Universal energy accuracy tradeoffs in nonequilibrium cellular sensing

We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can detect external concentrations. We show that if estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming non-equilibrium receptor that can be divided into signaling and non-signaling states can outperform an equilibrium two-state receptor. Moreover, we derive an energy accuracy tradeoff for such general non-equilibrium receptors when the estimation is performed by a simple observer of the duration the receptor is in signaling states. This tradeoff reveals that the simple observer can only attain the performance of the ideal observer in the limit of large receptor energy consumption and size. Our results generalize the classic 1977 Berg-Purcell limit on cellular sensing along multiple dimensions, and yield a novel thermodynamic uncertainty relation for the time a physical system spends in a pool of states.

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