Abstract
We quantify random migration of the social ameba Dictyostelium discoideum. We demonstrate that the statistics of cell motion can be described by an underlying Langevin-type stochastic differential equation. An analytic expression for the velocity distribution function is derived. The separation into deterministic and stochastic parts of the movement shows that the cells undergo a damped motion with multiplicative noise. Both contributions to the dynamics display a distinct response to external physiological stimuli. The deterministic component depends on the developmental state and ambient levels of signaling substances, while the stochastic part does not.