How Macromolecules Associate

In considering such equilibria we must first examine the individual interactions of different domains of a protein, one with another. These can be described by 

The extent of binding of a molecule X to another molecule P (Eqs. 7-1, 7-2) is measured by varying the concentrations of X and P and observing changes in the concentration of the complex [PX]. The first 

The property being measured (AA) reaches a maximum value AAmax at saturation and when all of compound P has been converted to PX. The ratio of [PX] to the total concentration of all forms of P present [Pit is known as the saturation fraction and is often given the symbol Y. If P has more than one binding site for X, Y is defined as the fraction of the total binding sites occupied. If n is the number of sites per molecule, the total number of sites is n[P], The value of Y is often taken as AA / AAmax, an equality that holds for multisite macromolecules only if the change in A is the same for each successive molecule of X added. This is not always true, but when it is Eq. 7-3 is followed. 

Here i represents the number of ligands X bound to P and may vary from 0 to n. When n = 1 the saturation fraction Y and AA are related to the concentration of free unbound X and the formation constant as follows  

This kind of plot is sometimes called an adsorption isotherm because it describes binding only at a constant temperature. Notice, from both Fig. 7-1 and Eq. 7-4, 

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