Active-gel Theory for Multicellular Migration of Polar Cells in the Extra-cellular Matrix

TL;DR

This paper develops an active-gel theoretical framework to understand multicellular migration in the extracellular matrix, revealing how cell-matrix interactions influence migration stability and patterning.

Contribution

It introduces a novel active-gel model combining cell polarity and ECM mechanics to analyze migration dynamics and stability.

Findings

Homogeneous migration predicted for small wave vectors.

Migration domains form for sufficiently extensile cells.

Stability is affected by matrix stiffness and cell alignment mechanisms.

Abstract

We formulate an active-gel theory for multicellular migration in the extra-cellular matrix (ECM). The cells are modeled as an active, polar solvent, and the ECM as a viscoelastic solid. Our theory enables to analyze the dynamic reciprocity between the migrating cells and their environment in terms of distinct relative forces and alignment mechanisms. We analyze the linear stability of polar cells migrating homogeneously in the ECM. Our theory predicts that, as a consequence of cell-matrix alignment, contractile cells migrate homogeneously for small wave vectors, while sufficiently extensile cells migrate in domains. Homogeneous cell migration of both extensile and contractile cells may be unstable for larger wave vectors, due to active forces and the alignment of cells with their concentration gradient. These mechanisms are stabilized by cellular alignment to the migration flow and matrix stiffness. They are expected to be suppressed entirely for rigid matrices with elastic moduli of order 10 kPa. Our theory should be useful in analyzing multicellular migration and ECM patterning at the mesoscopic scale.