some effort into improving the documentation so that others can more easily assess the code and reproduce the simulations.
The link to the code is given in the Data availability statement. However, this statement might not appear in the manuscript files that you are receiving (it is available online and in the article PDF downloadable from eLife), so I am providing the link here, as well. The Readme.md file now describes the code, and how to reproduce figures in the article.
https://github.com/danieltrpevski/Plasticity/tree/metaplasticity
Reviewer #2 (Public review):
Summary:
The manuscript proposes interesting synaptic plasticity rules grounded in experimental data. Its main features are:
(1) plasticity depends on local calcium concentration driven by presynaptic activity and is independent of somatic action potentials,
(2) the rules incorporate metaplasticity, and
(3) they demonstrate how a single neuron could address the feature-binding problem at the dendritic level.
The work extends a previous study (https://doi.org/10.7554/), to which the author also contributed.
The author models two calcium thresholds (LTP/LTD) from two different calcium sources (NMDA/VGCC), and these thresholds are flexible (metaplasticity rule, similar to BCM), which is claimed to be necessary for successful learning of both FBP and NFBP (linear and nonlinear feature binding problem with 1 or 2 patterns). The role of each threshold seems to be opposite and complementary. One extra condition has been added: an upper threshold for LTP. This threshold serves to stop synaptic strengthening once synapses are strong enough to evoke a plateau. With that, synapses are not strengthened to the maximal value, avoiding strong supralinear integration for irrelevant patterns.
This is summarizes the learning rule well. What I should probably add is that, as mentioned in the introductory response, the article’s first version may cause some confusion about the study’s goal. The goal was to study the role of metaplasticity in the two thresholds, not to solve feature binding in particular. Nevertheless, feature binding is a very useful task to demonstrate the roles of each threshold because the patterns share features: the synapses for the shared features experience both LTP and LTD, and metaplasticity is necessary to express (or to converge to) just one plasticity state (either LTP or LTD). More specifically, the threshold for one plasticity process (e.g. LTD) is necessary to express the opposite process (e.g. LTP). However, to be able to study metaplasticity using feature binding, a prerequisite is to have a rule that can solve it. (So, in that sense, it was first necessary to show that the rule solves the tasks before exploring the roles of metaplasticity. The article has been revised to clearly state this.)
Strengths:
The current model implements not only local synaptic plasticity but also metaplasticity and solves the FBP at the dendrite level. Another strong aspect of the model is that metaplasticity in the LTD threshold protects strengthened synapses from weakening. In this way, as the author mentioned, metaplasticity is able to protect learned patterns from being forgotten or weakened and prevent irrelevant patterns from being stored. This is a nice modelling example of metaplasticity being helpful in preventing the catastrophic interference or forgetting (as has been explicitly discussed in a recent article https://doi.org/10.1016/j.). The author might want to briefly mention or emphasize this aspect of the model, which might be interesting also for the AI community.
This is a great suggestion, thank you! I have instead emphasized a related aspect of the model: that it can solve the plasticity-stability dilemma (when taking away the closed-loop implementation of metaplasticity). I did not focus on catastrophic forgetting, because in machine learning it has a slightly more specific meaning: forgetting that occurs in sequential learning of different tasks. Instead, I exemplified the plasticity-stability dilemma using reversal learning (the reward policy is switched in the middle of the simulation), which can be viewed as a special case of sequential learning of opposite tasks. So, strictly speaking, there is no demonstration that metaplasticity prevents catastrophic forgetting (in the more general sense), but there is a demonstration that it retains (stabilizes) what has been learned (within the same task). The latter does suggest that metaplasticity could help prevent catastrophic forgetting, as well.
Weaknesses:
(1) What is novel in the current paper as compared to Khodadadi et al. eLife 2025? That is not completely clear and should be made clearer. Is it only a minor difference related to the fact that the new learning rule has metaplasticity in both calcium thresholds and is simpler? This seems to be just an incremental increase in knowledge/methods. Can the author defend his paper against this point from the „devil's advocate"? How is the conclusion of the author in the abstract that „metaplasticity in both thresholds is necessary" reconcilable with his previous publication (Khodadadi et al. eLife 2025), in which only metaplasticity in one threshold was successful in solving the nonlinear feature binding problem?
Thank you for raising this question, since the answer was not clear in the first version. The study may be an incremental increase in methods, but is (in my view) a solid increase in knowledge, giving concrete new insights into metaplasticity (an area that is still comparatively little understood). The two main conclusions are:
(1) In synapses that are exposed to both the LTP and the LTD process, metaplasticity is necessary to ultimately express just one of them (converge to either LTP or LTD).
(2) Metaplasticity in the threshold regulating one plasticity process is necessary for expressing the opposite process (metaplasticity in the LTD threshold is necessary for expressing LTP, and vice versa).
The article has been substantially revised to clearly state these main conclusions (as well as the study’s goal), while a full list of all conclusions is given in points 1-7 the Discussion.
The conclusion in the abstract that „metaplasticity in both thresholds is necessary" is stated too generally, and it was meant to refer to this rule only. I have now removed it from the abstract, since the study’s goal was not to solve feature binding. Instead, the focus is on the two conclusions above as well as other conclusions obtained from expanding the study with reversal learning and using a single threshold (prompted by the comments from yourself and reviewer #1).
