Local, calcium- and reward-based synaptic learning rule that enhances dendritic nonlinearities can solve the nonlinear feature binding problem

  1. Zahra Khodadadi
  2. Daniel Trpevski
  3. Robert Lindroos
  4. Jeanette Hellgren Kotaleski

  • Curated by eLife

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    eLife Assessment

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The study presents solid evidence that the location of synapses on dendritic branches, as well as synaptic plasticity of excitatory and inhibitory synapses, influences the ability of a neuron to discriminate combinations of sensory stimuli. The ideas in this work are very interesting, presenting an important direction in the computational neuroscience field about how to harness the computational power of "active dendrites" for solving learning tasks.

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Abstract

This study investigates the computational potential of single striatal projection neurons (SPN), emphasizing dendritic nonlinearities and their crucial role in solving complex integration problems. Utilizing a biophysically detailed multicompartmental model of an SPN, we introduce a calcium-based, local synaptic learning rule dependent on dendritic plateau potentials. According to what is known about excitatory corticostriatal synapses, the learning rule is governed by local calcium dynamics from NMDA and L-type calcium channels and dopaminergic reward signals. In order to devise a self-adjusting learning rule, which ensures stability for individual synaptic weights, metaplasticity is also used. We demonstrate that this rule allows single neurons to solve the nonlinear feature binding problem, a task traditionally attributed to neuronal networks. We also detail an inhibitory plasticity mechanism that contributes to dendritic compartmentalization, further enhancing computational efficiency in dendrites. This in silico study highlights the computational potential of single neurons, providing deeper insights into neuronal information processing and the mechanisms by which the brain executes complex computations.

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  1. Version published to 10.7554/elife.97274.2 on eLife
  2. Version published to 10.7554/elife.97274 on eLife
  3. eLife

    eLife Assessment

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The study presents solid evidence that the location of synapses on dendritic branches, as well as synaptic plasticity of excitatory and inhibitory synapses, influences the ability of a neuron to discriminate combinations of sensory stimuli. The ideas in this work are very interesting, presenting an important direction in the computational neuroscience field about how to harness the computational power of "active dendrites" for solving learning tasks.

  4. eLife

    Reviewer #1 (Public review):

    Summary:

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The authors construct a detailed biophysical and morphological model of a single striatal medium spiny neuron, and endow excitatory and inhibitory synapses with dynamic synaptic plasticity mechanisms that are sensitive to (1) the presence or absence of a dopamine reward signal, and (2) spatiotemporal coincidence of synaptic activity in single dendritic branches. The latter coincidence is detected by voltage-dependent NMDA-type glutamate receptors, which can generate a type of dendritic spike referred to as a "plateau potential." In the absence of inhibitory plasticity, the proposed mechanisms result in good performance on a nonlinear classification task when specific input features are segregated and clustered onto individual branches, but reduced performance when input features are randomly distributed across branches. Interestingly, adding inhibitory plasticity improves classification performance even when input features are randomly distributed.

    Strengths:

    The integrative aspect of this study is its major strength. It is challenging to relate low-level details such as electrical spine compartmentalization, extrasynaptic neurotransmitter concentrations, dendritic nonlinearities, spatial clustering of correlated inputs, and plasticity of excitatory and inhibitory synapses to high-level computations such as nonlinear feature classification. Due to high simulation costs, it is rare to see highly biophysical and morphological models used for learning studies that require repeated stimulus presentations over the course of a training procedure. The study aspires to prove the principle that experimentally-supported biological mechanisms can explain complex learning.

    Weaknesses:

    The high level of complexity of each component of the model makes it difficult to gain an intuition for which aspects of the model are essential for its performance, or responsible for its poor performance under certain conditions. Stripping down some of the biophysical detail and comparing it to a simpler model may help better understand each component in isolation.

  5. eLife

    Reviewer #2 (Public review):

    Summary:

    The study explores how single striatal projection neurons (SPNs) utilize dendritic nonlinearities to solve complex integration tasks. It introduces a calcium-based synaptic learning rule that incorporates local calcium dynamics and dopaminergic signals, along with metaplasticity to ensure stability for synaptic weights. Results show SPNs can solve the nonlinear feature binding problem and enhance computational efficiency through inhibitory plasticity in dendrites, emphasizing the significant computational potential of individual neurons. In summary, the study provides a more biologically plausible solution to single-neuron learning and gives further mechanical insights into complex computations at the single-neuron level.

    Strengths:

    The paper introduces a novel learning rule for training a single multicompartmental neuron model to perform nonlinear feature binding tasks (NFBP), highlighting two main strengths: the learning rule is local, calcium-based, and requires only sparse reward signals, making it highly biologically plausible, and it applies to detailed neuron models that effectively preserve dendritic nonlinearities, contrasting with many previous studies that use simplified models.

  6. eLife

    Author response:

    The following is the authors’ response to the original reviews

    Public Reviews:

    Reviewer #1 (Public Review):

    Summary:

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The authors construct a detailed biophysical and morphological model of a single striatal medium spiny neuron, and endow excitatory and inhibitory synapses with dynamic synaptic plasticity mechanisms that are sensitive to (1) the presence or absence of a dopamine reward signal, and (2) spatiotemporal coincidence of synaptic activity in single dendritic branches. The latter coincidence is detected by voltage-dependent NMDA-type glutamate receptors, which can generate a type of dendritic spike referred to as a "plateau potential." The proposed mechanisms result in moderate performance on a nonlinear classification task when specific input features are segregated and clustered onto individual branches, but reduced performance when input features are randomly distributed across branches. Given the high level of complexity of all components of the model, it is not clear which features of which components are most important for its performance. There is also room for improvement in the narrative structure of the manuscript and the organization of concepts and data.

    Strengths:

    The integrative aspect of this study is its major strength. It is challenging to relate low-level details such as electrical spine compartmentalization, extrasynaptic neurotransmitter concentrations, dendritic nonlinearities, spatial clustering of correlated inputs, and plasticity of excitatory and inhibitory synapses to high-level computations such as nonlinear feature classification. Due to high simulation costs, it is rare to see highly biophysical and morphological models used for learning studies that require repeated stimulus presentations over the course of a training procedure. The study aspires to prove the principle that experimentally-supported biological mechanisms can explain complex learning.

