Information efficiency of bacterial chemotaxis

Information transfer is central to the function of many biological systems. For example, the bacteria Escherichia coli climbs gradients of chemical attractants by modulating its rate of tumbling—randomly reorienting its swimming direction—when it senses time-changes in attractant concentration. But even in the absence of signal processing, the cell’s tumble behavior is correlated with the signal it sees. The transfer entropy rate I_φ→M from signal to tumble behavior removes these correlations and isolates the causal influence of the signal on the cell’s tumble decisions. We show that climbing a gradient with drift speed v_D requires an information rate of at least I_φ→M = 12 D_r (v_D/v₀)² (1-TB), where D_r is the rate of rotational diffusion, v₀ is the run speed, and TB is the fraction of time the cell is tumbling. To quantify E. coli cells' information rates, we measure, in single cells, signal transduction responses and fluctuations. Along with measurements of drift speeds, we determine how efficiently E. coli use information about the gradient during chemotaxis.