{"id":"f30bc32b-43df-4e74-93c0-9673ab1002cb","arxiv_id":"2602.22855","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"A mean-field constitutive model linking cell shape and shear rate to stress and T1-rearrangement yielding is constructed for a viscous (internally dissipative) vertex model and validated against large-amplitude oscillatory shear simulations.","lead":"Researchers built a mathematical model that predicts how a sheet of cells responds to being stretched and squeezed, including how cells rearrange. It is a step toward understanding tissue mechanics in embryos and organs from cell-level rules.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The load-bearing assumption is that R(t) depends only on instantaneous Q and v̇; the lone LAOS test shows deviations near flow reversal, and the acknowledged internal relaxation time suggests memory effects that would break the closure.","rationale":"The reader's weakest_assumption identifies exactly the Markov-in-Q closure as the most load-bearing assumption, and the text supports this: the model has no internal state variable beyond Q, the single non-steady predictive test (Fig. 9) shows deviations near yielding, and the authors explicitly invoke memory of deformation history. The reader's CONDITIONAL verdict already reflects this uncertainty; my stress-test does not move it. I agree with the reader that REJECT is inappropriate because the model is coherent, the fits are honest, and the central claim is explicitly framed as a mean-field closure that can be tested further. The concrete test I propose would directly probe whether the memory effect is significant enough to invalidate the closure for varying shear-rate protocols.","tokens_in":18260,"tokens_out":3685,"duration_ms":35838,"concrete_test":"Run the same large-amplitude oscillatory shear protocol at several frequencies, e.g. ω = 0.01, 0.03, 0.1, 0.3, and amplitudes γ0 = 0.5, 1, 2, keeping all model parameters fixed. Quantify the normalized L2 error in Q(t) and σ(t) between simulation and the mean-field prediction. If the error grows systematically with ω, or appears after the first shear reversal and grows with cycle number, the Markov-in-Q closure is falsified and a memory term is required. If the error remains small at all frequencies, the concern is settled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on Eqs. (12) and (19): tissue state is fully captured by average cell shape Q, so the rearrangement rate R and stress σ depend only on (Q, v̇). The only genuinely predictive test of this Markov closure is the single large-amplitude oscillatory shear protocol in Fig. 9. There, the predictions match 'relatively well,' but visible deviations appear near shear reversal, and the authors themselves attribute them to 'memory of the past deformation history' (Sec. III C 2). This is the same small-but-finite internal relaxation time already visible in the linear rheology at high frequency (Fig. 2b) and in the initial stress buildup in Fig. 4e. If R retains any dependence on the history of Q — through the distribution of cell shapes, slow relaxation of internal modes, or relaxation of cell shapes after T1 transitions — Eq. (12) is not a closed ODE and the model cannot be 'sufficiently general' for arbitrary morphogenetic histories, as claimed in the abstract. A secondary point: the steady-state check in Fig. 8 via Eq. (22) is not independent; Q_s is obtained by inverting the same fitted R, so it only confirms the fit, not the closure. Thus the evidence for the Markov-in-Q assumption rests on a single protocol with acknowledged deviations.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"Anand and Merkel propose a mean-field, cell-shape-based constitutive description for a 2D vertex model with internal (Galilean-invariant) viscous friction and two active stress mechanisms. Using the strain-decomposition framework of Merkel et al. [63], they write the shear rate as v = dQ/dt + R, where Q is the average cell shape and R is the rearrangement rate. They then posit closed relations: sigma(Q,v) = sigma_el(Q) + 2 eta(Q,R,v) v - rho T_act and R/v = (1/2) exp[b(v)(Q-Q0(v))]. The parameters are fitted to small-amplitude oscillatory, step, and constant-shear simulations for passive and active tissues; they identify a viscosity enhancement during T1 events and an exponential yielding law. Finally, they integrate dQ/dt = v - R to predict Q(t) and sigma(t) in large-amplitude oscillatory shear; predictions match simulations qualitatively, with deviations near shear reversal that the authors attribute to memory not captured by Q alone.","tokens_in":18537,"tokens_out":7457,"duration_ms":78982,"significance":"If established, this would be a useful tool for linking cell- and tissue-level mechanics, especially because it explicitly treats internal dissipation and separates reversible cell-shape change from plastic rearrangement. The paper is transparent, uses well-defined protocols, and is unusual in systematically fitting non-linear constitutive relations for a vertex model. Its main limitation is that the central closure is tested by only one out-of-sample protocol and a self-consistency check that is not independent. The stress and yield relations contain many fitted functions, so the 'prediction' is closer to a reparametrized interpolation over the same simulation data than to a parameter-free consequence of