Information Gain Limit of Biomolecular Computation

Biomolecules stochastically occupy different configurations that correspond to distinct functional states. Changing biochemical inputs such as rate constants alters the output probability distribution of configurations, and thus constitutes a form of computation. In the cell, such computations are often coupled to thermodynamic forces such as ATP hydrolysis that drive systems far from equilibrium, resulting in energy expenditure even during times when computations are not being performed. The information-theoretic advantage of this costly computational paradigm is unclear. Here we introduce a theoretical framework showing how much the thermodynamic force enables changes in probability distributions, quantified by the information gain, beyond what is possible at equilibrium. Using this framework, we derive a general expression relating the force to the maximum information gain in an arbitrary computation, revealing how small input changes can exponentially alter outputs. We numerically show that biomolecular systems can closely approach this universal bound, illustrating how energy expenditure is needed to achieve the information processing capabilities observed in nature.