Lastly, the differences compared to Khodadadi et al. 2025 (eLife) are:
(1) Yes, the rule is simpler and has metaplasticity in both calcium thresholds, instead of just one in Khodadadi et al. 2025 that operates according to a different mechanism (where the threshold, along with the entire LTP plasticity kernel, moves in a direction opposite of the calcium signal).
(2) Plateau potentials are used here, versus the “boosting” nonlinearities in Khodadadi et al. 2025.
(3) The most detailed calcium diffusion model to date for SPNs is implemented in this study (by Dorman et al. (2018)). This was a necessary addition to avoid non-monotonous increases in calcium (shown in Fig. 13A, B). No calcium diffusion between neuronal compartments is implemented in Khodadadi et al., 2025. This is indeed a small methodological difference, but not trivial to implement.
The relation to Khodadadi et al., 2025 is now stated both in the introduction in lines 137-144, and at greater length in the discussion in lines 856-870.
Perhaps I should note that the two learning rules (this one and that in Khodadadi et al. 2025) developed in parallel, this one being based on formulations similar to Gütig et al. 2003 by adding metaplasticity, while the rule in Khodadadi et al. 2025 was inspired from the ideas in Schiess et al. (2016) and Urbanczik and Senn (2014) (see list of references provided). The two studies have different goals (and in that sense one was not meant to be an extension of the other):
- Khodadadi et al. (2025) studies whether the NFBP can be solved by SPNs,
- this article studies the role of metaplasticity in the two calcium thresholds that exist in dSPNs; it uses feature binding as a task because the role of metaplasticity is exposed precisely by the shared features in the task (they cause shared synapses to undergo competing LTP and LTD, and metaplasticity is necessary to direct synapses into just one outcome); importantly, feature binding is also relevant for the striatum (now described in the introduction in lines 126-136)
Finally, to obtain the conclusions in this study about the roles of the two thresholds, it was necessary to devise a suitable rule. They cannot be obtained neither with the rule in Khodadadi et al. 2025, nor with any other rule, because none have a formulation with two separate thresholds for LTP and LTD. Phrased more generally, one needs a new/different rule (new/different assumptions) to obtain new/different conclusions, even if the new rule may be related to existing ones. That said, a rule with a single threshold would have reached conclusion 1. above, as is now shown in the article in Fig. 12 and Figure 12 – figure supplements 1 – 4, but SPNs have two thresholds, prompting the use of a rule with two thresholds. Also, although not demonstrated with the cascade model (by Fusi et al. (2005) and its extensions), conclusion 1. should be obtainable with it, and is implied by the dynamics of the cascade model (which uses one threshold to control transitions between strong and weak synapses). More on the cascade model is given below and in the revised article.
Hopefully that provided a clearer answer. If you have more questions, please let me know so I can try to clarify further.
(2) As far as I can judge without testing the model, metaplasticity causes thresholds to monotonically increase during systematic pattern presentation, which stabilizes weights and allows pattern separation. Due to the closed-loop nature of the current implementation, where metaplasticity only happens if plasticity happens, this also effectively locks patterns in place. However, flexible learning is an essential mechanism for survival. Imagine a mutation event takes place and bananas suddenly become red and/or strawberries turn yellow. It seems that the current model would be unable to adapt to these new patterns even if rewards were to be shifted. While out of the scope of the study, due to its importance, I feel that pattern shifting/relearning should at least be briefly discussed. How could the model be improved to allow relearning?
This is a very important question, and I think it is in fact within the scope of the study, so it is now addressed using reversal learning as a task (the reward policy is switched in the middle of the simulation, after the FBP and NFBP are learned). As you pointed out, the closed-loop formulation of metaplasticity effectively locks the patterns in the dendrites, and reversal learning cannot be solved (Fig. 9). On the other hand, if the conditions for metaplasticity are relaxed by allowing any calcium levels to trigger metaplasticity (i.e. no longer have a closed-loop formulation requiring that [Ca]<sub>NMDA</sub> or [Ca]<sub>L-type</sub> be above their thresholds), reversal learning in both the FBP and NFBP is solved (Fig. 10 and Figure 10 – figure supplements 1 – 3). (Note that [Ca]<sub>NMDA</sub> or [Ca]<sub>L-type</sub> still need to be above their thresholds for plasticity to occur.)
Recommendations for the authors:
Reviewing Editor Comments:
While the reviewers were very positive, they highlighted limitations on the strength of evidence. Addressing these points could help revise this assessment.
Reviewer #1 (Recommendations for the authors):
(1) Framing the problem as "feature binding" is easy to understand, but it's a slightly narrow view of learning in general. Some mention of how NFBP relates to the XOR problem in the introduction would help you relate your solution to the much broader class of computational problems, since XOR is a more fundamental computational primitive. Non-linear feature learning is very general and relates to all machine learning problems and to computations that occur across every brain region.
Since the goal of the study was not to solve the NFBP or feature binding (but to study metaplasticity), the relation of the NFBP to the XOR is put in the Discussion instead (to avoid further confusion about the study’s goal). Nevertheless, this connection is clearly made in the introduction of the new study that uses 100+ SPN models.
(2) Since the requirement for clustered synapses is one of the main limitations of this learning rule, it would help if there were some discussion of how clustering might occur (e.g., whether there are any other related learning rules or mechanisms that might promote clustering, or if you are assuming that this has to occur entirely through developmental wiring).
This is now discussed in lines 817-827 and related to developing a learning rule that would incorporate structural plasticity.
(3) Page 5, row 157: Another potentially relevant citation here is Bittner et al. 2017, showing that a dendritic plateau potential in silent CA1 neurons drives place field formation without any prior spiking activity.
