Markov state models of proton- and pore-dependent activation in a pentameric ligand-gated ion channel

  1. Cathrine Bergh
  2. Stephanie A Heusser
  3. Rebecca Howard
  4. Erik Lindahl

  • Curated by eLife

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    Evaluation Summary:

    This article presents molecular dynamics simulations of the pH-gated pentameric ion channel GLIC, which has been the subject of many structural and functional studies. GLIC can be considered as a model system for pentameric ligand-gated ion channels that are responsible for fast chemical-electrical communication between cells in animals. The findings include the solution of open- and closed-like channel forms, intermediates and a "pre-desensitised" state. The approach reproduces modulation by pH and mutation, surprisingly finding a predominance of closed channels, despite activating conditions, and suggest a role for asymmetry in channel gating. Overall, the sampling of channel dynamics is significant and the description of state interconversions sheds new light on pLGIC mechanisms.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

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Abstract

Ligand-gated ion channels conduct currents in response to chemical stimuli, mediating electrochemical signaling in neurons and other excitable cells. For many channels, the details of gating remain unclear, partly due to limited structural data and simulation timescales. Here, we used enhanced sampling to simulate the pH-gated channel GLIC, and construct Markov state models (MSMs) of gating. Consistent with new functional recordings, we report in oocytes, our analysis revealed differential effects of protonation and mutation on free-energy wells. Clustering of closed- versus open-like states enabled estimation of open probabilities and transition rates, while higher-order clustering affirmed conformational trends in gating. Furthermore, our models uncovered state- and protonation-dependent symmetrization. This demonstrates the applicability of MSMs to map energetic and conformational transitions between ion-channel functional states, and how they reproduce shifts upon activation or mutation, with implications for modeling neuronal function and developing state-selective drugs.

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  1. Version published to 10.7554/elife.68369 on eLife
  2. eLife

    Author Response:

    Reviewer #1:

    This manuscript applies extensive simulations with Markov state modelling to describe the activation of a pentameric ligand-gated ion channel (pLGIC). The authors have generated libraries of microsecond trajectories to sample the interconversion of channel functional states. They have described different Markov states of the pH-gated GLIC channel, including conformations that resemble open and closed functional forms, as well as possible intermediates and a "pre-desensitised" state. They have illustrated channel modulation by capturing shifts in the free energies of gating with pH, and a shift in the distribution of states due to a mutation that affects a hydrophobic gate within the narrow transmembrane pore. The authors suggest a role for asymmetry in GLIC gating that may explain experimentally observed structural diversity of the closed state and suggests entropically driven channel closure. Overall, the sampling of channel dynamics is significant and the description of state interconversions sheds some light on pLGIC mechanisms.

    Appreciated, thank you!

    The manuscript could include better descriptions of the simulation methods, accessible to both experts and nonexperts, avoiding jargon and better spelling out the motivations for choices made. Clearer relation to past simulation studies is needed to avoid any misapprehensions.

    Fair point. We have rewritten the methods section, particularly the MSM construction section, to improve clarity and better motivate choices made. To explain the motivation behind hyper-parameter selection we also added Figure 2-figure supplement 3. We have clarified the meaning of terms, such as tICA or eBDIMS, when they are first introduced on page 2, at the beginning of the results section. To address the second point we have added references 10, 11, and 15, and extended the description of them on pages 1-2 in the introduction:

    “[...] several studies have been conducted on GLIC to study short-timescale motions; such as simulations of the transmembrane domain only [1-3], studies of the ion permeation pathway through potential-of-mean- force calculations [4,5], and steady-state simulations reaching 100 ns to 1 μs timescales [6-8], some also with additional ligands or modulations [9-15].”

    The manuscript should include analysis to show that the MSM approach has converged and has yielded sampling independent of the starting elastic network/Brownian dynamics model. It is important that proof of equilibrium sampling is obtained in the subsequent free MD library: that it is not sampling just within the vicinity of the initial gating model path. How far afield from the initial ENM/BD path and how converged is the MSM solution?

