{"id":"fa1b9059-3c3f-413a-9c06-bc05a5a9c264","arxiv_id":"2505.06168","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Simulations of a minimal 3D active tissue model identify a phase diagram of liquid, crystal, glass, and viscosity-saturation states controlled by cell elasticity and size polydispersity.","lead":"A minimal computer model of 3D tissue, with elastic cell repulsion and active random motion, shows that cell softness and size variation can switch tissue between liquid, crystal, glass, and viscosity-saturating states. The map of these states could guide design of tissues with tailored mechanical properties.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The VS phase is defined by an unvalidated stress-autocorrelation proxy (Eq. 4); if it does not track true shear viscosity, the central phase is an artifact.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing concern: Eq. (4) is an unvalidated proxy for shear viscosity, and the VS phase is defined through it. I considered other candidate concerns: the categorical FDT claim in the abstract is indeed stronger than the negative evidence in SI Section VII, which itself concedes \"does not prove\" the absence of VS under FDT; however, even if that claim were softened, the active-model VS phase would still stand or fall on the validity of Eq. (4). The reported VFT fit with phi_0 ~ 0.70 while data extend to phi = 0.72 is an internal inconsistency, but it affects the quantitative description of the glassy state rather than the existence of the VS phase. The absence of deposited code or error bars is a reproducibility issue, not a specific technical flaw in the central argument. The most direct way to settle the proxy concern is an independent shear rheology measurement in the same model, which would confirm whether viscosity saturation is a real material response or an artifact of the chosen observable. Since the reader already conditioned the verdict on this issue, I recommend no change to the verdict.","tokens_in":24561,"tokens_out":5659,"duration_ms":63218,"concrete_test":"Run Lees-Edwards or SLLOD planar shear simulations with the identical Hertz-plus-white-noise dynamics at E = E0, Sigma = 8.5%, for phi = 0.70, 0.73, 0.76, and 0.79, spanning the reported phiS ~ 0.75. Measure the steady-state shear stress and compute the apparent shear viscosity eta_shear = -<P_xy>/gamma_dot at two shear rates, e.g., gamma_dot = 1e-4 and 1e-5 per microsecond, to check rate-independence. Compare eta_shear(phi) with the Eq. (4) proxy from unsheared runs. If eta_shear continues to increase past phiS, or if eta_shear and eta_eff disagree qualitatively in their dependence on phi, the VS phase is an artifact of the proxy rather than a true rheological property.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central phase diagram includes a viscosity-saturation (VS) phase, but that phase is operationally defined by Eq. (4), which computes eta_eff as the zero-frequency integral of the off-diagonal stress autocorrelation without the V/kBT prefactor and without a kinetic term. The paper explicitly calls eta_eff \"a proxy for shear viscosity\" and never compares it with a direct imposed-shear measurement. In an athermal active system there is no fluctuation-dissipation theorem to guarantee that this stress-correlation integral equals, or is even proportional to, the mechanical shear viscosity; the missing prefactor also leaves the quantity with an arbitrary scale. If the proxy saturates while the true shear viscosity continues to grow, the VS phase disappears as a material property. The proportionality eta_eff proportional to tau_alpha reported in SI Section II is not an independent validation, because tau_alpha is a separate dynamical observable used in the same phase classification. Thus the load-bearing condition, that Eq. (4) faithfully tracks shear viscosity in this active athermal regime, is unverified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports simulations of a minimal particle-based model of a non-confluent 3D tissue in which cells interact through short-range Hertz repulsion and are driven by white-noise active self-propulsion. By varying cell elasticity E and size polydispersity Sigma, the authors identify four dynamical regimes—liquid, viscosity saturation (VS), glass, and crystal—and construct a (Sigma, E) phase diagram. The VS phase is characterized by Vogel-Fulcher-Tammann growth of an effective viscosity up to a saturation packing fraction phi_S and saturation beyond it. The paper also reports absence of aging in the VS regime, emergence of aging at high E, and argues that the VS phase requires non-FDT active self-propulsion rather than thermal