Structure-based mechanism of RyR channel operation by calcium and magnesium ions

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Abstract

Ryanodine receptors (RyRs) serve for excitation-contraction coupling in skeletal and cardiac muscle cells in a noticeably different way, not fully understood at the molecular level. We addressed the structure of skeletal (RyR1) and cardiac (RyR2) isoforms relevant to gating by Ca 2+ and Mg 2+ ions (M 2+ ). Bioinformatics analysis of RyR structures ascertained the EF-hand loops as the M 2+ binding inhibition site and revealed its allosteric coupling to the channel gate. The intra-monomeric inactivation pathway interacts with the Ca 2+ -activation pathway in both RyR isoforms, and the inter-monomeric pathway, stronger in RyR1, couples to the gate through the S23*-loop of the neighbor monomer. These structural findings were implemented in the model of RyR operation based on statistical mechanics and the Monod-Wyman-Changeux theorem. The model, which defines closed, open, and inactivated macrostates allosterically coupled to M 2+ -binding activation and inhibition sites, approximated the open probability data for both RyR1 and RyR2 channels at a broad range of M 2+ concentrations. The proposed mechanism of RyR operation provides a new interpretation of the structural and functional data of mammalian RyR channels on common grounds. This may provide a new platform for designing pharmacological interventions in the relevant diseases of skeletal and cardiac muscles. The synthetic approach developed in this work may find general use in deciphering mechanisms of ion channel functions.

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    1. General Statements

    We thank the reviewers for their thorough and positive evaluation of the manuscript.

    2. Point-by-point description of the revisions

    We revised the manuscript following the suggestions of the reviewers to make the article more concise and comprehensible to a wider audience. Specifically, we rearranged Section 5, rewrote the difficult-to-understand sections 5 and 6, and removed unnecessary or overlapping text in Introduction and Discussion. We have also addressed the specific points raised by the reviewers. The responses to individual points are detailed below.

    Reviewer 1:

    The reviewer did not ask for any changes to the manuscript.

    We thank the reviewer for the positive evaluation of the manuscript.

    Reviewer 2:

    1/ Title: Structure-based mechanism of RyR channel operation by calcium and magnesium ions

    The authors may consider using an alternative term instead of "operation".

    Thank you for the suggestion. We considered and discussed the term "RyR channel operation" very thoroughly with several colleagues, including native English speakers, and we found it to represent the complex RyR behavior in situ and in experiments most exactly. Alternative terms such as "control" suggest a one-way deterministic action from the ion binding to the protein state, which is not the case. The terms such as "modulation" implicate the presence of a higher RyR state-governing principle, such as phosphorylation, nitrosylation, binding of auxiliary proteins, etc.

    2/ Abstract: Please spell out CFF and MWC theorem.

    Thank you for the proposal. CFF was changed to caffeine; MWC was changed to Monod-Wyman-Changeaux

    3/ Line 87-88: "In striated muscle cells, RyR channels cluster at discrete sites of sarcoplasmic reticulum attached to the sarcolemma where electrical excitation triggers transient calcium release by activation of RyRs."

    There is no attachment between sarcoplasmic reticulum and sarcolemma, please rewrite.

    We respectfully disagree, since there is strong evidence for the existence of discrete contact sites between the sarcolemma and sarcoplasmic reticulum both at triads of skeletal muscle (Rossi et al., 2019) and at dyads of cardiac muscle (Mackrill, 2022), at which both membranes are firmly attached.

    However, to avoid potential misunderstanding, we changed the sentence to "In striated muscle cells, RyR channels cluster at the discrete sites of sarcoplasmic reticulum attached to the sarcolemma in triads or dyads, where electrical excitation triggers transient calcium release by activation of RyRs" (lines 86-87).

