Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Public review):
Major comments:
(1) The main issue that I have with this study is the lack of exploration of "why" the model produces the results it does. Considering this is a model, it should be possible to find out why the three timescales of half-act/inact parameter modifications lead to different sets of results. Without this, it is simply an exploratory exercise. (The model does this, but we do not know the mechanism.) Perhaps this is enough as an interesting finding, but it remains unconvincing and (clearly) does not have the impact of describing a potential mechanism that could be potentially explored experimentally.
This is now addressed in a new section in Results (“Potential Mechanism”):
“To explore why the properties of the resulting bursters depend on the timescale of half-(in)activation adjustments, we examined what happens when SP1 is assembled under different half-(in)activation timescales: (1) fast, (2) intermediate (matching the timescale of ion channel density changes), and (3) infinitely slow (i.e., effectively turned off). The effects of these timescales can be seen by comparing the zoomed-in views of the SP1 activity profiles under each condition (Figure 4).
When half-(in)activations are fast, the time evolution of — which tracks how far the activity pattern is from its targets (see Methods)—shows an abrupt jump as it searches for a voltage-dependence configuration that meets calcium targets (Figure 4A). As this happens, the channel densities are slightly altered, and this process continues again. Slowing the half-(in)activations alterations reduces these abrupt fluctuations (Figure 4B). Making the alterations infinitely slow effectively removes half-(in)activation changes altogether, leaving the system reliant solely on slower alterations in maximal conductances (Figure 4C). Because each timescale of half-(in)activation produces a different channel repertoire at each time step, different timescales of half-(in)activation alteration led the model through a different path in the space of activity profiles and intrinsic properties. Ultimately, this resulted in distinct final activity patterns – all of which were consistent with the Ca2+ targets [22].
(2) A related issue is the use of bootstrapping to do statistics for a family of models, especially when the question is in fact the width of the distribution of output attributes. I don't buy this. One can run enough models to find say N number of models within a tight range (say 2% cycle period) and the same N number within a loose range (say 20%) and compare the statistics within the two groups with the same N.
We appreciate the reviewer’s skepticism regarding our statistical approach with the “Group of 5” and “Group of 20.” These groups arose from historical aspects of our analysis and this analysis does not directly advance the main point—that changes in the timescale of channel voltage-dependence alterations impact the properties of bursters to which the homeostatic mechanism converges. Therefore, we removed the references to the Group of 5 and focus on how the Group of 20 responds to variations in the timescale of voltage-dependent alterations.
(3) The third issue is that many of the results that are presented (but not the main one) are completely expected. If one starts with gmax values that would never work (say all of them 0), then it doesn't matter how much one moves the act/inact curves one probably won't get the desired activity. Alternately, if one starts with gmax values that are known to work and randomizes the act/inact midpoints, then the expectation would be that it converges to something that works. This is Figure 1 B and C, no surprise. But it should work the other way around too. If one starts with random act/inact curves that would never work and fixes those, then why would one expect any set of gmax values would produce the desired response? I can easily imagine setting the half-act/inact values to values that never produce any activity with any gmax.
We appreciate this observation and agree that it highlights a limitation of our initial condition sampling. Our claim that the half-(in)activation mechanism is subordinate to the maximal conductance mechanism is not intended as a general statement. Rather, we make this observation only within the specific range of initial conditions we explored. Within this restricted set, we found that the conductance mechanism was sufficient for successful assembly, while the half-(in)activation mechanism alone was not. We have revised the manuscript to limit the claim.
“The results shown in Figure 1A require activity-dependent regulation of the maximal conductances. When activity-dependent regulation of the maximal conductances is turned off, the model failed to assemble SP1 into a burster (Figure 1B). This was seen in the other 19 Starting Parameters (SP2-SP20), as well [22].
(4) A potential response to my previous criticism would be that you put reasonable constraints on gmax's or half-act/inact values or tie the half-act to half-inact. But that is simply arbitrary ad hoc decisions made to make the model work, much like the L8-norm used to amplify some errors. There is absolutely no reason to believe this is tied to the biology of the system.
Here the reviewer highlights that model choices (e.g., constraints on maximal conductance and half-(in)activation, use of the L8 norm) are not necessarily justified by biology. A discussion of the constraints on maximal conductance and half-(in)activation are in the Model Assumptions section at the end of Methods. The Methods also contains a longer discussion of the use of the L8 norm:
“To compute this match score, we adapted a formulation from Alonso et al (2023), who originally used a root-mean-square (RMS) or norm to combine the sensor mismatches. In that approach, each error (, , and ) is divided by its allowable tolerance (, , and ) to produce a normalized error. These normalized errors are then squared, summed, and square-rooted to produce a single scalar score that reflects how well the model matches the target activity pattern.
