{"id":"afd85911-64f0-401a-ac86-d298081aca30","arxiv_id":"2501.19366","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A voltage-dependent four-state Markov chain model of Piezo1 is fitted to patch-clamp data, but when placed in a myocyte model it cannot reproduce the key finding that alternating electrical and mechanical pacing loses capture faster than mechanical pacing alone.","lead":"This paper builds a computer model of the stretch-sensitive Piezo1 ion channel, adding voltage effects that earlier models lacked, and puts it into a heart-cell simulation. It reproduces several lab measurements of the channel, but when tested against heart-pacing experiments it fails to explain why alternating mechanical and electrical stimuli lose their effect faster than mechanical stimuli alone.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Negative fitted rates (r4–r8) make the model invalid as a continuous-time Markov chain, so the quantitative and cell-level claims are not supported as stated.","rationale":"The reader's weakest assumption identifies exactly the load-bearing flaw: the model is presented as a continuous-time Markov chain, but Table 1 contains negative rate coefficients. This is not a minor technicality. The transition rates appear as r_i exp(...), so a negative r_i makes the rate negative for all pressure and voltage values. Negative rates break the generator-matrix structure, can drive probabilities outside [0,1], and remove the stochastic-process interpretation that justifies the term 'Markov chain'. Since the channel-level fits and the integrated myocyte simulations all use these parameters, the abstract's claim of quantitative reproduction and the cell-level pacing conclusions lose their foundation. The paper's honest reporting of limitations and the deposited CellML files are positive features, but they do not cure the mathematical invalidity of the model as written. I also checked the stated detailed-balance constraint and found that the printed parameters do not satisfy it, which strengthens the concern: either the table contains sign errors or the constraint was not enforced. The concrete test of evaluating the generator at nominal conditions and simulating probabilities would settle the issue quickly. If the negative rates are simply typographical errors in the table and the CellML code uses corrected positive values, then the paper could be revised; but the manuscript as submitted does not support its central claim. Hence I agree with the reader's rejection and recommend no change to the verdict.","tokens_in":24199,"tokens_out":4474,"duration_ms":46698,"concrete_test":"Download the deposited CellML files and construct the generator matrix Q at p=0, Δμ=0 using the Table 1 values; if any off-diagonal entry q_{ij} = r_i exp(...) is negative, the model is not a CTMC. Then simulate the stated protocol from the paper's initial condition C=1, I1=I2=O=0 and check whether any probability becomes negative or the sum leaves 1 at any time. Also verify the detailed-balance relation r2 = r1*r3*r5/(r4*r6) algebraically with the printed numbers; if it fails, the parameter table is internally inconsistent and the actual CellML parameter values must be checked against the table.","verdict_should_be":"UNCHANGED","load_bearing_attack":"A continuous-time Markov chain requires every transition rate to be nonnegative for all pressures and voltages. In the proposed model, the transition rate from O to I1 is k4 = r4 exp(c4m p + c4e Δμ), with r4 = -0.008945307 from Table 1. Since the exponential is always positive, k4 < 0 everywhere; the same holds for r5 = -1.3529515e-5, r6 = -6.206403e-5, r7 = -6.603723e-6, and r8 = -0.00079357607. Such negative off-diagonal entries in the generator matrix are not a Markov chain: probability can leave [0,1] and the master equation has no stochastic interpretation. The paper neither constrains r_i >= 0 nor explains how a negative rate should be interpreted. Additionally, the printed parameter set does not satisfy the paper's own detailed-balance constraint: r1*r3*r5 is negative while r2*r4*r6 is positive, so the relation r2 = r1*r3*r5/(r4*r6) cannot hold with these signs. This suggests either a misprinted table or an unenforced constraint. Because the channel fits in Figures 3-4 and the Mahajan-Shiferaw pacing results all use these rates, the central claim that the model quantitatively reproduces experiments and explains electromechanical pacing rests on an invalid stochastic process. The model could potentially be repaired by re-optimizing with positivity constraints, but as written the central claim is not supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a four-state continuous-time Markov chain model of the Piezo1 ion channel with voltage- and pressure-dependent transition rates, fits the rate parameters to voltage-clamp current traces from Moroni et al. (2018), and integrates the resulting channel model into the Mahajan-Shiferaw rabbit ventricular myocyte model. The integrated model