Calculation of thermodynamic properties of species of biochemical reactants using the inverse Legendre transform

The determination of apparent equilibrium constants and heats of enzyme-catalyzed reactions provides a way to determine Δ(f)G° and ΔH-f° of species of biochemical reactants. These calculations are more difficult than the calculation of transformed thermodynamic properties from species properties, and they are an application of the inverse Legendre transform. The Δ(f)G° values of species of a reactant can be calculated from an apparent equilibrium constant if the Δ(f)G° values are known for all the species of all the other reactants and the pKs of the reactant of interest are known. The ΔH-f° of species of a reactant can be calculated from the heat of reaction if the ΔH-f° values are known for all species of the other reactants and Δ(f)G° values are known for all species in the reaction. The standard enthalpies of acid dissociation of the reactant of interest are also needed. The inverse Legendre transformation is accomplished by using computer programs to set up the simultaneous equations that involve the ΔH-f° of the species and solving them. Thirty two new species matrixes providing Δ(f)G° values and eight new species matrixes providing ΔH-f° values are calculated. It is the specificity and speed of enzyme-catalyzed reactions that make it possible to determine standard thermodynamic properties of complicated species in aqueous solution that could never have been obtained classically.