  Migrating cells exhibit various motility patterns, resulting from different
migration mechanisms, cell properties, or cell-environment interactions. The
complexity of cell dynamics is reflected, e.g., in the diversity of the
observed forms of velocity autocorrelation function -- that has been widely
served as a measure of diffusivity and spreading -- . By analyzing the dynamics
of migrating dendritic cells in vitro, we disentangle the contributions of
direction and speed to the velocity autocorrelation. We find that the ability
of cells to maintain their speed or direction of motion is unequal, reflected
in power-law decays of speed and direction autocorrelation functions with
different exponents. The larger power-law exponent of the speed autocorrelation
function indicates that the cells lose their speed memory considerably faster
than the direction memory. Using numerical simulations, we investigate the
influence of speed and direction memories as well as the direction-speed
cross-correlation on the search time of a persistent random walker to find a
randomly located target in confinement. Although the direction memory and
direction-speed coupling play the major roles, we find that the speed
autocorrelation can be also tuned to minimize the search time. Adopting an
optimal speed memory can reduce the search time even up to 10% compared to
uncorrelated spontaneous speeds. Our results suggest that migrating cells can
improve their search efficiency, especially in crowded environments, through
the directional or speed persistence or the speed-direction correlation.