    The point regarding sampling and convergence is indeed important! It is also an area where we want to be careful about claims since no method can truly converge or exhaustively sample systems of this size to guarantee independence e.g. of starting paths. We previously presented plots of the implied timescales displaying convergence of the slowest timescale, which is a common way to validate the eigenvalues of the MSMs. To this figure, Figure 2-figure supplement 2, we have added Chapman-Kolmogorov tests to further assess the eigenvectors, resulting in good agreement between our propagated models at kτ and independently estimated models at the same time points. We also added plots with a measure of the symmetry of the transition probability matrix, indicating the level of reversible sampling achieved and enable the reader to see how far simulations are from full equilibrium sampling. Although we are obviously not able to achieve full reversible sampling, we find that the gating transition of interest is generally well-sampled. To further show that our simulations were not severely restricted to the vicinity of the eBDIMS seeds, we added Figure 2-figure supplement 1 showing sampling along the two main principal components extracted from known X-ray structures. These plots display overall broad sampling of the space around the transition pathway, indicating orthogonal sampling of up to 4.9 Å away from the interpolation path, more than the difference between open and closed X-ray structures at 2.7 Å. This too is of course still limited compared to e.g. unfolding of a domain, but it should help the reader assess the magnitude of structural changes that can and cannot be captured.

    The early results (around figure 2) could include better visualisation and description of the coordinates used for Markov state modelling. tICA1 is presumed to represent the slowest transition, and it appears to capture channel closure. But many readers may wonder what the tICA1/2 vectors represents physically. Perhaps some vector mapping onto the structure can illustrate protein movements for each vector, with relevant discussion.

    The point about the meaning of the tICA coordinates is well taken. In fact, clearly understanding these motions is something we have wrestled with ourselves. Following the advice from the reviewer, we have added Figure 2-figure supplement 4 showing the 20 largest eigenvector components projected onto the protein structure as arrows. Unlike e.g. PCA, it can be difficult to interpret exactly which motions the tICA eigenvectors represent, but we can conclude that both tIC1 and tIC2 represent complex motions involving particularly the transmembrane helices - with the tIC 1 eigenvectors slightly more focused on the M2 helices and tIC 2 more interspersed between multiple transmembrane helices. This is also mentioned in text on page 4.

    Moreover, the likely pathway through the Markov states between closed and open states could be better discussed.

    Sorry this was not more clear in our initial manuscript. We have now clarified in the results section that the most likely transition pathway between open and closed states will follow the path of lowest free energy, generally through State III (page 7).

    The claims have been justified, but the importance of the findings could be better relayed. This includes newly identified states, where the roles of the intermediately closed forms could be better explained, and the role of any locally-closed form in the gating transition could be described. Note that in Fig2 both closed and LC are projected onto the state 1 cluster with narrow pore and wide ECD. Why was LC not one with compact ECD (by definition), or is this because ECD spreading vanished from the gating mechanism within this MSM?

    We agree that the features of intermediate conformations could be more extensively described. First, we have described more features of state III in text, particularly on pages 6-9 and 12.

    Regarding the locally closed state, we have extended the results and discussion with new simulations of the H235Q mutation (see Response 2.2) to better address the questions of ECD spread in relation to the locally closed state. Our conclusion from the discussion now reads:

    “Surprisingly, our MSMs of protonated H235Q resulted in only a modest deepening of the free energy minimum around the projected locally closed structures, but also in a heightened free energy barrier between open and closed states, potentially facilitating a single state to be captured in experiments. This, in combination with our other observation that ECD compaction seems to be pH- rather than state-dependent, means that the most probable conformation for the H235Q variant at low pH has a closed-like TMD and more open-like ECD, similarly to the locally closed state.”

    Additionally, we regret that there was a sentence in our previous manuscript describing state 1 with narrow pore and expanded ECD. This statement came from visual inspection of a few conformations but is not supported as a general feature by the probability distributions in Figure 5. We have corrected this mistake. Regarding whether ECD spreading vanished from the MSMs we refer to the longer answer to comment 1.14.

    Moreover, I do not see dots for LC near the state I-II border, as the text suggests on page 8.

