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

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