is then used to simulate idealized cardiac cycles and electromechanical pacing protocols modeled on the experiments of Quinn and Kohl (2016). The authors report that the channel model reproduces a wide range of Piezo1 experimental observations, and that the cell-level model qualitatively captures some rate-dependent features of mechanical capture and loss of capture, although it does not reproduce all experimental findings.","tokens_in":24437,"tokens_out":5781,"duration_ms":57080,"significance":"If the model were valid, it would be a valuable contribution: it is, to the authors' knowledge, the first Markov-chain-based Piezo1 model integrated into a ventricular myocyte model, it is provided in open CellML form with reproducible simulation scripts, and it is calibrated against independent patch-clamp data rather than only against the target pacing experiments. The experimental comparisons in Figures 3 and 4 show qualitatively reasonable behavior, and the authors are transparent about the model's limitations. However, the paper's central quantitative claim is undermined by a fundamental mathematical flaw in the fitted rate parameters, as detailed in the major comments. The pacing-level conclusions are also weakened by the fact that the two cell-level free parameters (scaling and prNaK) are fitted to the very Quinn-Kohl capture counts the model is then said to explain.","major_comments":[{"comment":"The fitted rate coefficients r4, r5, r6, r7, and r8 in Table 1 are negative, while the transition rates are defined as k_i = r_i * exp(...) with exponential factors that are always positive. For example, k4 = r4 exp(cm4 p + ce4 Δμ) is negative for all p and Δμ because r4 = -0.008945307. A continuous-time Markov chain requires every transition rate to be non-negative for all states and all conditions; negative off-diagonal entries in the generator mean that probability mass is not conserved and the process has no stochastic interpretation. Since all subsequent simulations (Figures 3-7) use these parameters, the central claim that the model quantitatively reproduces experimental observations is not supported as stated. This is a load-bearing error that affects the entire model, not a cosmetic issue.","section":"§2.1.2, Table 1"},{"comment":"The authors state that detailed balance is enforced by requiring r1*r3*r5 = r2*r4*r6, leading to r2 = r1*r3*r5/(r4*r6). With the printed parameter values, r1, r2, r3 are positive while r4, r5, r6 are negative, so the left-hand side r1*r3*r5 is negative and the right-hand side r2*r4*r6 is positive. The equality cannot hold. This means either the table is misprinted or the constraint was not actually enforced during optimization. In either case, the manuscript presents an internally inconsistent parameter set, and the relationship between the stated constraint and the reported fit is not credible. The authors need to re-examine their optimization code and either report a parameter set that satisfies detailed balance with all non-negative r_i or explain and justify the discrepancy.","section":"§2.2 (detailed balance constraint)"},{"comment":"The cell-level claim that the model can 'qualitatively explain some of the experimental observations from Quinn and Kohl' is weakened by the in-sample nature of the parameter choice. The free parameters scaling and prNaK are explicitly varied 'to reproduce the total number of captured mechanical stimuli recorded in the experiments' (Section 3), and Figure 7 shows the loss surface over these parameters. The paper then reports that no parameter combination reproduces all experimental findings, and specifically that no simulation reproduces the observation that alternating electrical and mechanical stimuli cause faster loss of mechanical capture than mechanical pacing alone. The abstract's phrasing ('qualitatively reproduce some aspects') is accurate but the discussion should more clearly state that the pacing-level result is a partial in-sample fit rather than a validated prediction, especially since the channel model itself is invalid for the reasons above.","section":"§3, Figs. 6-7 and §4"}],"minor_comments":[{"comment":"There are several typos and spacing errors, e.g., 'an thus' (Section 2.1.3), 'T able 1' (Table 1 caption), 'eletromechanical' (Section 4.2), and a run-on 'the proposedmodelisabletoreproduce' (Section 3). A careful proofread is needed.","section":"§1 and §4.2"},{"comment":"The transition rate labels in Figure 1 are hard to read: the subscripts and exponents (e.g., ce7Δμp) are not clearly formatted, and the figure does not indicate that the parameters in Table 1 are for normalized p and Δμ even though the text says p and Δμ are normalized in the optimization. Please clarify.","section":"Fig. 1"},{"comment":"The loss function in Eq. (6) is described as a 'Huber-type Lasso loss' with H(x) = min(|x|, x^2). The notation 'min(|x|, x^2)' is not standard; for |x|>1 this is x^2, which grows unboundedly, so it is not the usual Huber loss. Please define the