    4/ Lines 104-107: "Recently, mathematical modeling of the cardiac calcium release site (Iaparov et al., 2022) confirmed that Mg2+ ions could at the same time act as the negative competitor at the calcium activation site and as an inhibitor at the inhibition site. Unfortunately, the structural counterpart of RyR inactivation, an inhibitory binding site for divalent ions, has not been located yet in RyR structures."

    Note that the exact structural counterpart exists (Nayak et al., 2022, 2024), where Ca and Mg were found both at the activation and inhibition sites. The paragraph should be updated accordingly.

    We respectfully disagree. In the cited works of Nayak et al. (2022; 2024) it was shown that Ca and Mg ions bind firmly at the activation site. Both atoms were also observed at the ACP molecule bound at the ATP binding site. However, they were not observed at the divalent ion-binding inhibition site, which is distinct from the ATP binding site and resides in the loops of the EF-hand region.

    However, to clarify the meaning of the disputed sentence, we have changed it to: "Although binding of Ca2+ or Mg2+ to an inhibitory binding site has not been observed yet in RyR structures, a consensus is emerging that the EF-hand loops constitute this site (Gomez et al., 2016; Zheng and Wen, 2020; Nayak et al., 2024; Chirasani et al., 2024 )" (lines 107-109).

    5/ Lines 108-110: The activation of RyR by agonists was shown to be accompanied by a conformational change around the Ca2+ binding site that leads to a decrease in the free energy and to a concomitant increase of the Ca2+ binding affinity and a population shift between the closed and open conformations (Dashti et al., 2020).

    Please clarify to what state does the "decrease in free energy" refer, to the open or to the closed state?

    Thank you for the proposal. The text was changed to: "The activation of RyR by agonists was shown to be accompanied by a conformational change around the Ca2+ binding site that leads to a decrease in the free energy of the open state and concomitantly to an increase of the Ca2+ binding affinity of the activation site. As a result, the occurrence probability of a RyR state/conformation shifts from the closed toward the open (Dashti et al., 2020)" (lines 110-113).

    6/ Figure 2: please indicate if distances were measured between the C-alphas or side chains.

    Thank you for the proposal. The figure legend was modified to "Distances D1 between the Cα atoms of E4075 and R4736* or equivalent. Right - Distances D2 between the Cα atoms of K4101 and D4730* or equivalent."

    7/ Line 353-357: "These data suggest that interactions between the basic arginine residue R4736* and the acidic residues at the start of the initial helix E of the EF1-hand are specific for Ca2+-dependent inactivation in RyR1, whereas the interactions between the lysine K4101 that immediately follows the F helix of EF1 and the middle of the S23* loop (corresponding to D4730* and I4731* in RyR1) may play a part in the inactivation of both RyR1 and RyR2 isoforms.

    Sentence is unclear; please rewrite. Overall, the entire section "Spatial interactions between the EF-hand and S23* regions" should be simplified and shortened.

    Thank you for the proposal. The text was changed to: "These data suggest that interactions between the basic arginine residue R4736* and the acidic residues E4075 and D4079 are specific for Ca2+-dependent inactivation in RyR1, whereas the interactions between the lysine K4101 and the residues D4730 and I4731 (rRyR1 notation)** may play a part in the inactivation of both RyR1 and RyR2 isoforms." (lines 334-337).

    We did not find a way how to make the whole section simpler and shorter at the same time without losing clarity.

    8/ Lines 246-249 and Table 1. "all structures corresponding to rRyR1 residues 4063-4196 were
    subjected to energy minimization and submitted to the MIB2 server for evaluation of the ion binding score (IBS) of individual amino acid residues and the number of ion binding poses (NIBP) for Ca and Mg ions."

    Please elaborate on the "ion binding score" and "number of ion binding poses" concepts and provide reference for the MIB2 server.

