Adair equation generalized

The general Adair equation for the binding of a ligand X to a multisite protein where K represents the thermodynamic macroscopic association constant for the fth site and where n is the total number of sites is... 

Using these assumptions, it is possible to describe the binding of oxygen by four successive binding constants. This is formally equivalent to the Adair equation the KNF model may be considered as a molecular interpretation of that equation. In general, the number of constants required is equal to the number of binding sites, unlike the situation in the MWC model, which always uses three. 

Show that if Kt = X2 = X3 = X4, the four-site Adair equation becomes that of a rectangular hyperbola. Note that the statistical factors in the numerator and denominator of the four-site Adair equation, and in fact in the general n-site equation, are the coefficients of the binomial expansion, i.e., the coefficients of the expansion of (1 — jr)". In the present case with n = 4, Eq. (9.50) applies and... 

This equation is sometimes known as the Adair equation, after the British biophysical chemist Gilbert Smithson Adair. Its general form is as shown in Figure 11.2 at high concentrations of ligand, v n, while at low concentrations v 0. However, equation (11.18) is not useful as it stands, since it would be impossible to evaluate the constants from an experimental curve. To make such an analysis of experimental results, some special cases must be considered. 

Hemoglobin Structure-Function Relationship by the Use of the Generalized Adair Equation... 

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