functions precisely to avoid confusion.","section":"§2.2"},{"comment":"The sentence about Buonocunto et al. mentions 'their experimental work suggests that the reversal potential ... around -15 mV', but the citation [8] is a computational characterization paper; please verify whether this is an experimental or computational finding.","section":"§4.1"}],"recommendation":"major_revision","confidential_remarks":"The negative-rate issue is serious and must be resolved before the manuscript can be considered further. I recommend the editor ask the authors to re-run the parameter optimization with explicit non-negativity constraints (and verify detailed balance), then re-simulate all figures. If the negative rates turn out to be a transcription error, the authors must check that the correct table and code are in the supplementary materials. I also recommend that the authors tone down the abstract's 'quantitatively reproduce' claim until the model is mathematically valid. The CellML and code availability are strong points, but the current manuscript's central results are not reliable. The paper may be salvageable with substantial revision, which is why I recommend major_revision rather than reject."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth reading if you work on stretch-activated channels or mechano-electric feedback, but the central quantitative claim is not supported: the fitted rates in Table 1 violate the definition of a continuous-time Markov chain. This is a fixable flaw, so the paper deserves referee time, but it needs major revision before the conclusions can be trusted.\n\nWhat is genuinely new: a four-state Piezo1 Markov chain with voltage-dependent transitions and a pressure-driving-force product coupling, and the first integration of such a channel model into the Mahajan-Shiferaw ventricular myocyte model. The channel-level fits in Figs. 3-4 are visually plausible, the authors clearly separate calibration from validation, and they deposit CellML files plus simulation scripts. They also explicitly report that the model cannot reproduce the alternating electrical/mechanical stimulus finding from Quinn and Kohl, which is unusually candid. The citation pattern looks appropriate, with the relevant experimental and modeling literature well covered.\n\nThe load-bearing problem is in Table 1. The coefficients r4 through r8 are negative, so the corresponding transition rates (e.g., k4 = r4 exp(...)) are negative for all pressures and voltages. Negative off-diagonal entries in the generator mean the process is not a Markov chain; probabilities can leave [0,1] and the master equation has no stochastic interpretation. The paper also states a detailed balance constraint, but the printed parameters do not satisfy it: r1*r3*r5 is negative while r2*r4*r6 is positive, so r2 = r1*r3*r5/(r4*r6) cannot hold with these signs. Either the table is misprinted or the constraint was not enforced. Either way, all the channel-level and cell-level simulations inherit the problem.\n\nBeyond that, the pacing study fits scaling and prNaK to the experimental capture counts, so those reproductions are fits, not predictions. The abstract's \"quantitatively reproduce\" is stronger than what the results sections claim; most matches are qualitative and partial. These are not independent flaws, but they compound the mismatch between the abstract and the actual evidence.\n\nWho is this for? Modelers building Piezo1 or stretch-activated current models, and anyone interested in how Markov chain models are parameterized and validated. The framework and the honest limitations section are useful. But as written, the central conclusion about the role of Piezo1 in electromechanical pacing rests on an invalid stochastic process. I would send it to a serious peer review, not desk reject, because the idea is new, the execution is mostly careful, and the flaw is concrete and correctable. The authors should re-optimize with r_i >= 0 and either verify or drop the detailed balance claim.","headline":"Sensible model idea, honest limitations, but the fitted parameter table makes the Markov chain invalid as written; re-fit needed before the pacing claims can stand.","tokens_in":119,"tokens_out":2075,"would_cite":false,"duration_ms":48576,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A four-state Markov chain model of the Piezo1 stretch-activated channel quantitatively reproduces voltage-clamp inactivation and desensitization data and, in a ventricular myocyte model, qualitatively explains rate-dependent loss of…","keywords":["Piezo1","stretch-activated ion channel","continuous-time Markov chain","voltage-dependent inactivation","desensitization","electromechanical pacing","ventricular myocyte model","mechano-electric feedback"],"falsifier":"A decisive check is to compute the generator matrix entries from Table 1 at physiological pressure and voltage; if any off-diagonal rate is negative, the channel is not a Markov chain and the fitted equations as written