The determination of thermodynamic allosteric parameters of an enzyme undergoing steady-state turnover

The free energy description of protein-ligand and ligand-ligand interactions, originally proposed by Weber [Weber, G., Biochemistry 11, 864-878 (1972)] is applied to allosteric enzymes. The free energy of interaction between an allosteric ligand and the substrate can be obtained from the ratio of Michaelis constants at zero and saturating concentrations of allosteric ligand even if the "rapid equilibrium" assumption does not apply to the substrate. It is only necessary that the allosteric ligand achieve equilibrium with the various enzyme forms of the steady state. All allosteric mechanisms can be described by combination of three basic types of constants: dissociation (or Michaelis) constants of each ligand (or substrate) from free enzyme, fractional influence of each modifier on maximal velocity, and the free energy of interaction between various combinations of ligands simultaneously bound to the enzyme. A single free energy of interaction appears in the rate expression for a single substrate-single modifier system. Four parameters completely describe the interactions of a single substrate-double modifier system from which the free energy interaction between all possible combinations of ligands can be derived. Suggestions are made for the graphical estimation of these allosteric parameters. Application of this approach to more complex systems involving cooperativity or multiple allosteric interactions is discussed and compared to evaluating allosteric enzymes with more conventional "two-state" approaches.