    This might not have been clear in our initial figures. We have modified the colors in Figure 2 so that the projected locally closed structures are more easily distinguishable from the closed structures. We have also added labels marking closed, locally closed, and open clusters more clearly to Figure 3 and Figure 4.

    The outcome of a predominantly closed channel irrespective of pH could be better related to experiments, including electrophysiology and recent cryo-EM in Ref.33. In the discussion section the authors write that the minority of channels being open is consistent with electrophysiology, apparently in contrast to what is written in the beginning of the results section. The authors previously wrote that Po is not established by electrophysiology but that cryoEM (Ref.33) may suggest it is more closed than open, regardless of pH. How do the solved "open" states compare to the proposed closed low pH state reported in that preprint (ref.33) and how do the propensities (if any) relate?

    The reviewer raises an interesting point regarding how the pH 3 cryo-EM structure from Ref. 39 (previously 33) relates to the closed channels at low pH. First, we wish to point out that there is actually no conflict between the two statements mentioned by the reviewer since maximal conduction in electrophysiology does not necessarily require 100% of the channels to be open. We have clarified this in the results section (page 3).

    To compare the low-pH structure from Ref. 39 with our open conformations, we first added those structures (along with the other two from Ref. 39) to the set of experimental structures projected onto the tICA landscapes in Figure 2, Figure 3, and Figure 4. Additionally, we added the low-pH structures to plots in Figure 5 and Figure 5-figure supplement 1 to enable better comparison to the different macrostates. We also added panel F to Figure 5, which shows local backbone rearrangement around E35 - thought to be the main proton sensor in GLIC and whose side-chain rearrangements were identified as the main difference between the structures in ref.39. Observations and discussion were added to pages 9 and 12.

    Finally, the relationship of ECD asymmetry to published crystal structures, and the importance of this asymmetry to the functions of pLGICs could be better explained.

    We have extended the discussion of asymmetry on page 13 to include two additional references (ref. 56 and 57) describing published structures that display asymmetric features in the ECD.

    Reviewer #2:

    The authors are trying to explain fundamental and functional aspects of ligand-gated ion channels using extensive molecular dynamics simulations. In particular they examine the effect of pH on GLIC, a pH-gated ion channel, and also the effect of (one) mutation. They successfully account for energy barriers levels as well as free energy levels in GLIC wild-type open and closed states as well as in one gain-of-function mutant, mutated in the one of the pore-lining residues. They also uncover a protonation-dependent symmetrisation in the subunits, which had seen by crystallography but not clearly demonstrated by other techniques before. The approach, based on clustering and Markov-state-models allows to find the transition rates between the different substates and could be used for other ion channels as well.

    The study is overall well conducted and convincing. However, it suffers from the very limited scope of the mutations examined. Indeed, only one mutant is analysed, whereas dozens of mutants of GLIC have been characterised both functionally and structurally, especially some that fall in the so-called "locally-closed" (LC) state. One thus wonders how the existence of mutants that are known to adopt an intermediate conformation (LC state) fits into the scheme of this study.

    Thank you! As we wrote at the start of our response, we are indeed happy that we took the time to add a second mutant (despite initially worrying that it would mostly be related to ECD motions instead).

    The impact of this study would be undoubtedly strengthened if at least one more mutant was examined in details, namely one that is blocked in the LC state.

    We have now run an additional 120 μs of simulations and constructed two additional MSMs of the H235Q mutant, known to crystallize in a LC state at low pH. We have done similar analysis as in our previous submission and appended the results to all figures and extended results and discussion sections accordingly.

    Also, it is not entirely clear how much the results are sensitive (or not) to the protonation protocol.

    This is indeed worthwhile to cover better. We have added a paragraph comparing our protonation protocol to two experimental studies and six simulation studies on pages 13-14. Admittedly, fully resolving the question will require studies using different protonation states, or better constant-pH simulation methods, which we are working on.

    Reviewer #3:

    The gating mechanism of ligand-gated ion channels offers a challenge to both the experimentalists and the modellers; existing experimental methods lack the ability to access detailed information about conformational changes during the transient events that correspond to the opening of the channel that lets ion flows, while simulations are able to access these levels of details but do not give access to the relevant timescales of the process. At a fundamental level, this makes cross-validating the two approaches a difficult task.

