Narrow Results

In this paper, we construct a model to describe the spatial motion of a monolayer of cells occupying a two-dimensional dish. By taking care of nonlocal contact inhibition, quiescence phenomenon, and the cell cycle, we derive porous media-like equation with nonlocal reaction terms. The first part of this paper is devoted to the construction of the model. In the second part we study the well-posedness of the model. We conclude the paper by presenting some numerical simulations of the model and we observe the formation of colonies.

We simulate the aggregation of zoospores of the green alga Pediastrum simplex into a planar colony — including radially outward cell orientation. The model assumptions are: cells are randomly kicked by flagella, an ellipsoidal boundary repells cells and flagella, overlapping cell surfaces lead to dissipative cell-cell repulsion, cell-cell attractive forces occur around arches close to the cell's surfaces, there is friction of the cells with the medium; the process ends by an extension of the attractive arches followed by the stop of flagellar propulsion and finally a change of cell shapes from spherical to nearly triangular with contact-inhibited horn-like extensions. These assumptions are directly observed or indirectly inferred from the literature, light microscopy (video recordings) and scanning electron microscopy. We perform calculations with cell numbers ranging from 4 to 64. Additional simulations permit to discard alternative models, including planarization via cell-cell attraction only, chemotaxis or cohesive intercellular gliding. Our model yields patterns agreeing well with symmetrical as well as with disordered natural aggregates.