    Weaknesses:

    The high level of complexity of each component of the model makes it difficult to gain an intuition for which aspects of the model are essential for its performance, or responsible for its poor performance under certain conditions. Stripping down some of the biophysical detail and comparing it to a simpler model may help better understand each component in isolation. That said, the fundamental concepts behind nonlinear feature binding in neurons with compartmentalized dendrites have been explored in previous work, so it is not clear how this study represents a significant conceptual advance. Finally, the presentation of the model, the motivation and justification of each design choice, and the interpretation of each result could be restructured for clarity to be better received by a wider audience.

    Thank you for the feedback! We agree that the complexity of our model can make it challenging to intuitively understand the underlying mechanisms. To address this, we have revised the manuscript to include additional simulations and clearer explanations of the mechanisms at play.

    In the revised introduction, we now explicitly state our primary aim: to assess to what extent a biophysically detailed neuron model can support the theory proposed by Tran-Van-Minh et al. and explore whether such computations can be learned by a single neuron, specifically a projection neuron in the striatum. To achieve this, we focus on several key mechanisms:

    (1) A local learning rule: We develop a learning rule driven by local calcium dynamics in the synapse and by reward signals from the neuromodulator dopamine. This plasticity rule is based on the known synaptic machinery for triggering LTP or LTD in the corticostriatal synapse onto dSPNs (Shen et al., 2008). Importantly, the rule does not rely on supervised learning paradigms and neither is a separate training and testing phase needed.

    (2) Robust dendritic nonlinearities: According to Tran-Van-Minh et al., (2015) sufficient supralinear integration is needed to ensure that e.g. two inputs (i.e. one feature combination in the NFBP, Figure 1A) on the same dendrite generate greater somatic depolarization than if those inputs were distributed across different dendrites. To accomplish this we generate sufficiently robust dendritic plateau potentials using the approach in Trpevski et al., (2023).

    (3) Metaplasticity: Although not discussed much in more theoretical work, our study demonstrates the necessity of metaplasticity for achieving stable and physiologically realistic synaptic weights. This mechanism ensures that synaptic strengths remain within biologically plausible ranges during training, regardless of initial synaptic weights.

    We have also clarified our design choices and the rationale behind them, as well as restructured the interpretation of our results for greater accessibility. We hope these revisions make our approach and findings more transparent and easier to engage with for a broader audience.

    Recommendations for the authors:

    Reviewer #1 (Recommendations For The Authors):

    This study extends three previous lines of work:

    (1) Prior computational/phenomenological work has shown that the presence of dendritic nonlinearities can enable single neurons to perform linearly non-separable tasks like XOR and feature binding (e.g. Tran-Van-Minh et al., Front. Cell. Neurosci., 2015).

    Prior computational and phenomenological work, such as Tran-Van-Minh et al. (Front. Cell. Neurosci., 2015), directly inspired our study, as we now explicitly state in the introduction (page 4, lines 19-22). While Tran-Van-Minh theoretically demonstrated that these principles could solve the NFBP, it remains untested to what extent this can be achieved quantitatively in biophysically detailed neuron models using biologically plausible learning rules - which is what we test here.

    (2) This study and a previous biophysical modeling study (Trpevski et al., Front. Cell. Neurosci., 2023) rely heavily on the finding from Chalifoux & Carter, J. Neurosci., 2011 that blocking glutamate transporters with TBOA increases dendritic calcium signals. The proposed model thus depends on a specific biophysical mechanism for dendritic plateau potential generation, where spatiotemporally clustered inputs must be co-activated on a single branch, and the voltage compartmentalization of the branch and the voltage-dependence of NMDARs is not enough, but additionally glutamate spillover from neighboring synapses must activate extrasynaptic NMDARs. If this specific biophysical implementation of dendritic plateau potentials is essential to the findings in this study, the authors have not made that connection clear. If it is a simple threshold nonlinearity in dendrites that is important for the model, and not the specific underlying biophysical mechanisms, then the study does not appear to provide a conceptual advance over previous studies demonstrating nonlinear feature binding with simpler implementations of dendritic nonlinearities.

    We appreciate the feedback on the hypothesized role of glutamate spillover in our model. While the current manuscript and Trpevski et al. (2023) emphasize glutamate spillover as a plausible biophysical mechanism to provide sufficiently robust and supralinear plateau potentials, we acknowledge, however, that the mechanisms of supralinearity of dendritic integration, might not depend solely on this specific mechanism in other types of neurons. In Trpevski et al (2023) we, however, realized that if we allow too ‘graded’ dendritic plateaus, using the quite shallow Mg-block reported in experiments, it was difficult to solve the NFBP. The conceptual advance of our study lies in demonstrating that sufficiently nonlinear dendritic integration is needed and that this can be accounted for by assuming spillover in SPNs—but regardless of its biophysical source (e.g. NMDA spillover, steeper NMDA Mg block activation curves or other voltage dependent conductances that cause supralinear dendritic integration)—it enables biophysically detailed neurons to solve the nonlinear feature binding problem. To address this point and clarify the generality of our conclusions, we have revised the relevant sections in the manuscript to state this explicitly.

    (3) Prior work has utilized "sliding-threshold," BCM-like plasticity rules to achieve neuronal selectivity and stability in synaptic weights. Other work has shown coordinated excitatory and inhibitory plasticity. The current manuscript combines "metaplasticity" at excitatory synapses with suppression of inhibitory strength onto strongly activated branches. This resembles the lateral inhibition scheme proposed by Olshausen (Christopher J. Rozell, Don H. Johnson, Richard G. Baraniuk, Bruno A. Olshausen; Sparse Coding via Thresholding and Local Competition in Neural Circuits. Neural Comput 2008; 20 (10): 2526-2563. doi: https://doi.org/10.1162/neco.2008.03-07-486). However, the complexity of the biophysical model makes it difficult to evaluate the relative importance of the additional complexity of the learning scheme.

    We initially tried solving the NFBP with only excitatory plasticity, which worked reasonably well, especially if we assume a small population of neurons collaborates under physiological conditions. However, we observed that plateau potentials from distally located inputs were less effective, and we now explain this limitation in the revised manuscript (page 14, lines 23-37).

    To address this, we added inhibitory plasticity inspired by mechanisms discussed in Castillo et al. (2011) , Ravasenga et al., and Chapman et al. (2022) , as now explicitly stated in the text (page 32, lines 23-26). While our GABA plasticity rule is speculative, it demonstrates that distal GABAergic plasticity can enhance nonlinear computations. These results are particularly encouraging, as it shows that implementing these mechanisms at the single-neuron level produces behavior consistent with network-level models like BCM-like plasticity rules and those proposed by Rozell et al. We hope this will inspire further experimental work on inhibitory plasticity mechanisms.