    In this work, the authors tackle the second challenge by sampling the gating transition over a cumulated simulation time that exceeds 100 microseconds - thus generating very large datasets. While the analysis of these large datasets used to require a significant amount of supervised clustering (e.g. involving manual feature definitions), the authors have decided to apply the protocol of Markov State Model (MSM) construction which has matured into a semi-unsupervised approach. Indeed, it was shown that these kinetic models could be variationally optimized.

    Major strengths:

    The authors have shown a great technical expertise in showing that such simulations could be generated and analyzed, yielding results that are overall consistent with a lot of previous results, both experimental and computational. An interesting and original observation regarding the role of pH on compaction rather than gating directly is mentioned.

    Major weaknesses:

    While the intention of constructing a Markov State Model is very interesting, it does not seem to have been fully executed, by lack of convergence despite a rather large computational effort. The ability to produce an (variationally) optimized kinetic model would have been a much stronger result.

    More precisely, the authors built an MSM and optimized it using the VAMP method, but were not satisfied with the result because the kinetic model obtained emphasized "exploratory behavior" rather than "convergence of a few [slowest] interesting processes". The most likely reason for this, as pointed out by the authors, is lack of convergence: their simulations might have started to explore processes that are even slower than the ones they are interested in (desensitization? artifact? something else?) but not to convergence. To test this, maybe they should try the deflation method proposed by Husic & Noe (https://doi.org/10.1063/1.5099194) and use it to show that they did sample well the processes that they intended to sample well (gating, not desensitization)?

    A demonstration of convergence (or lack thereof) and sampling would help clarify how the VAMP approach did not work, beyond the blanket statement that optimizing MSMs are "a feasible approach for peptide- sized systems, [but the authors] find it practically unfeasible for large-scale motions in ion channels".

    We thank the reviewer for the suggestion to try the deflation method proposed by Husic et al. This is indeed something we tried but turned out to be challenging for our system. In the paper from Husic et al. the method was demonstrated on smaller peptide-sized systems, and scaling up, especially using distance features, makes it more difficult to deflate processes since components to be deflated may appear in many parts of the system (i.e. the basis is not so sparse). After correspondence with Husic, we were informed that deflation becomes difficult when the basis is not sparse. The point about convergence and sampling is of course an important one where we have now added more data & analysis - see our response to comment 1.2.

    Also, since they were not satisfied with the variationally optimized MSM, the authors decided to work on an un-optimized one and cluster it to extract states and transitions, in a way that appears to be more supervised than unsupervised. Here too, additional details on the methods and the motivation behind the choices made for clustering would help. Since insights are drawn from these analysis, it would seem important to give a sense of how robust the conclusions would be to slightly different choices in the clustering decisions, for example.

    The point about better motivating methodological choices is well taken and we have extended the methods section to make motivations clearer. Regarding the robustness of our results to different hyperparameter combinations, our previous submission included two figures in the SI showing how the estimation of open probabilities vary for many different combinations of hyperparameters (tICA lag time, commute or kinetic mappings, and the number of microstate clusters). We have now combined these two figures into Figure 2- figure supplement 3 and added a new panel C, which shows the slowest timescales for different hyperparameter combinations. We have selected parameters variationally optimal (in terms of the second largest eigenvalue) for the deprotonated conditions and used the same parameters for all models for consistency reasons. However, we note that for the protonated conditions timescales are almost within the error margin of the optimal model. In Figure 2-figure supplement 3A-B, we already showed how the open probabilities depend on different combinations of hyperparameters. We can conclude the results are robust for hyperparameters within the ranges identified in the methods section.

    Overall, the authors have shown a method that has potential in achieving their aims, and that will yield better results as more computational effort will become possible - which realistically is a lot to ask for. Given the resources available, the results obtained support the conclusions drawn.

    Unfortunately, limitations in this respect also limits the impact on our understanding of how these molecules work. Yet, the data generated, if made available, could potentially be used beyond the aims of this paper and be made useful for drug discovery, drug design, etc.

