Calculation of equilibrium compositions of biochemical reaction systems involving water as a reactant

In the thermodynamic treatment of reactions involving water as a reactant in dilute aqueous solutions, the activity of water is taken as unity in expressions for equilibrium constants, but the calculation of equilibrium constants using tables involves the standard Gibbs energy of formation of water. This convention, which is quite satisfactory for simple systems, causes problems in the thermodynamics of biochemical reaction systems in dilute aqueous solutions. One reason is that the identification of components in these systems is very important, and this involves the use of conservation matrixes and stoichiometric number matrixes. These matrixes can be interconverted, and this is especially useful in computer programs for calculating equilibrium compositions. When water is a reactant in a system of reactions, there is a sense in which oxygen atoms are not conserved because they can be brought into reactants or expelled from reactants without altering the activity of water in the solution. These problems can be avoided by using a Legendre transform to define a further transformed Gibbs energy that provides the criterion for spontaneous change and equilibrium when a(H2O) = 1. The equations that are derived here are illustrated by equilibrium calculations on a system of three enzyme-catalyzed reactions in the citric acid cycle. This system of reactions also illustrates the fact that the mechanisms of enzyme-catalyzed reactions may introduce constraints in addition to element balances.