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.