Multiple ligand binding sites independent

Figure 3.3 Kinetics of four site ligand binding curves (1) to (5) represent the zero-, mono-, di-, tri- and fully liganded tetramers. Curve (6) represents the total concentration of liganded sites, (a) is based on the reaction of identical and independent sites with statistical multiplication factors (see p. 68) given to the intrinsic rate constant it = Is , (b) is based on a cooperative system (identical sites) with intrinsic rate constants of 0.04 for the first step and 1.0 for the subsequent three steps of ligand binding. In this graph lines 2,3 and 4 are omitted because they all straddle the baseline.

In the above expression, n gives the number of ligands bound to one protein molecule (stoichiometry). Scatchard plots consider multiple binding sites as noncooperative (equivalent and independent) for the calculation of K. However, this linearization is not really necessary in the age of computer-based curve fitting, and in fact it is somewhat problematic because the ordinate and abscissa are not independent. Figure 15.15 provides an example where a nonlinear least-squares fit was used instead of linearization. 

The first case of multiple-site bindings involves a biomacromolecule with n equivalent sites (each of the n sites has the same affinity, K for the ligand) and the binding is non-cooperative (each of the n sites is noninteracting/independent). Consideration of the stereochemistry of the bounded A for n equivalent sites suggests that there are... 

For the case of multiple-site bindings involving a biomacromolecule with n nonequivalent, but not interacting/cooperative sites, the macromolecule is considered to display m classes of independent sites (n > m > 1), each class i (1 < i < m) having Uj sites with an intrinsic binding constant, Ki (Klotz and Hunston, 1971). The total number of sites occupied by a ligand per macromolecule will simply be the sum of the number of sites of each class occupied per macromolecule ([A] will be written simply as A for the clarity here), i.e. ... 

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