Reformulation of thermodynamic systems with aggregation and theoretical methods for the analysis of ligand binding in proteins with monomer-multimer equilibria.

The reformulation of complex thermodynamic systems is a useful tool for their analysis as demonstrated by the theoretical analysis of conformationally mediated cooperativity in a dimeric protein. Many chemical and biochemical systems exhibit monomer-multimer equilibria, behavior not addressed in the original reformulation. A method for reformulating such systems, and the mathematical methods necessary for relating alternative models, are therefore developed. The basic principles of the reformulation are illustrated on homodimeric and heterodimeric systems. The mathematical methods necessary to relate alternative models are then derived from probabilistic considerations. Higher-order models (more interacting subunits) are related to lower-order models (fewer interacting subunits) by a polynomial expansion of the sum of species in the lower-order model to give the sum of species in the higher-order model. Using these methods, the equations describing the ligand binding behavior of a homomeric monomer-dimer system are derived. These methods are also used to relate the two alternative models for cooperativity for a homotetrameric protein; one model where the dimer is the cooperative unit and the other where the tetramer is the cooperative unit.