# Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes Source: [Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes]() Collection index: [llms.txt]() Data updated: 2025-10-23T21:02:26.782Z Authors: Hong Qian, X. Sunney Xie Published: 2005-07-27T22:08:37.000Z ## Abstract 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 idential non-exponential distributions: $\\QQ\_+(t)=\\QQ\_-(t)$. 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, $\\Delta\\mu$. More interestingly, the moment generating function of the stochastic number of substrate cycle $\\nu(t)$, $\$ follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When $\\lambda$ = $\\Delta\\mu/k\_BT$, we obtain the Jarzynski-Hatano-Sasa-type equality: $\$ $\\equiv$ 1 for all $t$, where $\\nu\\Delta\\mu$ is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force {\\it in situ} from turnover data via single-molecule enzymology. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()