Thank you, that is indeed a very relevant citation here! It is now added in line 222.
(4) Figure 4C: It would be helpful to add a sentence in the figure legend explaining what the dashed lines represent (even though you also mention it in the main text).
Added, thank you!
(5) Across all figures, the author should consider using color combinations that are more colorblindfriendly (e.g., cyan/red). As a R/G colorblind person, I find it slightly difficult to see which line is which in the panels that compare scores in the NFBP.
The panels showing the NFBP scores have been changed throughout the article, and all other figures have been checked. If there are any more difficult color combinations, please let me know.
(6) The conventional, widely used abbreviation for dopamine is "DA", not "Da".
Now changed.
(7) A few typos I spotted in the paper:
(a) Row 117 (page 3): missing parenthesis around citation
(b) Row 173 (page 5): "uner" --> under
(c) Row 248 (page 7): repeated sentence "...are first seen above..."
(d) Row 255 (page 7): "NBFP" --> NFBP
These are now fixed, thank you for reporting them!
Reviewer #2 (Recommendations for the authors):
(1) How are synapses distributed in the nonlinear integration case? Are pattern combinations branch-specific, or are features distributed randomly across the whole dendritic tree? Does this matter in any way? In any case, it should be clarified.
Yes, they are branch-specific. In the NFBP, the feature combinations from Figure 3 – figure supplement 1 (and later from Figure 10 – figure supplement 1) are placed on two dendrites, chosen at random from 8 dendrites, in a 20-micrometre dendritic stretch starting around 120 micrometers away from the soma. 12 different trials are run for each feature combination, meaning that 12 randomly chosen pairs of dendrites were tested for each feature combination. In the FBP, the clusters are placed in one dendrite chosen at random from 8 dendrites, at the same distance from the soma as in the NFBP. This information is now added in the caption of Fig. 3.
The idea behind placing clusters on the same dendrite is that, after learning, two strong clusters will produce a plateau (e.g. ‘red’ and ‘strawberry’), while one strong and one weak cluster will not (e.g. ‘yellow’ and ‘strawberry’), as in Figs. 3C<sub>2</sub>, 3C<sub>3</sub> (with the weights shown in Figs. 4B<sub>2</sub>, 4B<sub>3</sub>). For this the clusters need to be in the same branch, so that two features are “bound” together “into” a larger, plateau-evoking cluster. Also, a strong and a weak cluster should evoke a sufficiently lower somatic amplitude so that any additional noise will not cause somatic spiking. This is assured by the large voltage jump in the plateau (the all-or-none quality of the plateaus, Fig. 2D<sub>1</sub>).
If the clusters are distributed randomly on different dendrites, it might or it might not work. Fig. 10 of Oikonomou et al. (2012) shows that dendritic spikes (that individually do not evoke somatic spiking) summate sublinearly at the soma in pyramidal neurons: weak + weak cluster = no spiking (Fig. 10A); strong + strong = no spiking (Fig. 10B); but also strong + strong = spiking (Fig. 10C). To reliably solve the NFBP, a large enough supralinearity is necessary instead, so one should test how the soma integrates dendritic spikes/plateaus in SPNs. As the goal of this study was not to solve the NFBP, this is left for the future (perhaps within the new ongoing study focusing on the NFBP).
(2) To produce dendritic plateau potentials, the model (as in the previously published model - Trpevski et al. 2023) implements glutamate spillover activating extrasynaptic NMDARs. This is an interesting mechanism, but is there empirical evidence supporting this way of generating plateau potentials? Are synaptic NMDARs not sufficient? If not, which experiments support the role of nonsynaptic ones?
This is still an ongoing area of research, indicating that glutamate spillover is regulated by reuptake from glial cells, which could even reverse function and excrete glutamate (Rusakov and Stewart, 2021; Malarkey and Parpura, 2014).
Except for the experiments from Szapiro and Barbour, 2007 showing that climbing fibers in the cerebellum signal to molecular-layer interneurons exclusively through glutamate spillover, there are no other “in-vivo-like” experimental conditions which show that spillover activates extrasynaptic NMDARs (eNMDARs). The strongest other in vitro data come from the following experiments:
(1) Chalifoux and Carter (2011), where glutamate reuptake by transporters was blocked with TBOA, which promoted NMDA spikes evoked by synaptic stimulation, suggesting that glutamate spillover activates eNMDARs. A similar experiment was done in Suzuki et al. (2008), where, in addition, synaptic NMDARs were blocked, leaving only eNMDARs available to trigger plateaus.
(2) Glutamate iontophoresis, which ejects glutamate directly into the extrasynaptic space, activates plateaus once the iontophoretic current is strong enough (Oikonomou et al., 2012), with or without blocking glutamate reuptake (Suzuki et al. 2008).
(3) Repetitive synaptic stimulation is thought to produce glutamate spillover (Suzuki et al. 2008; Oikonomou et al., 2012). For example, two synaptic shocks trigger NMDA spikes, while 5 synaptic shocks trigger plateaus in pyramidal neurons (Oikonomou et al., 2012).
On the other hand, studies that employ glutamate uncaging at spines, which should activate eNMDARs much less, evoke NMDA spikes instead (Losonczy and Magee, 2006; Branco et al. 2010). Compared to plateaus, these have much smaller amplitudes, and the size of the supralinearity (the voltage jump) is much smaller than in the plateaus obtained with glutamate iontophoresis (compare Fig. 3 in Losonczy and Magee, (2006), Fig. 3B in Branco et al. (2010) to Fig. 4C in Oikonomou et al. (2012), Fig. 6 in Oikonomou et al. (2014)).
