Assessing the ability of the 2D Fisher–KPP equation to model cell-sheet wound closure

• Nonlinear parameter identification, and advanced image processing are used.
• Detailed study of the profiles of the classically used cost functions is performed.
• The “wound constant speed” assumption, and the use of area-error function are studied.
• Fisher–KPP accurately predicts, in control assays, the wound area and speed.
• Fisher–KPP fails to predict the wound closure features, in activated or inhibited assays.

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.