Migration of immune cells is believed to be optimized in the course of evolution to reduce their search time. Nevertheless, so far the optimality of the search for pathogens and other targets by immune cells has not been verified. Mediated by retrograde actin flows, the speed of migrating cells is coupled to their directional persistence in such a way that they decelerate to change the direction of motion. We prove that the coupling between directional persistence and migration speed enables dendritic cells to search for pathogens more efficiently. A new class of random search optimization problems is introduced by minimizing the mean first-passage time (MFPT) with respect to the strength of the coupling between influential parameters. An analytical expression for the MFPT in a confined geometry has been derived which verifies that the correlated motion enhances the search efficiency if the mean persistence length is sufficiently shorter than the confinement size. Our correlated search optimization approach provides an efficient searching recipe and predictive power in a broad range of correlated stochastic processes.
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