Generalized Haldane equation and fluctuation theorem in the steady-state cycle kinetics of single enzymes

Enyzme kinetics are cyclic. We study a Markov renewal process model of single-enzyme turnover in nonequilibrium steady state (NESS) with sustained concentrations for substrates and products. We show that the forward and backward cycle times have identical nonexponential distributions: ₊(t)=_–(t). This equation generalizes the Haldane relation in reversible enzyme kinetics. In terms of the probabilities for the forward (p₊) and backward (p_–) cycles, k_BT  ln(p₊/p_–) is shown to be the chemical driving force of the NESS, µ. More interestingly, the moment generating function of the stochastic number of substrate cycle (t), e^–(t), follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When =µ/k_BT, we obtain the Jarzynski-Hatano-Sasa-type equality e^{–(t)µ/k_BT} 1 for all t, where µ is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force in situ from turnover data via single-molecule enzymology.

©2006 The American Physical Society