Quantitative Analysis and Interpretation of Allosteric Behavior
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Even complex allosteric enzymes can be analyzed in a manner guided by the principles of thermodynamic linkage. Apparent coupling parameters between pairs of ligands can be determined regardless of the oligomeric nature of the enzyme. Except in the simplest of cases the associated coupling free energies will be equal to the sum of the individual unique coupling parameters that exist between the multiple binding sites for each ligand. If the coupling free energy is divided by the stoichiometry, the average coupling free energy will be obtained. The overall value will include a contribution from homotropic interactions only if the degree of cooperativity changes in the presence of the other ligand. The sum or average nature of these coupling parameters compromises their utility only to the same extent as does the fact that K 0.5 represents an average dissociation constant. The coupling free energy, even if a composite of more fundamental couplings, still quantitatively describes both the nature and magnitude of the allosteric effect, and as such it provides a means of monitoring how another experimental variable, for example, the introduction of a site-specific mutation, might alter the action of an allosteric ligand. Thus, even without a precise understanding of the individual interactions that comprise the coupling free energy, it provides a model-independent basis for interpreting experiments. One might draw an analogy to the value of the kinetic parameter V/K in a kinetic analysis of a nonallosteric enzyme. Even before (or without) knowing the precise kinetic mechanism for an enzyme, the meaning of V/K is clear, and its evaluation assists in the eventual determination of that mechanism. Other principles of linkage are also useful to keep in mind-in particular, the principle of reciprocity, the principle of the independence of binding affinity and allosteric efficacy, and the principle that ultimately it is the poise of a disproportionation equilibrium, such as Eq. (13), that must be understood. In particular, the properties of the ternary complex are the key to understanding any structural basis for the allosteric function. The ternary complex is too important to leave its true nature to mere presumptions, or worse yet to the seemingly irrelevant ambiguity of a two-state model.
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