Numerical analysis of homogeneous and inhomogeneous intermittent search strategies

TL;DR

This paper analyzes the efficiency of homogeneous and inhomogeneous intermittent search strategies in various search problems, demonstrating that spatially inhomogeneous strategies often outperform homogeneous ones in terms of mean first-passage time.

Contribution

The study introduces and evaluates spatially inhomogeneous search strategies, inspired by cellular structures, showing their potential for significantly improved search efficiency over homogeneous strategies.

Findings

Inhomogeneous strategies often outperform homogeneous ones in search efficiency.

Spatial dependence of transition rates enhances search performance.

Application to biological contexts like cellular transport.

Abstract

A random search is a stochastic process representing the random motion of a particle (denoted as the searcher) that is terminated when it reaches (detects) a target particle or area the first time. In intermittent search the random motion alternates between two or more motility modes, one of which is non-detecting. An example is the slow diffusive motion as the detecting mode and fast, directed ballistic motion as the non-detecting mode, which can lead to much faster detection than a purely diffusive search. The transition rate between the diffusive and the ballistic mode (and back) together with the probability distribution of directions for the ballistic motion defines a search strategy. If these transition rates and/or probability distributions depend on the spatial coordinates within the search domain it is a spatially inhomogeneous search strategy, if both are constant, it is a homogeneous one. Here we study the efficiency, measured in terms of the mean first-passage time, of spatially homogeneous and inhomogeneous search strategies for three paradigmatic search problems: 1) the narrow escape problem, where the searcher has to find a small area on the boundary of the search domain, 2) reaction kinetics, which involves the detection of an immobile target in the interior of a search domain, and 3) the reaction-escape problem, where the searcher first needs to find a diffusive target before it can escape through a narrow region on the boundary. Using families of spatially inhomogeneous search strategies, partially motivated by the spatial organization of the cytoskeleton in living cells with a centrosome, we show that they can be made almost always more efficient than homogeneous strategies.