Activity-Dependent Changes in Ion Channel Voltage-Dependence Influence the Activity Patterns Targeted by Neurons

Reviewer #1 (Public review):

This computational study builds on a previous study (Liu et al) from the Marder lab from 1998, where a model was proposed that demonstrated activity-dependent homeostatic recovery of activity in individual bursting neurons, based on three "sensors" of intrinsic calcium concentration. The original model modified levels of ion channel conductances. The current model builds on that and adds activity-dependent modifications of the voltage-dependence of these ionic currents, implemented to happen concurrently with maximum conductance levels, but at a different timescale. The faster timescale change in voltage dependence is justified by the assumption that such changes can occur by neuromodulatory chemicals or similar second messenger-based mechanisms that presumably act at a faster rate than the regulation of channel densities. The main finding is that the difference in timescales between the two homeostatic mechanisms (channel density vs. voltage dependence) could result in distinct subsets of parameters, depending on how fast the second messenger mechanisms operate.

This study is an interesting and noteworthy extension of the theoretical ideas proposed by the classic study of Liu et al, 1998. It addresses a very important question: How do two known mechanisms of modifications of neuronal activity that occur at different timescales interact within an activity-dependent homeostatic framework? However, the study and its presentation have some major shortcomings that should be addressed to strengthen the claim.

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.

(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.

(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.

(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.

(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.

(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.

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.

(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?

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.

(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.

Author response:

We thank the reviewers for their detailed and constructive comments on our manuscript entitled “Activity-Dependent Changes in Ion Channel Voltage-Dependence Influence the Activity Patterns Targeted by Neurons.” We appreciate the time and effort the reviewers invested in critiquing our work and are grateful for the opportunity to clarify and improve our manuscript.

As noted by the reviewers, the main message of the manuscript is that the intrinsic properties and activity characteristics of targeted bursters depend on the timescale of half-(in)activation alterations in the homeostatic mechanism. However, the concerns of the reviewers reveal that the manuscript is organized in ways that detract from this message. Below we respond to the points the reviewers raise and close by outlining the changes that we will make to the manuscript as a result. Our goal will be to streamline the message of the paper while addressing the concerns of the reviewers.

Response to Reviewer #1:

Point 1: We interpret the reviewer’s question about “mechanism” to be: why do half-(in)activation alterations redirect degenerate bursters to different parameter regions? (A separate aspect of “mechanism,” namely how these alterations might be biologically implemented, is already addressed in the paper.)

We speculate that Figure 3 illustrates this process. As conductance densities slowly evolve, rapid half-(in)activation changes cause the sensor variable (α) to jump abruptly as it searches for a voltage-dependence configuration that meets calcium targets (Figure 3A). The channel densities are slightly altered and this process continues again. Slowing the half-(in)activations alterations reduces these abrupt fluctuations (Figure 3B). Making the alterations infinitely slow effectively removes half-(in)activation changes altogether, leaving the system reliant solely on slower alterations in maximal conductances (Figure 3C). Because each timescale of half-(in)activation produces a different channel repertoire at each time step, the neuron follows distinct trajectories through the space of activity characteristics and intrinsic properties over the long term.

Point 2: 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 plan to remove 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.

Point 3: Our paper claims that the half-(in)activation mechanism is subordinate to the maximal conductance mechanism. We agree with the reviewer that making this claim requires more care. The simulations we run are controls in the spirit described below.

The reviewer notes that in our simulations, half-(in)activations are already near the range required for bursting, which forces maximal conductances to undergo larger changes and thus appear more critical. We however note that the opposite can also occur: if half-(in)activation values were already positioned in ranges required for bursting, an arrangement of small maximal conductances may potentially produce bursting. The latter might give the impression that maximal conductance alterations and half-(in)activation alterations are equally important. The simulations we ran are simply suggested this wasn’t true for these models.

Points 4 - 6: In Point 4, the reviewer highlights model choices (e.g., constraints on maximal conductance and half-(in)activation, use of the L8 norm) are not clearly justified. In Point 5, the reviewer suggests that the paper provides excessive detail about other model choices. Point 6 appears to reiterate concerns about insufficient justification for some modeling decisions.

Our intent was to acknowledge every caveat, which led us to include long section on Model Assumptions in the Discussion. However, as Point 5 notes, this makes the Discussion cumbersome. The Discussion should focus on remarks regarding the impact that timescale of half-(in)activation alterations have on the family of bursters targeted by the homeostatic mechanism. Consequently, we will relocate the extended discussion of model assumptions from the Discussion to the Methods section. This section already touches on how the constraints on half-(in)activation alterations compare to earlier versions of the model (noted in Point 6) and will be expanded to further explain our choice of the L8 norm (Point 4).

