title: A phenomenological model of cell-cell adhesion mediated by cadherins.
abstract: We present a phenomenological model intended to describe at the protein population level the formation of cell-cell junctions by the local recruitment of homophilic cadherin adhesion receptors. This modeling may have a much wider implication in biological processes since many adhesion receptors, channel proteins and other membrane-born proteins associate in clusters or oligomers at the cell surface. Mathematically, it consists in a degenerate reaction-diffusion system of two partial differential equations modeling the time-space evolution of two cadherin populations over a surface: the first one represents the diffusing cadherins and the second one concerns the fixed ones. After discussing the stability of the solutions of the model, we perform numerical simulations and show relevant analogies with experimental results. In particular, we show patterns or aggregates formation for a certain set of parameters. Moreover, perturbing the stationary solution, both density populations converge in large times to some saturation level. Finally, an exponential rate of convergence is numerically obtained and is shown to be in agreement, for a suitable set of parameters, with the one obtained in some in vitro experiments.
authors: Laboratoire MAPMO, UMR 7349, Fédération D. Poisson, Université of Orléans, BP. 6759, 45067, Orléans, France. simona.mancini@univ-orleans.fr.
authors: Simona
authors: 0000-0003-4702-6761
authors: S
authors: Mancini
authors: Institut Jacques Monod, Centre National de la Recherche Scientifique, Université Paris Diderot, 75205, Paris, France.
authors: René-Marc
authors: RM
authors: Mège
authors: UPMC Univ Paris 06, Laboratoire Jacques-Louis Lions, Sorbonne Universités, 75005, Paris, France.|Laboratoire de Biologie Intégrative des Modéles Marins, 29680, Roscoff, France.
authors: Benoit
authors: B
authors: Sarels
authors: Institut Jacques Monod, Centre National de la Recherche Scientifique, Université Paris Diderot, 75205, Paris, France.
authors: Pierre-Olivier
authors: PO
authors: Strale
mesh_terms: D015820:Cadherins / Q000378:metabolism*; D002448:Cell Adhesion / Q000502:physiology*; D004058:Diffusion; D007365:Intercellular Junctions; D008954:Models, Biological
chemical_list: D015820:Cadherins
keywords: Adherens junctions; Cadherins; Cell adhesion; Degenerate reaction–diffusion system; Patterns formation; Protein clustering