Interface Conditions in Phenotype-Structured Models with Basement Membranes and Cell Layers

The purpose of this article is to identify the appropriate interface conditions to be coupled with phenotype-structured models, in which the motility terms depend on both cell density and phenotypic expression and where the cell population lives in a domain characterized by the presence of thin physical structures, such as basement membranes, vessel walls, and cell layers. A set of biophysically consistent transmission conditions is derived through an asymptotic method. The way in which they depend on the phenotype is found, determining the ability or inability of the cells to cross the membrane-like structure. In this way, the interface can act as a selector of more invasive phenotypes with respect to more residential ones. Numerical simulations confirm the analytical findings and provide additional insights into the influence of each model component. Overall, our results highlight how the interplay between phenotypic traits and migratory behaviour governs the spatial distribution of heterogeneous cell populations in the presence of physical interfaces, laying the groundwork for future theoretical and computational studies.