Calculation of Equilibrium Compositions of Large Systems of Biochemical Reactions

Abstract

A more global view of the thermodynamics of a system of biochemical reactions can be obtained by specifying concentrations of coenzymes such as adenosine triphosphate and adenosine diphosphate. These calculations are facilitated by use of conservation matrices that can be arranged in such a way that the coenzymes are components. In calculations at specified pH in dilute aqueous solutions, neither hydrogen atoms or oxygen atoms are conserved, and so the applicable conservation matrices are calculated from stoichiometric number matrices that omit the stoichiometric numbers for H2O. For a system of biochemical reactions, the number of components is generally greater than the number of elements other than hydrogen and oxygen because of constraints that arise in the mechanisms of the enzyme-catalyzed reactions. When concentrations of coenzymes are specified, the system can be described as being made up of pseudoisomer groups, each made up of one or several reactants. The values of apparent equilibrium constants K‘ ‘ for reactions between the pseudoisomer groups can be calculated if the standard transformed Gibbs energies of formation of the reactants are known at the desired pH or the apparent equilibrium constants K‘ are all known. These concepts and equations are applied to glycolysis plus the citric acid cycle, and it is shown that quantitative thermodynamic calculations can be made by working with 7 reactants, rather than 32, and 5 reactions, rather than 20.