A reaction-diffusion model of galvanotaxis coupling cell shape and sensor transport

Cells can polarize and migrate in response to external electric fields, a process known as galvanotaxis. It is believed that cells sense electric fields through redistribution of sensors, with recent experiments proposing that galvanin is a sensor candidate. In our study, we propose a 2D reaction-diffusion model to simulate cell motility driven by galvanotaxis. We constrain the transport of sensors to cell membrane, with sensor velocity linearly proportional to the magnitude of local electric fields, which, in turn, depend on the cell shape. The cell shape and movement are governed by a force balance equation that includes protrusion forces, membrane tension forces, and cytoplasmic pressure forces. We hypothesize that sensors are negatively charged, indicating that they migrate toward the cell rear. As a result, we let sensors act as inhibitors for active Rac proteins, which regulate cell motility by generating lamellipodia that provide protrusion forces. Protrusion forces determine the cell's speed and whether its long axis is perpendicular or parallel to external electric fields. Membrane tension forces resist changes in membrane length to maintain shape, while the cytoplasmic pressure forces prevent overexpansion. Our model predicts that the time required for a cell to respond to an applied field depends on both the sensor mobility and the strength of sensor inhibition of active Rac proteins.