Viktoria Freingruber: Heterogeneous structuring in traveling wave solutions of a trait-structured Keller-Segel model

Speaker
Viktoria Freingruber, TU Delft

Abstract
In this study we generalise the Keller-Segel (KS) model, a well-established framework used for investigating chemotaxis-driven invasion across diverse biological contexts. We extend the model to incorporate intrinsic heterogeneity within the cell population, represented by the percentage of occupied membrane receptors by ligands. This trait is subject to change through ligand attachment/detachment processes. The ligand serves a dual role as a chemoattractant and, in specific scenarios, a nutrient for cell proliferation. The resulting framework consists of a non-local partial differential equation governing the dynamics of the cell population, coupled with a diffusion-reaction equation capturing the evolution of the ligand. Employing a Hopf-Cole transformation, we formally derive properties of traveling wave solutions, offering analytical insights into the system’s behaviour. We also present the results of numerical simulations which align with the analytical findings.