cannot be integrated as probability dynamics.","tokens_in":23823,"feed_emoji":"🫀","tokens_out":9344,"duration_ms":87193,"temperature":0.7,"pith_summary":"What the paper tries to establish is that the voltage dependence of the Piezo1 stretch-activated channel is a primary mechanism behind the loss of mechanical capture in electromechanical pacing. To do this, the authors build a four-state continuous-time Markov chain whose transition rates depend exponentially on both pressure and transmembrane voltage, fit it to patch-clamp recordings, and show it reproduces voltage-dependent inactivation, weak rectification, desensitization during pressure trains, and the reset of desensitization at positive driving forces. When the channel is added to a rabbit ventricular myocyte model, the simulated cell shows the same qualitative pattern seen in Langendorff-perfused rabbit hearts: repeated mechanical stimuli depolarize until capture is lost, with the number of captured stimuli depending on pacing rate and on interleaved electrical stimuli. The authors are explicit that the integrated model does not quantitatively reproduce all pacing protocols with a single parameter set, and they conclude that Piezo1 alone may not be sufficient, but that the channel's voltage modulation is likely a major contributor. A reader should care because mechanical pacing is used in CPR and emergency bradycardia treatment, and no mechanistic explanation previously existed for why it works and why it fails.","feed_headline":"Four-state Piezo1 model explains lost mechanical capture in pacing","feed_subtitle":"Voltage dependence of Piezo1 may explain why mechanical pacing succeeds, then stops, at high rates.","key_machinery":"The engine of the paper is a four-state continuous-time Markov chain with states $O$ (open), $C$ (closed), $I_1$ (fast-inactivated), and $I_2$ (slow-inactivated). Transition rates have the Eyring-like form $r_i \\exp(c_i^m p + c_i^e \\Delta\\mu)$, where $p$ is pressure and $\\Delta\\mu$ is the electrochemical driving force, set equal to the membrane voltage because the Piezo1 reversal potential is near zero. Pressure dependence is kept on the closed-to-$I_1$ and $I_1$-to-open transitions, and the $I_2$-to-open transition depends on the product $p\\,\\Delta\\mu$; every edge also carries a voltage term, and detailed balance is enforced through parameter constraints. The channel's open probability drives separate Ohmic Na$^+$, K$^+$, and Ca$^{2+}$ currents that are added to the Mahajan-Shiferaw myocyte model, which is what lets voltage and pressure jointly shape capture and loss of capture.","core_discovery":"The central claim is that Piezo1's electromechanical response can be captured by a four-state continuous-time Markov chain in which every transition rate depends exponentially on pressure and on the electrochemical driving force, here identified with the transmembrane voltage. On that basis the paper reports quantitative agreement with the voltage-clamp recordings of Moroni et al. for voltage-dependent inactivation and weak rectification, and qualitative agreement for desensitization during repeated pressure stimuli and for the reset of desensitization when pressure is applied at positive driving forces. When the channel is coupled to the Mahajan-Shiferaw rabbit ventricular myocyte model, the simulations reproduce the essential pacing phenomenon: mechanical capture is lost after a number of mechanical stimuli, and that number depends on pacing rate and on alternating electrical stimuli, matching the direction of the Quinn-Kohl observations. The authors also state plainly that no tested parameter combination reproduces every experimental pacing outcome quantitatively, and that Piezo1 alone may not suffice.","pith_inferences":["If the transition rates from Table 1 are evaluated literally at physiological pressures and voltages, some generator-matrix entries are negative; the model would not define a Markov chain, and the pacing results may depend on how the solver handles these entries. Refitting with non-negativity constraints is the natural next step.","The paper's finding that a lower reversal potential of roughly $-30$ mV would be needed for reset during passive filling suggests that the assumption $\\Delta\\mu = $ membrane voltage is a sensitive point; if recent estimates near $-15$ mV hold, the model's reset dynamics could change substantially.","A direct experimental falsification would be to measure Piezo1 open probability under a two-pulse protocol at a series of positive voltages and compare the reset time constant to the model's prediction; because the model was fit only to current traces, the state probabilities themselves are an unvalidated prediction."],"forward_implications":["The voltage-modulated Markov chain gives a mechanistic explanation for why positive electrochemical driving forces reset Piezo1 desensitization: at positive voltages the channel population re-enters states that can open again on the next pressure step.","In