the model. With additional independent tests and explicit validity limits, the contribution would be significant.","major_comments":[{"comment":"The central assumption of the paper is that the plastic rate R depends only on the instantaneous pair (Q, v), making Eq. (12) a closed ODE. The only out-of-sample test of this Markov closure is the single large-amplitude oscillatory-shear protocol in Sec. III C 2 (Fig. 9). The authors themselves state that deviations near shear reversal 'may arise from some form of memory of the past deformation history that is not fully captured by the average cell shape Q alone.' This is consistent with the 'small, but finite relaxation time' already acknowledged in Sec. III A 3 and with the frequency dependence of G' in Fig. 2(b). Because the abstract and discussion claim generality for morphogenetic histories, a single protocol with acknowledged memory deviations is insufficient. Please test the closure on additional protocols (e.g., step-rate changes, repeated LAOS at different frequencies/amplitude","section":"Sec. III C and Eq. (12)"},{"comment":"The steady-state check in Fig. 8 is not independent evidence for the model. Equation (22) is obtained by setting R/v = 1 in the already-fitted exponential (19) and solving for Q. Consequently, Fig. 8 only demonstrates that Eq. (19) is invertible in the fitted regime; it does not validate either the closure (12) or the functional form. The text calls this a 'consistency check', which is appropriate, but the discussion later uses it to support the model and the activity-dependent Q0 phenomenology. A genuine validation would use shear rates not included in the fit, or a leave-one-out procedure, or a separate measure of R from the triangulation method rather than Eq. (11).","section":"Sec. III C 1, Eq. (22)"},{"comment":"The proposed stress law in the visco-plastic regime relies on the viscosity interpolation eta = eta0 + (R/v)(eta_s - eta0). This is an ad hoc form: eta_s is obtained from the same constant-shear data that the model is supposed to describe (Fig. 4c), and no microscopic derivation or direct measurement in a controlled state is provided. Moreover, the time-evolution test in Fig. 4e uses R(t) 'computed using a binned average' from the simulations; it therefore tests only the stress relation conditional on the simulated R, not the closed model. The LAOS prediction does use the closed model, but the deviations near reversal are exactly where Eq. (16) is least constrained. Please supply an independent determination of eta_s (e.g., in a protocol where R is directly observed) or replace Eq. (16) with a form derived from the dissipative microdynamics, and report the transient comparison using pred","section":"Sec. III A 3, Eq. (16)"},{"comment":"The constitutive model for yielding contains free functions b(v), Q0(v), and Delta q0(v) alongside the exponential ansatz. Because these functions are extracted from constant-shear simulations, and the LAOS protocol lies inside the fitted shear-rate range, the LAOS test is a consistency check of the interpolation between fitted constant-shear states. The exponential form is chosen after seeing the data; no independent derivation is provided. I recommend adding an identifiability analysis, testing the sensitivity of predicted LAOS trajectories to the chosen fitting functions, or reducing the shear-rate dependence to a compact parameterization with few coefficients. This would make the generality claim in the abstract testable and would strengthen the paper considerably.","section":"Sec. III B, Eq. (19)"}],"minor_comments":[{"comment":"In the text after Eq. (18), 'rho alt = 0.96' appears to be a typo for 'rho_ait = 0.96'. Please fix.","section":"Sec. III A 4"},{"comment":"The phrase 'R(t) is computed using a binned average' is vague. Please specify the binning procedure (bin widths, time windows, averaging over samples) and state whether R is obtained from the triangulation method or from Eq. (11).","section":"Fig. 4 and Sec. III A 3"},{"comment":"The notation 'ta_n' in Eq. (10) is undefined and inconsistent with Eq. (9), which uses 'ta_n' and 'T_act^n'. Please unify the notation for active tensions.","section":"Eq. (10)"},{"comment":"The phrase 'predicting the response' is stronger than the evidence provided. The LAOS protocol is the intended validation, but all parameters are fitted to the same model and parameter sets. Consider wording such as 'validating against' or 'reproducing' the large-amplitude oscillatory-shear response.","section":"Abstract"},{"comment":"Several grammatical slips: 'plots Fig. 7' should be 'the plots in Fig. 7', and 'the b(v), Q0_passive(v), and Delta q0(v) data from plots Fig. 7' should be rephrased. These do not affect the science but should be cleaned up.","section":"Sec. III C"}],"recommendation":"major_revision","confidential_remarks":"I see no issues of scientific misconduct; the concerns are about validation depth and the strength of the claims. The central Markov-in-(Q,v) closure is plausible but is only weakly tested, and the steady-state check is tautological. The paper would be suitable for this journal after the authors provide additional out-of-sample tests and temper the abstract/discussion claims accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a solid computational paper that builds a two-relation mean-field description of a vertex model with internal, Galilean-invariant friction: stress as a function of cell shape Q and shear rate v̇, plus an ODE for Q with a T1 rearrangement rate R(Q,v̇). The genuinely new bit is the systematic non-linear treatment, including activity and a shear-rate-dependent exponential yielding law. There's also a concrete and interesting result: the apparent viscosity roughly triples when the tissue is undergoing T1 rearrangements compared to the linear viscoelastic regime. The paper is honest about what is fit and what is predicted, and the LAOS check in Fig. 9 is a reasonable first test.