{"id":"ebc7afae-14f7-4789-ab2f-5bda0d9f85d6","arxiv_id":"2506.19475","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"A two-scale model coupling cell-scale multiphase-field dynamics to tissue-scale Helfrich bending reproduces known vesicle shapes and shows that neighbor-dependent bending rigidity can break symmetry and rotate the tissue.","lead":"The authors build a two-scale computational model in which individual deformable cells on a curved tissue surface influence the bending of that surface through their neighbor arrangement, and in turn move with the deforming surface. The work offers a route to simulate how small-scale cellular activity could drive large-scale tissue shape changes during development, currently tested only in idealized model systems.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The scale-separation premise in §2.3 is load-bearing but untested: cell-interface energies F_CH and F_Int are omitted from the surface evolution, so cell deformability and adhesion cannot directly shape the tissue.","rationale":"The reader's weakest_assumption identifies the same load-bearing point: the omission of F_CH and F_Int from the surface evolution equations is asserted via scale separation rather than demonstrated. My reading of §2.3 confirms that this omission is not a peripheral technicality but the mechanism that makes the model computationally cheap and conceptually simple: the tissue scale feels the cell scale only through the neighbor-number-dependent bending rigidity. If interface energies contribute comparably to normal forces, the model leaves out a direct channel by which cell deformability, cell-cell adhesion, and line tension influence tissue shape, which is precisely the influence the paper claims to study. The proposed test directly measures the relative magnitude of the omitted forces, so it would settle whether the assumption is quantitatively safe. The paper is otherwise a candid exploratory study with honest limitations, so a conditional verdict remains appropriate; the concern does not by itself invalidate the qualitative findings, but it should be checked before the two-scale coupling is presented as a route to morphogenetic prediction.","tokens_in":20927,"tokens_out":9463,"duration_ms":105230,"concrete_test":"On a saved N=32 snapshot (e.g., Vr=0.8, v0=0.2), compute the normal component of the shape derivative of F_CH + F_Int with respect to X using the same surface finite-element discretization, and compare its magnitude to the normal component of deltaF_Helf/deltaX from eq. (5). If max|(delta(F_CH+F_Int)/deltaX) dot n| is not at least an order of magnitude below max|(deltaF_Helf/deltaX) dot n| over the surface, the scale-separation premise is violated and the central two-scale coupling must be re-derived with the full energy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In §2.3 the authors state: 'Due to separation of scales we question the necessity of F_CH and F_Int to be considered in eqs. (2)-(4). Both are essentially only nonzero within the vicinity of the cell interfaces and thus on a small scale, which is not relevant for the large scale surface evolution.' This is the central load-bearing assumption. The coupled system is not a gradient flow of a single energy: the surface descends F_Helf while the phase fields descend F_CH+F_Int, with no cross-terms in the respective gradient flows. Spatial localization does not imply mechanical irrelevance: in two-component vesicle models line tension at interfaces produces budding and tubulation, and in epithelial sheets junctional and cortical tension is a primary source of tissue stress. With the values in Table 1 (Ca=10, In=0.05, epsilon=0.01) and kappa_bending between 0.008 and 0.030, the paper offers no order-of-magnitude estimate showing that the normal forces from F_CH+F_Int are small compared with deltaF_Helf/deltaX. Because the stated goal is to let 'cellular processes influence tissue deformations,' omitting the direct mechanical action of the very cell-scale energies that define deformability and cell-cell interactions weakens the central claim unless shown to be negligible. The companion omission of deltaF_Helf/delta_phi_i in eq. (8) means cells also do not respond energetically to bending, so the only back-coupling is geometric transport.