    We strongly agree with the reviewer on the importance of making more of our data open-access. In addition to the previously added sampled states from all 5-state models and simulation parameters, we have now uploaded all MSM models and trajectories to Zenodo (doi:10.5281/zenodo.5500174).

  3. eLife

    Evaluation Summary:

    This article presents molecular dynamics simulations of the pH-gated pentameric ion channel GLIC, which has been the subject of many structural and functional studies. GLIC can be considered as a model system for pentameric ligand-gated ion channels that are responsible for fast chemical-electrical communication between cells in animals. The findings include the solution of open- and closed-like channel forms, intermediates and a "pre-desensitised" state. The approach reproduces modulation by pH and mutation, surprisingly finding a predominance of closed channels, despite activating conditions, and suggest a role for asymmetry in channel gating. Overall, the sampling of channel dynamics is significant and the description of state interconversions sheds new light on pLGIC mechanisms.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

  4. eLife

    Reviewer #1 (Public Review):

    This manuscript applies extensive simulations with Markov state modelling to describe the activation of a pentameric ligand-gated ion channel (pLGIC). The authors have generated libraries of microsecond trajectories to sample the interconversion of channel functional states. They have described different Markov states of the pH-gated GLIC channel, including conformations that resemble open and closed functional forms, as well as possible intermediates and a "pre-desensitised" state. They have illustrated channel modulation by capturing shifts in the free energies of gating with pH, and a shift in the distribution of states due to a mutation that affects a hydrophobic gate within the narrow transmembrane pore. The authors suggest a role for asymmetry in GLIC gating that may explain experimentally observed structural diversity of the closed state and suggests entropically driven channel closure. Overall, the sampling of channel dynamics is significant and the description of state interconversions sheds some light on pLGIC mechanisms.

    The manuscript could include better descriptions of the simulation methods, accessible to both experts and nonexperts, avoiding jargon and better spelling out the motivations for choices made. Clearer relation to past simulation studies is needed to avoid any misapprehensions. The manuscript should include analysis to show that the MSM approach has converged and has yielded sampling independent of the starting elastic network/Brownian dynamics model. It is important that proof of equilibrium sampling is obtained in the subsequent free MD library: that it is not sampling just within the vicinity of the initial gating model path. How far afield from the initial ENM/BD path and how converged is the MSM solution?

    The early results (around figure 2) could include better visualisation and description of the coordinates used for Markov state modelling. tICA1 is presumed to represent the slowest transition, and it appears to capture channel closure. But many readers may wonder what the tICA1/2 vectors represents physically. Perhaps some vector mapping onto the structure can illustrate protein movements for each vector, with relevant discussion. Moreover, the likely pathway through the Markov states between closed and open states could be better discussed.

    The claims have been justified, but the importance of the findings could be better relayed. This includes newly identified states, where the roles of the intermediately closed forms could be better explained, and the role of any locally-closed form in the gating transition could be described. Note that in Fig2 both closed and LC are projected onto the state 1 cluster with narrow pore and wide ECD. Why was LC not one with compact ECD (by definition), or is this because ECD spreading vanished from the gating mechanism within this MSM? Moreover, I do not see dots for LC near the state I-II border, as the text suggests on page 8.

    The outcome of a predominantly closed channel irrespective of pH could be better related to experiments, including electrophysiology and recent cryo-EM in Ref.33. In the discussion section the authors write that the minority of channels being open is consistent with electrophysiology, apparently in contrast to what is written in the beginning of the results section. The authors previously wrote that Po is not established by electrophysiology but that cryoEM (Ref.33) may suggest it is more closed than open, regardless of pH. How do the solved "open" states compare to the proposed closed low pH state reported in that preprint (ref.33) and how do the propensities (if any) relate?

    Finally, the relationship of ECD asymmetry to published crystal structures, and the importance of this asymmetry to the functions of pLGICs could be better explained.