The reason why glutamate spillover was implemented is precisely this robust all-or-none quality of the plateaus, i.e. the large jump in somatic voltage (Fig. 2D<sub>1</sub>) after a threshold level of stimulation (when the stimulus intensity increases in equal amounts). Without spillover, plateaus are graded in amplitude (and duration, Fig. 2B<sub>1</sub> in Trpevski et al. (2023)), and the NFBP cannot be solved (Fig. 6 in Trpevski et al. (2023)).
(3) The check for dependence on initial conditions of theta_LTP/LTD is missing. Especially for the conditions of the thresholds being fixed. How do you decide what fixed value to use? How about having a corresponding limit for weights and not for thresholds? Why is there still an increase in threshold going on even when weights reach the maximum?
The initial conditions for θ<sub>LTP</sub> and θ<sub>LTD</sub> are also an important question. The idea behind starting with low values of the thresholds (or fixing them to low values) is to make the synapses flexible for learning. One can view metaplasticity’s role as a “lock” on the weights, locking them once learning is done, and unlocking them (making them flexible) when something needs to be learned. Which signals determine when to lock or unlock the weights is what the metaplasticity rule implements, and is insufficiently understood experimentally. In any case, it makes sense to start with flexible synapses (low thresholds) at the beginning of learning; otherwise, no/little learning will take place (Figure 9 – figure supplement 2, the panels for “thresholded” metaplasticity). Throughout the article I choose the initial values of the thresholds to be lower than the calcium evoked by weakened synapses, ensuring that any calcium signal will trigger plasticity (but higher values also work).
Instead of doing a scan over the initial conditions of θ<sub>LTP</sub> and θ<sub>LTD</sub>, I chose to show the following:
(1) An example with initial threshold values higher than the calcium amplitudes: these “lock” the weights (Figure 9 – figure supplement 2, panels for “thresholded” metaplasticity) from the start and no learning can occur.
(2) An example initialized with high values for the thresholds, but where metaplasticity can be triggered by any calcium amplitudes (no closed-loop in the metaplasticity rule, Figure 9 – figure supplement 2, panels for “relaxed” metaplasticity): here the thresholds adapt and learning can take place afterwards.
This is supposed to illustrate a mechanism that can “unlock” weights. A scan over the initial conditions of θ<sub>LTP</sub> and θ<sub>LTD</sub> will give the lowest calcium level that the thresholds can be initialized to so that “thresholded” metaplasticity will work. But it is not important to know these precise values to obtain the conclusions in the article, which is why I did not do such a scan. (The above is treated in the article in the section on reversal learning, lines 569-577 and 628-633.)
Also, when the rule is used for learning, it is not meant to have fixed thresholds, as synapses cannot stabilize and nothing will be stored (Figs. 5, 6, and 8). Fixing the thresholds to a low value was meant to show what happens without any metaplasticity (or if metaplasticity were “dysfunctional”). If in reality a mechanism exists to fix the thresholds to a low value or a high value, fixing would be temporary (until necessary to keep the weights flexible or locked, respectively).
I am probably not understanding this part of the comment: “How about having a corresponding limit for weights and not for thresholds?” There are two limits, the maximal and minimal weights in the rule w<sub>max</sub> and w<sub>min</sub>, and are initialized to random values within the interval [0.3, 0.35], but this is probably not what you mean.
When the weights reach their maximum, the thresholds still increase because they have not reached the calcium amplitudes evoked by the maximal weights. (This is most visible with supralinear integration, where strengthened weights evoke plateaus Fig. 4C<sub>2</sub>-C<sub>4</sub>.) The thresholds move towards the calcium amplitudes with a rate η<sub>θ</sub>, which if made very high (as in Figure 4 – figure supplement 11), will make the thresholds rise as fast as the weights. But this is not good, as it will “lock” the learning processes in the synapses too soon (i.e. shorten the window where they are flexible). Neither is a too low η<sub>θ</sub> good, as then the synapses are flexible for a very long time and learning of the NFBP is prolonged (Figure 4 – figure supplements 10B<sub>3</sub>, 10B<sub>4</sub>, 10E<sub>3</sub>, learning simulations last longer than in Fig. 4).
(4) Calcium modelling: The author writes that the largest voltage plateaus do not correspond to the largest calcium amplitude because of the plateau's voltage approaching the NMDAR reversal potentials, which might be a problem for the plasticity rule. To solve this, the author tried to implement a monotonic increase of calcium with increasing plateau by implementing axial calcium diffusion and buffering. My question is, is the monotonic increase realistic? Is not the NMDAR reversal effect, described above, a realistic scenario in dendrites?
It seems to be realistic. The closest experiment that I know of is in Fig. 2C<sub>2</sub>, D<sub>2</sub> in Oikonomou et al. (2012), where 2 synaptic shocks produce an NMDA spike, and 5 shocks produce a plateau. The calcium dye shows a higher response from the plateau, suggesting a higher calcium amplitude (with a monotonic increase). Moreover, in the detailed calcium model for SPNs by Dorman et al. (2018), larger synaptic clusters produce monotonically higher calcium amplitudes. These two pieces of evidence suggest the calcium amplitudes are not affected by the membrane voltage approaching to the reversal potential. Most likely, this happens because of strong intracellular calcium buffering.