In our version, we instead used an norm, which raises each normalized error to the 8th power before summing and taking the 1/8th root. This formulation emphasizes large deviations in any one sensor, making it easier to pinpoint which feature of the activity is limiting convergence. By amplifying outlier mismatches, this approach provided a clearer view of which sensor was driving model mismatch, helping us both interpret failure modes and tune the model’s sensitivity by adjusting the tolerances for individual sensor errors.
Although the norm emphasizes large deviations more strongly than the norm, the choice of norm does not fundamentally alter which models can converge—a model that performs well under one norm can also be made to perform well under another by adjusting the allowable tolerances. The biophysical mechanisms by which neurons detect deviations from target activity and convert them into changes in ion channel properties are still not well understood. Given this uncertainty, and the fact that using different norms ultimately shouldn’t affect the convergence of a given model, the use of different norms to combine sensor errors is consistent with the broader basic premise of the model: that intrinsic homeostatic regulation is calcium mediated [22].
(5) The discussion of this manuscript is at once too long and not adequate. It goes into excruciating detail about things that are simply not explored in this study, such as phosphorylation mechanisms, justification of model assumptions of how these alterations occur, or even the biological relevance. (The whole model is an oversimplification - lack of anatomical structure, three calcium sensors, arbitrary assumptions, and how parameter bounds are implemented.) Lengthy justifications for why channel density & half-act/inact of all currents are obeying the same time constant are answering a question that no one asked. It is a simplified model to make an important point. The authors should make these parts concise and to the point. More importantly, the authors should discuss the mechanism through which these differences may arise. Even if it is not clear, they should speculate.
We agree. A long discussion on Model Assumptions and potential biological mechanisms that implement alteration in channel voltage-dependence obscure this. The former is relocated to the Methods section. The latter discussion is shortened. A discussion of a potential mechanism is included in the Results (Figure 4).
(6) There should be some justification or discussion of the arbitrary assumptions made in the model/methods. I understand some of this is to resolve issues that had come up in previous iterations of this approach and in fact the Alonso et al, 2023 paper was mainly to deal with these issues. However, some level of explanation is needed, especially when assumptions are made simply because of the intuition of the modeler rather than the existence of a biological constraint or any other objective measure.
A discussion of Model Assumptions is included in the Methods.
Reviewer #2 (Public review):
Summary:
In this study, Mondal and co-authors present the development of a computational model of homeostatic plasticity incorporating activity-dependent regulation of gating properties (activation, inactivation) of ion channels. The authors show that, similar to what has been observed for activity-dependent regulation of ion channel conductances, implementing activity-dependent regulation of voltage sensitivity participates in the achievement of a target phenotype (bursting or spiking). The results however suggest that activity-dependent regulation of voltage sensitivity is not sufficient to allow this and needs to be associated with the regulation of ion channel conductances in order to reliably reach the target phenotype. Although the implementation of this biologically relevant phenomenon is undeniably relevant, the main conclusions of the paper and the insights brought by this computational work are difficult to grasp.
Strengths:
(1) Implementing activity-dependent regulation of gating properties of ion channels is biologically relevant.
(2) The modeling work appears to be well performed and provides results that are consistent with previous work performed by the same group.
Weaknesses:
(1) The writing is rather confusing, and the state of the art explaining the need for the study is unclear.
We reorganized the manuscript to make its focus clearer.
Introduction: We clarified our explanation of the state-of-the-art. Briefly, prior work on activity-dependent homeostasis has focused on regulating ion channel density. Neurons have also been documented to homeostatically regulate channel voltage-dependence. However, the consequences of channel voltage-dependence alterations on homeostatic regulation remain underexplored. To study this, we extend a computational model of activity-dependent homeostasis — originally developed to only alter channel density— to alter channel voltage-dependence.
Results: We reorganized this section to underscore the main point: that the timescale of half-(in)activation alterations influences the intrinsic properties and activity patterns targeted by a homeostatic mechanism. Figures 1A and 1B were retained to provide context—Figure 1A illustrates how activity can emerge from random initial conditions, while Figure 1B suggests that in these simulations, modulation of half-(in)activation played a specific limited role. Figure 2 builds on Figure 1A by summarizing how intrinsic properties and activity characteristics vary across a population of 20 bursters. Figure 3 then demonstrates that despite playing this specific limited role, altering the timescale of half-(in)activation in these simulations significantly impacted the intrinsic properties and activity characteristics of the bursters targeted by the homeostatic mechanism. Figure 4 supports this by offering a possible mechanistic explanation. Finally, Figure 5 reinforces the central message by showing how the same population responds to perturbation when the timescale of half-(in)activation alterations is varied—essentially extending the analysis of Figure 3 to a perturbed regime.