    P2, paragraph 2: Grammar: "multiple dendritic regions, preferentially responsive to different input values or features, are known to form with close dendritic proximity." The meaning is not clear. "Dendritic regions" do not "form with close dendritic proximity."

    Rewritten (current page 2, line 35)

    P5, paragraph 3: Grammar: I think you mean "strengthened synapses" not "synapses strengthened".

    Rewritten (current page 14, line 36)

    P8, paragraph 1: Grammar: "equally often" not "equally much".

    Updated (current page 10, line 2)

    P8, paragraph 2: "This is because of the learning rule that successively slides the LTP NMDA Ca-dependent plasticity kernel over training." It is not clear what is meant by "sliding," either here or in the Methods. Please clarify.

    We have updated the text and removed the word “sliding” throughout the manuscript to clarify that the calcium dependence of the kernels are in fact updated

    P10, Figure 3C (left): After reading the accompanying text on P8, para 2, I am left not understanding what makes the difference between the two groups of synapses that both encode "yellow," on the same dendritic branch (d1) (so both see the same plateau potentials and dopamine) but one potentiates and one depresses. Please clarify.

    Some "yellow" and "banana" synapses are initialized with weak conductances, limiting their ability to learn due to the relatively slow dynamics of the LTP kernel. These weak synapses fail to reach the calcium thresholds necessary for potentiation during a dopamine peak, yet they remain susceptible to depression under LTD conditions. Initially, the dynamics of the LTP kernel does not allow significant potentiation, even in the presence of appropriate signals such as plateau potentials and dopamine (page 10, lines 22–26). We have added a more detailed explanation of how the learning rule operates in the section “Characterization of the Synaptic Plasticity Rule” on page 9 and have clarified the specific reason why the weaker yellow synapses undergo LTD (page 11, lines 1–7).

    As shown in Supplementary Figure 6, during subthreshold learning, the initial conductance is also low, which similarly hinders the synapses' ability to potentiate. However, with sufficient dopamine, the LTP kernel adapts by shifting closer to the observed calcium levels, allowing these synapses to eventually strengthen. This dynamic highlights how the model enables initially weak synapses to "catch up" under consistent activation and favorable dopaminergic conditions.

    P9, paragraph 1: The phrase "the metaplasticity kernel" is introduced here without prior explanation or motivation for including this level of complexity in the model. Please set it up before you use it.

    A sentence introducing metaplasticity has been added to the introduction (page 3, lines 36-42) as well as on page 9, where the kernel is introduced (page 9, lines 26-35)

    P10, Figure 3D: "kernel midline" is not explained.

    We have replotted fig 3 to make it easier to understand what is shown. Also, an explanation of the Kernel midpoint is added to the legend (current page 12, line 19)

    P11, paragraph 1; P13, Fig. 4C: My interpretation of these data is that clustered connectivity with specific branches is essential for the performance of the model. Randomly distributing input features onto branches (allowing all 4 features to innervate single branches) results in poor performance. This is bad, right? The model can't learn unless a specific pre-wiring is assumed. There is not much interpretation provided at this stage of the manuscript, just a flat description of the result. Tell the reader what you think the implications of this are here.

    Thanks for the suggestion - we have updated this section of the manuscript, adding an interpretation of the results that the model often fails to learn both relevant stimuli if all four features are clustered onto the same dendrite (page 13, lines 31-42).

    In summary, when multiple feature combinations are encoded in the same dendrite with similar conductances, the ability to determine which combination to store depends on the dynamics of the other dendrite. Small variations in conductance, training order, or other stochastic factors can influence the outcome. This challenge, known as the symmetry-breaking problem, has been previously acknowledged in abstract neuron models (Legenstein and Maass, 2011). To address this, additional mechanisms such as branch plasticity—amplifying or attenuating the plateau potential as it propagates from the dendrite to the soma—can be employed (Legenstein and Maass, 2011).

    P12, paragraph 2; P13, Figure 4E: This result seems suboptimal, that only synapses at a very specific distance from the soma can be used to effectively learn to solve a NFBP. It is not clear to what extent details of the biophysical and morphological model are contributing to this narrow distance-dependence, or whether it matches physiological data.

    We have added Figure 5—figure supplement 1A to clarify why distal synapses may not optimally contribute to learning. This figure illustrates how inhibitory plasticity improves performance by reducing excessive LTD at distal dendrites, thereby enhancing stimulus discrimination. Relevant explanations have been integrated into Page 18, Lines 25-39 in the revised manuscript.

    P14, paragraph 2: Now the authors are assuming that inhibitory synapses are highly tuned to stimulus features. The tuning of inhibitory cells in the hippocampus and cortex is controversial but seems generally weaker than excitatory cells, commensurate with their reduced number relative to excitatory cells. The model has accumulated a lot of assumptions at this point, many without strong experimental support, which again might make more sense when proposing a new theory, but this stitching together of complex mechanisms does not provide a strong intuition for whether the scheme is either biologically plausible or performant for a general class of problem.

    We acknowledge that it is not currently known whether inhibitory synapses in the striatum are tuned to stimulus features. However, given that the striatum is a purely inhibitory structure, it is plausible that lateral inhibition from other projection neurons could be tuned to features, even if feedforward inhibition from interneurons is not. Therefore, we believe this assumption is reasonable in the context of our model. As noted earlier, the GABA plasticity rule in our study is speculative. However, we hope that our work will encourage further experimental investigations, as we demonstrate that if GABAergic inputs are sufficiently specific, they can significantly enhance computations (This is discussed on page 17, lines 8-15.).

    P16, Figure 5E legend: The explanation of the meaning of T_max and T_min in the legend and text needs clarification.

    The abbreviations Tmin and Tmax have been updated to CTL and CTH to better reflect their role in calcium threshold tracking. The Figure 5E legend and relevant text have been revised for clarity. Additionally, the Methods section has been reorganized for better readability.

    P16, Figure 5B, C: When the reader reaches this paper, the conundrums presented in Figure 4 are resolved. The "winner-takes-all" inhibitory plasticity both increases the performance when all features are presented to a single branch and increases the range of somatodendritic distances where synapses can effectively be used for stimulus discrimination. The problem, then, is in the narrative. A lot more setup needs to be provided for the question related to whether or not dendritic nonlinearity and synaptic inhibition can be used to perform the NFBP. The authors may consider consolidating the results of Fig. 4 and 5 so that the comparison is made directly, rather than presenting them serially without much foreshadowing.