Similarly, the experiments in Figs. 5 and 8 in Losonczy and Magee (2006) with glutamate uncaging at spine heads show a monotonic increase in calcium dye flourescence as the cluster size is increased. However, these experiments evoke NMDA spikes, which might not have approached the NMDAR reversal potential as closely as plateaus do (so, it is theoretically possible that monotonicity does not hold if a plateau were evoked, although it seems unlikely). This is now added to the Methods in lines 957-961.
(5) Function: What is the actual function of the SPN, and how does it relate to FBP/NFBP learning? SPNs are involved in motor control/decision making and generally in sensorimotor tasks. Rather, use an example for that than a visual stimulus, though I understand it is more easily illustrated. Is feature binding what SPNs do and have to solve?
It is not known yet what SPNs do precisely. The initial action selection role of the basal ganglia is currently being challenged or replaced by a role in movement initiation and/or invigoration (with action selection being done by the cortex, see e.g. Thura and Cisek (2017)). In any case, SPNs receive convergent input from sensory, motor, limbic and associative areas, as well as thalamic and neuromodulatory inputs (with topographical projections indicating functional specialization). In that sense, feature binding is particularly relevant for the striatum, as diverse features from different areas would arrive there. The basal ganglia participate in non-motor loops as well, so the striatum may have a role in initiation and termination of cognitive processes such as planning and attention, and in regulating emotional and motivated behavior (Purves et al. 2018).
The role of the striatum and the relevance of feature binding is now stated in the introduction in lines 126-136, and a task with features more suited for the striatum is given in Figure 1 – figure supplement 1 (inspired from similar tasks in Bernklau et al. (2024)). I have kept the example from the visual system in the main text simply because it is widely used throughout the literature and easily recognizable, while clearly stating that other features would be involved in the striatum and pointing to the example in Figure 1 – figure supplement 1. Hopefully this will make a good compromise between ease of reading and relevance to the striatum.
(6) The population of striatal projection neurons can express dopamine D2 receptors and not only D1 receptors. SPNs with different receptors thus undergo synaptic plasticity according to different rules. Would that lead to similar results? A combination of both populations?
This is also being tested in the new study, and preliminary results indicate the answer is “yes” (see Author response image 4). Contrary to the dSPNs, the indirect-pathway SPNs (iSPNs), which predominantly express D<sub>2</sub> receptors, are thought to be involved in suppressing competing or related movements. The learning rule is almost the opposite to dSPNs: to trigger LTP, a dopamine pause is needed, and to trigger LTD a dopamine peak is needed (Fig. 4B and Shen et al. (2008)). So, with such a rule, iSPNs will store the irrelevant patterns and spike to them, and be silent to the relevant patterns (which indeed happens after learning in Author response image 4F<sub>2</sub>, F<sub>3</sub>). This aligns well with their role to suppress movements – reaching for the irrelevant patterns will be suppressed, while reaching for the relevant patterns will be disinhibited (the indirect pathway inhibits movement initiation).
(7) Other synaptic plasticity & metaplasticity models (possible comparison or discussion): https://pubmed.ncbi.nlm.nih./ https://linkinghub.elsevier.(https://link.springer.com/ For example, in the last model, there is only one modification LTP/LTD threshold, but it is different from the voltage threshold (which would be comparable to calcium thresholds in the current paper - see the voltage threshold different from the modification threshold here: https://doi.org/10.1371/). The modification threshold favors LTP or LTD - depending on the previous spiking activity of the cell and effectively works as an anti-Hebbian firing rate „homeostasis" mechanism. How is the firing rate homeostasis maintained in the current paper/model? Can you explain how this model is related to the previous models of Benuskova and Abraham, and also Clopath (there was also a metaplasticity version of the Clopath model), in terms of firing rate stability? The current model implements not only local synaptic plasticity but also metaplasticity, which is a nice feature, and seems to not only solve the FBP but also maintain firing stability. Is the stability of firing a consequence of the hard bounds for synaptic weights, or is it also a consequence of plasticity and metaplasticity? I like that each synaptic weight is changed independently based on local calcium concentration, with its own LTP and LTD thresholds.
I will first describe what happens to the firing rate in this model, and then compare with the references you mentioned. In the FBP with linear integration, yes, the firing rate stability is only maintained because of the hard bounds for synaptic weights (Figure 4 – figure supplement 5A<sub>1</sub>, the neuron goes into depolarization block without w<sub>max</sub>). Without w<sub>max</sub>, the weights would grow until [Ca]<sub>NMDA</sub> saturates in the spine (which does not happen for most spines within the simulation time in Figure 4 – figure supplement 5B<sub>1</sub>).
In the FBP with supralinear integration and the NFBP, the weights are prevented from increasing by the upper threshold for LTP, θ<sub>LTP</sub>. If θ<sub>LTP</sub> and w<sub>max</sub> are gone, synapses also grow without bound (Figure 4 – figure supplement 5B<sub>2</sub>). Regardless of how high the synaptic weight becomes, firing rate stability is ensured by the plateau potential, as the maximally achievable voltage is limited by the NMDAR reversal potential (Figure 4 – figure supplement 5A<sub>2</sub>, a somatic depolarization block does not happen as in Figure 4 – figure supplement 5A<sub>1</sub>). This is part of the plateaus’ function to provide dynamic range compression, as shown experimentally in Figs. 3E, 4D and 12 in Oikonomou et al. (2012). (Of course, such high weights are unrealistic, but they happen in the model without w<sub>max</sub> and without θ<sub>LTP</sub>). This is now described in the text in lines 397-407.
