Mpemba-Like Sensory Withdrawal Effect

Biological sensors rely on the temporal dynamics of ligand concentration for signaling. The sensory performance is bounded by the distinguishability between the sensory state transition dynamics under different environmental protocols. This work presents a comprehensive theory to characterize arbitrary transient sensory dynamics of biological sensors. Here the sensory performance is quantified by the Kullback-Leibler (KL) divergence between the probability distributions of the sensor's stochastic paths. We introduce a novel benchmark to assess a sensor's transient sensory performance arbitrarily far from equilibrium. We identify a counterintuitive phenomenon in multistate sensors: while an initial exposure to high ligand concentration may hinder a sensor's sensitivity towards a future concentration up-shift, certain sensors may show a boost in sensitivity if the initial high concentration exposure is followed by a transient resetting at a low concentration environment. The boosted performance exceeds that of a sensor starting from an initially low concentration environment. This effect, reminiscent of a drug withdrawal effect, can be explained by the Markovian dynamics of the multistate sensor, similar to the Markovian Mpemba effect. Moreover, an exhaustive machine learning study of four-state sensors reveals a tight connection between the sensor's performance and the structure of the Markovian graph of its states. Published by the American Physical Society 2024