Optimality of spatially inhomogeneous search strategies

TL;DR

This paper analyzes how spatially inhomogeneous search strategies, combining diffusion and ballistic motion with position-dependent directions, can minimize search times in biological and physical systems, inspired by cellular cytoskeleton organization.

Contribution

It demonstrates that optimal search efficiency is achieved with a spatially organized directional distribution resembling cellular cytoskeleton arrangements.

Findings

Minimized mean first passage times for standard search problems.

Optimal strategies involve radial and boundary-focused ballistic transport.

Cellular cytoskeleton organization mirrors these optimal search strategies.

Abstract

We consider random search processes alternating stochastically between diffusion and ballistic motion, in which the distribution function of ballistic motion directions varies from point to point in space. The specific space dependence of the directional distribution together with the switching rates between the two modes of motion establishes a spatially inhomogeneous search strategy. We show that the mean first passage times for several standard search problems - narrow escape, reaction partner finding, reaction-escape - can be minimized with a directional distribution that is reminiscent of the spatial organization of the cytoskeleton filaments of cells with a centrosome: radial ballistic transport from center to periphery and back, and ballistic transport in random directions within a concentric shell of thickness $\Delta_{\rm opt}$ along the domain boundary. The results suggest that living cells realize efficient search strategies for various intracellular transport problems economically through a spatial cytoskeleton organization that involves radial microtubules in the central region and only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments.