The ability to navigate environmental gradients is often critical for survival. When gradients are shallow or noisy, URLanisms move by alternating straight motion (runs) with random reorientations (tumbles) . Navigation is achieved by transiently reducing the probability to tumble when attractant signal increases. One drawback of this strategy is that occasional runs in the wrong direction reduce progress up the gradient. Here we discovered a positive feedback regime inherent in this strategy that strongly mitigates this problem. In an attractant field, motion up the gradient reduces tumble probability, which further boosts drift up the gradient. This positive feedback can drive large fluctuations in the internal state of URLanism away from its mean, resulting in long runs in favorable directions but short ones otherwise. In this new regime URLanism achieves a "ratchet-like" gradient climbing behavior unexpected from mean field theory, and drift speeds much faster than previously believed possible .
URLanisms 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 URLanism 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 URLanism. 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 .
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The ability to navigate environmental gradients is often critical for survival. When gradients are shallow or noisy, URLanisms move
URLanisms navigate gradients
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motion
motions
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. Navigation is achieved by transiently reducing the probability to tumble when
, transiently suppressing tumbles whenever
R
One drawback of this strategy is that occasional runs in the wrong direction reduce progress up the gradient. Here we discovered a positive feedback regime inherent in this strategy that strongly mitigates this problem. In an attractant field,
This induces a functional coupling between movement and sensation, since tumbling probability is controlled by the internal state of URLanism 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
R
tumble probability, which further boosts
tumbling probability, further boosting
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This
Importantly, such
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of URLanism away from its mean, resulting in long
, 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
R
but short ones otherwise. In this new regime URLanism achieves
and abbreviating others. The result is
R
unexpected from mean field theory, and drift speeds much faster than previously believed possible
with drift speeds that can approach half the maximum run speed of URLanism. 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