Use of the matrix form of the fundamental equations for transformed gibbs energies of biochemical reaction systems at three levels

The thermodynamics of a biochemical reaction system can be treated at three levels. At level 1 the fundamental equation for the Gibbs energy G is written in terms of species, at level 3 the equilibrium pH is specified and the fundamental equation for the transformed Gibbs energy G' is written in terms of reactants (sums of species), and at level 3 the equilibrium pH and equilibrium concentrations of one or more reactants are specified and the fundamental equation for the further transformed Gibbs energy G" is written in terms of pseudoisomer groups of reactants. At each level it is convenient to use matrix notation because the conservation matrixes A, A', and A" are useful for identifying components and choosing alternate sets of components. These conservation matrixes can also be used to calculate the corresponding stoichiometric number matrixes v, v', and v", which are useful for grouping terms for an independent set of reactions in the fundamental equation. The treatments of reactions at the three levels are similar, and there are mathematical relations between the thermodynamic properties at the three levels. The matrix form of the fundamental equation at each level is useful for identifying the set of properties that have to be specified to describe the extensive state of the system at equilibrium. These variables are used to specify the criterion for spontaneous change and equilibrium The matrix form of the Gibbs-Duhem equation at each level is useful for identifying the set of intensive properties required to describe the intensive state of the system at equilibrium. The total number of degrees of freedom F is the same at all three levels.