Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime.

Marc Durand

doi:10.1371/journal.pcbi.1008576

Abstract

Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent n = 1/4 independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.

Highlights

Collective cell behaviors are involved in many morphogenetic events, such as embryo development, organ regeneration, wound healing, and the progression of metastatic cancer [1]
Because of the high sensibility of this process to finite-size and finite-time effects, no clear consensus has emerged on the scaling law of cell sorting driven by differential adhesion
No clear consensus has emerged from these studies on the kinetics law of cell sorting driven by differential adhesion: in their seminal papers [4, 5], Graner and Glazier found—on a somewhat smaller system—that the boundary length, defined as the number of mismatched cell contacts, decays logarithmically

Summary

Introduction

Collective cell behaviors are involved in many morphogenetic events, such as embryo development, organ regeneration, wound healing, and the progression of metastatic cancer [1]. One of the simplest and best studied examples of such behavior is the spontaneous separation of two randomly mixed cell populations, in a process called cell sorting [2]. In the 1960s, Steinberg proposed the differential adhesion hypothesis (DAH) as a mechanism to explain cell sorting [3]. Since Steinberg’s hypothesis statement, several numerical studies have proven that the DAH could reproduce cell sorting phenomena similar to those observed experimentally [4,5,6,7,8]. No clear consensus has emerged from these studies on the kinetics law of cell sorting driven by differential adhesion: in their seminal papers [4, 5], Graner and Glazier found—on a somewhat smaller system—that the boundary length, defined as the number of mismatched cell contacts, decays logarithmically. Cochet-Escartin et al [8] reported power-law decays, but with significantly higher exponents: n 2 [0.49, 0.74] from experiments, while n 2 [0.55, 0.59] from simulations

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Conclusion