Free boundary problem for cell protrusion formations: theoretical and numerical aspects

Abstract : In this paper, we derive a free boundary problem for cell protrusion formation in which the cell membrane is precisely described thanks to a level-set function, whose motion is due to specific signalling pathways. The model consists in Laplace equation with Dirichlet condition inside the cell coupled to Laplace equation with Neumann condition in the outer domain. The motion of the interface is due the gradient of the inner quantity. We prove the well-posedness of our free boundary problem under a sign condition on the datum similarly to the Taylor criterion in water waves. We also propose an accurate numerical scheme to solve the problem and we exhibit the main biological features that can be accounted for by the model. Even though simplistic from the modeling point of view, we claim that this paper provides the theoretical and numerical grounds for single cell migration modeling. In particular, specific chemical reactions that occurred at the cell membrane could be precisely described in forthcoming works.
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Contributor : Olivier Gallinato <>
Submitted on : Monday, November 14, 2016 - 11:39:14 AM
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Olivier Gallinato, Masahito Ohta, Clair Poignard, Takashi Suzuki. Free boundary problem for cell protrusion formations: theoretical and numerical aspects. [Research Report] RR-8810, INRIA; Institut de Mathématiques de Bordeaux; Université de Bordeaux; Tokyo University of Science; Osaka University. 2016. ⟨hal-01228013v3⟩

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