noise. The SI extends the analysis to 2D and provides free-volume and connectivity-based interpretations of the viscosity behavior.","tokens_in":24787,"tokens_out":7391,"duration_ms":72334,"significance":"If the central claims hold, the paper offers a useful framework for relating single-cell mechanical properties to tissue-scale morphologies and dynamics, with potential relevance to cancer cell softness and metastasis. The explicit phase diagram, the demonstration that polydispersity suppresses crystallization, the consistency between 2D and 3D results, and the free-volume/connectivity analyses are valuable strengths. The simulation protocols are described in sufficient detail to reproduce the qualitative results. However, the two most load-bearing claims—that the VS behavior is a genuine viscosity phenomenon and that it cannot occur under FDT dynamics—rest on an unvalidated stress-autocorrelation proxy and on a limited negative search in parameter space, respectively; both need to be substantiated before the results can be accepted at face value.","major_comments":[{"comment":"Equation (10) appears to have the elastic modulus ratio inverted. The printed expression, F_ij^el = h^{3/2} (3/2) ((1-nu^2)/E) sqrt(1/R_i + 1/R_j), predicts that the contact force decreases as E increases, whereas the standard Hertz contact law scales as E/(1-nu^2) and the text and Fig. 10(b) state that larger E produces larger forces. Since all phase assignments depend on E through this force law, please correct the equation and confirm that the simulations used the corrected form.","section":"Materials and Methods, Eq. (10)"},{"comment":"The effective viscosity eta_eff defined in Eq. (4) is a zero-frequency integral of the stress autocorrelation with no V/k_BT prefactor and no kinetic term; in this athermal active system there is no FDT guarantee that this integral equals, or is even proportional to, the mechanical shear viscosity. The paper calls eta_eff a 'proxy' but never validates it against an imposed-shear measurement, and the proportionality eta_eff proportional to tau_alpha reported in SI Section II is not independent because tau_alpha is another observable used in the same phase classification. If the proxy saturates while the true shear viscosity continues to grow, the viscosity-saturation phase is an artifact of the observable; please validate against a direct shear protocol (e.g., Lees-Edwards or SLLOD) or, at minimum, restrict the phase label to 'relaxation-time saturation'.","section":"Viscosity Saturation regime, Eq. (4) and Fig. 2"},{"comment":"The categorical claim that 'The VS phase does not form in systems at finite temperature in which the dynamics satisfies the Fluctuation Dissipation Theorem' is stronger than the evidence. The SI explicitly states that the absence of saturation under FDT dynamics 'does not prove that saturation of tau_alpha cannot arise using Eqn. (4) if a broader range of cell softness and Sigma are explored,' and the main text reports only two E values and one Sigma value for the thermal simulations. Please soften the claim to 'was not observed in the parameter range tested' or perform a systematic search over E and Sigma before making a universal statement.","section":"Abstract; SI Section VII"},{"comment":"The phase diagram in Fig. 9(g) is the central summary of the paper, but the phase assignments and boundaries are presented with no statistical uncertainty: the VFT fits for eta_eff and tau_alpha, the extracted phi_S values in Figs. 2(c) and 2(f), and the boundary locations (e.g., the liquid-to-crystal transition 'near E ~ 0.3E0') are all reported without error bars or sensitivity analysis. In addition, SI Section III cautions that finite-size independence cannot be established from the narrow range N = 250-800; this caveat should be stated in the main text and ideally addressed with at least one larger system at a phase boundary.","section":"Fig. 9(g); SI Section III"}],"minor_comments":[{"comment":"The same symbol mu is used for the friction coefficient mu_i and for the active-noise strength mu in Eq. (12); these are independent parameters and should have distinct notation.","section":"Eq. (12)"},{"comment":"The sentence reporting the aging exponent is incomplete: 'The value of x is for data in Fig. 8 (a), (Fig. 8 (b)), (Fig. 8 (c)) and (Fig. 8 (d) ~ 0.9 (~ 1)' does not state which exponent corresponds to which panel; please rewrite.","section":"Aging in 3D tissues, around Eq. (9)"},{"comment":"The sentence 'In the absences of mu, the cell system is frozen at all times because the value of mu is so large that thermal motion is suppressed' is internally contradictory; presumably the model has zero temperature, so no thermal motion exists even with mu present.","section":"Discussion, 'On the importance of cell propulsion'"},{"comment":"There are numerous encoding artifacts in the rendered text (e.g., 'Äalpha', 'Ã', 'Ïð', 'omega t') that obscure the equations and figure captions; these should be fixed in the final version.