Discussion: The Discussion concentrates on more specifically on how the timescale of half-(in)activation alterations shape bursters targeted he homeostatic mechanism. Extended content on model assumptions is moved to Methods. The discussion of biological pathways that implement channel voltage-dependence is shortened to avoid distracting from the main message.
Methods: Aside from moving model assumptions here, we removed discussion of the “Group of 5” and explained in more detail why we chose the L8 norm.
(2) The main outcomes and conclusions of the study are difficult to grasp. What is predicted or explained by this new version of homeostatic regulation of neuronal activity?
Our message is general: the timescale of half-(in)activation alterations influences the intrinsic properties and activity characteristics of bursters targeted by a homeostatic mechanism. As such, the implications are general. Their value lies in circumscribing a conceptual framework from which experimentalists may devise and test new hypotheses. We do not aim to predict or explain any specific phenomenon in this work. To address this concern the Discussion highlights two potential implications of our findings—one to neuronal development and another to pathologies that may arise from disruptions to homeostatic processes:
“One application for the simulations involving the self-assembly of activity may be to model the initial phases of neural development, when a neuron transitions from having little or no electrical activity to possessing it (Baccaglini & Spitzer 1977). As shown in Figure 6, the timescale of (in)activation curve alterations define a neuron's activity characteristics and intrinsic properties. As such, neurons may actively adjust these timescales to achieve a specific electrical activity aligned with a developmental phase’s activity targets. Indeed, developmental phases are marked by changes in ion channel density and voltage-dependence, leading to distinct electrical activity at each stage (Baccaglini & Spitzer 1977, Gao & Ziskind-Conhaim 1998, Goldberg et al 2011, Hunsberger & Mynlieff 2020, McCormick & Prince 1987, Moody & Bosma 2005, O'Leary et al 2014, Picken Bahrey & Moody 2003).
Additionally, our results show that activity-dependent regulation of channel voltage-dependence can play a critical role in restoring neuronal activity during perturbations (Figure 5). Specifically, the presence and timing of half-(in)activation modulation influenced whether the model neuron could successfully return to its target activity pattern. Many model neurons only achieved recovery when a half-(in)activation mechanism was present. Moreover, the speed of this modulation shaped recovery outcomes in nuanced ways: some model neurons reached their targets only when voltage-dependence was adjusted rapidly, while others did so only when these changes occurred slowly. These observations all suggest that impairments in a neuron’s ability to modulate the voltage-dependence of its channels may lead to disruptions in activity-dependent homeostasis. This may have implications for conditions such as addiction (Kourrich et al 2015) and Alzheimer’s disease (Styr & Slutsky 2018), where disruptions in homeostatic processes are thought to contribute to pathogenesis.”
Reviewer #3 (Public review):
Mondal et al. use computational modeling to investigate how activity-dependent shifts in voltage-dependent (in)activation curves can complement activity-dependent changes in ion channel conductance to support homeostatic plasticity. While changes in the voltage-dependent properties of ion channels are known to modulate neuronal excitability, their role as a homeostatic plasticity mechanism interacting with channel conductance has been largely unexplored. The results presented here demonstrate that activity-dependent regulation of voltage-dependent properties can interact with plasticity in channel conductance to allow neurons to attain and maintain target activity patterns, in this case, intrinsic bursting. These results also show that the rate of channel voltage-dependent shifts can influence steady-state parameters reached as the model stabilizes into a stable intrinsic bursting state. That is, the rate of these modifications shapes the range of channel conductances and half-(in)activation parameters as well as activity characteristics such as burst period and duration. A major conclusion of the study is that altering the timescale of channel voltage dependence can seamlessly shift a neuron's activity characteristics, a mechanism that the authors argue may be employed by neurons to adapt to perturbations. While the study's conclusions are mostly well-supported, additional analyses, and simulations are needed.
