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.
Highlights
A wide variety of organisms, from animals to single cells, are capable of searching for odor sources
By comparing the optimality models with the E. coli chemotactic responses measured experimentally [13,17– 21], one can understand how close to the physical limit a cell can perform chemotaxis and whether its biochemical signaling pathway is organized in a reasonable way to achieve efficient chemotaxis
We investigated the connection between the derived optimal strategy and a well-characterized biochemical model of the signaling pathway of E. coli
Summary
A wide variety of organisms, from animals to single cells, are capable of searching for odor sources. By inhibiting tumbles when sensing an increase in ligand concentration and vice versa, E. coli can selectively enhance positive displacement along the gradient’s increasing direction Such a sensory-motor cycle has been theoretically. By comparing the optimality models with the E. coli chemotactic responses measured experimentally [13,17– 21], one can understand how close to the physical limit a cell can perform chemotaxis and whether its biochemical signaling pathway is organized in a reasonable way to achieve efficient chemotaxis. In addition to motor control, previous optimality models have failed to include the nonlinear responses observed (for example, in the biochemical pathway of E. coli chemotaxis [16,21]). They considered only linear responses and derived the optimal strategy in that class by assuming a weak ligand gradient [22–25].
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