the Mahajan-Shiferaw cell, adding Piezo1 raises intracellular Na$^+$ and Ca$^{2+}$ by roughly 8--10%, shortens the action potential, and depresses its peak; stronger pressure steps increase Na$^+$ more than Ca$^{2+}$, a prediction that could be tested ion-selectively.","The integrated model reproduces the qualitative ranking that alternating mechanical and electrical stimuli (2:1 E:M) causes faster loss of capture than 3:1 E:M for some parameterizations, supporting the claim that voltage modulation contributes to capture loss.","Because no single parameter set matches all Quinn-Kohl protocols quantitatively, the authors conclude that mechanisms beyond Piezo1, possibly other stretch-activated currents or tissue-level conduction, are needed for full quantitative agreement."],"supporting_citations":[{"why":"Supplies the voltage-clamp recordings from N2a cells used to fit and validate the Markov chain parameters.","marker":"[52]"},{"why":"Supplies the four-state topology with two inactivation states and the frequency-dependent band-pass behavior that the model extends with voltage dependence.","marker":"[41]"},{"why":"Supplies the rabbit ventricular myocyte model into which the Piezo1 current is integrated.","marker":"[49]"},{"why":"Provides the electromechanical pacing experiments whose rate-dependent loss of capture the integrated model aims to explain.","marker":"[66]"},{"why":"Gives single-channel conductances and reversal information used to set the magnitudes of the Piezo1 Na, K, and Ca currents.","marker":"[27]"},{"why":"Supplies dwell-time evidence that detailed balance should hold, motivating the parameter constraints.","marker":"[80]"},{"why":"Provides independent voltage-dependent inactivation observations used to check the model's qualitative behavior after pressure release.","marker":"[81]"},{"why":"Provides the earlier three-state Piezo1 Markov chain from which the topology evolved.","marker":"[6]"}],"fun_headline_variants":["Voltage-modulated Piezo1 model explains mechanical capture loss","Piezo1 voltage dependence drives pacing capture drop","Markov chain model links Piezo1 to pacing failures","Simple Piezo1 model reproduces electromechanical pacing loss"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model is a probability model only if all transition rates are non-negative for every pressure and voltage used, but the fitted parameters include negative rate coefficients and the paper gives no rule for interpreting a negative rate.","fun_headline_variants_meta":{"raw":{"variants":["Voltage-modulated Piezo1 model explains mechanical capture loss","Piezo1 voltage dependence drives pacing capture drop","Markov chain model links Piezo1 to pacing failures","Simple Piezo1 model reproduces electromechanical pacing loss"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000614,"raw_usage":{"total_tokens":2850,"prompt_tokens":940,"completion_tokens":1910,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":556,"completion_tokens_details":{"reasoning_tokens":1842}},"tokens_in":556,"tokens_out":1910,"duration_ms":14575,"temperature":1.0,"reasoning_tokens":1842,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T20:21:38.045080+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check is to compute the generator matrix entries from Table 1 at physiological pressure and voltage; if any off-diagonal rate is negative, the channel is not a Markov chain and the fitted equations as written cannot be integrated as probability dynamics.","supporting_citations":[{"cited_title":"Rocio Servin-Vences, Raluca Fleischer, Oscar Sánchez-Carranza, and Gary R","cited_arxiv_id":null,"evidence_quote":"Supplies the voltage-clamp recordings from N2a cells used to fit and validate the Markov chain parameters."},{"cited_title":"Lewis, Alisa F","cited_arxiv_id":null,"evidence_quote":"Supplies the four-state topology with two inactivation states and the frequency-dependent band-pass behavior that the model extends with voltage dependence."},{"cited_title":"Alexander Quinn and Peter Kohl","cited_arxiv_id":null,"evidence_quote":"Provides the electromechanical pacing experiments whose rate-dependent loss of capture the integrated model aims to explain."},{"cited_title":"Gottlieb, and Frederick Sachs","cited_arxiv_id":null,"evidence_quote":"Gives single-channel conductances and reversal information used to set the magnitudes of the Piezo1 Na, K, and Ca currents."},{"cited_title":"Wijerathne, Alper D","cited_arxiv_id":null,"evidence_quote":"Supplies dwell-time evidence that detailed balance should hold, motivating the parameter constraints."},{"cited_title":"Lewis, Ashley N","cited_arxiv_id":null,"evidence_quote":"Provides independent voltage-dependent inactivation observations used to check the model's qualitative behavior after pressure release."},{"cited_title":"Gottlieb, and Frederick Sachs","cited_arxiv_id":null,"evidence_quote":"Provides the earlier three-state Piezo1 Markov chain from which the topology evolved."}],"review_version":1}