    Thank you for the proposal. We added the reference for the server (Lu et al., 2022) (line 228) and added the information: "IBS values of individual residues are determined using sequence and structure conservation comparison with 409 and 209 respective templates from the PDB database for Ca2+ and Mg2+ (Lin et al., 2016) and assessing the similarity of the configuration of the residue to its configurations in known structures of its complexes with the given metal (Lu et al., 2012)****. Ion binding sites are determined by locally aligning the query protein with the metal ion-binding templates and calculating its score as the RMSD-weighted scoring function Z. The site is accepted if it has a scoring function Z>1, and based on the local 3D structure alignment between the query protein and the metal ion-binding template, the metal ion in the template is transformed into the query protein structure (Lin et al., 2016)****. The larger the IBS value, the higher the tendency of the residue to bind the ion. The larger the NIBP value, the larger the number of such complexes with acceptable structure" (lines 224-234).

    9/ Lines 460-466: Nine structural models of RyR were selected, and then these are referred to in the text only with the pdb code. The reviewer understands that it would be difficult to recapitulate all conditions but either a table in the main manuscript file or a minimal description in the text following the pdb code would increase clarity and help readers to follow the content.

    Thank you for the proposal. We added a new Table 2 "Model structures used for identifying the allosteric pathways****" on line 452 that contains the required information, and inserted a reference to it in the text at line 446 "According to these criteria we selected five RyR1 model structures (Table 2)..."

    10/ Line 467: "In the selected structures, we identified residues with high allosteric coupling intensities (ACI) for both the inhibition and activation network and compared them with residues important for ligand binding and gating of RyR (Table 2)."

    Please define further the concept of "allosteric coupling intensities". The corresponding methods section appears to focus on the outputs of the OHM server without delving too much on the algorithm or principles followed. Is the allosteric coupling between neighboring residues, or reflect movement of the residues due to ligand binding? Is there a "reference" state or are the comparisons carried out within each allosteric state? This would help to introduce better the sections "The inhibition network" and "The activation network".

    Thank you for this suggestion. We have lately realized, considering both the server output and the original work of Wang et al. (2020), that a better term for the variable depicting the role of the residue in the allosteric pathway would be the residue importance RI rather than the ACI. The allosteric pathway is determined on the basis of the network of contacts between pairs of residues in the given structure. The more contacts are present between two residues, the higher is the probability that a perturbation will be propagated from one to the other residue (Eq. 3 of Wang et al. (2020)). An allosteric pathway is then defined as the pathway that transmits the signal the whole way from the allosteric site to the active site.

    Based on this we have changed in the manuscript the term "allosteric coupling intensity" to "residue importance" throughout the text and figures of the manuscript. It should be underlined, that this change has no effect whatsoever on presented data and conclusions. We inserted the following formulation in the Results section:

    "The term residue importance defines the extent to which the given residue is involved in the propagation of a perturbation from the allosteric site to the active site, i.e., the fraction of simulated perturbations transmitted through this particular residue. The more contacts are present between two residues, the higher is the probability that a perturbation will be propagated from one to the other residue (Wang et al., 2020)****." (lines 439-443).

    We also inserted the following formulations into the Methods section: "The simulation of the perturbation propagation was performed 10 000 times per structure and pathway to estimate the values of residue importance." (lines 1093-1095), and we expanded the relevant sentence: "Allosteric pathways were traced using the server OHM (https://dokhlab.med.psu.edu/ohm/#/home, (Wang et al., 2020)), in which the allosteric pathway is determined on the basis of the network of contacts between pairs of residues in the given structure." (lines 1082-1084).

    11/ Figure 8: The figure would be more meaningful if the pathways were drawn in the context of the 3D structure.

    Thank you for the proposal. The pathways described in Fig. 8 are too complex for description in the RyR 3D structure, therefore they were not presented in the original manuscript. However, to follow the reviewer's proposal we have illustrated the pathways observed in the inactivated RyR1 channel (7tdg) and the open RyR2 channel (7u9) in Expanded View Figure EV1 and added the corresponding Expanded View Movie EV1 and EV2. These RyR structures were selected for displaying both the intra- and inter-monomeric inactivation pathways.

