Multi-Cellular Aggregates, A Model For Living Matter

This review presents the different physical descriptions of cell assemblies. After a short presentation of discrete models, very popular in studies of epithelial tissues, we focus more on multi-cellular spheroids containing a variety of components. In particular, we highlight both an approach based on the Smoluchowski theory of aggregation that does not consider the spatial structure of the aggregates and a continuous model for cell mixtures based on the Onsager formalism combined with the Rayleigh principle for the dynamics of dissipative systems. We show how the first approach allows to obtain the physical constants of the cells by comparison with experimental aggregates comprising a single cancerous cell line, while the second one determines the fate of interacting and proliferating cell mixing as a function of the access to nutrients. For both models, the formalism is deeply revisited to be adapted to the specificity and diversity of biological multi-component tissues. Finite element numerical simulations are shown to illustrate the potential of these physical studies. (C) 2021 Elsevier B.V. All rights reserved.