Inverse Legendre Transform in Biochemical Thermodynamics: Illustrated with the Last Five Reactions of Glycolysis

Abstract

Legendre transforms are needed to introduce intensive variables into the description of thermodynamic systems. But when experimental thermodynamic data involve an inconveniently large number of intensive variables, inverse Legendre transforms are needed to reduce the number of independent intensive variables. This is illustrated by the elimination of pH in the calculation of standard Gibbs energies of formation of species from apparent equilibrium constants of enzyme-catalyzed reactions. Apparent equilibrium constants have been determined for about 500 enzyme-catalyzed reactions involving about 1000 different reactants at various pHs and ionic strengths. However, these apparent equilibrium constants cannot be compared directly with each other because of differences in pH and ionic strength. More than one pathway can be used to calculate standard Gibbs energies of formation of the species involved. This discussion of inverse Legendre transforms provides guidance on how to write computer programs to elimina...