A bacterium in a drop of water is looking for food. Around it, there's a chemical gradient: more food molecules on one side, fewer on the other. How should it move to reach the tasty spot fastest? It could steer smoothly, like a cyclist dodging a puddle. Or, like a bacterium, it could periodically stop, tumble, and swim off in a random direction.
Scientists asked: why did bacteria choose the second, seemingly clumsy approach? They modeled the search as a problem: what's the fastest way to climb a gradient if you only get a limited amount of directional information per unit time? It turns out that without precise knowledge of which way to turn, discrete actions, jerks and tumbles, beat smooth steering. When information is scarce, it pays to turn around 180 degrees: if you were heading the wrong way, you quickly get back. With more information, full tumbles with a random new direction are optimal. And with even more data, turning at a few fixed angles becomes the best strategy.
This result isn't just about microbes. It shows how nature often picks simple, discrete solutions even though the underlying physics is continuous. The bacterium doesn't compute a perfect trajectory; it follows a simple rule: "swim until things get worse, then tumble." And such a rule turns out to be nearly optimal for life in murky water.
as written by the authors arXiv:2602.23324
Navigation up a smooth sensory gradient is one of the simplest behavioural tasks, and some organisms solve it by making continuous adjustments to their course. Bacteria instead employ a variety of discrete strategies, including run and tumble motion, direction reversals, and turns by specific angles. Here we ask what drives the choice of these strategies, framing the problem as maximising up-gradient speed with a given amount of sensory information per unit time. We find that, without directional information on which way to turn, behavioural strategies that take discrete actions perform better than gradual steering. As the amount of information is increased, we see a series of transitions between optimal strategies, including a shift from direction reversals to fully re-orienting tumbles. Among more complex re-orientation strategies, we show that discrete turn angles are best, and observe transitions in the number of angles employed by the optimal strategy. More broadly, such emergent simplicity in behaviour is a tractable example of a widespread phenomenon in which biology chooses a discrete solution, despite the underlying physics being continuous.
When searching for food, E. coli tumbles about once per second, and each tumble changes its direction by a random angle.