From random to directed motion: Understanding chemotaxis in E. Coli within a simplified model

The bacterium E.Coli swims in a zig-zag manner, in a series of straight runs and tumbles occurring alternately, with the run-durations dependent on the local spatial gradient of chemo-attractants/repellants. This enables the organism to move towards nutrient sources and move away from toxins. The signal transduction network of E.Coli has been well-characterized, and theoretical modeling has been used, with some success, in understanding its many remarkable features, including the near-perfect adaptation to spatially uniform stimulus. We study a reduced form of this network, with 3 methylation states for the receptor instead of 5. We derive an analytical form of the response function of the tumbling rate and use it to compute the drift velocity of the bacterium in the presence of a weak spatial attractant gradient.