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For navigation, microscopic agents such as biological cells rely on noisysensory input. In cells performing chemotaxis, such noise arises from thestochastic binding of signaling molecules at low concentrations. Usingchemotaxis of sperm cells as application example, we address the classicproblem of chemotaxis towards a single target. We reveal a fundamentalrelationship between the speed of chemotactic steering and the strength ofdirectional fluctuations that result from the amplification of noise in thechemical input signal. This relation implies a trade-off between slow, butreliable, and fast, but less reliable, steering.  By formulating the problem of optimal navigation in the presence of noise asa Markov decision process, we show that dynamic switching between reliable andfast steering substantially increases the probability to find a target, such asthe egg. Intriguingly, this decision making would provide no benefit in theabsence of noise. Instead, decision making is most beneficial, if chemicalsignals are above detection threshold, yet signal-to-noise ratios of gradientmeasurements are low. This situation generically arises at intermediatedistances from a target, where signaling molecules emitted by the target arediluted, thus defining a `noise zone' that cells have to cross.  Our work addresses the intermediate case between well-studied perfectchemotaxis at high signal-to-noise ratios close to a target, and random searchstrategies in the absence of navigation cues, e.g. far away from a target. Ourspecific results provide a rational for the surprising observation of decisionmaking in recent experiments on sea urchin sperm chemotaxis. The general theorydemonstrates how decision making enables chemotactic agents to cope with highlevels of noise in gradient measurements by dynamically adjusting thepersistence length of a biased persistent random walk.

Optimal decision making for sperm chemotaxis in the presence of noise