DEGREES OF FREEDOM IN BIOCHEMICAL REACTION SYSTEMS AT SPECIFIED PH AND PMG

When pH and pMg are specified for a biochemical reaction system, thermodynamic properties are described in terms of transformed thermodynamic properties. Under these conditions, chemical reactions am written in terms of sums of species, so that the stoichiometric number matrix nu for the reaction system is replaced by an apparent stoichiometric number matrix nu' and the conservation matrix A is replaced by an apparent conservation matrix A'. The number N of species in a biochemical reaction system may be very large because a reactant like ATP exists as an equilibrium mixture of species. Under certain conditions. ATP exists as ATP4-, HATP3-, H2ATP2-, MgATP2-, MgHATP-, and Mg2ATP. Thus ATP contributes 1 to the number N' of reactants and 6 to the number N of species. Similarly, the number C' of apparent components is smaller than the number C of components. The equilibrium constants of biochemical reactions are referred to as apparent equilibrium constants K' because they are written in terms of reactants (sums of species) rather than particular species. Apparent equilibrium constants depend on T, P, pH, pMg, and ionic strength. The number F' of apparent degrees of freedom is given by C' - p + 2, where C' is the number of apparent components and p is the number of phases. The criterion of equilibrium at T, P, pH, and pMg is the transformed Gibbs energy G'. The fundamental equation for G' provides the means for calculating the transformed entropy S' and transformed enthalpy H'. There is a Gibbs-Duhem equation written in terms of the transformed entropy S', the transformed chemical potentials mu(Ci') of components, and the amounts n(Ci)' of apparent components in the system. Matrix notation is emphasized because of its utility in treating systems involving many reactions.