Connection between the Bacterial Chemotactic Network and Optimal Filtering

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers binary whether it swimming up or down along exponential ligand gradient from noisy signals. Then show standard biochemical model mathematically equivalent to information-theoretically dynamics. Moreover, demonstrate experimentally observed nonlinear response relation can be reproduced These results suggest chemotaxis designed extract in condition.