Optimal sensing and control of run-and-tumble chemotaxis

TL;DR

This paper develops a fully nonlinear, optimal control strategy for run-and-tumble chemotaxis that accounts for noisy sensing, combining filtering and decision-making theories, and relates it to biological data from E. coli.

Contribution

It introduces a novel, fully nonlinear optimal control framework for chemotaxis that incorporates stochastic sensory noise and links to biological models.

Findings

Derived the optimal filtering and control strategy for noisy chemotactic sensing.

Connected the theoretical model with E. coli's biochemical chemotaxis data.

Demonstrated the framework's potential to analyze chemotactic efficiency and optimality.

Abstract

Run-and-tumble chemotaxis is one of the representative search strategies of an odor source via sensing its spatial gradient. The optimal ways of sensing and control in the run-and-tumble chemotaxis have been analyzed theoretically to elucidate the efficiency of strategies implemented in organisms. However, because of theoretical difficulties, most of attempts have been limited only to either linear or deterministic analysis even though real biological chemotactic systems involve considerable stochasticity and nonlinearity in their sensory processes and controlled responses. In this paper, by combining the theories of optimal filtering and Kullback-Leibler control of partially observed Markov decision process (POMDP), we derive the optimal and fully nonlinear strategy for controlling run-and-tumble motion depending on noisy sensing of ligand gradient. The derived optimal strategy consists of the optimal filtering dynamics to estimate the run-direction from noisy sensory input and the control function to regulate the motor output. We further show that this optimal strategy can be associated naturally with a standard biochemical model and experimental data of the Escherichia coli's chemotaxis. These results demonstrate that our theoretical framework can work as a basis for analyzing the efficiency and optimality of run-and-tumble chemotaxis.