    In order to facilitate readability, we have updated the following sections of the manuscript to clarify how inhibitory plasticity resolves challenges from Figure 4:

    Figure 5B and Figure 5–figure supplement 1B: Two new panels illustrate the role of inhibitory plasticity in addressing symmetry problems.

    Figure 5–figure supplement 1A: Shows how inhibitory plasticity extends the effective range of somatodendritic distances.

    P18, Figure 6: This should be the most important figure, finally tying in all the previous complexity to show that NFBP can be partially solved with E and I plasticity even when features are distributed randomly across branches without clustering. However, now bringing in the comparison across spillover models is distracting and not necessary. Just show us the same plateau generation model used throughout the paper, with and without inhibition.

    Figure updated. Accumulative spillover and no-spillover conditions have been removed.

    P18, paragraph 2: "In Fig. 6C, we report that a subset of neurons (5 out of 31) successfully solved the NFBP." This study could be significantly strengthened if this phenomenon could (perhaps in parallel) be shown to occur in a simpler model with a simpler plateau generation mechanism. Furthermore, it could be significantly strengthened if the authors could show that, even if features are randomly distributed at initialization, a pruning mechanism could gradually transition the neuron into the state where fewer features are present on each branch, and the performance could approach the results presented in Figure 5 through dynamic connectivity.

    To model structural plasticity is a good suggestion that should be investigated in later work, however, we feel that it goes beyond what we can do in the current manuscript. We now acknowledge that structural plasticity might play a role. For example we show that if we can assume ‘branch-specific’ spillover, that leads to sufficiently development of local dendritic non-linearities, also one can learn with distributed inputs. In reality, structural plasticity is likely important here, as we now state (current page 22, line 35-42).

    P17, paragraph 2: "As shown in Fig. 6B, adding the hypothetical nonlinearities to the model increases the performance towards solving part of the NFBP, i.e. learning to respond to one relevant feature combination only. The performance increases with the amount of nonlinearity." This is not shown in Figure 6B.

    Sentence removed. We have added a Figure 6 - figure supplement 1 to better explain the limitations.

    P22, paragraph 1: The "w" parameter here is used to determine whether spatially localized synapses are co-active enough to generate a plateau potential. However, this is the same w learned through synaptic plasticity. Typically LTP and LTD are thought of as changing the number of postsynaptic AMPARs. Does this "w" also change the AMPAR weight in the model? Do the authors envision this as a presynaptic release probability quantity? If so, please state that and provide experimental justification. If not, please justify modifying the activation of postsynaptic NMDARs through plasticity.

    This is an important remark. Our plasticity model differs from classical LTP models as it depends on the link between LTP and increased spillover as described by Henneberger et al., (2020).

    We have updated the method section (page 27, lines 6-11), and we acknowledge, however, that in a real cell, learning might first strengthen the AMPA component, but after learning the ratio of NMDA/AMPA is unchanged ( Watt et al., 2004). This re-balancing between NMDA and AMPA might perhaps be a slower process.

    Reviewer #2 (Public Review):

    Summary:

    The study explores how single striatal projection neurons (SPNs) utilize dendritic nonlinearities to solve complex integration tasks. It introduces a calcium-based synaptic learning rule that incorporates local calcium dynamics and dopaminergic signals, along with metaplasticity to ensure stability for synaptic weights. Results show SPNs can solve the nonlinear feature binding problem and enhance computational efficiency through inhibitory plasticity in dendrites, emphasizing the significant computational potential of individual neurons. In summary, the study provides a more biologically plausible solution to single-neuron learning and gives further mechanical insights into complex computations at the single-neuron level.

    Strengths:

    The paper introduces a novel learning rule for training a single multicompartmental neuron model to perform nonlinear feature binding tasks (NFBP), highlighting two main strengths: the learning rule is local, calcium-based, and requires only sparse reward signals, making it highly biologically plausible, and it applies to detailed neuron models that effectively preserve dendritic nonlinearities, contrasting with many previous studies that use simplified models.

    Weaknesses:

    I am concerned that the manuscript was submitted too hastily, as evidenced by the quality and logic of the writing and the presentation of the figures. These issues may compromise the integrity of the work. I would recommend a substantial revision of the manuscript to improve the clarity of the writing, incorporate more experiments, and better define the goals of the study.

    Thanks for the valuable feedback. We have now gone through the whole manuscript updating the text, and also improved figures and added some supplementary figures to better explain model mechanisms. In particular, we state more clearly our goal already in the introduction.

    Major Points:

    (1) Quality of Scientific Writing: The current draft does not meet the expected standards. Key issues include:

    i. Mathematical and Implementation Details: The manuscript lacks comprehensive mathematical descriptions and implementation details for the plasticity models (LTP/LTD/Meta) and the SPN model. Given the complexity of the biophysically detailed multicompartment model and the associated learning rules, the inclusion of only nine abstract equations (Eq. 1-9) in the Methods section is insufficient. I was surprised to find no supplementary material providing these crucial details. What parameters were used for the SPN model? What are the mathematical specifics for the extra-synaptic NMDA receptors utilized in this study? For instance, Eq. 3 references [Ca2+]-does this refer to calcium ions influenced by extra-synaptic NMDARs, or does it apply to other standard NMDARs? I also suggest the authors provide pseudocodes for the entire learning process to further clarify the learning rules.

    The model is quite detailed but builds on previous work. For this reason, for model components used in earlier published work (and where models are already available via model repositories, such as ModelDB), we refer the reader to these resources in order to improve readability and to highlight what is novel in this paper - the learning rules itself. The learning rule is now explained in detail. For modelers that want to run the model, we have also provided a GitHub link to the simulation code. We hope this is a reasonable compromise to all readers, i.e, those that only want to understand what is new here (learning rule) and those that also want to test the model code. We explain this to the readers at the beginning of the Methods section.

    ii. Figure quality. The authors seem not to carefully typeset the images, resulting in overcrowding and varying font sizes in the figures. Some of the fonts are too small and hard to read. The text in many of the diagrams is confusing. For example, in Panel A of Figure 3, two flattened images are combined, leading to small, distorted font sizes. In Panels C and D of Figure 7, the inconsistent use of terminology such as "kernels" further complicates the clarity of the presentation. I recommend that the authors thoroughly review all figures and accompanying text to ensure they meet the expected standards of clarity and quality.

