How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models

TL;DR

This paper investigates how cells form stable clusters during tissue development using continuum models, demonstrating the effectiveness of local approximations in capturing nonlocal cell interactions and cluster stability.

Contribution

It applies a recent local approximation to nonlocal models with biologically-based interactions, analyzing cluster formation, size, stability, and the approximation's accuracy.

Findings

Local approximation effectively captures nonlocal cell interactions.

Cluster stability depends on specific attraction-repulsion parameters.

The model predicts conditions for robust cell cluster formation.

Abstract

Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal continuum models by Falc\'o, Baker, and Carrillo (2023). We apply their theoretical results by specifying biologically-based cell-cell interactions, showing how such cell communication results in an effective attraction-repulsion Morse potential. We then explore the clustering instability, the existence and size of the cluster, and its stability. We also extend their work by investigating the accuracy of the local approximation relative to the full nonlocal model.