The information gain limit of molecular computation
Biomolecules stochastically occupy different possible configurations with probabilities given by non-equilibrium steady-state distributions. These distributions are determined by the transition rate constants between different configurations. Changing these biochemical parameters (inputs) alters the resulting distributions (outputs), and thus constitutes a form of computation. The information-theoretic advantage of performing computations using non-equilibrium distributions, which require a thermodynamic driving force and thus continual energy expenditure to maintain, is unclear. Here we show how much driving can change probability distributions beyond what is possible at equilibrium. First, we establish a tight limit on how much the driving force can change the probability of observing any configuration of an arbitrary molecular system. We then derive a concise expression relating the driving force to the maximum information gain -- the change in the full probability distribution over configurations -- in any computation, showing how small input changes can exponentially alter outputs. Finally, we numerically show that synthetic systems and Ras signaling can closely approach this bound, illustrating the necessity of energy expenditure to enable the computational capabilities observed in nature.