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a two-scale model for tissue morphogenesis in which each cell is resolved as a phase field on an evolving surface, while the surface itself evolves under a Canham-Helfrich bending energy whose rigidity depends locally on the number of neighbors of the underlying cell. Cell activity is introduced through a self-propulsion term with rotational noise. The authors validate the passive limit against the classical Helfrich phase diagram and against known optimal arrangements of cells on a sphere, then study active cases with N=12, N=32, and N=92 cells, reporting collective rotation, rigid-body rotation of the surface, activity-dependent shifts in neighbor-number statistics, and correlations between local mean curvature and neighbor number. The paper is explicitly framed as a qualitative step toward quantitative morphogenesis modeling, and it discusses several limitations in the final section.","tokens_in":21315,"tokens_out":5302,"duration_ms":61329,"significance":"If the central modeling assumptions are accepted, the paper offers a computationally tractable route from cellular-scale activity to tissue-scale shape change, with a numerical method that scales essentially with the number of cells. The consistency checks are genuine strengths: the passive limit reproduces the Helfrich phase diagram from [74], and the N=12 and N=32 configurations reproduce known Thomson/Tammes arrangements on a sphere. The authors are also transparent about the phenomenological nature of the neighbor-dependent bending rigidity and about the computational constraints. However, the central claim that cellular processes influence tissue deformations rests on a scale-separation premise that is asserted rather than quantified, and the coupling via Eq. (12) is chosen by hand without sensitivity analysis. These issues affect the load-bearing mechanism of the model, so the manuscript requires substantial revision before the central claim can be considered established.","major_comments":[{"comment":"The central scale-separation assumption is asserted, not demonstrated. The text states, \"Due to separation of scales we question the necessity of F_CH and F_Int to be considered in eqs. (2)-(4). Both are essentially only nonzero within the vicinity of the cell interfaces and thus on a small scale, which is not relevant for the large scale surface evolution,\" but spatial localization is not a sufficient criterion. In two-component vesicle models, interface line tension is localized at the interface and yet directly drives budding and tubulation. For the parameters in Table 1 (Ca=10, In=0.05, epsilon=0.01, and kappa_bending in [0.008, 0.03]), the normal forces from F_CH and F_Int are never compared with delta(F_Helf)/delta(X). Since the stated objective is to let cellular processes influence tissue deformations, omitting the direct mechanical action of the very energies that define cell deformability and cell-cell adhesion weakens the central claim unless an order-of-magnitude estimate or a direct inclusion of these terms is provided.","section":"Section 2.3, Eqs. (2)-(5) and (8)"},{"comment":"The neighbor-dependent bending rigidity is introduced phenomenologically as kappa_bending = kfac(tanh(-|n_neigh-6|)+1) + klower, with no derivation from cell mechanics and no calibration against experimental or defect-mechanics data. Since Eq. (12) is the only mechanism by which cellular topology affects the tissue-scale curvature evolution, the arbitrariness of the chosen form and of the parameters kfac and klower is load-bearing. The authors acknowledge the phenomenological character, but the manuscript would need at least a sensitivity study over kfac and klower, or a comparison with an independently derived defect-based estimate, to support the general conclusions drawn from Figures 4-16.","section":"Section 2.3, Eq. (12)"},{"comment":"The N=92 results appear to be based on single stochastic trajectories. Because the active force contains a Wiener process and neighbor rearrangements are stochastic, the reported averages, standard deviations, and shape-change measures are not statistically characterized. Multiple realizations, or at least time-block averaging with confidence intervals, are needed before the monotonic trends in v0 and Vr claimed in Figures 11, 12, and 16 can be considered robust.","section":"Section 3.4, Figs. 11-16"},{"comment":"The numerical scheme is validated only by reference to previous convergence results for v0=0, a single phase field, and a stronger area-conservation constraint. The coupled system here involves an evolving surface with kappa_bending depending on the discrete neighbor number n_neigh, which changes discontinuously during T1-type rearrangements. No convergence or mesh-resolution study is provided for this coupled regime, so the quantitative accuracy of the averaged quantities in Section 3.4 is not established.","section":"Section 2.4"}],"minor_comments":[{"comment":"The word \"resamples\" is used repeatedly where \"resembles\" is intended (e.g., Sections 3.1 and 3.2, including the caption of Figure 4).","section":"Throughout"},{"comment":"The reference to Wenzel and Voigt lists volume 184, which is not a valid Physical Review E volume; the correct volume appears to be 103 (article 054410, 2021).","section":"Reference [36]"},{"comment":"The axis labels in Figure 15 contain LaTeX markup artifacts (\"D ´ cell H´ cell 1\") that make the figure