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

TL;DR

This study uses large-scale simulations of the cellular Potts model to explore how collective cell migration and tissue organization influence each other, revealing complex phase behaviors and hysteresis phenomena.

Contribution

It uncovers a rich phase diagram with multiple orientational orders and demonstrates how actin polymerization drives phase transitions and phenotypic hysteresis in epithelial tissues.

Findings

Gradual increase in actin polymerization induces a transition to flocking state.

Quasi-long-range nematic order emerges at large scales due to directed motion.

Phenotypical hysteresis observed across the epithelial-mesenchymal transition.

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.