How Cells Stay Together: A Mechanism for Maintenance of a Robust Cluster Explored by Local and Non-local Continuum Models

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 non-local continuum models by Falcó et al. (SIAM J Appl Math 84:17–42, 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. For attractant–repellent chemotaxis, we derive an explicit condition on cell and chemical properties that guarantee the existence of robust clusters. We also extend their work by investigating the accuracy of the local approximation relative to the full non-local model.