The role of tumbling frequency and persistence in optimal run-and-tumble chemotaxis

TL;DR

This paper investigates how tumble frequency and directional persistence influence the efficiency of run-and-tumble chemotaxis, revealing optimal strategies and the impact of finite tumble times on navigation performance.

Contribution

It provides a comprehensive analysis of the parameter space for run-and-tumble chemotaxis, identifying optimal persistence and tumble frequency combinations, and explores how species-specific reorientation affects navigation.

Findings

Optimal persistence exists for given tumble frequency.

A continuum of solutions is optimal in the full parameter space.

Finite tumble times influence the selection of persistence strategies.

Abstract

One of simplest examples of navigation found in nature is run-and-tumble chemotaxis. Tumbles reorient cells randomly, and cells can drift toward attractants or away from repellents by biasing the frequency of these events. The post-tumble swimming directions are typically correlated with those prior, as measured by the variance of the reorientation angle distribution. This variance can range from large, in the case of bacteria, to so small that tumble events are imperceptible, as observed in choanoflagellates. This raises the question of optimality: why is such a range of persistence observed in nature? Here we study persistent run-and-tumble dynamics, focusing first on the optimisation of the linearised chemotactic response within the two-dimensional parameter space of tumble frequency and angular persistence. Although an optimal persistence does exist for a given tumble frequency, in the full parameter space there is a continuum of optimal solutions. Introducing finite tumble times that depend on the persistence can change this picture, illuminating one possible method for selecting tumble persistence based on species-specific reorientation dynamics. Moving beyond linear theory we find that optimal chemotactic strengths exist, and that these maximise reaction when swimming in a wrong direction, but have little or no reaction when swimming with even the slightest projection along the chemoattractant gradient.