Chirality across scales in tissue dynamics

Doruk Efe G\"okmen; Michel Fruchart; Miriam Krumbein; Pascal Silberzan; Sihan Chen; Victor Yashunsky; Vincenzo Vitelli

REVIEW 4 major objections 4 minor 5 cited by

Chirality across scales in tissue dynamics

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A microscopic model with a single chiral parameter, inferred from cell movies, predicts the macroscopic edge flows of a living tissue without any adjustable constants.

desk verdict Novel chiral vertex model and NADA inference tool, but the headline parameter-free prediction (Eq. 6) lacks a valid stated derivation and conflicts with the paper's own liquid-phase moduli. read the letter →

arxiv 2506.12276 v1 pith:7JQOS6XT submitted 2025-06-13 cond-mat.soft physics.bio-ph

Sihan Chen , Doruk Efe Gökmen , Michel Fruchart , Miriam Krumbein , Pascal Silberzan , Victor Yashunsky , Vincenzo Vitelli This is my paper

classification cond-mat.softphysics.bio-ph

keywords chiralitytissuedynamicsVoronoigraphmodeloddviscoelasticityactiveinferencecellproliferationrigiditytransitionautomaticdifferentiation

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

The paper aims to show that the handedness of forces generated inside a single cell can be followed, without empirical adjustment, all the way up to the circulation of a whole tissue. It builds a Voronoi graph model in which each cell's contractile force acquires a transverse component set by one parameter, and derives from it a continuum odd viscoelastic theory. The authors then use a noise-regularized inference algorithm to extract model parameters from movies of cell monolayers, and show that those parameters, with no fitted macroscopic moduli, predict the measured ratio of chiral edge flow to converging flow across channel widths. If right, this gives a concrete route from molecular-level chirality to tissue-scale flow, and a general recipe for inferring interpretable cell-level models from noisy snapshots.

What carries the argument

The load-bearing object is the chiral Voronoi graph model, whose dynamics add a non-variational chiral force acting on cell vertices, making the system impossible to write as a gradient of an energy. Its macroscopic counterpart is odd viscoelasticity: a constitutive law whose modulus tensor lacks the usual symmetry, giving active moduli and viscosities such as the odd shear modulus and odd bulk modulus. The quantitative bridge is a mean-field computation of these moduli on a hexagonal lattice, which yields the ratio identity used to compare with experiment without fitted macroscopic parameters. NADA, a nudged automatic differentiation algorithm, supplies the microscopic parameters by nudging noisy cell centers just enough to repair Voronoi topology changes before gradient descent.

What would settle it

Measure the actual odd and normal elastic moduli of the tissue in the liquid phase, for example by applying controlled bulk and shear deformations and reading the induced torque and stress, and compare them with the mean-field values used to derive the ratio identity; a clear mismatch would show that the prediction's agreement with flow data rides on the extrapolation. Alternatively, test the ratio identity on a cell line with independently measured chirality and preferred perimeter in channels outside the widths already examined.

Watch

Extended reading notes

Core claim

The central claim is quantitative chirality transfer across scales. Starting from a chiral Voronoi cell model whose only new ingredient is a non-variational transverse force applied at cell vertices rather than centers, the paper coarse-grains a mean-field hexagonal version to obtain odd elastic moduli, and obtains a closed-form prediction for the ratio of edge-parallel to edge-perpendicular flow driven by self-pinching, namely inhomogeneous proliferation and extrusion. With the two microscopic parameters inferred from bulk velocity fields, this parameter-free formula reproduces the measured ratio of chiral edge flow to converging flow for several channel widths. This is presented as evidence that the chiral machinery inside cells leaves a measurable, quantitatively predictable imprint on tissue-scale flow.

Load-bearing premise

The prediction borrows elasticity constants computed for a perfect hexagonal cell packing in the solid phase and applies them to the disordered, liquid-like tissue in the experiment; if that extrapolation is not justified, the parameter-free agreement could be coincidental.

