To steer or not to steer? Information-limited navigation selects discrete jumps

In order to perform chemotaxis, microscopic organisms use diverse navigation strategies. For example, E. coli perform run-and-tumble motion, while V. cholerae do run-reverse-flick, while some larger organisms implement continuous steering. These qualitatively distinct strategies are implemented by differing mechanical structures, and in different environments, and it is possible that they reflect different mechanical constraints or evolutionary happenstance. Here, we consider a simpler possibility – that given a limited information budget, qualitatively different strategies might be optimal. Under our information theoretic constraint an organism that can measure the direction of the gradient should always perform continuous steering, becoming more accurate as their information rate increases. By contrast, an organism able only to measure the time derivative of concentration should instead alternate straight running with reversals when information is sparse. But as the amount of sensory information available increases, the optimal strategy undergoes a series of transitions to incorporate progressively smaller flicks. These strategies remain discrete for all information rates. Our results could help explain qualitative features of the diverse strategies used by organisms to chemotax.