difficult to read and should be typeset properly.","section":"Figure 15"},{"comment":"The distinction between collective rotation on a fixed shape and rigid-body rotation of the surface is inferred from the behavior of q_l and |q_3^m|, but no quantitative threshold or statistical test is given; a precise criterion would strengthen this central phenomenological claim.","section":"Section 3.3"}],"recommendation":"major_revision","confidential_remarks":"The main technical risk is the unquantified scale-separation assumption in Section 2.3, which is the load-bearing element of the proposed two-scale coupling. I see no indications of misrepresentation; the authors are transparent about the phenomenological nature of Eq. (12) and about the limitations of the numerical validation. If the authors can supply an order-of-magnitude estimate for the omitted cell-scale forces, or include them directly, and add sensitivity or statistical analyses, the paper could become suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Plainly: this is a competent and honest exploratory modeling paper, and the coupling it proposes is genuinely new. The new piece is the two-scale coupling itself—resolved multiphase-field cells on an evolving Helfrich surface, with the bending rigidity depending on local neighbor number. That goes beyond earlier stationary-surface work and beyond the capsid-buckling model, and the paper does the right consistency checks: it reproduces the Helfrich phase diagram from Seifert, recovers known cell packings on a sphere, and quantifies symmetry breaking for N=32. The small-cell results also give a clean transition from collective rotation on a fixed shape to rigid-body rotation of the surface, which is worth taking seriously.\n\nThe soft spots are real and the authors mostly name them, but one deserves more weight than they give it. The scale-separation assumption in Section 2.3—that F_CH and F_Int are localized at interfaces and can be dropped from the surface evolution equations—is load-bearing and untested. Spatial localization does not imply mechanical irrelevance; line tension at interfaces is what drives budding and tubulation in two-component vesicles, and junctional tension is a primary source of tissue stress. The paper supplies no order-of-magnitude estimate showing that normal forces from F_CH/F_Int are small compared with the Helfrich variation for the Table 1 parameters. So \"cellular processes influence tissue deformations\" currently flows through a single, hand-chosen channel: kappa_bending(n_neigh). That is a legitimate modeling choice, but it should be framed as a fragile premise, not settled scale separation.\n\nTwo further issues. The 92-cell results appear to be single runs; no error bars or ensemble averages are given, so trends like the shift in mean neighbor number are not statistically grounded. And the authors explicitly defer convergence for the coupled system, relying on the two-phase flat-space case—honest, but another gap. The code is not released, so the numbers in Figures 11–16 are not independently reproducible. The citation pattern is fine; the self-citations are to the prior work the paper extends, which is appropriate.\n\nWho is this for? People designing cell-resolved models of morphogenesis and anyone interested in defect-dependent tissue rigidity. It is not a quantitative prediction of a specific experiment. I would send it to a serious referee with a request for revision that addresses the scale-separation assumption, either by estimating the omitted terms or including a test case, and by clarifying the statistical basis of the N=92 data. That is my recommendation: peer review yes, with expectations of heavy revision.","headline":"A genuinely new two-scale coupling, benchmarked in the passive limit, but the central scale-separation assumption is asserted rather than demonstrated, and the 92-cell statistics are too thin for strong claims.","tokens_in":21749,"tokens_out":3805,"would_cite":true,"duration_ms":40155,"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 two-scale model proposes that the local number of a cell's neighbors sets the tissue's bending stiffness, so cellular rearrangements directly reshape the tissue.","keywords":["two-scale model","morphogenesis","multiphase-field model","bending rigidity","topological defects in epithelia","active deformable cells","evolving surfaces","cell neighbor number"],"falsifier":"Re-run the N=12 and N=32 computations with the cell-interface and interaction energies kept in the surface evolution equations; if the equilibrium shapes change appreciably, the scale-separation premise fails. A complementary experimental check is whether five-neighbor cells in a curved epithelial monolayer sit in regions of measurably lower local bending stiffness, as the rigidity relation