    12/ Lines 610-612: "The structure of the inactivated RyR2 has not been determined yet; however, it is plausible to suppose that it exists at high concentrations of divalent ions and differs from the inactivated RyR1 structure by the extent of EF-hand - S23* coupling. "

    The speculation would be more fit for the discussion section.

    Thank you for the proposal; however, the sentence introduces a logical supposition, necessary there for reasoning on the construction of the model. We reformulated the sentence to: "In the absence of a structure of the inactivated RyR2, the model assumes that such a structure exists at high concentrations of divalent ions and differs from the inactivated RyR1 structure by the extent of EF-hand - S23 coupling.*" (lines 573-575).

    13/ Lines 617-619: Closed and primed macrostates could be combined into a single closed macrostate of the model since both are closed and cannot be functionally distinguished at a constant ATP concentration.

    The rationale for combining closed with primed does not seem a good idea, especially since the authors also mention that "the primed state is structurally very close to the open state" (lines 925-926). If the COI model is based on the structural findings, in principle it seems that primed should be treated separately.

    Thank you for the proposal. The use of both the closed and primed states was crucial for solving the model. As a matter of fact, although the primed and closed states are in part structurally different, functionally they are identical, that is, closed. Consequently, to be distinguished in a functional model we would need to incorporate single-channel data obtained under conditions when the ratio of closed and primed channels was modulated under otherwise identical conditions. Unfortunately, such a set of data, for instance at a varying ATP concentration for a range of cytosolic Ca2+ concentrations, does not exist for either RyR1 or RyR2 channels. Moreover, while there are several RyR1 high-resolution structures in the primed state (such as the 7tzc that we used; 2.45 Å; Melville et al. (2022)), the resolution of the corresponding RyR2 structures (6jg3, 6jh6, 6jhn; 4.5 - 6.1 Å; Chi et al. (2019)) is not sufficient for determination of allosteric pathways. Fortunately, however, the two sets of conditions for RyR2 open probability data that were available in the literature turned out to represent activation of channels either selectively from the closed state (Fig. 10C), or almost selectively from the primed state (Fig. 10A, B). This allowed us to interpret the difference in the allosteric coefficients as a consequence of this fact.

    To better clarify the idea, the corresponding text of the Discussion was modified as follows (lines 926-931): "RyR channels can be considered mostly in the primed state under these conditions since the binding of ATP analogs induces the primed structural macrostate in RyRs even in the absence of Ca2+ (Cholak et al., 2023). Fortunately, the two sets of conditions for RyR2 open probability data that were available in the literature turned out to represent activation of channels either selectively from the closed state (Fig. 10C), or selectively from the primed state (Fig. 10A, B).", and "construction of such a model is at present hampered by the lack of open probability data at a sufficiently wide range of experimental conditions and the absence of high-resolution structures of WT RyR2 in the primed state" (lines 934-937).

    14/ Line 619. Please define the "COI" acronym. I assume it is closed, open and inactivated but this is not mentioned.

    We thank the reviewer for noticing the insufficiency. We expanded the specific sentence as follows: Therefore, we constructed the model of RyR operation, termed the COI (closed-open-inactivated) model, in which we assigned a functional macrostate corresponding to each of the closed, open, and inactivated structural macrostates (Figure 9A)" (line 582).

    15/ Figure 9: The diagrams are difficult to follow. Something that could improve it is to differentiate more between open and closed gates, but further elaboration would help the reader.

    We thank the reviewer for paying attention to details. The open state was differentiated in Figure 9 (after line 603) by adding a pore opening to the gate.

    To elaborate on the gating transitions and to keep the manuscript concise, we added a new Expanded View Figure EV2, which illustrates the relationship between the ion binding within macrostates and the transitions between macrostates.