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version. They simulate a minimal 3D athermal active tissue model (Hertz repulsion + white-noise self-propulsion) and map out phases in the (E, Sigma) plane: liquid, viscosity-saturation (VS), glass, crystal. The 3D phase diagram, the crystallization boundary, and the aging/no-aging crossover are new relative to their earlier 2D eLife paper; the VS phase itself is a 2D carryover. The simulations look carefully done: stretched-exponential fits, finite-size checks (though limited N range), free-volume analysis, and CNA crystal identification. The aging results in Fig. 8, where active noise seems to enhance aging compared to thermal, are the most interesting piece.\n\nSoft spots, in order of importance:\n\n1. The abstract's categorical claim that \"The VS phase does not form in systems at finite temperature in which the dynamics satisfies the Fluctuation Dissipation Theorem\" is not supported by their own evidence. SI Section VII says explicitly that their FDT simulations only covered a limited range of E and Sigma, and \"does not prove\" VS cannot arise there. The claim should be softened to \"was not observed in the range we tested.\" This is a genuine overstatement, not a stylistic quibble.\n\n2. Eq. (4) defines effective viscosity as a stress-autocorrelation integral without the V/kBT prefactor and without a kinetic term. In an athermal active system there is no general fluctuation-dissipation guarantee that this equals the mechanical shear viscosity. The paper never validates it against imposed-shear measurements. This matters because the VS phase is partly defined by eta_eff saturation. That said, the paper also shows tau_alpha saturates (Fig. 2e) and free volume saturates (Fig. S5a), so the phenomenon is not purely an artifact of the proxy. Still, a direct comparison with shear rheology would make the claim solid.\n\n3. The VFT fit for the glassy state in Fig. 4 reports phi_0 ~ 0.70 while data extend to phi = 0.72. A divergence at 0.70 with finite relaxation times at 0.72 is unphysical. The fit probably should be restricted to phi < phi_0, or another divergence form used. The reader flagged this; it's real.\n\n4. No error bars on eta_eff or tau_alpha, and no code/data release. For a simulation paper this is fixable and should be requested.\n\nOverall, the central picture is plausible and the aging-active-noise result is worth having. The FDT overclaim and the viscosity-proxy validation are the two things a referee should force them to address. This deserves a serious referee — the phase diagram is a concrete control rule for tissue engineering — but not acceptance in its current form.","headline":"Solid 3D phase-diagram simulation study with a real overclaim about FDT that needs fixing before acceptance.","tokens_in":25345,"tokens_out":2759,"would_cite":true,"duration_ms":27603,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In a minimal three-dimensional active tissue model, cell elasticity and size polydispersity select among liquid, viscosity-saturation, glass, and crystal phases, with the viscosity-saturation phase requiring active self-propulsion that…","keywords":["active matter","tissue morphogenesis","Hertz repulsion","viscosity saturation","glass transition","polydispersity","cell mechanics","phase diagram"],"falsifier":"Simulate the same model under a steady shear flow at $E=E_0$, $\\Sigma=8.5\\%$, and $\\phi>\\phi_S$ and measure the shear stress divided by strain rate; if the true shear viscosity keeps rising past $\\phi_S$ while Eq. (4) plateaus, the VS phase is an artifact of the proxy.","tokens_in":24352,"feed_emoji":"🧫","tokens_out":7159,"duration_ms":67653,"temperature":0.7,"pith_summary":"This paper claims that in a minimal three-dimensional tissue model, where cells are soft repelling spheres pushed by random self-propulsion, two physical properties—cell elasticity $E$ and size polydispersity $\\Sigma$—control both the morphology and the collective dynamics. Varying these parameters yields four distinct regimes: liquid at low $E$, viscosity saturation (VS) at intermediate $E$ with $\\Sigma$ above about 8.5%, glass at high $E$, and crystal at low $\\Sigma$ once $E$ is large enough. The load-bearing claim is that the VS regime, in which effective viscosity rises following the Vogel-Fulcher-Tammann law and then saturates