prescribes.","tokens_in":20739,"feed_emoji":"🧫","tokens_out":10058,"duration_ms":99775,"temperature":0.7,"pith_summary":"The paper aims to establish that tissue-scale deformations can be driven by the arrangement of individual cells: each cell is resolved as a deformable phase field on an evolving surface, and the surface's bending stiffness is lowered wherever a cell has other than six neighbors. Because cells with five or seven neighbors are the defects of epithelial packing, this turns neighbor-count differences into local curvature changes, and shape changes feed back into the cell arrangement. The numerical explorations show transitions, such as cells rotating on a fixed vesicle-like shape versus carrying the whole shape around with them, and show that activity broadens the neighbor-number distribution and shifts its mean toward five. If the model is right, it provides a concrete computational route from cell-scale behavior to quantitative morphogenesis predictions.","feed_headline":"Neighbor counts bend tissue: a two-scale morphogenesis model","feed_subtitle":"A model links each cell's neighbor count to tissue stiffness, a step toward predicting embryo shape from cell behavior.","key_machinery":"The load-bearing object is the relation $\\kappa_{\\mathrm{bending}}(x,t) = k_{\\mathrm{fac}}(\\tanh(-|n_{\\mathrm{neigh}}(x,t)-6|)+1)+k_{\\mathrm{lower}}$, which assigns a reduced bending rigidity to a cell whose neighbor count $n_{\\mathrm{neigh}}$ deviates from six, the hexagonal-packing ideal. This single function carries the two-scale coupling: through it the cellular network modifies the surface's bending-energy evolution, while the surface's motion feeds back by advecting and deforming the phase fields. The second piece of machinery is the explicit scale-separation assumption that the cell-interface and cell-cell interaction energies are confined to thin interfaces and can be omitted from the surface evolution equations; this keeps the scheme computable while leaving the neighbor-dependent rigidity as the only cellular channel to the tissue scale. Each phase field is solved on its own refinement of the evolving surface, with neighbor interactions communicated on a common mesh, so the numerical cost scales essentially with the number of cells.","core_discovery":"The central claim is that a two-scale coupling through a neighbor-dependent bending rigidity is sufficient to capture how cellular processes influence tissue deformations. The surface evolves by the standard bending energy of a thin elastic sheet, with constraints on constant area and enclosed volume; on it, each cell is a phase field with its own self-propulsion, and the bending rigidity at a point is reduced the further the nearest cell's neighbor count deviates from six. The paper's computations show that this minimal coupling already produces symmetry breaking: for 12 cells, a prolate shape deforms below a reduced volume of roughly $V_r \\approx 0.96$; for 32 cells, the six five-neighbor cells shape a truncated-icosahedral surface at higher $V_r$; and active rotation transitions from collective motion on a stationary surface to rigid rotation of the whole shape. For 92 cells, the mean neighbor number shifts from six toward five with activity, cells with five neighbors sit in regions of stronger negative curvature, mean-curvature gradients grow, and relative shape change increases with activity while absolute deviation from the equilibrium prolate decreases. These results are presented as qualitative numerical evidence, not as quantitative biological predictions.","pith_inferences":["Editorial inference: the scale-separation assumption can be tested directly by re-running the same computations with the cell-interface and interaction energies kept in the surface evolution equations; if equilibrium shapes change materially, the neighbor-dependent rigidity is not the only coupling that matters.","Editorial inference: the predicted shift of the mean neighbor number toward five with increasing activity is a measurable signature; time-lapse imaging of curved epithelial monolayers or organoids could look for whether local curvature correlates with five-neighbor cells as prescribed by the rigidity relation.","Editorial inference: the same coupling mechanism could be extended to cell growth or division by letting the rigidity field respond to newly created neighbors, turning the constant-cell-size assumption into a testable extension."],"forward_implications":["Neighbor exchanges (cellular rearrangements) become shape-changing events, because changing a cell's neighbor count locally softens or stiffens the surface.","Topological defects localize curvature: cells with five neighbors concentrate strong negative curvature, so the defect network determines the symmetry axes of the deformed tissue.","Cellular activity alone can switch the tissue between two dynamical regimes: collective rotation of cells on a