Nonequilibrium steady state of a nanometric biochemical system: Determining the thermodynamic driving force from single enzyme turnover time traces

A single enzyme molecule in a living cell is a nanometric system that catalyzes biochemical reactions in a nonequilibrium steady-state condition. The chemical driving force, Delta mu, is an important thermodynamic quantity that determines the extent to which the reaction system is away from equilibrium. Here we show that Delta mu for an enzymatic reaction in situ can be determined from the nonequilibrium time traces for enzymatic turnovers of individual enzyme molecules, which can now be recorded experimentally by single-molecule techniques. Three different Delta mu estimators are presented from principles of nonequilibrium statistical mechanics: fluctuation theorem, Kawasaki identity, and fluctuation dissipation theorem, respectively. In particular, a maximum likelihood estimation method of Delta mu has been derived based on fluctuation theorem. The statistical precisions of these three Delta mu estimators are analyzed and compared for experimental time traces with finite lengths.