Self-similarity in collective cell migration
Collective cell migration plays a substantial role in maintaining the cohesion of cell layers in the context of wound healing, embryonic development, and the progression of cancer. We extend and develop continuum mechanical models of cell layer migration based on an assumption of elastic deformation of the cell layer that leads to a generalized Stefan problem. In the case where there is no cell proliferation, we study similarity under scaling solutions where substitution of the similarity ansatz reduces the model equations to a nonlinear second-order ordinary differential equation on the half-line with Neumann boundary conditions at both boundaries. The existence and uniqueness of solutions is proven using Ważewski’s Principle.