Understanding mechanisms of topography sensing in migrating cells through simulations of a coupled excitable network model

Motility in social amoeba, Dictyostelium, is regulated by two coupled excitable networks: the diffusive and slower signal transduction excitable network (STEN), which connects to and organizes the faster and less diffusive cytoskeletal excitable network (CEN). Additionally, feedback from CEN to STEN helps polarize the cell enabling directional migration. Waves arise from these excitable networks and the patterns of actin polymerization waves determine how a cell moves on the substrate. In experiments we observe that differences in substrate topography can change the wave patterns. We hypothesized and confirmed using computational methods that mechanical stimulus from ridges affect the threshold of activation of the two excitable networks, guiding the waves along the ridges. Experiments also suggested that the height, spacing and curvature of the ridges might influence wave activity. Through simulations, we investigated the effect of these characteristics on CEN and STEN waves. Our model confirmed that the mechanical stimulus from short ridges enters solely through the CEN network, the observed changes in the STEN waves come about from the feedback loop from CEN to STEN, and that this effect is inhibitory. In contrast, when plated on tall ridges, double streak patterns are observed in experiments. We hypothesized that these patterns are a result of differences in surface curvature and their effect on the biochemical signaling pathway for actin polymerization. Using our model, we showed that CEN is activated by negative curvature, whereas positive or zero curvature across wider regions can directly stimulate STEN waves. STEN also coordinates CEN activity in regions of negative curvature giving rise to patterns like the double streak. In conclusion, our computational methods have gone a long way in revealing the mechanisms of curvature sensing and contact guidance.