Thermodynamics of information transfer between subunits in oligomeric enzymes and kinetic cooperativity. 2. Thermodynamics of kinetic cooperativity.

The principles of structural kinetics allow one to define the thermodynamic conditions that are sufficient to generate a certain type of kinetic behavior. If subunits are loosely coupled, that is if no quaternary constraint exists between them, the kinetic behavior of the polymeric enzyme is qualitatively defined by the behavior of an ideal dimer. The nature and the extent of the kinetic cooperativity are defined by the energy of interaction, delta G rho, between two subunits. This energy of interaction is that of an ideal dimer relative to that of the A2 and B2 states. This thermodynamic formulation of a given type of cooperativity holds whatever the degree of polymerization of the enzyme. Under these conditions of loose coupling between subunits, positive kinetic cooperativity cannot be associated with any sigmoidicity of the rate curve. The range of energy coupling where positive kinetic cooperativity must, of necessity, be observed becomes more and more narrow as the number of subunit interactions is increased. This range, however, is independent of the number of subunits. The same situation is not observed for negative cooperativity which appears to be independent of both the number of subunits and the number of subunit interactions. If the subunits are tightly coupled, that is if quaternary constraints exist between them, three thermodynamic parameters, delta G' rho, delta G lambda, delta G mu, are required to define the nature of kinetic cooperativity. delta G' rho is the free energy of an ideal strained dimer relative to that of strained A2 and B2 states. delta G lambda and delta G mu represent the difference of strain energies between conformations A and B and B and B relative to that existing between conformations A and A. One may determine in the parametric space (delta G' rho, delta G lambda, delta G mu) the boundaries between the sufficient conditions that generate a certain type of cooperativity and the lack of these conditions. The kinetic parameters of the rate equation are not all independent. A number of constraint conditions exist between them which depend upon the subunit design of the polymeric enzyme. The existence of these constraint conditions may be diagnostic of a certain type of subunit interactions.