Regarding the other studies, the second link did not work, so I will refer to Jedlicka et al. (2015), Clopath et al. (2010) and Zenke et al. (2013). (The rule in Jedlicka et al. (2015) is the same as in Benuskova and Abraham, (2007) but with a more detailed neuron model.) In these studies, there is a threshold representing a (weighted) average of the postsynaptic activity (postsynaptic voltage or spiking). In Clopath et al. (2010) and Zenke et al. (2013) it modulates only the amount of LTD, while in Jedlicka et al. (2015) it modulates the amounts of both LTP and LTD that occur due to plasticity. The threshold is global for a neuron (i.e. all synapses use the same threshold), and allows for heterosynaptic effects that compensate increased excitation from synaptic strengthening with stronger weakening in depressed synapses (thus maintaining stable firing rates). (However, the rule in Jedlicka et al. (2015) and Benuskova and Abraham, (2007) has only one threshold, there is no separate voltage threshold. Indeed, the threshold is a low-pass filtered variable of the input spike train, so is similar to calcium concentration.)
There are no such effects in the current learning rule. Some compensatory effects are visible when comparing supralinear integration with and without an upper threshold θ<sub>LTP</sub>, as e.g. in Fig. 4B<sub>2</sub> and Figure 4—figure supplement 3B<sub>1</sub>. With θ<sub>LTP</sub>, synapses do not increase to w<sub>max</sub>, and without it, they do. As a consequence, the weakened synaptic cluster is weakened less when using θ<sub>LTP</sub> (‘yellow’ synapses in Fig. 4B<sub>2</sub>), and more without θ<sub>LTP</sub> (‘yellow’ synapses in Figure 4—figure supplement 2B<sub>1</sub>). The increased weakening in the latter case is because the strengthened ‘strawberry’ synapses have reached w<sub>max</sub>, and contribute to spiking for the irrelevant pattern (‘yellow strawberry’). As a result, the weakened ‘yellow’ synapses have to decrease more so no spiking for the irrelevant pattern occurs. In effect, the increased strengthening in the ‘strawberry’ synapses drives increased weakening in the ‘yellow’ synapses. However, this is a result of the task structure, i. e. that the patterns share features, and not from the learning rule.
The above is briefly explained in the Discussion in lines 778-786.
(8) The last sentence in the discussion is a bold claim: SPN can completely solve NFBP alone. Is that statement too strong, or is it a sign of multiple different mechanisms implementing the same function (i.e., degeneracy)?
The sentence was not meant to be a bold claim. It currently says:
“This indicates that ... SPNs might completely solve the task ... Whether this is true will be explored in another study …”
I have now toned this claim down, as the purpose was only to point to the new study that explores this question (using with 100+ SPN models, in two learning regimes and varying cluster location). Nevertheless, the preliminary results in the new study suggest that SPNs can indeed solve the NFBP (if the plateaus are all-or-none), so I agree that it is a sign of multiple mechanisms implementing the same function.
Figures/Table:
(1) Figure 2: The layout of the figure is confusing. B shows distributed input as in upper A, and C shows clustered input as in lower A. This should be illustrated better (e.g., as in Figure 3 or 4). The term cluster size is confusing as well because it also refers to the distributed inputs; better use the number of synapses here. The color choice is difficult, as similar colors are chosen for cluster size and for differentiating linear and nonlinear integration in D.
Thank you for the detailed comments! The figure has been reworked accordingly.
(2) Figure 4: C What are dashed lines?
They indicate the upper threshold for LTP, θ<sub>LTP</sub>.Thank you for noticing this, it is now added in the figure caption, and in other figures where it was missing.
(3) Figure 5 and Figure 6: B is missing.
These figures have been reworked to match the revision of the text describing the role of metaplasticity in the shared synapses. Now, the FBP is described first, followed by the NFBP, so the figures have been merged with their figure supplements (where the FBP results used to be in the first version).
(4) Figure 4 Supplement 1: What do the colors and regions mean in B3? Why show here and not for others?
The main text in lines 311-312, 331-333, and 358-359 refers to these regions when explaining the dynamics of the calcium, the thresholds and the weights (e.g. the pink region shows that [Ca]<sub>L-type</sub> in the ‘strawberry’ synapses evoked by ‘yellow strawberry’ is much lower than the calcium threshold for ‘strawberry’, protecting these synapses from weakening). They are simply highlighted with different colors, so readers know precisely where to look when reading the main text. The figure caption has been updated to state this.
Also, the figure caption says that the same regions exist in all panels, although they have not been highlighted. I could have chosen any panel to mark these regions, and I chose B<sub>3</sub> because it looked like it had the least visual clutter.
(5) Table 1: Typo for LTD
Now fixed.
(6) Line 21: „thehsold"
Now fixed.
(7) Line 50: Closing parentheses missing.
Now fixed.
(5) Line 55: "All metaplasticity models so far have only one modifiable threshold". This is not true as it stands. Multiple sliding thresholds have been proposed before:
- experimentally by Ngezahayo et al. (2000)
- multiple pathways reviewed by Abraham (2008)
- multiple structural LTP thresholds observed experimentally by Ueda et al. (2022)
- models of synaptic states and cascade models can be considered to employ multiple thresholds (depending on state); e.g., Fusi et al. (2005)
Thank you for providing these references! The sentence has been changed (it was supposed to refer only to computational models), and the studies have been added in the text where appropriate.
