  Animal cells can sense chemical gradients without moving, and are faced with
the challenge of migrating towards a target despite noisy information on the
target position. Here we discuss optimal search strategies for a chaser that
moves by switching between two phases of motion ("run" and "tumble"),
reorienting itself towards the target during tumble phases, and performing a
persistent random walk during run phases. We show that the chaser average run
time can be adjusted to minimize the target catching time or the spatial
dispersion of the chasers. We obtain analytical results for the catching time
and for the spatial dispersion in the limits of small and large ratios of run
time to tumble time, and scaling laws for the optimal run times. Our findings
have implications for optimal chemotactic strategies in animal cell migration.
