Components and coupling in enzyme-catalyzed reactions

Many enzyme-catalyzed reactions involve coupling of two or more reactions that could otherwise be catalyzed separately. When biochemical reactions are coupled, the equilibrium composition is very different from that when the reactions are not coupled. The number of components in a chemical reaction is equal to the number of independent conservation equations for atoms of elements, but the number of components in an enzyme-catalyzed reaction that is coupled is larger than the number of independent conservation equations for atoms of elements. The investigation of these additional conservation equations by use of linear algebra is complicated by the fact that in dilute aqueous solutions, the activity of water is taken to be unity. This causes an incompatibility of conservation matrices and stoichiometric number matrices that can be avoided by use of the further transformed Gibbs energy G' ' that provides the criterion for spontaneous change and equilibrium when the standard transformed Gibbs energy of water is constant. In the most striking example discussed, the enzyme mechanism of a ligase reaction introduces three constraints in addition to conservation of atoms of elements. This is completely unheard of in chemical reaction thermodynamics.