A Gallavotti-Cohen-Type Symmetry in the Steady-state Kinetics of Single Enzyme Turnover Reactions

Abstract

We study a Markov renewal model for the turnover kinetics of single-enzyme reactions $A+E$ $\rightleftharpoons$ $...$ $\rightleftharpoons$ $B+E$ in steady-state with sustained concentrations for substrate $A$ and product $B$. We introduce the exponential average, $$, for the net number of turnovers $\nu(t)$ and show that it exhibits a Gallavotti-Cohen-type symmetry discovered by Kurchan, Lebowitz and Spohn. When $\lambda = \Delta\mu$, the nonequilibrium chemical driving force, we obtain the Jarzynski-type equality: $$ $\equiv$ 1. These results provide a useful method to experimentally determine the thermodynamic free energy from turnover data in single-molecule enzymology and the possibility of a direct verification of the stochastic theory of nonequilibrium steady-state.