Editorial extensions

If this is right

A tissue-scale flow measurement becomes a direct readout of the single-cell chirality parameter: in the relevant parameter range, the edge flow ratio gives roughly half the chirality parameter.
Tissues inferred to sit near the solid-liquid transition are predicted to show a vanishing bulk modulus, a sign-changing viscosity, and time-dependent chirality that switches off as the tissue evolves.
The inference algorithm should work for any confluent tissue where cell positions and velocities can be measured, yielding interpretable Voronoi models from single noisy snapshots.
If inhomogeneous net proliferation is suppressed, the model predicts the chiral edge flow disappears, providing a direct experimental toggle for the mechanism.
Because the chiral graph model coarse-grains to the same equations as convection-pattern phase diffusion, wall-mode chiral flows in rotating convection are predicted to be describable by the same discrete formalism.

Reading between the lines

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

Beyond the paper, the approximate proportionality between the edge flow ratio and the chirality parameter suggests that high-throughput monolayer flow imaging could screen for drugs or mutations that alter the molecular origin of cell chirality without single-cell mechanical measurements.
The nudging idea generalizes: any inference problem where noise moves data across a topological boundary, such as jamming, foams, or epithelial rearrangements, can be regularized by co-optimizing a small data displacement rather than only the model parameters.
The hexatic-lattice mean field leaves a concrete gap: a controlled coarse-graining of the disordered liquid phase would either validate the closed-form prediction or reveal why the extrapolation works, and would sharpen predictions near the phase transition.
If the parameter-free collapse holds across more cell types, chirality transfer may be approximately scale-free, in which case the only biology that needs measurement is whatever sets the single-cell chirality parameter.

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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

This one is worth reading, but the central quantitative claim has a derivation gap that needs attention before I'd trust it. The genuinely new pieces are solid: a vertex model with non-variational chiral forces applied at vertices rather than centers, and NADA, a nudged automatic differentiation scheme that tames T1-induced discontinuities in the loss landscape. The authors use it to infer parameters from three cell types, build a phase diagram with a chiral liquid/solid transition, and then go on to predict boundary flows in HT1080 channels. That arc—from subcellular force parameter to tissue-scale flow prediction—is the right kind of claim to make. What's less solid is the derivation of Eq. (6), the parameter-free prediction. Methods VII says it comes from substituting mean-field solid-phase moduli into Eq. (33). But the paper's own Table I lists liquid-phase moduli for HT1080 (B=2.2, A=-7.1, mu=0, K_o=0). Plug those into Eq. (5) and you get vy/vx about -3.2, not the -1.33 from Eq. (6). The MFT formulas in Methods V don't obviously give Eq. (6) either, unless you drop terms that aren't dropped. So the reader is left without a valid derivation for the headline number. The extrapolation from solid to liquid is asserted, not justified. This is load-bearing: if Eq. (6) is wrong, the agreement in Fig. 3C could be luck. On the plus side, the numerical simulations in Extended Data Fig. 5D seem to show that Eq. (6) holds in the liquid phase for a range of parameters, so the relation may be right even if the derivation is missing. And the independent estimate of alpha_o from edge flows (3.6 vs 2.9) is reassuring. But the paper needs to show exactly how Eq. (6) follows from the model, or present it as an empirical observation of the simulations. Other soft spots are minor: no code/data, no error bars on the NMSE, and the proliferation/extrusion rates in the simulations are fitted. These are fixable. Overall, it's a novel paper with a potentially important result, but the central prediction isn't yet backed by a clear derivation. I'd send it to peer review, but ask for a rewritten derivation of Eq. (6), and the data/code behind Fig. 3C before I'd trust the result.

Referee Report

4 major / 4 minor

Summary. The paper proposes a multiscale framework for chirality transfer in tissues, combining a non-variational chiral vertex model, a new inference algorithm (NADA) for noisy cell-position data, and experiments on HT1080, C2C12, and HBEC cultures. The central quantitative claim is that a parameter-free prediction of the ratio of chiral edge flow to converging flow, Eq. (6), obtained from bulk-inferred microscopic parameters (α_o = 2.9, P0/ℓ0 = 4.0), matches boundary-flow measurements in channels of varying width. The paper also presents a phase diagram for the chiral graph model, derives odd viscoelastic moduli via mean-field theory, and discusses applications to rotating Rayleigh-Bénard convection.

