Dispersion for two classes of random variables: general theory and application to inference of an external ligand concentration by a cell

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 estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg-Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)0006-349510.1016/S0006-3495(77)85544-6] on cellular sensing along multiple dimensions.

Learning nonequilibrium control forces to characterize dynamical phase transitions

Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem, based on importance sampling, cloning, and spectral approximations, have yielded significant insight into nonequilibrium systems but tend to scale poorly with the size of the system, especially near dynamical phase transitions. Here we propose a machine learning algorithm that samples rare trajectories and estimates the associated large deviation functions using a many-body control force by leveraging the flexible function representation provided by deep neural networks, importance sampling in trajectory space, and stochastic optimal control theory. We show that this approach scales to hundreds of interacting particles and remains robust at dynamical phase transitions.

Proof of the finite-time thermodynamic uncertainty relation for steady-state currents

The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a recently conjectured finite-time thermodynamic uncertainty relation for steady-state current fluctuations. Our proof is based on a quadratic bound to the large deviation rate function for currents in the limit of a large ensemble of many copies.

Optimal inference strategies and their implications for the linear noise approximation

We study the information loss of a class of inference strategies that is solely based on time averaging. For an array of independent binary sensors (e.g., receptors, single electron transistors) measuring a weak random signal (e.g., ligand concentration, gate voltage) this information loss is up to 0.5  bit per measurement irrespective of the number of sensors. We derive a condition related to the local detailed balance relation that determines whether or not such a loss of information occurs. Specifically, if the free-energy difference arising from the signal is symmetrically distributed among the forward and backward rates, time integration mechanisms will capture the full information about the signal. As an implication, for the linear noise approximation, we can identify the same loss of information, arising from its inherent simplification of the dynamics.

Dissipation Bounds All Steady-State Current Fluctuations

Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linear-response-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations.