Characteristics of Speed–Acceleration Phase Diagram of Migrating Cells

Cell movement behavior is one of the most interesting biological problems in physics, biology, and medicine. We experimentally investigate the characteristics of random cell motion during migration. Observing cell motion trajectories under a microscope, we employ a nonlinear dynamics method to construct a speed–acceleration phase diagram. Our analysis reveals the presence of a fixed point in this phase diagram, which suggests that migrating cells possess a stable state. Cells that deviate from this stable state display a tendency to return to it, following the streamline trends of an attractor structure in the phase diagram. We derive a set of characteristic values describing cell motion, encompassing inherent speed, inherent acceleration, characteristic time for speed change, and characteristic time for acceleration change. We develop a differential equation model based on experimental data and conduct numerical calculations. The computational results align with the findings obtained from experiments. Our research suggests that the asymmetrical characteristics observed in cell motion near an inherent speed primarily arise from properties of inherent acceleration of cells.