Parameterizing cell movement when the instantaneous cell migration velocity is ill-defined

Cell crawling has usually been characterized by a diffusion constant D and instantaneous velocity 〈|v→|2〉. However, experimentally 〈|v→|2〉 diverges. A three regime (diffusive-ballistic-diffusive) modified Fürth equation parameterized by D, the dimensionless excess diffusion coefficient S and the persistence time P is compatible with experiment. S allows comparison of trajectories across experiments and sets limits on the intervals and duration of experiments required to assess cell movement. Cell trajectories in a variety of published experiments are consistent with longitudinal Langevin dynamics and a transverse Wiener process with S∼1+constant∗D−1.