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.
Highlights
Intercellular junctions are macromolecular structures built at the interface between cell membranes and holding animal cells together within a tissue
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
Adherens junction formation deserves much interest among experimental biologists, since it initiates the formation of all the other types of intercellular junctions, including desmosomes, and it is at the centre of the cohesion and mechanical resistance of biological tissues
Summary
Intercellular junctions are macromolecular structures built at the interface between cell membranes and holding animal cells together within a tissue. It is important to understand how the trans-interaction of cadherins leads to their clustering and anchoring to F-actin, so to form discrete size-defined junctions, see [?,?,?] To overcome these difficulties we described earlier an experimental approach where single cells are allowed to spread on surfaces covered with purified cadherin extracellular domains, mimicking the cell-cell contact formation, see [?]. On such a substratum, cells adopt an isotropic morphology with radial accumulations of cadherin adhesion complexes on their ventral face that colocalize with F-actin, showing the formation of adherens junctions (Fig. 1).
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