    Nevertheless, for the complexity of the model, which would need a multidimensional presentation, we had to limit the illustration to only the binding of the first ions at the binding sites. We hope that it will help the reader to grasp the principle of the model function more easily.

    16/ One comment is that the manuscript is too long; the manuscript exceeds the typical length required by most journals. To enhance its suitability for publication, the content needs to be synthesized and streamlined. The manuscript is written for an audience specialized in the RyR field and may be challenging for outsiders or for readers unfamiliar with structure and/or biophysical models.

    We thank the reviewer for opening this problem. The specific contribution to the understanding of RyR operation communicated by this manuscript was achieved by the synergy of approaches coming from different fields of RyR research - the structural, the functional, and the synthetic/systems ones. This needed deep immersion into complex studies performed over several decades to unwrap their complementary contributions. Only then we could synthesize the stepwise advances and integrate the mosaic of partial discoveries into the COI model. When conceptualizing the manuscript we were also considering a two-paper version, one on structural aspects and the other on modeling aspects. We realized that the two papers would need to have a very high overlap at the allosteric mechanism to be understandable in separation and would be difficult to publish in the same journal. We also anticipated a typical side effect that structuralists and modelers would read just their parts and would not appreciate enough the feedback from alternative views - how to design and interpret future structural, functional, and modeling studies.

    Compacting the manuscript would be extremely difficult for us. In our view, the dense text would make it even more challenging for readers unfamiliar with some of the numerous approaches used here, as often happens to prominent multidisciplinary journals. Maybe it would be possible with the help of AI, but for now, we prefer to remain authentic.

    Nevertheless, we made some effort. To shorten the manuscript, we have removed the paragraph describing the timeline of the search for the RyR inhibition site that was originally on lines 126-151 and replaced it with the paragraph on lines 129-134: "The regulatory domains involved in both, activation and inactivation of RyRs (Figure 1) are located in the C-terminal quarter of the RyR. The Central domain participates in the Ca2+ binding activation site; the C-terminal domain bears several residues of Ca-, ATP- and caffeine-binding activation sites; the U-motif participates at the ATP- and caffeine-binding sites; the EF-hand region contains the putative Ca-binding pair EF1 and EF2; and the S23 loop bears one residue of the caffeine-binding site and two residues interacting with the EF-hand region of a neighboring monomer (Samso, 2017; Hadiatullah et al., 2022)". We also removed the statements about the proposed kinetic mechanism of inactivation by Nayak et al. (2022), originally on lines 175-184. Finally, we removed the discussion of the work of Gomez et al. (2016) originally on lines 882-889, since it fully overlapped with the statements in Results on lines 358-367 (now lines 338-347). We also moved the text of the subsection "Relationship between the COI model and RyR allosteric pathways" (originally lines 670-685) into subsection "Construction of the model of RyR operation", lines 592-603 and 645-662 of the revised version.

    17/ Another comment is the limited consideration of two relevant published works. One is by Chirasani et al. (2024), focused on allosteric pathways similar to the ones described here. The other work is by Nayak et al (2024), with cryo-EM structures of RyR1 focused on the interplay with Mg2+ and Ca2+. Overall, the manuscript would be strengthened by incorporating such related results in the literature.

