Controlling the morphologies and dynamics in three-dimensional tissues

D. Thirumalai; Rajsekhar Das; Sumit Sinha; Xin Li

REVIEW 4 major objections 4 minor 81 references

Controlling the morphologies and dynamics in three-dimensional tissues

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict Solid 3D phase-diagram simulation study with a real overclaim about FDT that needs fixing before acceptance. read the letter →

arxiv 2505.06168 v1 pith:Z5KBQEBT submitted 2025-05-09 cond-mat.soft physics.bio-ph

Rajsekhar Das , Xin Li , Sumit Sinha , D. Thirumalai This is my paper · ORCID

classification cond-mat.softphysics.bio-ph

keywords activemattertissuemorphogenesisHertzrepulsionviscositysaturationglasstransitionpolydispersitycellmechanicsphasediagram

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

Soft spots, in order of importance:

1. 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.

2. 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.

3. 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.

4. 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.

Overall, 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.

Referee Report

4 major / 4 minor

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.

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 (4)

[Materials and Methods, Eq. (10)] 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.
[Viscosity Saturation regime, Eq. (4) and Fig. 2] 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'.
[Abstract; SI Section VII] 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.
[Fig. 9(g); SI Section III] 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.

minor comments (4)

[Eq. (12)] 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.
[Aging in 3D tissues, around Eq. (9)] 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.
[Discussion, 'On the importance of cell propulsion'] 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.
[Throughout] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase diagram is an empirical simulation result, VFT fits are descriptive, and tau_alpha is used as a validated proxy, not as a circular input.

full rationale

This is a simulation study, not a derivation, so the circularity burden is low. The phase classification is based on explicitly defined observables — Fs(q,t) (Eq. 1), g(r) (Eq. 2), tau_alpha (Eq. 3), and eta_eff (Eq. 4) — computed from the same nonequilibrium dynamics described by Eq. 12. The VFT and Arrhenius fits are descriptive fits to simulated data, not first-principles predictions, and the paper does not claim otherwise. The substitution of tau_alpha for eta_eff is justified by an explicit empirical proportionality check in SI Section II, and phi_S from tau_alpha is compared with phi_S from eta_eff (Fig. 2f), so this is a surrogate validation rather than a circular definition. The claim that the VS phase does not occur under FDT-satisfying dynamics is tested directly in SI Section VII with a separate Brownian-dynamics equation of motion; the authors also state the limitation that the absence of VS in those simulations does not prove it cannot occur for untested parameters. Self-citations (e.g., refs. 19, 33, 61) supply the prior particle model, parameter choices, and free-volume interpretation, but the 3D free-volume calculation and phase boundaries are performed here rather than imported. The only substantive concern — that Eq. 4 is called 'a proxy for shear viscosity' and is not validated against imposed shear — is a measurement-validity caveat, not circularity, because the paper does not derive the phase behavior from a claimed equality between the proxy and the true shear viscosity.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central results rest on the Hertz active-noise model with several parameters taken from prior work and fitted VFT parameters. No code or data are shipped, and no new physical entities are introduced.

free parameters (6)

Active noise strength mu = 0.045 um/sqrt(s)
Fixed from prior work [2]; the phase diagram is attributed to self-propulsion but mu is not varied, so the location of phase boundaries may depend on this value.
Friction coefficient gamma_0 = 0.1 kg/(um s)
Taken from prior work [2]; sets the time scale of the overdamped dynamics.
VFT fragility parameter D = e.g., D approximately 0.78 for E = 5E0, Sigma = 8.5%
Fitted to tau_alpha(phi) or eta_eff(phi) data; used to assert super-Arrhenius VFT behavior in glass and VS states.
VFT divergence packing fraction phi_0 = e.g., approximately 0.70 for E = 5E0, Sigma = 8.5%; approximately 0.69 and 0.68 for Sigma = 8.5% and 24.8%
Fitted to data; the reported phi_0 approximately 0.70 conflicts with plotted data up to phi = 0.72 for Eq. (6).
Saturation packing fraction phi_S = varies with E, around 0.74 to 0.76 in the VS regime
Extracted from where eta_eff or tau_alpha stops growing; used for the scaling collapse in Fig. 2(d).
Poisson ratio nu = 0.5
Fixed for all cells from prior tissue models [14,15]; affects the Hertz force magnitude.