Importantly, Fusi et al. (2005) is now being discussed throughout the text, as it contains important results and conclusions about metaplasticity which are used as comparison. (In the first version of the article I did not include it because I was not sure about the interpretation of the thresholds – strictly speaking there is only one plasticity threshold (q, determining whether a synapse will switch sign), while the other is a metaplasticity threshold (p, determining whether the synapse will change its metaplastic state). However, the precise number of thresholds is not as important, as the study’s results are relevant to compare with.)
(9) Lines 117/118: Missing parentheses around reference.
Fixed.
(10) Line 140: "a small difference". I feel like "small" is a bit of an understatement here, as from what I can see, the differences are almost a magnitude -- see blue/black traces in Figure 2B4 vs. 2C4.
Thank you for noticing this. It was meant to refer only to the amplitude of the somatic voltage when the cluster size is small (in Fig 2D<sub>1</sub>). The text has been clarified now.
(11) I think it's unnecessary to rewrite Eq. 1 in Eq. 3.
I decided to keep this.
(12) Lines 181-183: It would probably still be useful to show that NFBP can't be solved by distributed inputs.
It is now shown in Figure 4 – figure supplement 1, and briefly described in the text in lines 298300.
(13) Line 210: Typo, double "(the"
Fixed, thank you.
(14) Lines 248-249: Typo, double partial sentence.
Now fixed.
(15) Line 760: The year in the „STDP rule endowed with the BCM sliding threshold accounts for hippocampal heterosynaptic plasticity" should be corrected to 2007. Also, all other references should be checked for mistakes and missing pages, etc. (see e.g., also line 882).
Thank you for noticing this! The references have been checked.
References
Benuskova, L., Abraham, W.C. STDP rule endowed with the BCM sliding threshold accounts for hippocampal heterosynaptic plasticity. J Comput Neurosci 22, 129–133 (2007). https://doi.org/10.1007/s10827-006-0002-x
Bernklau TW, Righetti B, Mehrke LS, Jacob SN. (2024) Striatal dopamine signals reflect perceived cue–action–outcome associations in mice. Nature Neuroscience 27(4):747–757. doi: 10.1038/
Branco, T., Clark, B. A., & Häusser, M. (2010). Dendritic Discrimination of Temporal Input Sequences in Cortical Neurons. Science, 329(5999), 1671–1675. http://www.jstor.org.focus.lib.kth.se/stable/40803162
Chalifoux JR, Carter AG (2011) Glutamate Spillover Promotes the Generation of NMDA Spikes. J. Neurosci. 31(45):16435–16446. doi:10.1523/JNEUROSCI.2777-11.2011
Clopath, C., Büsing, L., Vasilaki, E. et al. Connectivity reflects coding: a model of voltage-based STDP with homeostasis. Nat Neurosci 13, 344–352 (2010). https://doi.org/10.1038/nn.2479
Dorman, D. B., Jędrzejewska-Szmek, J., Blackwell, K. T. (2018) Inhibition enhances spatiallyspecific calcium encoding of synaptic input patterns in a biologically constrained model. elife 7:e38588 https://doi.org/10.7554/eLife.38588
Du K., Wu Y., Lindroos R., Liu Y., Rózsa B., Katona G., Ding J.B., & Kotaleski J.H. (2017) Celltype–specific inhibition of the dendritic plateau potential in striatal spiny projection neurons, Proc. Natl. Acad. Sci. U.S.A. 114 (36) E7612-E7621, https://doi.org/10.1073/pnas.1704893114.
Gjorgjieva J., Clopath C., Audet J., & Pfister J. (2011) A triplet spike-timing–dependent plasticity model generalizes the Bienenstock–Cooper–Munro rule to higher-order spatiotemporal correlations, Proc. Natl. Acad. Sci. U.S.A. 108 (48) 19383-19388, https://doi.org/10.1073/pnas.1105933108
Gütig R., Aharonov R., Rotter S., Sompolinsky H (2003) Learning Input Correlations through Nonlinear Temporally Asymmetric Hebbian Plasticity. J. Neurosci. 23 (9) 3697-3714; DOI: 10.1523/JNEUROSCI.23-09-03697.2003
Hedrick, N.G., Lu, Z., Bushong, E. et al. (2022) Learning binds new inputs into functional synaptic clusters via spinogenesis. Nat Neurosci 25, 726–737 . https://doi.org/10.1038/s41593-022-01086-6
Hwang F, Roth R, Wu Y et al. (2022) Motor learning selectively strengthens cortical and striatal synapses of motor engram neurons Neuron 110, 2790-2801.e5
Jedlicka P, Benuskova L, Abraham WC. (2015) A Voltage-Based STDP Rule Combined with Fast BCM-Like Metaplasticity Accounts for LTP and Concurrent “Heterosynaptic” LTD in the Dentate Gyrus In Vivo. PLOS Comput Biol 11(11):1–24. https://doi.org/10.1371/journal.pcbi.1004588
Kirchner, J.H., Gjorgjieva, J. (2021) Emergence of local and global synaptic organization on cortical dendrites. Nat Commun 12, 4005. https://doi.org/10.1038/s41467-021-23557-3
Lindroos R, Hellgren Kotaleski J (2021) Predicting complex spikes in striatal projection neurons of the direct pathway following neuromodulation by acetylcholine and dopamine. Eur J Neurosci. 53:2117–2134. https://doi.org/10.1111/ejn.14891
Losonczy A, Magee J (2006) Integrative Properties of Radial Oblique Dendrites in Hippocampal CA1 Pyramidal Neurons. Neuron 50: 291-307
Malarkey EB, Parpura V (2008) Mechanisms of glutamate release from astrocytes, Neurochemistry International 52(1–2): 142-154, doi: 10.1016/j.neuint.2007.06.005.
