Optimality of the sensory system of Escherichia coli

Escherichia coli chemotaxis is one of the model systems from which we can obtain insights for understanding the biological sensory system. To realize chemotaxis, an E. coli cell has to detect temporal changes of ligand concentration caused by its motion based on noisy sensing of the ligand in the environment. How efficiently is the sensory system of E. coli designed to infer the dynamically changing environment behind the noise? While several works have analyzed the effect of noise on the signaling pathway and predicted the necessary feature for the sensory system to operate against noise, these analyses relied on the linear response approximation, which may limit the predictive capacity of the model. In this work, we utilize the nonlinear filtering theory to explore the requisite for information acquisition in chemotaxis. First, we derive the optimal dynamics for extracting the necessary information for chemotaxis, i.e., temporal concentration change. Then, we show how the derived dynamics can be linked to a biochemical model of the sensory system of E. coli. Furthermore, we demonstrate that the optimal dynamics obtained can reproduce a nonlinear response relation observed experimentally. These results indicate that the bacterial sensory system may be developed so as to obtain environmental information from a noisy and dynamic signal.