Definition of the Average Correlation in Any Binding System

It is assumed that we have experimental data on the binding isotherm of a system known to consist of m binding sites. We denote by the average number 

If the system is known to have m identical sites, either in a strict or in a weak sense, then K.J. = mk, where k is the intrinsic binding constant. On the other hand, if we know that the system has m different binding sites, each having a different intrinsic binding constant k, then we must determine each of these from the limiting slope of the corresponding individual BI, i.e.. 

The first, 7(0, can be determined from the experimental data for any finite value of C. The second, 7, 0, may be interpreted as the same integral 7(0, but computed for a hypothetical system of independent sites. As we shall see below, this interpretation is somewhat risky and should be avoided. The function 7,.(Q is better viewed as defined in Eq. (5.8.10), with the binding constants determined in Eq. (5.8.8). 

In terms of the two functions 7(0 and I C) and the intrinsic binding constants we define the quantity 

We now show that for any finite value of C, the quantity g(0 is a proper average of the correlations in the system. Note that g C) can be determined directly from the experimental data. The units of the concentration C should be the same as those of (A ) hence Ck is a dimensionless quantity. 

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