Oikonomou KD, Short SM, Rich MT and Antic SD (2012) Extrasynaptic Glutamate Receptor Activation as Cellular Bases for Dynamic Range Compression in Pyramidal Neurons. Front. Physio. 3:334. doi: 10.3389/fphys.2012.00334
Oikonomou KD, Singh MB, Sterjanaj EV and Antic SD (2014) Spiny neurons of amygdala, striatum, and cortex use dendritic plateau potentials to detect network UP states. Front. Cell. Neurosci. 8:292. doi: 10.3389/fncel.2014.00292
Purves D, Augustine GJ, Fitzpatrick D, Hall WC, LaMantia AS, White LE, et al. (2018) Neuroscience. 6 ed. New York:Oxford University Press
Rusakov DA, Stewart MG (2021) Synaptic environment and extrasynaptic glutamate signals: The quest continues, Neuropharmacology 195: 108688, https://doi.org/10.1016/j.neuropharm.2021.108688
Schiess M, Urbanczik R, Senn W (2016) Somato-dendritic Synaptic Plasticity and Errorbackpropagation in Active Dendrites. PLoS Comput Biol 12(2): e1004638. https://doi.org/10.1371/journal.pcbi.1004638
Suzuki, T., Kodama, S., Hoshino, C., Izumi, T. and Miyakawa, H. (2008), A plateau potential mediated by the activation of extrasynaptic NMDA receptors in rat hippocampal CA1 pyramidal neurons. European Journal of Neuroscience, 28: 521-534. https://doi.org/10.1111/j.14609568.2008.06324.x
Thura D, Cisek P. (2017) The Basal Ganglia Do Not Select Reach Targets but Control the Urgency of Commitment. Neuron 95(5):1160–1170.e5. doi: 10.1016/j.neuron.2017.07.039)
Tran-Van-Minh A, Cazé RD, Abrahamsson T, Cathala L, Gutkin BS and DiGregorio DA (2015) Contribution of sublinear and supralinear dendritic integration to neuronal computations. Front. Cell. Neurosci. 9:67. doi: 10.3389/fncel.2015.00067
Trpevski D, Khodadadi Z, Carannante I and Hellgren Kotaleski J (2023) Glutamate spillover drives robust all-or-none dendritic plateau potentials—an in silico investigation using models of striatal projection neurons. Front. Cell. Neurosci. 17:1196182. doi: 10.3389/fncel.2023.1196182
Urbanczik R, Senn W (2014) Learning by the Dendritic Prediction of Somatic Spiking. Neuron 81: 521-528
Author response image 1.
Plateau potentials (A1, B1) and their somatic amplitudes in dSPNs (A) and iSPNs (B) when the location of the synaptic cluster is varied. Distally evoked plateaus have a smaller somatic amplitude in both dSPNs and iSPNs, bust still exhibit a nonlinear jump in the somatic voltage. In (A2, B2) all 71 dSPN and 34 iSPN models were tested, color coded with respect to their excitability to a synaptic cluster of 10 synapses.

Author response image 2.
Two learning simulations on the NFBP where different metaplasticity rates for LTP and LTD were used. (Top) The metaplasticity rate for LTD is higher, stopping the LTD process prematurely (D1, D2), resulting in less weakening of the synapses (B1, B2) and spiking for one irrelevant pattern (A1). (Bottom) The metaplasticity rate for LTP is higher, preventing frequent synaptic strengthening(C1, C2). As a result, it takes a longer time for synapses to strengthen and trigger plateaus (B3, B4).

Author response image 3.
Learning on the NFBP with a nonlinear (quadratic) metaplasticity rule, which implements the BCM rule. (A) Somatic and dendritic voltage before and after learning. (B-D) Evolution of synaptic weights (B), LTP (C) nad LTD thresholds (D). Weights in (B) seem to stabilize around a high value once the LTP threshold reaches the maximal [Ca]NMDA; however, the value is too high and triggers plateau potentials for all patterns.

Author response image 4.
Learning to solve the NFBP in one dSPN and one iSPN model. (A, B) Schemes describing the requirements for cortico-striatal synaptic plasticity in dSPNs (A) and iSPNs (B). (C) Dopamine peaks are emitted from the midbrain after the relevant patterns, and dopamine pauses after the irrelevant patterns. (D) Stimulation protocol. (E, F) A single learning simulation in a dSPN (E) and an iSPN (F) model. Before learning the neurons spike to all patterns (due to additional feature-unspecific distributed inputs, shown with the third panels in E3, F3). After learning, the dSPN spikes only for the relevant patterns (E2) and the iSPN only for the irrelevant ones (F2). (E3, F3) The evolution of clustered and distributed synptic weights (In dendrite 1 of the iSPN, the synapses for 'red' experienced some strengtheneing after being weakened, but this does not seem to affect learning in this example.) The neurons in th enew study receive less background synaptic input than in the current article, and additional distributed synapses are needed along with a plateau for somatic spiking, making for a more challenging learning scenario.
