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

2024/06/05 by Andreas Buttenschön, Buttenschön, Andreas, Shona Sinclair +3 · 1 citation
Mathematics · #95B05 #Cell Behavior (q-bio.CB) #FOS: Biological sciences #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2406.02846

openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Falcó, 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.

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