\n\nWhere it's soft: the central stress relation (Eqs. 13–16) is a phenomenological ansatz with parameters (G0, η0, G2, ηs) fitted to simulation output. The choice between 'higher viscosity during rearrangements' vs 'higher-order elasticity' is made by comparing time trajectories, not derived from the vertex model energy and friction. That's a legitimate inference, but it keeps the theory at the level of a fitted surrogate.\n\nThe larger issue is the Markov-in-Q closure: R is assumed to depend only on instantaneous Q and v̇. The only genuinely predictive test is the single LAOS protocol, and the deviations near flow reversal are acknowledged as 'memory of the past deformation history.' The internal relaxation time already appears in the linear rheology at high frequency and in the initial stress buildup. As the stress-test note says, if R remembers the history of Q—through shape distributions, slow internal modes, or post-T1 relaxation—then Eq. (12) is not a closed ODE for arbitrary protocols. The abstract's claim that the approach is 'sufficiently general for any cell-based model' is not supported; it's a description of one vertex model variant in a limited regime.\n\nAlso, the steady-state check (Eq. 22) only inverts the fitted R, so it confirms the fit, not the closure. No simulation code or data is shipped, and fit uncertainties are absent. The comparison to published linear moduli (Tong et al.) is qualitative; a quantitative check of G0 and η0 against the normal-mode prediction would strengthen the link to prior work.\n\nNone of this sinks the paper's main contribution. The mean-field decomposition is well motivated, the fits are systematic, and the authors openly flag the deviations. But the title and abstract promise more generality than the evidence delivers. I'd send this to peer review and ask for: (1) code/data/parameter tables and fit uncertainties, (2) LAOS tests at several frequencies and amplitudes or an explicit relaxation-time term, and (3) a quantitative comparison to the linear rheology of Tong et al. for the same model. If the authors tighten the claims accordingly, it's a publishable contribution for the vertex-model rheology community.\n\nMy vote: accept for peer review with major revisions; the core is sound but the closure needs more testing and the scope needs to be reduced.","headline":"Useful mean-field rheology for a viscous vertex model, but the constitutive relations are fitted closures and the generality claim outruns the evidence.","tokens_in":19132,"tokens_out":3353,"would_cite":true,"duration_ms":31913,"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":"Tissue shear in the vertex model reduces to two coupled mean-field relations: stress and rearrangement rate depend only on instantaneous cell shape and shear rate.","keywords":["vertex model","tissue rheology","cell shape anisotropy","T1 transitions","visco-elasto-plastic","mean-field constitutive relation","active stress","large-amplitude oscillatory shear"],"falsifier":"Perform a shear-reversal or step-and-hold experiment in the vertex model in which two different histories arrive at the same instantaneous (Q, v) but with different accumulated past strain, then compare the immediately subsequent R and σ; if they differ beyond statistical error, the Markov-in-Q assumption fails. Alternatively, run large-amplitude oscillatory shear at higher frequency than ω=0.1 and check whether the deviations near yield reversal grow, as they should if finite internal relaxation times matter.","tokens_in":18027,"feed_emoji":"🧫","tokens_out":5339,"duration_ms":51294,"temperature":0.7,"pith_summary":"The paper tries to show that the complex shear behavior of a two-dimensional vertex model of epithelial tissue—covering elasticity, viscosity, plasticity, and active stresses—can be reduced to two coupled mean-field relations. The first gives shear stress as a function of instantaneous average cell shape and shear rate, with a viscosity that grows when cells undergo T1 rearrangements. The second states that the rate of plastic rearrangements is an exponential function of cell shape, so tissue shear splits into a reversible part (cell shape change) and an irreversible part (T1 events). If these relations hold, tissue-scale rheology can be predicted from cell-level simulations, and cell shape alone is a sufficient internal state variable for the tested regimes. The authors validate the model by predicting cell shape and stress trajectories under large-amplitude oscillatory shear.","feed_headline":"Two equations capture tissue rheology from elastic to plastic regimes","feed_subtitle":"Viscous vertex model with internal friction predicts cell shape and stress under large-amplitude oscillatory shear.","key_machinery":"The central object is the decomposition of tissue shear rate