title: Assessing the ability of the 2D Fisher-KPP equation to model cell-sheet wound closure.
abstract: We address in this paper the ability of the Fisher-KPP equations to render some of the dynamical features of epithelial cell-sheets during wound closure. Our approach is based on nonlinear parameter identification, in a two-dimensional setting, and using advanced 2D image processing of the video acquired sequences. As original contribution, we lead a detailed study of the profiles of the classically used cost functions, and we address the "wound constant speed" assumption, showing that it should be handled with care. We study five MDCK cell monolayer assays in a reference, activated and inhibited migration conditions. Modulo the inherent variability of biological assays, we show that in the assay where migration is not exogeneously activated or inhibited, the wound velocity is constant. The Fisher-KPP equation is able to accurately predict, until the final closure of the wound, the evolution of the wound area, the mean velocity of the cell front, and the time at which the closure occurred. We also show that for activated as well as for inhibited migration assays, many of the cell-sheet dynamics cannot be well captured by the Fisher-KPP model. Finally, we draw some conclusions related to the identified model parameters, and possible utilization of the model.
authors.affiliation: Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, Parc Valrose, 06108 Nice, France. Electronic address: habbal@unice.fr.
authors.forename: Abderrahmane
authors.initials: A
authors.lastname: Habbal
authors.affiliation: Univ. Nice Sophia Antipolis, CNRS, IPMC, UMR 7275, 06560 Sophia Antipolis, France. Electronic address: barelli@ipmc.cnrs.fr.
authors.forename: Hélène
authors.initials: H
authors.lastname: Barelli
authors.affiliation: INRIA, 2004 route des Lucioles, 06900 Sophia Antipolis, France. Electronic address: Gregoire.Malandain@inria.fr.
authors.forename: Grégoire
authors.initials: G
authors.lastname: Malandain
mesh_terms: D000818:Animals; D002465:Cell Movement / Q000502:physiology*; D004285:Dogs; D004847:Epithelial Cells / Q000502:physiology*; D007091:Image Processing, Computer-Assisted; D061985:Madin Darby Canine Kidney Cells; D008954:Models, Biological; D014741:Video Recording; D014945:Wound Healing / Q000502:physiology*
keywords: 2D simulation; Cell-sheet; Fisher–KPP; Image processing; MDCK; Wound edge dynamics