Abstract
Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and reverse fluxes and free energy for any chemical process operating in a steady state. This relationship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state in dilute solution, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.
Highlights
For a reaction occurring in an isothermal and isobaric system the chemical driving force DG—the Gibbs free energy difference— characterizes how far a chemical reaction is away from equilibrium
If we take a simple bimolecular reaction in a dilute solution k{1 as an example, DG is related to the concentrations of the reactants and products, as well as the equilibrium constant Keq, through the well-known thermodynamic equation
Hill Equation for Catalytic Cycles For the case of a catalytic cycle with J+/J2 equal to the ratio of the forward-to-reverse cycle flux and DG equal to the thermodynamic driving force for the cycle, Equation (4) is identical to the relationship introduced by Hill [2,5,10] and proved by Kohler and Vollmerhaus [11] and by Qian et al [12] for cycles in Markov systems. (See Equations (3.7) and (7.8) in [5].) the relationship between J+/J2 and DG introduced by Hill for linear cycle kinetics is a special case of Equation (4)
Summary
For a reaction occurring in an isothermal and isobaric system the chemical driving force DG—the Gibbs free energy difference— characterizes how far a chemical reaction is away from equilibrium. If we further assume that the law of mass action governs the reaction’s kinetics, the forward and reverse reaction fluxes and equilibrium constant are. For reversible enzyme reactions governed by MichaelisMenten kinetics, both J+ and J2 are complex, nonlinear functions of reactant and substrate concentrations, Equation (4) still holds true. Another nontrivial example of Equation (4) that arises in cycle kinetics in unimolecular systems is due to T.L. Hill [2,3,4,5]. The most significant insight from the present work is that the relation between one-way-fluxes and DG can be established without any supposition on the dynamics of a system
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