fixed shape and rigid-body rotation of the whole tissue.","The model predicts enhanced gradients of mean curvature at the cell scale, a proposed source of active geometric forces, so cellular-scale activity could initiate further large-scale morphogenesis.","Because the numerics scale with the number of cells, simulations with hundreds of cells become feasible, enabling statistical comparisons with continuous tissue models."],"supporting_citations":[{"why":"provides the bending-surface energy and Lagrange-multiplier evolution that the tissue surface follows.","marker":"[41, 42]"},{"why":"supplies the active deformable-particle phase-field description used for each individual cell.","marker":"[35]"},{"why":"gives the spherical baseline in which cell arrangements and collective rotation on a stationary surface were previously observed.","marker":"[39]"},{"why":"extends the cell phase-field model to curved surfaces, the starting point for the evolving-surface formulation.","marker":"[40]"},{"why":"supplies the evolving-surface phase-field transport formulation and the notation used for the coupled problem.","marker":"[52]"},{"why":"uses a similar neighbor-dependent bending-rigidity coupling for buckling of viral capsids and is the direct precedent for the rigidity relation.","marker":"[64]"},{"why":"provides the prolate/oblate phase diagram used to validate the passive bending-only limit.","marker":"[74]"},{"why":"defines the rotation-symmetry descriptors used to quantify cell shape on curved surfaces.","marker":"[81]"},{"why":"provides the active-geometric-force surface model whose velocity coupling and shape-change measures are compared.","marker":"[15]"}],"fun_headline_variants":["Cell neighbor count tunes tissue stiffness and shape","Two-scale model links cell contacts to tissue deformations","Neighbor numbers drive symmetry breaking in tissue","Active cells reshape tissue via neighbor-dependent bending"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model assumes that the forces concentrated in cell boundaries are too small to move the tissue surface, leaving the neighbor-dependent bending stiffness as the only channel from cell behavior to tissue shape; if those boundary forces matter, the coupling misses its main load.","fun_headline_variants_meta":{"raw":{"variants":["Cell neighbor count tunes tissue stiffness and shape","Two-scale model links cell contacts to tissue deformations","Neighbor numbers drive symmetry breaking in tissue","Active cells reshape tissue via neighbor-dependent bending"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000256,"raw_usage":{"total_tokens":1545,"prompt_tokens":888,"completion_tokens":657,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":504,"completion_tokens_details":{"reasoning_tokens":600}},"tokens_in":504,"tokens_out":657,"duration_ms":7051,"temperature":1.0,"reasoning_tokens":600,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:32:02.317704+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the N=12 and N=32 computations with the cell-interface and interaction energies kept in the surface evolution equations; if the equilibrium shapes change appreciably, the scale-separation premise fails. A complementary experimental check is whether five-neighbor cells in a curved epithelial monolayer sit in regions of measurably lower local bending stiffness, as the rigidity relation prescribes.","supporting_citations":[{"cited_title":"Physical Review Letters 125, 038003 (2020)","cited_arxiv_id":null,"evidence_quote":"supplies the active deformable-particle phase-field description used for each individual cell."},{"cited_title":"EPL 138, 67002 (2022)","cited_arxiv_id":null,"evidence_quote":"gives the spherical baseline in which cell arrangements and collective rotation on a stationary surface were previously observed."},{"cited_title":"Physical Review Letters 132, 078401 (2024)","cited_arxiv_id":null,"evidence_quote":"extends the cell phase-field model to curved surfaces, the starting point for the evolving-surface formulation."},{"cited_title":"Journal of Fluid Mechanics 977, 41 (2023)","cited_arxiv_id":null,"evidence_quote":"supplies the evolving-surface phase-field transport formulation and the notation used for the coupled problem."},{"cited_title":"Multiscale Modeling & Simulation 10, 82–110 (2012)","cited_arxiv_id":null,"evidence_quote":"uses a similar neighbor-dependent bending-rigidity coupling for buckling of viral capsids and is the direct precedent for the rigidity relation."},{"cited_title":"Advances in Physics 46, 13–137 (1997)","cited_arxiv_id":null,"evidence_quote":"provides the prolate/oblate phase diagram used to validate the passive bending-only limit."},{"cited_title":"arXiv:2506.13880 (2025)","cited_arxiv_id":null,"evidence_quote":"defines the rotation-symmetry descriptors used to quantify cell shape on curved surfaces."}],"review_version":2}