Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation*

Many organisms navigate the environment by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles as attractant signal increases. This induces a feedback between motion and sensation where the current tumble rate affects future signals. Previous studies have used mean field theory, assuming small fluctuations in the internal state that passes signaling information to the motor. Here we discover a new dynamical regime where this assumption breaks down, showing large fluctuations driven by the feedback. We demonstrate how these large fluctuations emerge from transient growths caused by non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the feedback. We further identify a nonlinearity that aymmetrically amplifies this effect. This elongates runs up-gradient and truncates those down-gradient, resulting in "ratchet-like" swimming behavior. Our results thus show that the classical drawback of run-and-tumble navigation -- wasteful runs in the wrong direction -- can be mitigated by exploiting fluctuations and non-normal dynamics implicit in the run-and-tumble strategy.