into reversible and irreversible parts, v = dQ/dt + R, where Q is the average cell-shape anisotropy tensor and R is the shear rate contributed by T1 neighbor exchanges. The load-bearing constitutive ingredient is the exponential yielding law R/v = (1/2) exp[b(v)(Q − Q0(v))], which states that the fraction of shear accommodated by rearrangements rises exponentially once cell shape exceeds a shear-rate-dependent threshold Q0(v). The stress relation combines a cubic elastic stress in Q with a viscosity that is linearly interpolated by the irreversible fraction R/v, so plastic flow is more dissipative than elastic deformation.","core_discovery":"On its own terms, the paper establishes a closed mean-field description of the vertex model's shear response. The tissue shear rate splits as v = dQ/dt + R, where Q is the average cell-shape anisotropy and R is the shear contributed by T1 neighbor exchanges. The stress is given by σ(Q,v) = σ_el(Q) + 2η(Q,v)v − ρT_act, with σ_el(Q) a nonlinear (cubic) elastic function of Q and η(Q,v) a viscosity that is roughly three times larger when deformation is carried by T1 rearrangements than when it is carried by cell-shape change. The rearrangement rate obeys R/v = (1/2) exp[b(v)(Q − Q0(v))], an exponential yielding law with a shear-rate-dependent threshold Q0(v); activity shifts both the stress and","pith_inferences":["An extension the authors leave implicit: for arbitrary deformation histories, the Markov-in-Q assumption may need an additional internal variable such as the relaxation state of subcellular degrees of freedom; the deviations near shear reversal reported in the paper suggest a testable memory effect.","The exponential yielding law has the form of an activated process with a shape-dependent barrier; one could derive b and Q0 from a mesoscopic model of T1 rates, turning the fit into a prediction.","The scheme should transfer to other cell-based models as long as the strain decomposition into shape change and rearrangements can be computed; comparing the resulting coefficients across models would reveal which rheological features are universal and which depend on model details.","A testable extension: measuring steady-state cell shape as a function of shear rate in epithelial monolayer experiments gives a direct route to the yielding threshold Q0 and can distinguish the two active mechanisms."],"forward_implications":["If correct, tissue-scale constitutive equations for vertex models with internal dissipation can be built from two scalar relations, and cell shape Q serves as an experimentally measurable state variable.","The model predicts the steady-state cell shape under constant shear, Q_s = Q0 + ln 2 / b, reproducing the observed increase of Q_s with shear rate and the different behaviors of the two active mechanisms.","Viscosity during T1-driven plastic flow is about three times the viscosity during elastic cell-shape change, so dissipation is concentrated in cell rearrangements.","Active anisotropic stresses act as linear offsets: they shift the stress by a constant ρ T_act and shift the yielding threshold Q0 by T_act Δq0(v), which can reverse the direction of cell elongation for crawling activity.","The same two-relation scheme, with the same strain decomposition, is proposed as general enough to construct nonlinear mean-field rheology for any cell-based tissue model."],"fun_headline_variants":["Shear splits into cell-shape change plus T1 swaps in viscous model","Exponential yielding law predicts tissue stress under large shear","Viscosity triples when tissue deforms by cell swapping vs shape change","Two mean-field equations link cell mechanics to tissue visco-plasticity"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing assumption is that the plastic rearrangement rate R at any instant depends only on the current average cell shape Q and current shear rate v—no memory of past deformation history—and this is tested against a time-varying shear protocol only once, where the model shows visible deviations near shear reversal.","fun_headline_variants_meta":{"raw":{"variants":["Shear splits into cell-shape change plus T1 swaps in viscous model","Exponential yielding law predicts tissue stress under large shear","Viscosity triples when tissue deforms by cell swapping vs shape change","Two mean-field equations link cell mechanics to tissue visco-plasticity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000168,"raw_usage":{"total_tokens":1081,"prompt_tokens":714,"completion_tokens":367,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":458,"completion_tokens_details":{"reasoning_tokens":290}},"tokens_in":458,"tokens_out":367,"duration_ms":4460,"temperature":1.0,"reasoning_tokens":290,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T20:33:29.877847+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform a shear-reversal or step-and-hold experiment in the vertex model in which two different histories arrive at the same instantaneous (Q, v) but with different accumulated past strain, then compare the immediately subsequent R and σ; if they differ beyond statistical error, the Markov-in-Q assumption fails. Alternatively, run large-amplitude oscillatory shear at higher frequency than ω=0.1 and check whether the deviations near yield reversal grow, as they should if finite internal relaxation times matter.","supporting_citations":[],"review_version":1}