Significance. If the central prediction were valid, the paper would constitute a notable step in quantitatively connecting subcellular chiral forces to tissue-scale flows, and it would introduce a generally useful inference algorithm (NADA) that handles topological noise in Voronoi-based tissue models. The derivation of odd viscoelastic moduli from a microscopic chiral graph model and the phase diagram for chiral active solids/liquids are also valuable contributions. However, the headline claim of a parameter-free quantitative prediction is currently not supported by the derivation presented, which is a load-bearing issue for the paper's main message.

major comments (4)

[Methods VII, Eq. (6)] The derivation of Eq. (6) is not reproducible from the stated mean-field results. Substituting the MFT moduli of Eq. (29), namely B = 0.31γK_P(P0/ℓ0), μ = 1.4γK_P(3.72 − P0/ℓ0), A = 0, and K_o = 1.7γK_P α_o, into (A − K_o)/(B + μ) gives −1.7α_o / [0.31(P0/ℓ0) + 1.4(3.72 − P0/ℓ0)], which for the HT1080 values (α_o = 2.9, P0/ℓ0 = 4.0) evaluates to approximately −5.8, not the Eq. (6) value of −α_o/(3 − aP0/ℓ0) ≈ −1.33. The text states that substituting the MFT results yields Eq. (6), but no combination of the moduli given in Eq. (29) or in the small-q dynamical matrices of Methods V produces this expression. This is load-bearing because the paper's headline claim is that Eq. (6) is a parameter-free prediction from the bulk-inferred parameters.
[Table I and Eq. (5)] The paper's own inferred liquid-phase moduli for HT1080 (B = 2.2, A = −7.1, μ = 0, K_o = 0) substituted into Eq. (5) give v_y/v_x = (A − K_o)/(B + μ) = −7.1/2.2 ≈ −3.2, which is roughly a factor of 2.4 away from Eq. (6)'s prediction of −1.33 and from the experimental points in Fig. 3C. The manuscript does not explain why the liquid-phase moduli that appear in Table I are not the ones used in Eq. (5) for the boundary-flow prediction; the only stated justification is an uncontrolled 'extrapolation' of solid-phase mean-field moduli into the liquid phase, which is further contradicted by the observation that the extrapolated Eq. (29) also does not yield Eq. (6), as shown above.
[Methods VII.3 and Extended Data Fig. 5D] The numerical 'validation' of Eq. (6) in Extended Data Fig. 5D is presented as supporting the derivation, but it measures the instantaneous velocity response to an artificially imposed displacement field in simulations of the discrete graph model. The connection between this instantaneous response and the zero-frequency viscoelastic moduli that enter the continuum Eq. (5) is not established. In the liquid phase, where μ = K_o = 0, the zero-frequency response would give v_y/v_x = A/B, which for the inferred values is about −3.2 rather than Eq. (6)'s result. Unless the boundary flow is governed by a different, finite-frequency or solid-like response, the agreement in Fig. 3C lacks a theoretical foundation.
[Main text, paragraph after Eq. (6)] The claim that 'the ratio v_y/v_x we predict without fitting any macroscopic moduli (black line in Fig. 3C) captures measurements' is not accompanied by any uncertainty estimate on the prediction. The inferred parameters α_o = 2.9 and P0/ℓ0 = 4.0 ± 0.2 are reported with an error bar on the latter only, and the experimental data in Fig. 3C appear to have error bars, but the theoretical curve has no propagated uncertainty. Given the ~30% normalized mean-squared error reported for the velocity-field inference, a statistical statement (e.g., confidence intervals on Eq. (6) from the parameter uncertainties) is necessary to support the quantitative claim.

minor comments (4)

[Fig. 3C caption] The caption says to see panel F for error bars, but it would be clearer to state explicitly that the colored dots in panel C are experimental with error bars and whether the black line has any uncertainty band.
[Notation in main text] The symbols ℓ0, P0, and A0 are used in the main text without explicit definitions; they are defined only in Methods. A brief definition in the main text would improve readability.
[Methods VI, paragraph 3] There is a typo: 'we are unbale to track down' should read 'we are unable to track down'.
[Reference numbering] In the Supplementary Information, the nematic-defect discussion refers to 'Ref. [5]', but the reference list in the SI begins with [1] for odd elasticity; ensure that the in-text citations in the SI match the SI reference numbering rather than the main-text numbering.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: bulk-inferred parameters predict an independent boundary-flow ratio; the derivation of Eq. (6) has an internal gap that is a correctness issue, not a circular reduction.