    We thank the reviewer for the concerns, but we cannot fully agree. The paper of Chirasani et al. (2024 ) was cited in the manuscript as its online-first version, Chirasani et al. (2023). The manuscript now refers to the printed version proposed by the reviewer. The Chirasani et al. work was discussed on lines 870-881. The paper concentrates on the interaction between the EF-hand region and the S23 segment and its effect on RyR inactivation, which we referenced in the manuscript, but not on the allosteric pathways as mentioned by the reviewer. To broaden the consideration of this important work, we have introduced a more detailed discussion of Chirasani et al. (2024 ) by adding the following text to the manuscript: Lines 881-888: "Based on their structural analysis of the open RyR1 structure 5tal, Chirasani et al. (2024 ) proposed that narrowing the gap between the EF-hand domain and S23 loop, resulting in H-bonding interactions between the EF-hand residue K4101 and the S23 loop residue D4730, and those between the EF-hand residues E4075, Q4076, D4079 and the S23 loop residue R4736, is a consequence of the binding of Ca2+ to the EF-hands. However, our PDBePISA analysis revealed a similar number of interactions between the EF-hand region and the S23* loop not only in open and inactivated but also in primed RyR1 structures (Figure 3). The presence of EF hand-S23 hydrogen bonds in the primed and open RyR1 structures suggests that the proximity of the EF-hand domain and S23 loop is a structural trait distinguishing RyR1 from RyR2, not a consequence of Ca2+ binding to the EF hand.**"

    The data and ideas of the illuminating work of Nayak et al. (2024) were discussed and referred to in the manuscript in several places, originally lines 74, 77, 164 (Introduction), 311, 340 (Results), 892-893, and 971 (Discussion). To broaden consideration of this work, we have expanded the discussion of this paper by adding the text shown in bold into the Introduction: "Recent studies reporting RyR structure at a high divalent ion concentration provide only indirect support for the molecular mechanism of Ca2+/Mg2+-dependent inactivation. Wei et al. (2016) and Nayak et al. (2024) observed a change in the conformation of the RyR1 EF-hands in the presence of 100 µM Ca2+ and 10 mM Mg2+, respectively, compared to low-calcium or low-magnesium conditions****." (lines 135-138) and in the Discussion (lines 889-891): "The recent RyR1 structure 7umz (Nayak et al., 2024) provided evidence of Mg2+ ion bound in the RyR activation site, thus confirming the functional studies that established competition between Ca2+ and Mg2+ at this activation site (Laver et al., 1997; Zahradnikova et al., 2003; Zahradnikova et al., 2010)****."

    Reviewer 3:

    Minor comment: While I am not an expert in allosteric model construction and therefore cannot fully assess their methodological approach, I observed that the authors fixed a number of parameters to achieve model convergence. A more detailed explanation of the rationale behind these fixed parameters would enhance clarity. Currently, these parameters are not clearly specified in the text and are somewhat obscured by the broader description of all parameters included in the model.

    We thank the reviewer very much for this comment, which made us realize that the relevant sections were written in a too technical manner, without sufficient explanation of the ideas behind the derivation and optimization of the model. To clarify the rationale of this process, we have rewritten the subsection "Derivation of the model open probability equation" and the section "Description of RyR operation by the COI model". In the subsection "Derivation of the model open probability equation", we have explained the simplification of the full set of equations (Eqs. 3A-C) into Eqs. 4A-C (lines 642 - 666). In the section "Description of RyR operation by the COI model", we have explained the extent of over-parametrization and the rationale of reducing it by three methods: combining the data into groups with common parameter values; eliminating parameter interdependence by fixation of one parameter at a preset value taken from the literature or postulated a priori; and sharing parameter values between data groups when no significant difference between these values was observed (lines 683-685, 702-710, 719-740).

    We hope that these changes make the manuscript more comprehensible.

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    Referee #3

    Evidence, reproducibility and clarity

    The authors conducted a meta-analysis of a large set of deposited structures of ryanodine receptors (RyR) 1 and 2, aiming to elucidate the gating and inactivation mechanisms of these channels. This work is significant as the functional understanding of this giant ion channel remains limited, despite extensive research efforts. The challenges primarily stem from its large size and complexity, with numerous modulating and activating ligands as well as post-translational modifications.
    This is a comprehensive and well-executed study, providing valuable insights into the differences in ligand sensitivities between RyR1 and RyR2. Notably, the authors clarify the role of the EF-hand pairs in the inhibition mechanism and how these differences drive the distinct inhibition sensitivities between the two isoforms. Additionally, they constructed an allosteric model that effectively recapitulates single-channel measurements available in the literature.

