Mechanochemical Feedback Enables Efficient Navigation in Complex Chemical Gradients

Neutrophils move through narrow pores, convoluted channels, and tight spaces in tissue to find infection sites. Their ability to sense weak chemical gradients, undergo directed motion, and solve such path-finding problems rests on internal GTPase signaling circuits that control the front protrusion and rear retraction of the cell. Here we explore several variants of known core polarity circuits, with local and long-ranged negative feedback, including inhibitor downstream of Rac, Rac-Rho antagonism, and effects of membrane tension. The resulting reaction-diffusion (RD) equations for Rac and Rho are then used to simulate protrusion-retractions along the edge of a simulated motile cell. We visualize how cells navigate through narrow tracks with sharp corners and weak chemical gradients in 2D. Our metrics for cell performance include polarity initiation, wall-collision intensity, and track completion. In this way, we expose how Rac and Rho, together with their immediate down and upstream components can fine-tune neutrophil motility through complex environments. Author SummaryWhite blood cells, attracted to sites of infection, migrate through complex tissues to find their target. Such movement requires a balance between robust polarity in one direction versus flexibility in response to spatial cues such as obstacles and sharp turns. Here we use mathematical modeling to explore known intracellular circuits that regulate front protrusion and rear retraction in directed cell migration. We test several such circuits in simulations of cells moving along zigzag tracks with sharp turns. We demonstrate that a basic cell polarity circuit, on its own, has limited success, since cells tend to get trapped in sharp corners. Known modulators of this core, which add local negative feedback, mutual front-back antagonism, and long-range feedback from membrane tension, improve cell performance. A cell with the full front-back-membrane tension regulatory circuit avoids delays due to traps and obstacle collisions, and moves swiftly through a convoluted passage to its target site.