    Thanks for directing our attention to these oversights. We have gone through the entire manuscript, updating the figures where needed, and we are making sure that the text and the figure descriptions are clear and adequate and use consistent terminology for all quantities.

    iii. Writing clarity. The manuscript often includes excessive and irrelevant details, particularly in the mathematical discussions. On page 24, within the "Metaplasticity" section, the authors introduce the biological background to support the proposed metaplasticity equation (Eq. 5). However, much of this biological detail is hypothesized rather than experimentally verified. For instance, the claim that "a pause in dopamine triggers a shift towards higher calcium concentrations while a peak in dopamine pushes the LTP kernel in the opposite direction" lacks cited experimental evidence. If evidence exists, it should be clearly referenced; otherwise, these assertions should be presented as theoretical hypotheses. Generally, Eq. 5 and related discussions should be described more concisely, with only a loose connection to dopamine effects until more experimental findings are available.

    The “Metaplasticity” section (pages 30-32) has been updated to be more concise, and the abundant references to dopamine have been removed.

    (2) Goals of the Study: The authors need to clearly define the primary objective of their research. Is it to showcase the computational advantages of the local learning rule, or to elucidate biological functions?

    We have explicitly stated our goal in the introduction (page 4, lines 19-22). Please also see the response to reviewer 1.

    i. Computational Advantage: If the intent is to demonstrate computational advantages, the current experimental results appear inadequate. The learning rule introduced in this work can only solve for four features, whereas previous research (e.g., Bicknell and Hausser, 2021) has shown capability with over 100 features. It is crucial for the authors to extend their demonstrations to prove that their learning rule can handle more than just three features. Furthermore, the requirement to fine-tune the midpoint of the synapse function indicates that the rule modifies the "activation function" of the synapses, as opposed to merely adjusting synaptic weights. In machine learning, modifying weights directly is typically more efficient than altering activation functions during learning tasks. This might account for why the current learning rule is restricted to a limited number of tasks. The authors should critically evaluate whether the proposed local learning rule, including meta-plasticity, actually offers any computational advantage. This evaluation is essential to understand the practical implications and effectiveness of the proposed learning rule.

    Thank you for your feedback. To address the concern regarding feature complexity, we extended our simulations to include learning with 9 and 25 features, achieving accuracies of 80% and 75%, respectively (Figure 6—figure supplement 1A). While our results demonstrate effective performance, the absence of external stabilizers—such as error-modulated functions used in prior studies like Bicknell and Hausser (2021)—means that the model's performance can be more sensitive to occasional incorrect outcomes. For instance, while accuracy might reach 90%, a few errors can significantly affect overall performance due to the lack of mechanisms to stabilize learning.

    In order to clarify the setup of the rule, we have added pseudocode in the revised manuscript (Pages 31-32) detailing how the learning rule and metaplasticity update synaptic weights based on calcium and dopamine signals. Additionally, we have included pseudocode for the inhibitory learning rule on Pages 34-35. In future work, we also aim to incorporate biologically plausible mechanisms, such as dopamine desensitization, to enhance stability.

    ii. Biological Significance: If the goal is to interpret biological functions, the authors should dig deeper into the model behaviors to uncover their biological significance. This exploration should aim to link the observed computational features of the model more directly with biological mechanisms and outcomes.

    As now clearly stated in the introduction, the goal of the study is to see whether and to what quantitative extent the theoretical solution of the NFBP proposed in Tran-Van-Minh et al. (2015) can be achieved with biophysically detailed neuron models and with a biologically inspired learning rule. The problem has so far been solved with abstract and phenomenological neuron models (Schiess et al., 2014; Legenstein and Maass, 2011) and also with a detailed neuron model but with a precalculated voltage-dependent learning rule (Bicknell and Häusser, 2021).

    We have also tried to better explain the model mechanisms by adding supplementary figures.

    Reviewer #2 (Recommendations For The Authors):

    Minor:

    (1) The [Ca]NMDA in Figure 2A and 2C can have large values even when very few synapses are activated. Why is that? Is this setting biologically realistic?

    The elevated [Ca²⁺]NMDA with minimal synaptic activation arises from high spine input resistance, small spine volume, and NMDA receptor conductance, which scales calcium influx with synaptic strength. Physiological studies report spine calcium transients typically up to ~1 μM (Franks and Sejnowski 2002, DOI: 10.1002/bies.10193), while our model shows ~7 μM for 0.625 nS and around ~3 μM for 0.5 nS, exceeding this range. The calcium levels of the model might therefore be somewhat high compared to biologically measured levels - however, this does not impact the learning rule, as the functional dynamics of the rule remain robust across calcium variations.

    (2) In the distributed synapses session, the study introduces two new mechanisms "Threshold spillover" and "Accumulative spillover". Both mechanisms are not basic concepts but quantitative descriptions of them are missing.

    Thank you for your feedback. Based on the recommendations from Reviewer 1, we have simplified the paper by removing the "Accumulative spillover" and focusing solely on the "Thresholded spillover" mechanism. In the updated version of the paper, we refer to it only as glutamate spillover. However, we acknowledge (page 22, lines 40-42) that to create sufficient non-linearities, other mechanisms, like structural plasticity, might also be involved (although testing this in the model will have to be postponed to future work).

    (3) The learning rule achieves moderate performance when feature-relevant synapses are organized in pre-designed clusters, but for more general distributed synaptic inputs, the model fails to faithfully solve the simple task (with its performance of ~ 75%). Performance results indicate the learning rule proposed, despite its delicate design, is still inefficient when the spatial distribution of synapses grows complex, which is often the case on biological neurons. Moreover, this inefficiency is not carefully analyzed in this paper (e.g. why the performance drops significantly and the possible computation mechanism underlying it).

    The drop in performance when using distributed inputs (to a mean performance of 80%) is similar to the mean performance in the same situation in Bicknell and Hausser (2021), see their Fig. 3C. The drop in performance is due to that: i) the relevant feature combinations are not often colocalized on the same dendrite so that they can be strengthened together, and ii) even if they are, there may not be enough synapses to trigger the supralinear response from the branch spillover mechanism, i.e. the inputs are not summated in a supralinear way (Fig. 6B, most input configurations only reach 75%).

    Because of this, at most one relevant feature combination can be learned. In the several cases when the random distribution of synapses is favorable for both relevant feature combinations to be learned, the NFBP is solved (Figs. 6B, some performance lines reach 100 % and 6C, example of such a case). We have extended the relevant sections of the paper trying to highlight the above mentioned mechanisms.

    Further, the theoretical results in Tran-Van-Minh et al. 2015 already show that to solve the NFBP with supralinear dendrites requires features to be pre-clustered in order to evoke the supralinear dendritic response, which would activate the soma. The same number of synapses distributed across the dendrites i) would not excite the soma as strongly, and ii) would summate in the soma as in a point neuron, i.e. no supralinear events can be activated, which are necessary to solve the NFBP. Hence, one doesn’t expect distributed synaptic inputs to solve the NFBP with any kind of learning rule.

