Universal lower bound on the free-energy cost of molecular measurements

Behavior of information flow near criticality

Recent experiments have indicated that many biological systems self-organize near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains unclear how information transmission depends on the dynamics of the input signal, the distance over which the information needs to be transmitted, and the distance to the critical point. Here we employ stochastic simulations of a driven two-dimensional Ising system and study the instantaneous mutual information and the information transmission rate between a driven input spin and an output spin. The instantaneous mutual information varies nonmonotonically with the temperature but increases monotonically with the correlation time of the input signal. In contrast, there exists not only an optimal temperature but also an optimal finite input correlation time that maximizes the information transmission rate. This global optimum arises from a fundamental trade-off between the need to maximize the frequency of independent input messages, the necessity to respond fast to changes in the input, and the need to respond reliably to these changes. The optimal temperature lies above the critical point but moves toward it as the distance between the input and output spin is increased.

Prediction and Dissipation in Nonequilibrium Molecular Sensors: Conditionally Markovian Channels Driven by Memoryful Environments

Biological sensors must often predict their input while operating under metabolic constraints. However, determining whether or not a particular sensor is evolved or designed to be accurate and efficient is challenging. This arises partly from the functional constraints being at cross purposes and partly since quantifying the prediction performance of even in silico sensors can require prohibitively long simulations, especially when highly complex environments drive sensors out of equilibrium. To circumvent these difficulties, we develop new expressions for the prediction accuracy and thermodynamic costs of the broad class of conditionally Markovian sensors subject to complex, correlated (unifilar hidden semi-Markov) environmental inputs in nonequilibrium steady state. Predictive metrics include the instantaneous memory and the total predictable information (the mutual information between present sensor state and input future), while dissipation metrics include power extracted from the environment and the nonpredictive information rate. Success in deriving these formulae relies on identifying the environment's causal states, the input's minimal sufficient statistics for prediction. Using these formulae, we study large random channels and the simplest nontrivial biological sensor model-that of a Hill molecule, characterized by the number of ligands that bind simultaneously-the sensor's cooperativity. We find that the seemingly impoverished Hill molecule can capture an order of magnitude more predictable information than large random channels.