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François Graner

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cond-mat.soft Biological Physics Cell Behavior

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preprint2026arXiv

Multiscale order, flocking and phenotypic hysteresis in the cellular Potts model of epithelia

In epithelia, how do collective cell migration and tissue spatial organization feedback on each other? We address this question through large-scale numerical simulations of the cellular Potts model. By accounting for both cell morphology and cytoskeletal activity, we uncover a remarkably rich phase diagram featuring multiple types of orientational order, either as distinct phases or coexisting across length scales. We identify a specific pathway in parameter space along which a gradual increase in the actin polymerization rate drives a phase transition into a long-range flocking state. Simultaneously, quasi-long-range nematic order emerges at length scales much larger than the cell size due to the combined effects of directed motion and lateral cell-cell interactions. At length scales comparible to cell size, however, cells adopt an approximatively hexagonal morphology, resulting in hexanematic order, similar to that observed in reconstituted Madin-Darby Canine Kidney (MDCK) cell monolayers. With further increases in actin polymerization, nematic order becomes fully long-range, while hexatic order remains quasi-long-range and confined to short length scales, but independent of cytoskeletal activity. When noise is sufficiently low to allow crystallization at finite actin polymerization rate, cycling the cell-monolayer across the melting transition yields an example of phenotypical hysteresis, reminiscent of that observed across the epithelial-mesenchymal transition.

preprint2015arXiv

3D simulations of wet foam coarsening evidence a self similar growth regime

In wet liquid foams, slow diffusion of gas through bubble walls changes bubble pressure, volume and wall curvature. Large bubbles grow at the expenses of smaller ones. The smaller the bubble, the faster it shrinks. As the number of bubbles in a given volume decreases in time, the average bubble size increases: i.e. the foam coarsens. During coarsening, bubbles also move relative to each other, changing bubble topology and shape, while liquid moves within the regions separating the bubbles. Analyzing the combined effects of these mechanisms requires examining a volume with enough bubbles to provide appropriate statistics throughout coarsening. Using a Cellular Potts model, we simulate these mechanisms during the evolution of three-dimensional foams with wetnesses of $ϕ=0.00$, $0.05$ and $ 0.20$. We represent the liquid phase as an ensemble of many small fluid particles, which allows us to monitor liquid flow in the region between bubbles. The simulations begin with $2 \times 10^5$ bubbles for $ϕ= 0.00$ and $1.25 \times 10^5$ bubbles for $ϕ= 0.05$ and $0.20$, allowing us to track the distribution functions for bubble size, topology and growth rate over two and a half decades of volume change. All simulations eventually reach a self-similar growth regime, with the distribution functions time independent and the number of bubbles decreasing with time as a power law whose exponent depends on the wetness.

preprint2010arXiv

Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams

We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities, such as the elastic strain of the structure, the yield strain and the yield function. The past history of the sample plays no explicit role, except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective, global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress and velocity gradient. We write the differential equations which predict their elastic and plastic behaviour in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications, including: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain.

preprint2007arXiv

Experimental growth law for bubbles in a "wet" 3D liquid foam

We used X-ray tomography to characterize the geometry of all bubbles in a liquid foam of average liquid fraction $ϕ_l\approx 17 %$ and to follow their evolution, measuring the normalized growth rate $\mathcal{G}=V^{-{1/3}}\frac{dV} {dt}$ for 7000 bubbles. While $\mathcal{G}$ does not depend only on the number of faces of a bubble, its average over $f-$faced bubbles scales as $G_f\sim f-f_0$ for large $f$s at all times. We discuss the dispersion of $\mathcal{G}$ and the influence of $V$ on $\mathcal{G}$.

preprint2005arXiv

Rounding of aggregates of biological cells: Experiments and simulations

The influence of surface tension and size on rounding of cell aggregates are studied using chick embryonic cells and numerical simulations based on the cellular Potts model. Our results show exponential relaxation in both cases as verified in previous studies using 2D Hydra cell aggregates. The relaxation time decreases with higher surface tension as expected from hydrodynamics laws. However, it increases faster than linearly with aggregate size. The results provide an additional support to the validity of the cellular Potts model for non-equilibrium situations and indicate that aggregate shape relaxation is not governed by the hydrodynamics of viscous liquids.