Broad-tailed force distributions and velocity ordering in a heterogeneous membrane model for collective cell migration

Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a “wound”. We argue that a simple physical model of a force-driven heterogeneous elastic membrane sliding over a viscous substrate can qualitatively explain a few experimentally observed facts: (i) the growth of velocity ordering which spreads from the wound boundary to the interior, (ii) the exponential tails of the traction force distributions, and (iii) the swirling pattern of velocities in the interior of the tissue.

💡 Research Summary

The paper addresses three hallmark phenomena observed during collective cell migration in wound‑healing assays: (i) the emergence and spatial spread of velocity ordering from the wound edge into the tissue interior, (ii) the presence of broad‑tailed, approximately exponential tails in the probability distribution of traction forces exerted on the substrate, and (iii) the appearance of swirling, vortex‑like velocity patterns deep within the cell sheet. To rationalize these observations, the authors construct a minimal physical model consisting of a heterogeneous elastic membrane sliding over a viscous substrate, driven by a localized “front” force applied only at the wound boundary.

The membrane is discretized on a two‑dimensional lattice. Each lattice node represents a cell and is connected to its nearest neighbours by springs whose stiffnesses (k_{ij}) are drawn from a broad distribution (e.g., log‑normal). The nodes also experience a viscous drag (\gamma) that models the interaction with the underlying substrate. The dynamics are assumed to be overdamped, so the velocity (\mathbf{v}_i) of node (i) satisfies
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