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

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation Mathématique pour l'Oncologie [MONC]
dc.contributor.authorGALLINATO, Olivier
hal.structure.identifierTokyo University of Science [Tokyo]
dc.contributor.authorOHTA, Masahito
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation Mathématique pour l'Oncologie [MONC]
dc.contributor.authorPOIGNARD, Clair
hal.structure.identifierOsaka University [Osaka]
dc.contributor.authorSUZUKI, Takashi
dc.date.created2016-12-05
dc.date.issued2016-12-05
dc.identifier.issn0303-6812
dc.description.abstractEnIn this paper, a free boundary problem for cell protrusion formation is studied theoretically and numerically. The cell membrane is precisely described thanks to a level set function, whose motion is due to specific signalling pathways. The aim is to model the chemical interactions between the cell and its environment, in the process of invadopodia or pseudopodia formation. The model consists of Laplace equation with Dirichlet condition inside the cell coupled to Laplace equation with Neumann condition in the outer domain. The actin polymerization is accounted for as the gradient of the inner signal, which drives the motion of the interface. We prove the well-posedness of our free boundary problem under a sign condition on the datum. This criterion ensures the consistency of the model, and provides conditions to focus on for any enrichment of the model. We then propose a new first order Cartesian finite-difference method to solve the problem. We eventually exhibit the main biological features that can be accounted for by the model: the formation of thin and elongated protrusions as for invadopodia, or larger protrusion as for pseudopodia, depending on the source term in the equation. The model provides the theoretical and numerical grounds for single cell migration modeling, whose formulation is valid in 2D and 3D. In particular, specific chemical reactions that occured at the cell membrane could be precisely described in forthcoming works.
dc.description.sponsorshipInitiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
dc.language.isoen
dc.publisherSpringer
dc.subject.enon Cartesian grids
dc.subject.enMathematics Subject Classification (2000) 65M06
dc.subject.en65M12
dc.subject.en92C37
dc.subject.enMathematical Biology
dc.subject.enCell Protrusion Formation
dc.subject.enFree boundary problem
dc.subject.enFinite differences
dc.title.enFree boundary problem for cell protrusion formations: theoretical and numerical aspects
dc.typeArticle de revue
dc.identifier.doi10.1007/s00285-016-1080-7
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalJournal of Mathematical Biology
bordeaux.peerReviewedoui
hal.identifierhal-01412264
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01412264v1
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