Feedback Between Motion and Sensation Provides Nonlinear Boost in Run-and-tumble Navigation

TL;DR

This paper reveals how positive feedback between motion and sensation in run-and-tumble navigation can create nonlinear effects that enhance gradient climbing efficiency, especially through non-normal dynamics and asymmetry in run durations.

Contribution

It demonstrates that positive feedback can dominate in certain conditions, leading to nonlinear transient behaviors that improve navigation performance.

Findings

Positive feedback can lead to large transient fluctuations in internal state.

Non-normal dynamics cause asymmetric run durations, enhancing gradient climbing.

Run-and-tumble navigation can be optimized by exploiting nonlinear feedback effects.

Abstract

Many organisms navigate gradients by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles whenever attractant signal increases. This induces a functional coupling between movement and sensation, since tumbling probability is controlled by the internal state of the organism which, in turn, depends on previous signal levels. Although a negative feedback tends to maintain this internal state close to adapted levels, positive feedback can arise when motion up the gradient reduces tumbling probability, further boosting drift up the gradient. Importantly, such positive feedback can drive large fluctuations in the internal state, complicating analytical approaches. Previous studies focused on what happens when the negative feedback dominates the dynamics. By contrast, we show here that there is a large portion of physiologically-relevant parameter space where the positive feedback can dominate, even when gradients are relatively shallow. We demonstrate how large transients emerge because of non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the positive feedback, and further identify a fundamental nonlinearity that strongly amplifies their effect. Most importantly, this amplification is asymmetric, elongating runs in favorable directions and abbreviating others. The result is a "ratchet-like" gradient climbing behavior with drift speeds that can approach half the maximum run speed of the organism. Our results thus show that the classical drawback of run-and-tumble navigation --- wasteful runs in the wrong direction --- can be mitigated by exploiting the non-normal dynamics implicit in the run-and-tumble strategy.