Small GTPases, such as Rac and Rho, are well known central regulators of cell morphology and motility, whose dynamics also play a role in coordinating collective cell migration. Experiments have shown GTPase dynamics to be affected by both chemical and mechanical cues, but also to be spatially and temporally heterogeneous. This heterogeneity is found both within a single cell, and between cells in a tissue. For example, sometimes the leader and follower cells display an inverted GTPase configuration. While progress on understanding GTPase dynamics in single cells has been made, a major remaining challenge is to understand the role of GTPase heterogeneity in collective cell migration.
 
Motivated by recent one-dimensional experiments (in micro-channels) we introduce a one-dimensional modelling framework allowing us to integrate cell bio-mechanics, changes in cell size, and detailed intra-cellular signalling circuits (reaction-diffusion equations). Using this framework, we build models of single cell migration, and cell-cell collisions. We use numerical simulations, and bifurcation analysis, to provide insights into the regulatory mechanisms coordinating single cell migration and cell-cell collisions. We observe a wide variety of dynamics, resembling both normal and pathological behaviours.
 
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