beyond a packing fraction $\\phi_S$, is produced only by active self-propulsion; a thermal drive obeying the fluctuation-dissipation theorem gives glassy dynamics but no saturation. If this is right, it explains a striking saturation of tissue viscosity seen in embryos and identifies cell softness and size spread as design knobs for tissue material properties.","feed_headline":"Tissue viscosity saturation needs active motility, not thermal noise","feed_subtitle":"A minimal 3D model maps cell elasticity and size spread onto liquid, viscosity-saturation, glass, and crystal states.","key_machinery":"The machinery is a minimal particle model: each cell is a soft deformable sphere interacting through a short-range Hertz repulsion $F_{ij}^{\\rm el} \\propto h_{ij}^{3/2}$, where $h_{ij}$ is the overlap of two radii; motion follows the overdamped equation $\\dot{\\mathbf r}_i = \\mathbf F_i/\\mu_i + \\mu \\mathbf W_i(t)$, with $\\mu_i$ a size-dependent friction and $\\mu$ the strength of active uncorrelated white noise. Because $\\mu$ and $\\mu_i$ are not linked by any fluctuation-dissipation relation, the system is genuinely out of equilibrium. The observable that defines the VS regime is an effective viscosity $\\eta_{\\rm eff}$ computed from a Green-Kubo-like integral of the stress autocorrelation (Eq. 4), and relaxation times from the self-intermediate scattering function; VFT fits identify $\\phi_S$, and a Voronoi-based free-volume calculation in the SI shows that $\\phi_{\\rm free}$ saturates beyond $\\phi_S$, which is the mechanism offered for viscosity saturation.","core_discovery":"The central discovery, stated on the paper's own terms, is that a purely athermal active model with Hertz repulsion and white-noise self-propulsion generates a phase diagram in the $(E,\\Sigma)$ plane with four regimes: fluid, viscosity-saturation, glass, and crystal. The viscosity-saturation regime is the novel piece: for intermediate cell elasticity ($E$ around $E_0 = 10^{-3}$ MPa) and modest polydispersity, the effective viscosity $\\eta_{\\rm eff}$ and relaxation time $\\tau_\\alpha$ follow the VFT relation up to a saturation packing fraction $\\phi_S$, then stop growing as cells are compressed further; $\\phi_S$ decreases with increasing $E$, and data collapse when plotted against $\\phi/\\phi_S$. The phase requires active self-propulsion: in simulations whose equations of motion obey the fluctuation-dissipation theorem, the saturation does not appear, and aging appears only at the stiffest cells. The paper also reports that aging is absent in the VS and moderately stiff glass regimes, and that at high $E$ both active and thermal systems age.","pith_inferences":["Beyond the paper: if free-volume saturation is the mechanism, then tuning polydispersity or cell softness should move $\\phi_S$ in a predictable way; measuring $\\phi_S$ under controlled cell-size spread would directly test that mechanism.","Beyond the paper: the phase diagram implies that metastatic cells, which are typically softer, should sit in the liquid regime; a testable corollary is that more heterogeneous tumor cell populations should show fluidization rather than jamming.","Beyond the paper: because the viscosity plateau appears only with non-FDT driving, observing such a plateau in a tissue rheology experiment could serve as a marker for active, out-of-equilibrium cell motility rather than passive viscoelasticity."],"forward_implications":["Soft cells ($E \\lesssim 0.2E_0$) remain fluid at all simulated polydispersities, even at packing fractions above the hard-sphere jamming point.","At intermediate elasticity and $\\Sigma \\gtrsim 8.5\\%$, viscosity and relaxation time follow VFT up to $\\phi_S$ and then saturate; $\\phi_S$ shifts with $E$, and the data collapse onto one curve when scaled by $\\phi/\\phi_S$.","At high elasticity and sufficient polydispersity, the tissue is a fragile glass, and at sufficiently high $E$ it ages, with relaxation times depending on the waiting time.","At low polydispersity and $E \\gtrsim 0.3E_0$, the tissue crystallizes, with the crystal type (FCC, BCC, HCP mixes at softer $E$; near-perfect FCC at larger $E$) depending on cell rigidity.","None of these phases form without active self-propulsion; a thermal drive obeying the fluctuation-dissipation theorem produces glassy dynamics and no viscosity-saturation phase."],"supporting_citations":[{"why":"Reports the experimental viscosity saturation in zebrafish blastoderm that the VS regime is built to explain.","marker":"[6]"},{"why":"Provides the two-dimensional predecessor simulation and free-volume explanation for viscosity saturation, along with parameter choices used