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

arXiv (Cornell University)

Abstract

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.

Authors 4

1. Calvin C. Bakker Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Leiden Institute of Physics , Universiteit Leiden , P.O. Box 9506 , 2300 RA Leiden , The Netherlands

2. Marc Durand

   Centre National de la Recherche Scientifique · Université Paris Cité · Laboratoire Matière et Systèmes Complexes

   Affiliation as printed

   Université Paris Cité , CNRS , Matière et Systèmes Complexes , F-75013 Paris , France

3. François Graner

   Centre National de la Recherche Scientifique · Université Paris Cité · Laboratoire Matière et Systèmes Complexes

   Affiliation as printed

   Université Paris Cité , CNRS , Matière et Systèmes Complexes , F-75013 Paris , France

4. Luca Giomi Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Leiden Institute of Physics , Universiteit Leiden , P.O. Box 9506 , 2300 RA Leiden , The Netherlands