Modelling how lamellipodia-driven cells maintain persistent migration and interact with external barriers

Cell motility is fundamental to many biological processes, and cells exhibit a variety of migration patterns. Many motile cell types follow a universal law that connects their speed and persistency, a property that can originate from the intracellular transport of polarity cues due to the global actin retrograde flow. This mechanism was termed the "Universal Coupling between cell Speed and Persistency"(UCSP). Here we implemented a simplified version of the UCSP mechanism in a coarse-grained "minimal-cell" model, which is composed of a three-dimensional vesicle that contains curved active proteins. This model spontaneously forms a lamellipodia-like motile cell shape, which is however sensitive and can depolarize into a non-motile form due to random fluctuations or when interacting with external obstacles. The UCSP implementation introduces long-range inhibition, which stabilizes the motile phenotype. This allows our model to describe the robust polarity observed in cells and explain a large variety of cellular dynamics, such as the relation between cell speed and aspect ratio, cell-barrier scattering, and cellular oscillations in different types of geometric confinements. Significance StatementCoupling curved membrane proteins to active protrusive forces that arise from recruited actin polymerization, can lead, in the presence of adhesion, to self-organization of a leading-edge cluster and a motile "minimal-cell". However, this polarized and motile shape can become unstable, and due to fluctuations or interactions with external perturbations transform to an immotile, symmetric shape. Here we couple the spatial organization of the curved active proteins to a global advection of a polarity cue along the cells activity axis. Introducing long-range inhibition, the resultant gradient of the polarity-cue stabilizes the motile, polarized "minimal-cell" vesicle. We thereby present a robust model of cell motility that can explain a variety of cellular shape-migration relations, cell-barrier scattering and spontaneous oscillations of confined cells.