  Cell crawling is critical to biological development, homeostasis and disease.
In many cases, cell trajectories are quasi-random-walk. In vitro assays on flat
surfaces often described such quasi-random-walk cell trajectories as
approximations to a solution of a Langevin process. However, experiments show
quasi-diffusive behavior at small timescales, indicating that instantaneous
velocity and velocity autocorrelations are not well-defined. We propose to
characterize mean-squared cell displacement using a modified F\"urth equation
with three temporal and spatial regimes: short- and long-time/range diffusion
and intermediate time/range ballistic motion. This analysis collapses
mean-squared displacements of previously published experimental data onto a
single-parameter family of curves, allowing direct comparison between movement
in different cell types, and between experiments and numerical simulations. Our
method also show that robust cell-motility quantification requires an
experiment with a maximum interval between images of a few percent of the
cell-motion persistence time or less, and a duration of a few
orders-of-magnitude longer than the cell-motion persistence time or more.