  5. eLife

    Reviewer #2 (Public Review):

    The authors are trying to explain fundamental and functional aspects of ligand-gated ion channels using extensive molecular dynamics simulations. In particular they examine the effect of pH on GLIC, a pH-gated ion channel, and also the effect of (one) mutation. They successfully account for energy barriers levels as well as free energy levels in GLIC wild-type open and closed states as well as in one gain-of-function mutant, mutated in the one of the pore-lining residues. They also uncover a protonation-dependent symmetrisation in the subunits, which had seen by crystallography but not clearly demonstrated by other techniques before. The approach, based on clustering and Markov-state-models allows to find the transition rates between the different substates and could be used for other ion channels as well.

    The study is overall well conducted and convincing. However, it suffers from the very limited scope of the mutations examined. Indeed, only one mutant is analysed, whereas dozens of mutants of GLIC have been characterised both functionally and structurally, especially some that fall in the so-called "locally-closed" (LC) state. One thus wonders how the existence of mutants that are known to adopt an intermediate conformation (LC state) fits into the scheme of this study.

    The impact of this study would be undoubtedly strengthened if at least one more mutant was examined in details, namely one that is blocked in the LC state. Also, it is not entirely clear how much the results are sensitive (or not) to the protonation protocol.

  6. eLife

    Reviewer #3 (Public Review):

    The gating mechanism of ligand-gated ion channels offers a challenge to both the experimentalists and the modellers; existing experimental methods lack the ability to access detailed information about conformational changes during the transient events that correspond to the opening of the channel that lets ion flows, while simulations are able to access these levels of details but do not give access to the relevant timescales of the process. At a fundamental level, this makes cross-validating the two approaches a difficult task.

    In this work, the authors tackle the second challenge by sampling the gating transition over a cumulated simulation time that exceeds 100 microseconds - thus generating very large datasets. While the analysis of these large datasets used to require a significant amount of supervised clustering (e.g. involving manual feature definitions), the authors have decided to apply the protocol of Markov State Model (MSM) construction which has matured into a semi-unsupervised approach. Indeed, it was shown that these kinetic models could be variationally optimized.

    Major strengths:

    The authors have shown a great technical expertise in showing that such simulations could be generated and analyzed, yielding results that are overall consistent with a lot of previous results, both experimental and computational. An interesting and original observation regarding the role of pH on compaction rather than gating directly is mentioned.

    Major weaknesses:

    While the intention of constructing a Markov State Model is very interesting, it does not seem to have been fully executed, by lack of convergence despite a rather large computational effort. The ability to produce an (variationally) optimized kinetic model would have been a much stronger result.

    More precisely, the authors built an MSM and optimized it using the VAMP method, but were not satisfied with the result because the kinetic model obtained emphasized "exploratory behavior" rather than "convergence of a few [slowest] interesting processes". The most likely reason for this, as pointed out by the authors, is lack of convergence: their simulations might have started to explore processes that are even slower than the ones they are interested in (desensitization? artifact? something else?) but not to convergence. To test this, maybe they should try the deflation method proposed by Husic & Noe (https://doi.org/10.1063/1.5099194) and use it to show that they did sample well the processes that they intended to sample well (gating, not desensitization)?

    A demonstration of convergence (or lack thereof) and sampling would help clarify how the VAMP approach did not work, beyond the blanket statement that optimizing MSMs are "a feasible approach for peptide- sized systems, [but the authors] find it practically unfeasible for large-scale motions in ion channels ".

    Also, since they were not satisfied with the variationally optimized MSM, the authors decided to work on an un-optimized one and cluster it to extract states and transitions, in a way that appears to be more supervised than unsupervised. Here too, additional details on the methods and the motivation behind the choices made for clustering would help. Since insights are drawn from these analysis, it would seem important to give a sense of how robust the conclusions would be to slightly different choices in the clustering decisions, for example.

    Overall, the authors have shown a method that has potential in achieving their aims, and that will yield better results as more computational effort will become possible - which realistically is a lot to ask for. Given the resources available, the results obtained support the conclusions drawn.

    Unfortunately, limitations in this respect also limits the impact on our understanding of how these molecules work. Yet, the data generated, if made available, could potentially be used beyond the aims of this paper and be made useful for drug discovery, drug design, etc.

  7. Version published to 10.1101/2021.03.12.435097v1 on bioRxiv