(1) A main conclusion of this study is that the speed at which (in)activation dynamics change determines the range of possible electrical patterns. The authors propose that neurons may dynamically regulate the timescale of these changes (a) to achieve alterations in electrical activity patterns, for example, to preserve the relative phase of neuronal firing in a rhythmic network, and (b) to adapt to perturbations. The results presented in Figure 4 clearly demonstrate that the timescale of (in)activation modifications impacts the range of activity patterns generated by the model as it transitions from an initial state of no activity to a final steady-state intrinsic burster. This may have important implications for neuronal development, as discussed by the authors.
However, the authors also argue that the model neuron's dynamics - such as period, and burst duration, etc - could be dynamically modified by altering the timescale of (in)activation changes (Figure 6 and related text). The simulations presented here, however, do not test whether modifications in this timescale can shift the model's activity features once it reaches steady state. In fact, it is unlikely that this would be the case since, at steady-state, calcium targets are already satisfied. It is likely, however, as the authors suggest, that the rate at which (in)activation dynamics change may be important for neuronal adaptation to perturbations, such as changes in temperature or extracellular potassium. Yet, the results presented here do not examine how modifying this timescale influences the model's response to perturbations. Adding simulations to characterize how alterations in the rate of (in)activation dynamics affect the model's response to perturbations-such as transiently elevated extracellular potassium (Figure 5) - would strengthen this conclusion.
The reviewer suggests that our core message — namely, that the timescale of half-(in)activation alterations influences the intrinsic properties and activity patterns targeted by a homeostatic mechanism — should also hold during perturbations. We agree that this extension strengthens the central message and have incorporated it into the subsection of the Results (“Half-(in)activation Alterations Contribute to Activity Homeostasis”) and Figure 5.
(2) Another key argument in this study is that small, coordinated changes in channel (in)activation contribute to shaping neuronal activity patterns, but that, these subtle effects may be obscured when averaging across a population of neurons. This may be the case; however, the results presented don't clearly demonstrate this point. This point would be strengthened by identifying correlations, if they exist, between (in)activation curves, conductance, and the resulting bursting patterns of the models for the simulations presented in Figure 2 and Figure 4, for example. Alternatively, or additionally, relationships between (in)activation curves could be probed by perturbing individual (in)activation curves and quantifying how the other model parameters compensate, which could clearly illustrate this point.
In part of the Discussion, we noted that small, coordinated shifts in half-(in)activation curves could be obscured when averaging across a population of neurons. Our intention was not to present this as a primary result, but to highlight an emergent consequence of the model: that distinct initial maximal conductances may converge to activity targets via different small shifts in half-(in)activation, making such changes difficult to detect at the population level. However, we did not systematically examine correlations between (in)activation parameters, conductances, and activity features, nor how these correlations might vary with the timescale of (in)activation modulation. While this observation is consistent with model behavior, it does not directly advance the study’s main point — that the timescale of half-(in)activation modulation influences the types of bursting patterns that satisfy the activity target. To keep the focus clear, we have removed this remark from the Discussion, though we agree that a more detailed analysis of these correlations may offer a fruitful direction for future work.
Reviewer #1 (Recommendations for the authors):
Minor comments:
(1) Page 5: remove "an" from "achieve a given an activity..."
The sentence containing this error has been removed.
(2) Page 7, bottom of page. Explain what prespecifying means here. This requires a conceptual explanation, even if the equations are given in the methods. Was one working ad hoc model built from which the three sensor values were chosen? What was this model and how was it benchmarked? The sensors are never shown. In any figure, but presumably they have different kinetics. What is meant by "average value"? What was the window of averaging and why?
The intention of this passage was to provide a broad overview of the homeostatic mechanism, with the rationale for using sensor “averages” as homeostatic targets explained in detail in the Methods. We have replaced the word “average” with “target” to maintain this focus.
(3) Page 9: add "the" in "electrical activity of the neuron as [the] model seeks...".
Done
(4) Page 9: say briefly what alpha is before using it. Also, please be consistent in either using the symbol for alpha or spelling it out across the manuscript and the figures.
Done
(5) Page 10: the paragraph "In general, ..." is confusing although it becomes clear later on what this is all about. Please rewrite and expand this to clarify some points. For instance, the word "degenerate" is first used here and it is unclear in what sense these models are degenerate. Then it is unclear why the first 5 models were chosen and then 15 more added. What was the point of doing this? What is the intent? Set this up properly before saying that you just did it. This also would clarify the weird terminology used later on of Group of 20 vs. Group of 5. The 20 and 5 are arbitrary. Say what the purpose is. Finally, is the "mean" at the very end the same 416 ms? If not, what do you mean by "the mean"? In fact, I find these 2% and 20% to be imprecise substitutes of (say) two distinct values of CV which are an order of magnitude different. Is that the intent?