    Minor comment: While I am not an expert in allosteric model construction and therefore cannot fully assess their methodological approach, I observed that the authors fixed a number of parameters to achieve model convergence. A more detailed explanation of the rationale behind these fixed parameters would enhance clarity. Currently, these parameters are not clearly specified in the text and are somewhat obscured by the broader description of all parameters included in the model.

    Significance

    Overall, this study marks a significant advance in understanding the mechanism of this channel, which plays a critical role in excitation-contraction coupling. It also lays the groundwork for more robust and thorough methods to study allosteric mechanisms in large protein complexes.
    Insights from this study may be used for the rational design of allosteric drugs targetting this channel to treat heart and muscular diseases.

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    Referee #2

    Evidence, reproducibility and clarity

    This is an interesting contribution by Zahradnikova et al. on the structure-based mechanism of RyR by calcium and magnesium. To this effect, they systematically and quantitatively compare multiple structures from the pdb database using bioinformatics. The comparisons between structures are rigorous and include RyR reconstructions in multiple conditions. They represent the more comprehensive structural comparison to date. The study proposes main long-allosteric pathways between the activation and inhibition ion binding sites and the ion gate and reasons the different inactivation properties of RyR1 and RyR2, which is an important question on the field.

    Based on the allosteric model, they built a model of "RyR operation" using Monod-Wyman-Changeaux and Markov theorems. While the reviewer cannot comment on the mathematical model due lack of expertise, it appears to have high predictive power and strong agreement with single channel functional data.

    Specific issues are noted below.

    Title: Structure-based mechanism of RyR channel operation by calcium and magnesium ions

    The authors may consider using an alternative term instead of "operation".

    Abstract: Please spell out CFF and MWC theorem.

    Line 87-88: "In striated muscle cells, RyR channels cluster at discrete sites of sarcoplasmic reticulum attached to the sarcolemma where electrical excitation triggers transient calcium release by activation of RyRs."

    There is no attachment between sarcoplasmic reticulum and sarcolemma, please rewrite.

    Lines 104-107: "Recently, mathematical modeling of the cardiac calcium release site (Iaparov et al., 2022) confirmed that Mg2+ ions could at the same time act as the negative competitor at the calcium activation site and as an inhibitor at the inhibition site. Unfortunately, the structural counterpart of RyR inactivation, an inhibitory binding site for divalent ions, has not been located yet in RyR structures."

    Note that the exact structural counterpart exists (Nayak et al., 2022, 2024), where Ca and Mg were found both at the activation and inhibition sites. The paragraph should be updated accordingly.

    Lines 108-110: The activation of RyR by agonists was shown to be accompanied by a conformational change around the Ca2+ binding site that leads to a decrease in the free energy and to a concomitant increase of the Ca2+ binding affinity and a population shift between the closed and open conformations (Dashti et al., 2020).

    Please clarify to what state does the "decrease in free energy" refer, to the open or to the closed state?

    Figure 2: please indicate if distances were measured between the C-alphas or side chains.

    Line 353-357: "These data suggest that interactions between the basic arginine residue R4736* and the acidic residues at the start of the initial helix E of the EF1-hand are specific for Ca2+-dependent inactivation in RyR1, whereas the interactions between the lysine K4101 that immediately follows the F helix of EF1 and the middle of the S23* loop (corresponding to D4730* and I4731* in RyR1) may play a part in the inactivation of both RyR1 and RyR2 isoforms.

    Sentence is unclear; please rewrite. Overall, the entire section "Spatial interactions between the EF-hand and S23* regions" should be simplified and shortened.

    Lines 246-249 and Table 1. "all structures corresponding to rRyR1 residues 4063-4196 were
    subjected to energy minimization and submitted to the MIB2 server for evaluation of the ion binding score (IBS) of individual amino acid residues and the number of ion binding poses (NIBP) for Ca and Mg ions."

