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.
Highlights
Chemotaxis, the ability to navigate concentration fields of chemicals, is a ubiquitous feature of the microscopic world
To understand what sets the optimal chemotactic strength, we seek an analytical approach, but since there is no perturbative small parameter we examine instead a Fourier-Hermite expansion of the form p(θ, q) =
In this study we have taken an approach to understanding run-and-tumble chemotaxis based on global parameter optimisation
Summary
Chemotaxis, the ability to navigate concentration fields of chemicals, is a ubiquitous feature of the microscopic world. This is the case in colonies of choanoflagellates [8], within which the flagella beat independently [9] and a reorientation event may arise from slight modulation of the beating of a single flagellum (Fig. 1b) These smaller tumbles, or directionally persistent tumbles, add up to a smoother swimming while still allowing navigation. Theory [16] and simulation [20] of chemotactic bacteria have showed that for otherwise equal chemotactic parameters, directional persistence of tumbles, as observed in experiments, can lead to enhanced chemotaxis. This raises a more general question: could the effect of changing one parameter, such as directional persistence,.
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