    (4) Figure 5B demonstrates that on average adding inhibitory synapses can enhance the learning capabilities to solve the NFBP for different pattern configurations (2, 3, or 4 features), but since the performance for excitatory-only setup varies greatly between different configurations (Figure 4B, using 2 or 3 features can solve while 4 cannot), can the results be more precise about whether adding inhibitory synapses can help improve the learning with 4 features?

    In response to the question, we added a panel to Figure 5B showing that without inhibitory synapses, 5 out of 13 configurations with four features successfully learn, while with inhibitory synapses, this improves to 7 out of 13. Figure 5—figure supplement 1B provides an explanation for this improvement: page 18 line 10-24

    (5) Also, in terms of the possible role of inhibitory plasticity in learning, as only on-site inhibition is studied here, can other types of inhibition be considered, like on-path or off-path? Do they have similar or different effects?

    This is an interesting suggestion for future work. We observed relevant dynamics in Figure 6A, where inhibitory synapses increased their weights on-site when randomly distributed. Previous work by Gidon and Segev (2012) examined the effects of different inhibitory types on NMDA clusters, highlighting the role of on-site and off-path inhibition in shunting. In our context, on-site inhibition in the same branch, appears more relevant for maintaining compartmentalized dendritic processing.

    (6) Figure 6A is mentioned in the context of excitatory-only setup, but it depicts the setup when both excitatory and inhibitory synapses are included, which is discussed later in the paper. A correction should be made to ensure consistency.

    We have updated the figure and the text in order to make it more clear that simulations are run both with and without inhibition in this context (page 21 line 4-13)

    (7) In the "Ca and kernel dynamics" plots (Fig 3,5), some of the kernel midlines (solid line) are overlapped by dots, e.g. the yellow line in Fig 3D, and some kernel midlines look like dots, which leads to confusion. Suggest to separate plots of Ca and kernel dynamics for clarity.

    The design of the figures has been updated to improve the visibility of the calcium and kernel dynamics during training.

    (8) The formulations of the learning rule are not well-organized, and the naming of parameters is kind of confusing, e.g. T_min, T_max, which by default represent time, means "Ca concentration threshold" here.

    The abbreviations of the thresholds ( Tmin, Tmax in the initial version) have been updated to CTL and CTH, respectively, to better reflect their role in tracking calcium levels. The mathematical formulations have further been reorganized for better readability. The revised Methods section now follows a more structured flow, first explaining the learning mechanisms, followed by the equations and their dependencies.

  7. Version published to 10.1101/2024.03.12.584462v3 on bioRxiv
  8. Version published to 10.1101/2024.03.12.584462v2 on bioRxiv
  9. Version published to 10.7554/elife.97274.1 on eLife
  10. eLife

    Author response:

    Reviewer #1 (Public Review):

    Summary:

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The authors construct a detailed biophysical and morphological model of a single striatal medium spiny neuron, and endow excitatory and inhibitory synapses with dynamic synaptic plasticity mechanisms that are sensitive to (1) the presence or absence of a dopamine reward signal, and (2) spatiotemporal coincidence of synaptic activity in single dendritic branches. The latter coincidence is detected by voltage-dependent NMDA-type glutamate receptors, which can generate a type of dendritic spike referred to as a "plateau potential." The proposed mechanisms result in moderate performance on a nonlinear classification task when specific input features are segregated and clustered onto individual branches, but reduced performance when input features are randomly distributed across branches. Given the high level of complexity of all components of the model, it is not clear which features of which components are most important for its performance. There is also room for improvement in the narrative structure of the manuscript and the organization of concepts and data.

    To begin with, we will better explain the goal of the study in the introduction and explain that it relies on earlier theoretical work. The goal of the study was to investigate whether and how detailed neuron models with biologically-based morphologies, membrane properties, ion channels, dendritic nonlinearities, and biologically plausible learning rules can quantitatively account for the theoretical results obtained with more abstract models.

    We will further evaluate and clarify the roles of several components in our model regarding their impact on the results. These include a) the role of sufficiently robust and supralinear plateau potentials in computing the NFBP; and b) the importance of metaplasticity for individual synapses, allowing them to start or stop responding to relevant or irrelevant stimuli, respectively, over the training period.

    Strengths:

    The integrative aspect of this study is its major strength. It is challenging to relate low-level details such as electrical spine compartmentalization, extrasynaptic neurotransmitter concentrations, dendritic nonlinearities, spatial clustering of correlated inputs, and plasticity of excitatory and inhibitory synapses to high-level computations such as nonlinear feature classification. Due to high simulation costs, it is rare to see highly biophysical and morphological models used for learning studies that require repeated stimulus presentations over the course of a training procedure. The study aspires to prove the principle that experimentally-supported biological mechanisms can explain complex learning.

    Weaknesses:

    The high level of complexity of each component of the model makes it difficult to gain an intuition for which aspects of the model are essential for its performance, or responsible for its poor performance under certain conditions. Stripping down some of the biophysical detail and comparing it to a simpler model may help better understand each component in isolation. That said, the fundamental concepts behind nonlinear feature binding in neurons with compartmentalized dendrites have been explored in previous work, so it is not clear how this study represents a significant conceptual advance. Finally, the presentation of the model, the motivation and justification of each design choice, and the interpretation of each result could be restructured for clarity to be better received by a wider audience.

    To achieve the goal of the study as described above, we chose to use a biophysically and morphologically detailed neuron model to see if it could quantitatively account for the theoretically-based nonlinear computations, for instance, those discussed in Tran-Van-Minh, A. et al. (2015).

    We will explain the role of each component of the learning rule, as well as the dendritic nonlinearities, for the performance on the NFBP.

    Reviewer #2 (Public Review):

    Summary:

    The study explores how single striatal projection neurons (SPNs) utilize dendritic nonlinearities to solve complex integration tasks. It introduces a calcium-based synaptic learning rule that incorporates local calcium dynamics and dopaminergic signals, along with metaplasticity to ensure stability for synaptic weights. Results show SPNs can solve the nonlinear feature binding problem and enhance computational efficiency through inhibitory plasticity in dendrites, emphasizing the significant computational potential of individual neurons. In summary, the study provides a more biologically plausible solution to single-neuron learning and gives further mechanical insights into complex computations at the single-neuron level.

