chemotaxis*

The bacteria Escherichia coli climbs shallow gradients by tumbling - randomly reorienting their directed runs - when they sense they are moving away from chemical attractants. In the absence of any information from their receptors E. coli would be unable to move in a directed fashion, moving stochastically by runs and tumbles with an effective long-scale diffusion constant D. Here we show that to climb a gradient with average speed V requires a transfer entropy rate, I, from direction of motion, through receptor activity, and ultimately to tumbling behavior of at least I = V²/2D. This provides a lower bound on the requirements of the signaling cascade that can be inferred from single bacteria trajectories. We discuss how this bound constrains the design of the receptor and signaling system.