full rationale

The central claim is that Eq. (6), evaluated with NADA-inferred bulk parameters (αo=2.9, P0/ℓ0=4.0), predicts the independently measured edge-flow ratio vy/vx as a function of channel width. The parameters are inferred by fitting the microscopic model to bulk velocity data, not to the boundary-flow data; Methods even derives an independent estimate αo≈3.6 from the edge-flow linear regression, which would be superfluous if the edge-flow ratio had been used as a fitting target. The MFT moduli (Eq. 29) and the numerical universal relation (Extended Data Fig. 5D) provide a derivation path for Eq. (6) from the microscopic model rather than from the measured edge flow. I therefore find no reduction of the prediction to its inputs. I do flag an internal derivation gap that is a correctness, not circularity, issue: the paper states in Methods VII that Eq. (6) follows from substituting MFT elastic moduli extrapolated to the liquid phase, but substituting the paper's own liquid-phase moduli for HT1080 (B=2.2, A=-7.1, µ=0, Ko=0; Table I) into Eq. (5) gives vy/vx=(A-Ko)/(B+µ)≈-3.2, not Eq. (6)'s -1.33. Eq. (6) appears to rest on the numerically established universal relation of Extended Data Fig. 5D rather than on the stated solid-phase MFT substitution. This weakens the 'no adjustable macroscopic parameters' derivation but does not make the edge-flow comparison circular, so it should be treated as an omitted-derivation/correctness concern.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the inferred parameters α_o, P0/ℓ0, and K_A, plus the NADA spring constant and the proliferation/extrusion rates. The main axioms are the Voronoi representation, overdamped 2D monolayer assumptions, uniform chirality, and the crucial extrapolation of mean-field solid-phase moduli into the liquid phase. No new particles, forces, or dimensions are introduced; α_o is a parameter, not an invented entity.

free parameters (5)

α_o (cortical chirality) = α_o = 2.9 for HT1080; -0.8 to 0.0 for HBEC; 0 for myoblast
Fitted to experimental velocity fields using NADA. Central to the chiral force term in Eq. (2).
P0/ℓ0 (preferred perimeter / cell size) = P0/ℓ0 = 4.0 ± 0.2 for HT1080; 4.5 start for HBEC; 3.9 for myoblast
Inferred from data; controls the solid-liquid transition and appears in Eq. (6).
K_A (area stiffness) = K_A = 0 (inferred)
The inference returns K_A=0, interpreted as K_A << K_P ℓ0^2. Used in MFT and simulations.
NADA spring constant k = not specified numerically
Chosen by the heuristic that the spring term and the velocity loss contribute similarly at the end of optimization; not a measured quantity.
k0, d_prolif, d_extr (proliferation/extrusion rates and decay lengths) = k0=0.33/h, d_prolif=6.25 µm, d_extr=35 µm
Chosen to reproduce the measured steady-state density profile; not independently measured, and used in the proliferation/extrusion simulation.

assumptions (6)

domain assumption Instantaneous Voronoi tessellation of cell centers accurately represents cell shapes and connectivity.
The entire model is built on this; wrong topology would invalidate the dynamics in Eq. (2).
domain assumption Cells are a 2D confluent monolayer with overdamped dynamics and substrate friction.
Basis for the force-balance equation (8) and the continuum momentum equation (12).
domain assumption Cortical chirality α_o is uniform within each cell and across the tissue.
The model sets a single α_o per cell type; the authors acknowledge fluctuations between cells are likely (Methods VI).
ad hoc to paper Mean-field elastic moduli computed on a perfect hexagonal lattice (with K_A=0) remain valid when extrapolated into the disordered liquid phase.
Methods VII extrapolates the solid-phase MFT results to the liquid phase to obtain Eq. (6).
domain assumption The inhomogeneous density field is maintained by spatially exponential proliferation and extrusion profiles; the steady-state approximation is used.
Used in Eq. (4) and in the self-pinching mechanism; the profiles are chosen to match the observed density and inferred net proliferation.
domain assumption Viscous stresses can be neglected in the momentum balance when deriving Eq. (5) from Eq. (3).
The paper states 'Neglecting viscous terms in (3)'; this is a simplification that may affect the quantitative accuracy of Eq. (6).