    Strengths:

    The paper introduces a novel learning rule for training a single multicompartmental neuron model to perform nonlinear feature binding tasks (NFBP), highlighting two main strengths: the learning rule is local, calcium-based, and requires only sparse reward signals, making it highly biologically plausible, and it applies to detailed neuron models that effectively preserve dendritic nonlinearities, contrasting with many previous studies that use simplified models.

    Indeed, the learning rule is local and reward-based, and we will highlight better in the paper that it is “always on”, i.e. there are no separate training and testing phases.

    Weaknesses:

    I am concerned that the manuscript was submitted too hastily, as evidenced by the quality and logic of the writing and the presentation of the figures. These issues may compromise the integrity of the work. I would recommend a substantial revision of the manuscript to improve the clarity of the writing, incorporate more experiments, and better define the goals of the study.

    We will revise the manuscript thoroughly to better present the figures and writing (more detailed below). We will also show supplementary figures showcasing the role of the different components of the learning rule.

    Major Points:

    (1) Quality of Scientific Writing: The current draft does not meet the expected standards. Key issues include:

    i. Mathematical and Implementation Details: The manuscript lacks comprehensive mathematical descriptions and implementation details for the plasticity models (LTP/LTD/Meta) and the SPN model. Given the complexity of the biophysically detailed multicompartment model and the associated learning rules, the inclusion of only nine abstract equations (Eq. 1-9) in the Methods section is insufficient. I was surprised to find no supplementary material providing these crucial details. What parameters were used for the SPN model? What are the mathematical specifics for the extra-synaptic NMDA receptors utilized in this study? For instance, Eq. 3 references [Ca2+]-does this refer to calcium ions influenced by extra-synaptic NMDARs, or does it apply to other standard NMDARs? I also suggest the authors provide pseudocodes for the entire learning process to further clarify the learning rules.

    The detailed setup of the model is described in the referenced papers, including equations and parameter values. The model is downloadable on github. For this reason we did not repeat the information here. That said, we will go through the manuscript and clarify all details, and provide supplemental figures and a GitHub link where necessary for reproducing the results.

    ii. Figure quality. The authors seem not to carefully typeset the images, resulting in overcrowding and varying font sizes in the figures. Some of the fonts are too small and hard to read. The text in many of the diagrams is confusing. For example, in Panel A of Figure 3, two flattened images are combined, leading to small, distorted font sizes. In Panels C and D of Figure 7, the inconsistent use of terminology such as "kernels" further complicates the clarity of the presentation. I recommend that the authors thoroughly review all figures and accompanying text to ensure they meet the expected standards of clarity and quality.

    We will revise the figures for consistency and clarity.

    iii. Writing clarity. The manuscript often includes excessive and irrelevant details, particularly in the mathematical discussions. On page 24, within the "Metaplasticity" section, the authors introduce the biological background to support the proposed metaplasticity equation (Eq. 5). However, much of this biological detail is hypothesized rather than experimentally verified. For instance, the claim that "a pause in dopamine triggers a shift towards higher calcium concentrations while a peak in dopamine pushes the LTP kernel in the opposite direction" lacks cited experimental evidence. If evidence exists, it should be clearly referenced; otherwise, these assertions should be presented as theoretical hypotheses. Generally, Eq. 5 and related discussions should be described more concisely, with only a loose connection to dopamine effects until more experimental findings are available.

    The reviewer is correct; the cited text does not present experimental facts but rather illustrates how the learning rule operates. We will revise the section on the construction of learning rules to clarify which aspects are explicit assumptions and which are experimentally verified. In particular, we will provide a more detailed description and motivation for metaplasticity

    (2) Goals of the Study: The authors need to clearly define the primary objective of their research. Is it to showcase the computational advantages of the local learning rule, or to elucidate biological functions?

    Briefly, the goal of the study was to investigate whether earlier theoretical results with more abstract models can be quantitatively recapitulated in morphologically and biophysically detailed neuron models with dendritic nonlinearities and with biologically based learning rules. (similar response to Summary and Weaknesses to Reviewer #1). We will update the introduction with this information.

    i. Computational Advantage: If the intent is to demonstrate computational advantages, the current experimental results appear inadequate. The learning rule introduced in this work can only solve for four features, whereas previous research (e.g., Bicknell and Hausser, 2021) has shown capability with over 100 features. It is crucial for the authors to extend their demonstrations to prove that their learning rule can handle more than just three features. Furthermore, the requirement to fine-tune the midpoint of the synapse function indicates that the rule modifies the "activation function" of the synapses, as opposed to merely adjusting synaptic weights. In machine learning, modifying weights directly is typically more efficient than altering activation functions during learning tasks. This might account for why the current learning rule is restricted to a limited number of tasks. The authors should critically evaluate whether the proposed local learning rule, including meta-plasticity, actually offers any computational advantage. This evaluation is essential to understand the practical implications and effectiveness of the proposed learning rule.

    As mentioned above, our intent is not to demonstrate the computational advantages of the proposed learning rule but to investigate and illustrate how biophysically detailed neuron models that also display dendritic plateau potential mechanisms, together with biologically-based learning rules, can support the theoretically predicted computational requirements for complex neuronal processing (e.g., Tran-Van-Minh, A. et al., 2015), as well as the results obtained with more abstract neuron models and plateau potential mechanisms (e.g., Schiess et al., 2016; Legenstein and Maass, 2011).

    In the revised manuscript, we will also discuss the differences between the supervised learning rule in Bicknell and Hausser (2021) and our local and reward-based learning rule. We will also show a critical evaluation of how our local learning rule and metaplasticity affect the synaptic weights and why the different components of the rule are needed.

    ii. Biological Significance: If the goal is to interpret biological functions, the authors should dig deeper into the model behaviors to uncover their biological significance. This exploration should aim to link the observed computational features of the model more directly with biological mechanisms and outcomes.

    We will make an attempt to better link the learning rule and dendritic supra-linearities and interpret their biological function.

  11. eLife

    eLife assessment

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The study presents valuable insights that the location of synapses on dendritic branches, as well as synaptic plasticity of excitatory and inhibitory synapses, influences the ability of a neuron to discriminate combinations of sensory stimuli. However, the evidence presented is incomplete - the major conclusions are only partially supported by the data presented, and there are identified gaps between the supporting evidence and the major conclusions.

