Characteristics of the Speed- Acceleration Phase Diagram of Migrating Cells

Abstract The behavior of cell movement is one of the most interesting biological problems in biology, physics and medicine. In this study, we conducted experiments to investigate the characteristics of random cell motion during migration. By observing cell motion trajectories under a microscope, we employed nonlinear dynamics method to construct a speed- acceleration phase diagram. Our analysis revealed 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 derived 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 developed a differential equation model based on experimental data and conducted numerical calculations. The computational results align with the findings obtained from experimental results. Our research suggests that the asymmetrical characteristics observed in cell motion near an inherent speed primarily arise from the characteristics of inherent acceleration of cells.