Protein interactions with small molecules. Relationships between stoichiometric binding constants, site binding constants, and empirical binding parameters

Abstract

The multiple equilibria for the binding of a ligand A by a macromolecule P with n binding sites may be formulated in terms of a stoichiometric analysis or on the basis of a site-oriented scrutiny. The dependence of binding on ligand concentration can always be correlated in terms of n stoichiometric binding constants,Ki, even if there are interactions between sites that accentuate or attenuate binding affinities. A corresponding correlation in terms of site binding constants, kj, under the most general circumstances depends on the definition of n2n-1 different constants of which 2n-1 are independent. If experimental data are correlated in terms of n parameters kalpha, kbeta ... klambda in an equation of the site-binding form, (see article for formular) then there is no guarantee that the values of ka, kb, etc., have any unique relationships to site binging constants. Examples are given to illustrate this point. Equation are derived for relating stoichiometric binding constants to site binding constants, for the general case and for various special circumstances. These equations make it possible to define and analyze binding insystems with interactions and conformational accommodations. Accordingly, a graphical procedure is described (in which iKi is plotted against i, the stoichiometric binding step) that provides an affinity profile for concise representation of magnitudes of binding constants and for detecting interactions that accentuate or attenuate site binding affinities.