Collective chemotaxis: how cells work together to migrate more efficiently

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Collective cell migration is a complex biological phenomenon observed, for example, in cancer and embryonic development. A simplifying modeling assumption is to consider a homogeneous population, where the individual members of a group behave identically. The aim of this thesis is to shed some light onto the collective cell migration of heterogeneous populations.\\ Collective cell migration is promoted by different cell-cell interactions, such as co-attraction and contact inhibition of locomotion. These mechanisms act on cell polarity, crucial for directed cell migration, through modulating the intracellular dynamics of small GTPases such as \textit{Rac1}. We propose a biased random walk model, where the bias depends on the internal state of \textit{Rac1}, and the \textit{Rac1} state is influenced by cell-cell and cell-environment interactions. We demonstrate the scope and applicability of the model in various scenarios in an extensive simulation study. Furthermore, we derive a corresponding system of partial differential equations.\\ We introduce a trait-structured Keller-Segel model to account for heterogeneity in migrating cell populations. The cell trait is given by the proportion of membrane receptors occupied by ligands, and cells change their trait by attaching or detaching ligands to or from their receptors. We assume that the trait is linked to the phenotype of a cell and, with that, to its ability to perform chemotaxis or proliferate. We formally derive properties of traveling wave solutions using the Hopf-Cole transformation and compare our analytical findings to results from numerical simulations.\\ For a modified trait-structured Keller-Segel model, we use a linear stability analysis to investigate (in-)stability conditions for a system of Keller-Segel models that stems from discretising the trait variable in the original model. For the simplest, two-state model, we derive instability conditions. We deduce corresponding criteria for cases with more than two states, and support these by numerical simulations.