  Cell movement, for example during embryogenesis or tumor metastasis, is a
complex dynamical process resulting from an intricate interplay of multiple
components of the cellular migration machinery. At first sight, the paths of
migrating cells resemble those of thermally driven Brownian particles. However,
cell migration is an active biological process putting a characterization in
terms of normal Brownian motion into question. By analyzing the trajectories of
wildtype and mutated epithelial (MDCK-F) cells we show experimentally that
anomalous dynamics characterizes cell migration. A superdiffusive increase of
the mean squared displacement, non-Gaussian spatial probability distributions,
and power-law decays of the velocity autocorrelations are the basis for this
interpretation. Almost all results can be explained with a fractional Klein-
Kramers equation allowing the quantitative classification of cell migration by
a few parameters. Thereby it discloses the influence and relative importance of
individual components of the cellular migration apparatus to the behavior of
the cell as a whole.
