Speaker
Description
Cell invasion is a striking example of self-organisation in biology, playing a central role in development, regeneration, and disease. Classically, invasion is modelled by the Fisher–KPP equation, which shows that the combination of cell proliferation and diffusion is sufficient to generate an invasive front whose speed is determined by the proliferation rate and cell diffusivity. When crowding constraints are incorporated into proliferation, these processes give rise to travelling wave solutions, namely invasion profiles that propagate at constant speed. In this talk, I will discuss recent work on analogous invasion phenomena in heterogeneous populations composed of two interacting cell types. Such heterogeneity may represent cells at different stages of the cell cycle, cells with distinct phenotypes such as invasive and proliferative subpopulations, chemotactic and consumer cells, or cells with different adhesive properties. I will highlight both the biological insights and the mathematical challenges arising in these systems. On the biological side, the results shed light on how population heterogeneity shapes invasion profile structure and regulates processes such as cell cycle progression or chemotactic migration efficiency. On the mathematical side, I will describe analytical approaches for studying the resulting travelling wave solutions, focusing on asymptotic and variational methods.