Response to Reviewer #2:

Weakness 1: The reviewer notes that the writing is “rather confusing.” This likely arises from the fact that we did not consistently emphasize the core message: the timescale of half-(in)activation alterations influences the intrinsic properties and activity characteristics of bursters targeted by the homeostatic mechanism. We will address this by reorganizing the manuscript to make that focus clearer, and we outline these planned revisions at the end of these responses.

The reviewer specifically points out that the state-of-the-art is not clearly articulated. We will reorganize the Introduction to highlight this. Briefly, work on activity-dependent homeostasis has historically focused on changes in channel density. This is supported by experiment and has been modelled theoretically. In comparison, changes in channel voltage-dependence, while documented, are less explored due to the challenges of measuring them. In this work, we attempt to study the impact that alterations in channel voltage-dependence have on activity-dependent homeostasis. To do this, we extend existing computational models of activity-dependent homeostasis—models that have hitherto only altered channel density—by incorporating a mechanism that also adjusts channel voltage-dependence.

Weakness 2: The Discussion highlights two potential implications of our findings—one for neuronal development and another for activity recovery following perturbations. However, they were outlined after the Model Assumptions section which, as Reviewer 1 points out, is quite detailed and cumbersome.

Another aspect that may contribute to the challenge in interpreting our results may be our conceptual approach to neuronal excitability, which relies on a computational model of activity-dependent homeostasis that abstracts much of the underlying biochemistry. 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 however, we will expand our discussion of how these findings may guide experimental considerations, particularly regarding neuronal development and activity recovery during perturbations, to better illustrate the practical utility of our results.

Response to Reviewer #3:

Point 1: This reviewer suggests that our core message—namely, that the timescale of half-(in)activation alterations affects the intrinsic properties and activity patterns targeted by a homeostatic mechanism—should also apply during perturbations. We plan to address this by extending our analysis on the Group of 20 models. We will perturb activity by increasing extracellular potassium concentration and change the timescale of half-(in)activation alterations during the perturbation. This should underscore how the neuron’s stabilized activity pattern depends on this timescale, reinforcing our central message.

Point 2: In this part of the Discussion, we noted that multiple half-activation shifts collectively shape the neuron’s global properties, and that averaging might obscure these effects. However, in light of the reviewers’ comments, we recognize that this observation alone does not directly advance the paper’s main message. To make it relevant, we would need to (1) identify correlations between intrinsic parameters (i.e., half-(in)activation and maximal conductance) and the resulting activity patterns, and (2) examine how these correlations shift under different timescales half-(in)activation alterations. Since we have not performed that analysis, we will revise this part of the Discussion to clarify its connection to the paper’s principal focus by noting that a deeper exploration of this notion using correlations will be the topic of future work.

Conclusion: We outline updates we will make to the paper here.

Introduction: In response to Reviewer 2, we will provide a clearer explanation of the state-of-the-art in activity-dependent homeostasis and highlight our specific contribution. We will emphasize that our conclusions, while generic, are relevant in experimental contexts.

Results: We will reorganize this section to underscore the main point: the timescale of half-(in)activation alterations affects the intrinsic properties and activity characteristics of bursters in the homeostatic mechanism. Figures 1 will remain as it is. It shows assembly from random initial conditions and explain that for these simulations we must always consider the half-(in)activation mechanism with a mechanism that alters maximal conductances as the half-(in)activation alterations alone cannot form bursters. Figure 2 will remain as is, but we will remove any discussion of the “Group of 5,” addressing Reviewer 1’s feedback. What is presently Figure 4 will then follow, illustrating how timescale differences shape the properties of 20 degenerate solutions. We then present Figure 3 to address Reviewer 1’s critique on mechanism. Here we will explain how different timescales of half-(in)activation alteration cause the homeostatic mechanism to update channel properties differently, leading to distinct trajectories through the space of intrinsic properties and activity characteristics (as described in the response of Point 1 of Reviewer 1’s feedback). Finally, following Point 1 of Reviewer 3, we will add a new figure highlighting the role of half-(in)activation timescale during perturbation.

Discussion: To streamline the Discussion, the “Model Assumptions” section will be moved to Methods. In line with Point 2 of Reviewer 3, we will clarify how the concept of "small half-(in)activation shifts lead to global changes in neuronal properties" aligns with our core message. Additionally, following Reviewer 2’s comments, we will expand our discussion of implications by including how experimentalists might use our findings to inform studies on perturbations and development.

Methods: We will expand “Model Assumptions” to explain in more detail why we chose the L8 norm.