Optimal sensing and control of run-and-tumble chemotaxis
Kento Nakamura, Tetsuya J. Kobayashi
Abstract
Run-and-tumble chemotaxis is a representative search strategy for odor sources by sensing its spatial gradients. The optimal ways of sensing and control in run-and-tumble chemotaxis have been theoretically analyzed to elucidate the efficiency of the strategies implemented in organisms. However, because of theoretical difficulties, most attempts have been limited 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 study, by combining the theories of optimal filtering and Kullback-Leibler control of a partially observed Markov decision process (POMDP), we derive an optimal and fully nonlinear strategy for controlling run-and-tumble motion depending on the noisy sensing of a ligand gradient. The derived optimal strategy comprises optimal filtering dynamics to estimate the run direction from the noisy sensory input and control function to regulate the motor output. Furthermore, we show that this optimal strategy can be naturally associated with a standard biochemical model and experimental data of the chemotaxis of Escherichia coli. Our results demonstrate that our theoretical framework can be used as a basis for analyzing the efficiency and optimality of run-and-tumble chemotaxis.