  12. eLife

    Reviewer #1 (Public Review):

    Summary:

    This computational modeling study builds on multiple previous lines of experimental and theoretical research to investigate how a single neuron can solve a nonlinear pattern classification task. The authors construct a detailed biophysical and morphological model of a single striatal medium spiny neuron, and endow excitatory and inhibitory synapses with dynamic synaptic plasticity mechanisms that are sensitive to (1) the presence or absence of a dopamine reward signal, and (2) spatiotemporal coincidence of synaptic activity in single dendritic branches. The latter coincidence is detected by voltage-dependent NMDA-type glutamate receptors, which can generate a type of dendritic spike referred to as a "plateau potential." The proposed mechanisms result in moderate performance on a nonlinear classification task when specific input features are segregated and clustered onto individual branches, but reduced performance when input features are randomly distributed across branches. Given the high level of complexity of all components of the model, it is not clear which features of which components are most important for its performance. There is also room for improvement in the narrative structure of the manuscript and the organization of concepts and data.

    Strengths:

    The integrative aspect of this study is its major strength. It is challenging to relate low-level details such as electrical spine compartmentalization, extrasynaptic neurotransmitter concentrations, dendritic nonlinearities, spatial clustering of correlated inputs, and plasticity of excitatory and inhibitory synapses to high-level computations such as nonlinear feature classification. Due to high simulation costs, it is rare to see highly biophysical and morphological models used for learning studies that require repeated stimulus presentations over the course of a training procedure. The study aspires to prove the principle that experimentally-supported biological mechanisms can explain complex learning.

    Weaknesses:

    The high level of complexity of each component of the model makes it difficult to gain an intuition for which aspects of the model are essential for its performance, or responsible for its poor performance under certain conditions. Stripping down some of the biophysical detail and comparing it to a simpler model may help better understand each component in isolation. That said, the fundamental concepts behind nonlinear feature binding in neurons with compartmentalized dendrites have been explored in previous work, so it is not clear how this study represents a significant conceptual advance. Finally, the presentation of the model, the motivation and justification of each design choice, and the interpretation of each result could be restructured for clarity to be better received by a wider audience.

  13. eLife

    Reviewer #2 (Public Review):

    Summary:

    The study explores how single striatal projection neurons (SPNs) utilize dendritic nonlinearities to solve complex integration tasks. It introduces a calcium-based synaptic learning rule that incorporates local calcium dynamics and dopaminergic signals, along with metaplasticity to ensure stability for synaptic weights. Results show SPNs can solve the nonlinear feature binding problem and enhance computational efficiency through inhibitory plasticity in dendrites, emphasizing the significant computational potential of individual neurons. In summary, the study provides a more biologically plausible solution to single-neuron learning and gives further mechanical insights into complex computations at the single-neuron level.

    Strengths:

    The paper introduces a novel learning rule for training a single multicompartmental neuron model to perform nonlinear feature binding tasks (NFBP), highlighting two main strengths: the learning rule is local, calcium-based, and requires only sparse reward signals, making it highly biologically plausible, and it applies to detailed neuron models that effectively preserve dendritic nonlinearities, contrasting with many previous studies that use simplified models.

    Weaknesses:

    I am concerned that the manuscript was submitted too hastily, as evidenced by the quality and logic of the writing and the presentation of the figures. These issues may compromise the integrity of the work. I would recommend a substantial revision of the manuscript to improve the clarity of the writing, incorporate more experiments, and better define the goals of the study.

    Major Points:

    (1) Quality of Scientific Writing: The current draft does not meet the expected standards. Key issues include:

    i. Mathematical and Implementation Details: The manuscript lacks comprehensive mathematical descriptions and implementation details for the plasticity models (LTP/LTD/Meta) and the SPN model. Given the complexity of the biophysically detailed multicompartment model and the associated learning rules, the inclusion of only nine abstract equations (Eq. 1-9) in the Methods section is insufficient. I was surprised to find no supplementary material providing these crucial details. What parameters were used for the SPN model? What are the mathematical specifics for the extra-synaptic NMDA receptors utilized in this study? For instance, Eq. 3 references [Ca2+]-does this refer to calcium ions influenced by extra-synaptic NMDARs, or does it apply to other standard NMDARs? I also suggest the authors provide pseudocodes for the entire learning process to further clarify the learning rules.

    ii. Figure quality. The authors seem not to carefully typeset the images, resulting in overcrowding and varying font sizes in the figures. Some of the fonts are too small and hard to read. The text in many of the diagrams is confusing. For example, in Panel A of Figure 3, two flattened images are combined, leading to small, distorted font sizes. In Panels C and D of Figure 7, the inconsistent use of terminology such as "kernels" further complicates the clarity of the presentation. I recommend that the authors thoroughly review all figures and accompanying text to ensure they meet the expected standards of clarity and quality.

    iii. Writing clarity. The manuscript often includes excessive and irrelevant details, particularly in the mathematical discussions. On page 24, within the "Metaplasticity" section, the authors introduce the biological background to support the proposed metaplasticity equation (Eq. 5). However, much of this biological detail is hypothesized rather than experimentally verified. For instance, the claim that "a pause in dopamine triggers a shift towards higher calcium concentrations while a peak in dopamine pushes the LTP kernel in the opposite direction" lacks cited experimental evidence. If evidence exists, it should be clearly referenced; otherwise, these assertions should be presented as theoretical hypotheses. Generally, Eq. 5 and related discussions should be described more concisely, with only a loose connection to dopamine effects until more experimental findings are available.

    (2) Goals of the Study: The authors need to clearly define the primary objective of their research. Is it to showcase the computational advantages of the local learning rule, or to elucidate biological functions?

    i. Computational Advantage: If the intent is to demonstrate computational advantages, the current experimental results appear inadequate. The learning rule introduced in this work can only solve for four features, whereas previous research (e.g., Bicknell and Hausser, 2021) has shown capability with over 100 features. It is crucial for the authors to extend their demonstrations to prove that their learning rule can handle more than just three features. Furthermore, the requirement to fine-tune the midpoint of the synapse function indicates that the rule modifies the "activation function" of the synapses, as opposed to merely adjusting synaptic weights. In machine learning, modifying weights directly is typically more efficient than altering activation functions during learning tasks. This might account for why the current learning rule is restricted to a limited number of tasks. The authors should critically evaluate whether the proposed local learning rule, including meta-plasticity, actually offers any computational advantage. This evaluation is essential to understand the practical implications and effectiveness of the proposed learning rule.

    ii. Biological Significance: If the goal is to interpret biological functions, the authors should dig deeper into the model behaviors to uncover their biological significance. This exploration should aim to link the observed computational features of the model more directly with biological mechanisms and outcomes.

  14. Version published to 10.1101/2024.03.12.584462v1 on bioRxiv