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Cite this review

Pith. "Pith review of Chirality across scales in tissue dynamics." pith.science (2026). https://pith.science/paper/7JQOS6XT

@misc{pith2026250612276,
  author       = {Pith},
  title        = {Pith review of: Chirality across scales in tissue dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7JQOS6XT}},
  note         = {Machine review of arXiv:2506.12276}
}

read the original abstract

Chiral processes that lack mirror symmetry pervade nature from enantioselective molecular interactions to the asymmetric development of organisms. An outstanding challenge at the interface between physics and biology consists in bridging the multiple scales between microscopic and macroscopic chirality. Here, we combine theory, experiments and modern inference algorithms to study a paradigmatic example of dynamic chirality transfer across scales: the generation of tissue-scale flows from subcellular forces. The distinctive properties of our microscopic graph model and the corresponding coarse-grained viscoelasticity are that (i) net cell proliferation is spatially inhomogeneous and (ii) cellular dynamics cannot be expressed as an energy gradient. To overcome the general challenge of inferring microscopic model parameters from noisy high-dimensional data, we develop a nudged automatic differentiation algorithm (NADA) that can handle large fluctuations in cell positions observed in single tissue snapshots. This data-calibrated microscopic model quantitatively captures proliferation-driven tissue flows observed at large scales in our experiments on fibroblastoma cell cultures. Beyond chirality, our inference algorithm can be used to extract interpretable graph models from limited amounts of noisy data of living and inanimate cellular systems such as networks of convection cells and flowing foams.

Figures

Figures reproduced from arXiv: 2506.12276 by the authors.

**Figure 2.** shows such a non-equilibrium phase diagram for the chiral dynamical system defined by the microscopic Equation (2), as a function of the optimal cell perimeter P0 and of the cortical chirality α o (ℓ 2 0 being the average cell area). We observe in Fig. 2A that a phase-transition line, drawn in white, separates a region where the tissue acts as a chiral solid (dark blue) from a region where it acts as a chiral liqui… view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Forward citations

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Reference graph

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pinching

Two mechanisms for macroscopic chiral ﬂows Chiral edge current is a prevalent phenomenon in chiral active systems. A steady-state cellular ﬂow indicates a persistent cellular force, which corresponds to a gradient of stress in the continuum limit. There are two possible mechanisms for stress gradients: the ﬁrst one is based on the spatial inhomogeneities,...
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For simplicity we approximate a ‘self pinching’ in x direction to an inhomo- geneous displacement ﬁeld ux, which results in a density ﬁeld ρ(x) = −∂xux

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self-pinching

Experimental ﬂow ﬁeld In Extended Data Figs. 6 AB we plot the density and proliferation proﬁles for various sample widths as func- tions of db, the distance to the boundaries. Both proﬁles peak near the boundaries, aligning the inhomogeneous growth mechanism. Moreover, we ﬁnd that ρ, vx and vy all follow the same exponential proﬁle, see Extended Data Fig....
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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

pinching

Two mechanisms for macroscopic chiral ﬂows Chiral edge current is a prevalent phenomenon in chiral active systems. A steady-state cellular ﬂow indicates a persistent cellular force, which corresponds to a gradient of stress in the continuum limit. There are two possible mechanisms for stress gradients: the ﬁrst one is based on the spatial inhomogeneities,...

[2] [2]

For simplicity we approximate a ‘self pinching’ in x direction to an inhomo- geneous displacement ﬁeld ux, which results in a density ﬁeld ρ(x) = −∂xux

In the chiral active solid phase, we neglect viscous stresses and obtain (γ/ℓ2 0) ( vx vy ) = ( (B + µ)∂2 xux + K o∂2 xuy (A − K o)∂2 xux + µ∂2 xuy ) (32) with u being the displacement ﬁeld. For simplicity we approximate a ‘self pinching’ in x direction to an inhomo- geneous displacement ﬁeld ux, which results in a density ﬁeld ρ(x) = −∂xux. In this case ...

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self-pinching

Experimental ﬂow ﬁeld In Extended Data Figs. 6 AB we plot the density and proliferation proﬁles for various sample widths as func- tions of db, the distance to the boundaries. Both proﬁles peak near the boundaries, aligning the inhomogeneous growth mechanism. Moreover, we ﬁnd that ρ, vx and vy all follow the same exponential proﬁle, see Extended Data Fig....

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Implementing proliferation and extrusion in graph models poses signiﬁcant challenges

Numerical simulation with proliferation and extrusion Can we reproduce the living mechanics of tissues and the resulting steady-state boundary ﬂows in numerical simulations? Here, we present a simulation method in- corporating both proliferation and extrusion, which qual- itatively captures the dynamics of cell turnover and the associated ﬂow ﬁelds. Imple...

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