Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

JOURNAL OF THEORETICAL BIOLOGY

卷:445

Article

Carrillo, Jose Antonio¹  Colombi, Annachiara²  Scianna, Marco² 

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Politecn Torino, Dept Math Sci, Corso Duca Abruzzi 24, I-10129 Turin, Italy

关键词: Interaction potentials;    Nonlocal models;    H-stability;    Cell sorting;    Cell-cell interactions;   

DOI  :  10.1016/j.jtbi.2018.02.022

来源: Elsevier

【 摘 要 】

The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters. The aim of the paper is to demonstrate how the concept of H-stability, deriving from statistical mechanics, can have important implications in this respect. For any given interaction kernel, it in fact allows to a priori predict the regions of the free parameter space that result in stable configurations of the system characterized by a finite and strictly positive minimal interparticle distance, which is fundamental when dealing with biological phenomena. The proposed analytical arguments are indeed able to restrict the range of possible variations of selected model coefficients, whose exact estimate however requires further investigations (e.g., fitting with empirical data), as illustrated in this paper by series of representative simulations dealing with cell colony reorganization, sorting phenomena and zebrafish embryonic development. (C) 2018 The Authors. Published by Elsevier Ltd.

【 授权许可】

Free