assumptions (6)

domain assumption Hertz contact force models cell-cell interactions (Eq. 10).
Assumes cells are elastic spheres with no adhesion, no cortical tension, and no division or apoptosis; this interaction is central to the model.
domain assumption Cell motility arises solely from active white noise with zero correlation time and no FDT (Eq. 12).
The paper explicitly states that in the absence of mu the tissue is frozen; this out-of-equilibrium driving is what creates the phases.
domain assumption Stokes friction law mu_i = 6 pi eta R_i describes drag on each cell.
Used in Eq. (12) and in the FDT-satisfying Brownian dynamics simulations.
domain assumption Green-Kubo-like stress autocorrelation (Eq. 4) gives a meaningful effective viscosity in an athermal active system.
The formula omits the kinetic term and the V/kBT factor; the paper calls it a proxy, but the VS phase characterization depends on it.
domain assumption Steady state is reached and Fs(q,t) relaxation time is a proxy for viscosity.
Justified in SI Section II by an observed proportionality between eta and tau_alpha, but only for the tested regimes.
domain assumption N = 500 periodic box represents bulk tissue.
Finite-size checks only cover N = 250 to 800, and the authors note they cannot be certain the results are truly system-size independent.

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Pith. "Pith review of Controlling the morphologies and dynamics in three-dimensional tissues." pith.science (2026). https://pith.science/paper/Z5KBQEBT

@misc{pith2026250506168,
  author       = {Pith},
  title        = {Pith review of: Controlling the morphologies and dynamics in three-dimensional tissues},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z5KBQEBT}},
  note         = {Machine review of arXiv:2505.06168}
}

abstract

A number of factors, such as, cell-cell interactions and self-propulsion of cells driven by cytoskeletal forces determine tissue morphologies and dynamics. To explore the interplay between these factors in controlling the dynamics at the tissue scale, we created a minimal three dimensional model in which short-range repulsive elastic forces account for cell-cell interactions. Self-propulsion is modeled as active uncorrelated random stochastic forces, with strength $\mu$, that act on individual cells and is the only source of cell motility. Strikingly, variations in polydispersity in cell sizes ($\Sigma$) and cell elasticity ($E$), results in the formation of a variety of distinct ``phases", driven entirely by $\mu$. At low $E$, the tissue behaves like a liquid, at all values of $\Sigma$, whereas at high $E$ and $\Sigma$, it has the characteristics of a glass. The tissue crystallizes at low $\Sigma$ provided $E$ exceeds a critical value. Over a narrow range of $E$ and $\Sigma$, that lies between the boundaries of the liquid and glass phase, the effective viscosity increases like in a glass as the cell density increases and saturates as the cells are compressed beyond a certain value, creating the viscosity saturation (VS) phase. The VS phase does not form in systems at finite temperature in which the dynamics satisfies the Fluctuation Dissipation Theorem. In the glass phase, the tissue exhibits aging (relaxation times depend on the waiting time) behavior at high $E$ values. Our findings provide a framework for designing tissues with tunable material properties by controlling the physical characteristics of cells.

Figures

Figures reproduced from arXiv: 2505.06168 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

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Reference graph

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The solid lines are the ﬁts to the VFT equation (Eqn

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8E0. VFT ﬁts are given by the solid line (Eqn. (6) for τα ). (f) φ S calculated using τα and ηeﬀ are linearly related. 7 the factor V kBT is not included in Eqn. (4) because temperature is not a relev ant variable in the highly over-damped model considered here. The eﬀective v iscosity of the 3D tissue as a function of ϕ (see Fig. 2 (b)) has the same tren...

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