here.","marker":"[33]"},{"why":"Supplies the Hertz-particle cell model and friction prescription, as well as the glass-to-fluid transition context for growing colonies.","marker":"[19]"},{"why":"Gives the Green-Kubo relation on which Eq. (4), the effective-viscosity proxy, is based.","marker":"[49]"},{"why":"Sets the random-close-packing fraction of monodisperse hard spheres used as the jamming reference.","marker":"[48]"},{"why":"Original Vogel-Fulcher-Tammann form used to fit viscosity and relaxation time below $\\phi_S$.","marker":"[46]"},{"why":"Companion VFT reference for the super-Arrhenius law used in the fits.","marker":"[47]"},{"why":"Motivates the active-force-driven glass-to-fluid transition in tissues that this model extends to three dimensions.","marker":"[29]"},{"why":"Supplies the adaptive common-neighbor analysis used to classify FCC, BCC, and HCP crystal motifs.","marker":"[51]"}],"fun_headline_variants":["Active cells, not heat, saturate tissue viscosity","Cell activity creates viscosity plateau that heat cannot","New tissue phase driven by cell self-propulsion alone","Athermal active tissue shows a viscosity-plateau phase","Tissue viscosity saturation: a purely active phenomenon"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim rests on treating the Green-Kubo-like stress autocorrelation, without the kinetic term and the $V/k_B T$ factor, as the effective shear viscosity; if that proxy fails to track a true imposed-shear viscosity, the viscosity-saturation phase may be an artifact of the observable rather than a real material property.","fun_headline_variants_meta":{"raw":{"variants":["Active cells, not heat, saturate tissue viscosity","Cell activity creates viscosity plateau that heat cannot","New tissue phase driven by cell self-propulsion alone","Athermal active tissue shows a viscosity-plateau phase","Tissue viscosity saturation: a purely active phenomenon"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001701,"raw_usage":{"total_tokens":6798,"prompt_tokens":1068,"completion_tokens":5730,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":684,"completion_tokens_details":{"reasoning_tokens":5656}},"tokens_in":684,"tokens_out":5730,"duration_ms":44576,"temperature":1.0,"reasoning_tokens":5656,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:47:08.137353+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the same model under a steady shear flow at $E=E_0$, $\\Sigma=8.5\\%$, and $\\phi>\\phi_S$ and measure the shear stress divided by strain rate; if the true shear viscosity keeps rising past $\\phi_S$ while Eq. (4) plateaus, the VS phase is an artifact of the proxy.","supporting_citations":[{"cited_title":"Cohen, Bradley T","cited_arxiv_id":null,"evidence_quote":"Reports the experimental viscosity saturation in zebrafish blastoderm that the VS regime is built to explain."},{"cited_title":"Motil ity-driven glass and jamming transitions in biological tissues","cited_arxiv_id":null,"evidence_quote":"Provides the two-dimensional predecessor simulation and free-volume explanation for viscosity saturation, along with parameter choices used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Hertz-particle cell model and friction prescription, as well as the glass-to-fluid transition context for growing colonies."},{"cited_title":"Discriminating bladder cancer cells through rheological mechanomarker s at cell and spheroid levels","cited_arxiv_id":null,"evidence_quote":"Gives the Green-Kubo relation on which Eq. (4), the effective-viscosity proxy, is based."},{"cited_title":"Ramos, Joanna Pabijan, Ricardo Garcia, and Malgorzata Lekka","cited_arxiv_id":null,"evidence_quote":"Sets the random-close-packing fraction of monodisperse hard spheres used as the jamming reference."},{"cited_title":"Direct eviden ce that tumor cells soften when navigating confined spaces","cited_arxiv_id":null,"evidence_quote":"Original Vogel-Fulcher-Tammann form used to fit viscosity and relaxation time below $\\phi_S$."},{"cited_title":"Hendriks-Balk, Rita Smajda, Donata Rimoldi, Martha Liley, Harry Heinzelmann, Andr´ e Meister, and Agnese Mariotti","cited_arxiv_id":null,"evidence_quote":"Companion VFT reference for the super-Arrhenius law used in the fits."},{"cited_title":"Cell division and death inhibit glassy behaviour of confluent tissues.Soft Matter, 13(17):3205–3212, 2017","cited_arxiv_id":null,"evidence_quote":"Motivates the active-force-driven glass-to-fluid transition in tissues that this model extends to three dimensions."},{"cited_title":"Tammann and W","cited_arxiv_id":null,"evidence_quote":"Supplies the adaptive common-neighbor analysis used to classify FCC, BCC, and HCP crystal motifs."}],"review_version":1}