A phenomenological model of cell–cell adhesion mediated by cadherins
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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.
KeywordsCell adhesion Cadherins Adherens junctions Protein clustering Degenerate reaction–diffusion system Patterns formation
Mathematics Subject Classification92C15 82B21 35J70
POS has been supported by an ANR funding (2010 Blan 1515). BS is supported by the Labex LMH (ANR-11-IDEX-003-02) and by the FMJH (ANR-Investissements d’Avenir). The authors thank the CNRS, INRIA and INSERM for the founding of the PEPS-MBI project “MAC: Modélisation d’Adhésion des Cadhérines” the ANR 2010 Blan 1515 and Human Frontier Science Program grant RTG0040/2012, and the ANR blanche project “Kibord” (ANR-13-BS01-0004) funded by the French Ministry of Research.
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