A Particle Model to Reproduce Collective Migration and Aggregation of Cells with Different Phenotypes

We here propose a theoretical framework where aggregates of cells are described as systems of pointwise agents. Each element is then set to move according to Newtonian laws, being both the speed and the direction of movement determined by its phenotype, which is here assumed to fall within the epithelialmesenchymal spectrum. In particular, the latter results from the balance of a given set of behavioural stimuli, each of them defined by a direction and a weight, that quantifies its relative importance. A constraint on the sum of the weights then avoids implausible simultaneous maximization/minimization of all movement traits. Further ingredients, such as cell duplication and simple chemical dynamics, are included as well. Numerical realizations are then provided in a perspective of analysis of critical model ingredients and parameters. The proposed approach is finally applied to reproduce selected aspects of a wound healing scenario. Some hints for its improvement are given in the last part of the chapter.