    Please elaborate on the "ion binding score" and "number of ion binding poses" concepts and provide reference for the MIB2 server.

    Lines 460-466: Nine structural models of RyR were selected, and then these are referred to in the text only with the pdb code. The reviewer understands that it would be difficult to recapitulate all conditions but either a table in the main manuscript file or a minimal description in the text following the pdb code would increase clarity and help readers to follow the content.

    Line 467: "In the selected structures, we identified residues with high allosteric coupling intensities (ACI) for both the inhibition and activation network and compared them with residues important for ligand binding and gating of RyR (Table 2)."

    Please define further the concept of "allosteric coupling intensities". The corresponding methods section appears to focus on the outputs of the OHM server without delving too much on the algorithm or principles followed. Is the allosteric coupling between neighboring residues, or reflect movement of the residues due to ligand binding? Is there a "reference" state or are the comparisons carried out within each allosteric state? This would help to introduce better the sections "The inhibition network" and "The activation network".

    Figure 8: The figure would be more meaningful if the pathways were drawn in the context of the 3D structure.

    Lines 610-612: "The structure of the inactivated RyR2 has not been determined yet; however, it is plausible to suppose that it exists at high concentrations of divalent ions and differs from the inactivated RyR1 structure by the extent of EF-hand - S23* coupling. "

    The speculation would be more fit for the discussion section.

    Lines 617-619: Closed and primed macrostates could be combined into a single closed macrostate of the model since both are closed and cannot be functionally distinguished at a constant ATP concentration.

    The rationale for combining closed with primed does not seem a good idea, especially since the authors also mention that "the primed state is structurally very close to the open state" (lines
    925-926). If the COI model is based on the structural findings, in principle it seems that primed should be treated separately.

    Line 619. Please define the "COI" acronym. I assume it is closed, open and inactivated but this is not mentioned.

    Figure 9: The diagrams are difficult to follow. Something that could improve it is to differentiate more between open and closed gates, but further elaboration would help the reader.

    Significance

    Overall, the work is a valuable conceptual contribution to the field that will help in the mechanistic understanding of RyR function.

    One comment is that the manuscript is too long; the manuscript exceeds the typical length required by most journals. To enhance its suitability for publication, the content needs to be synthesized and streamlined. The manuscript is written for an audience specialized in the RyR field and may be challenging for outsiders or for readers unfamiliar with structure and/or biophysical models.

    Another comment is the limited consideration of two relevant published works. One is by Chirasani et al. (2024), focused on allosteric pathways similar to the ones described here. The other work is by Nayak et al (2024), with cryo-EM structures of RyR1 focused on the interplay with Mg2+ and Ca2+. Overall, the manuscript would be strengthened by incorporating such related results in the literature.

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    Referee #1

    Evidence, reproducibility and clarity

    Summary: The data provides evidence for a novel model of divalent cation activation and inhibition of RyR1 and RyR2. The model defines allosterically coupled closed, open, and inactivated RyR states common for both RyR isoforms. The model is consistent with published single channel open probability data. The model is justified and brings together relevant novel and published structural and functional data and will provide a useful framework for discussion of future functional and structural findings. The manuscript will have the greatest appeal to a specialized audience dedicated to understanding the structure and function of the ryanodine receptor and excitation-contraction coupling.

    Major comments

    The claims and conclusions are supported by the data. I do not suggest any additional experiments. The data and methods are presented in an adequate fashion for reproduction by specialised investigators. The statistical analysis is adequate

    Minor comments

    Prior studies are appropriately referenced and clearly described.

    Significance

    The study is highly significant because the divalent cations are the primary regulators of ryanodine receptor activity during excitation-contraction coupling. The structural basis of this regulation if of the utmost importance in terms of understanding the basic molecular mechanisms and in future drug design.

    My expertise is in ryanodine receptor function and structure