This comment refers to a passage that was removed during revision.
(6) Page 10: this may be clear to you, but it took me a while to understand that in Figure 1C, you took the working model at the end of 1A, fixed the gmax values and randomized just the half-act/inact values to run it. Perhaps rewrite this to clarify?
This comment refers to a figure that was removed during revision.
(7) Page 13: why do channel densities not change much after the perturbation?
This comment refers to a figure that has since been reworked during revision. In particular, we only study what happens during perturbation. This question is interesting and is the subject of ongoing work.
Reviewer #2 (Recommendations for the authors):
The article should be carefully corrected, because the current quality of writing might obscure the interest of the study. Particular attention should be paid to the state-of-the-art section and to the discussion, but even the writing of the results should be carefully reworked. The current state of the article makes it very difficult to understand the motivation behind the study but also what the main result provided by this work is.
The Introduction, Results, and Discussion have been reworked to build on the central premise of the work: the timescale of half-(in)activation alterations influences the intrinsic properties and activity patterns targeted by the neuron’s homeostatic mechanism. These changes are detailed in Public Comment #1.
Reviewer #3 (Recommendations for the authors):
The manuscript presents an interesting computational study exploring how activity-dependent regulation of (in)activation dynamics interacts with conductance plasticity to shape neuronal activity patterns. While the study provides valuable insights, some aspects would benefit from clarification, further analyses, and/or additional simulations to strengthen the conclusions. Below, I outline concerns and comments related to specific details of the model and results presentation that were not included in the public review.
(1) The results presented in Figure 5 show that adaptation occurs in both channel conductances and (in)activation dynamics; however, the changes in conductance remain relatively permanent after the model recovers from the transient elevation in extracellular potassium. It therefore seems likely that the model would recover bursting more quickly in response to a subsequent exposure to simulated elevated extracellular potassium since large modifications in the slowly changing conductances would not be required. If this is the case, it could provide a plausible mechanism for adaptation to repeated high-potassium exposure, as demonstrated experimentally in Cancer borealis by this group (PMID: 36060056).
This is an astute observation and the subject of our present follow-up investigation.
(2) In the text relating to Figure 5, it is argued that the resulting shifts in (in)activation curves may be conceptualized as alterations in window currents. It would be helpful to illustrate this by plotting and comparing changes in window currents of these channels alongside the changes in their (in)activation curves.
This comment refers to a passage that was removed during revision.
(3) Some discussion of the role these homeostatic mechanisms may play when the neuron is synaptically integrated into a rhythmically active network could be informative. Surely, phasic and tonic inputs to the neuron would alter its conductance and voltage-dependent properties. Therefore, the model's parameters in an intact network could be very different from those in the synaptically isolated case.
This is an excellent point. We agree that synaptic context—particularly tonic and phasic inputs—would likely influence a neuron’s conductances and voltage-dependent properties, potentially leading to different homeostatic outcomes than in the isolated case. While our current study focuses on synaptically isolated neurons, the Marder lab has considered how homeostatically stabilized neurons might interact in network settings. For example, O'Leary et al (2014) presents an example network of three such neurons operating under homeostatic regulation. However, systematically exploring this question remains a challenge. We are currently developing ideas to study this in the context of a simplified half-center oscillator model, where network-level dynamics can be more tractably analyzed.
(4) Why are the transitions of alpha typically so abrupt, essentially either 1 or 0? Similarly, what happens in the model when there are transient transitions from what appears to be a steady-state alpha that abruptly shifts from 0 to 1 or 1 to 0? For example, what is occurring in Figure 1A at ~150s and ~180s when alpha jumps between 1 and 0, or in Figure 1B when the model transiently jumps up from 0 to 1 at ~400s and ~830s? In Figure 1A, does the bursting pattern change at all after ~250s, or is it identical to the pattern at c?
This is addressed in the revision (Lines 141 – 150).
(5) Are the final steady-state parameters of the 25 (sic) models consistent with experimental observations?
It is difficult to assess — it is hard to design an experiment to do what the reviewer is suggesting.
(6) Why isn't gL allowed to change dynamically? This seems like the most straightforward way to allow a neuron to adjust its excitability (aside from tonic synaptic inputs).
Passive currents could, in principle, be subject to homeostatic regulation. However, our study focused on active intrinsic currents. This focus stems from earlier investigations, which showed that active currents are dynamically regulated during homeostasis – for instance Turrigiano et al (1995) and (Desai et al 1999).
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