Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia.
We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University; Sorbonne Universités UPMC Univ Paris 06; CNRS;, 24 rue Lhomond, 75005 Paris, France.|Institut Universitaire de Cancérologie, Faculté de médecine, Université Pierre et Marie Curie-Paris 6, 91 Bd de l'Hôpital, 75013 Paris, France.
Martine
M
Ben Amar
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University; Sorbonne Universités UPMC Univ Paris 06; CNRS;, 24 rue Lhomond, 75005 Paris, France.|Institut Universitaire de Cancérologie, Faculté de médecine, Université Pierre et Marie Curie-Paris 6, 91 Bd de l'Hôpital, 75013 Paris, France.|Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University; Sorbonne Universités UPMC Univ Paris 06; CNRS;, 24 rue Lhomond, 75005 Paris, France.
Carlo
C
Bianca
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