Binding Thermodynamics and Correlation Functions

As in previous sections, we can define the Helmholtz energy change for binding the first, second, third, and fourth ligand and the corresponding intrinsic binding constants. Pair, triplet, and quadruplet correlation functions can also be defined for this model. 

We shall very briefiy present the definitions of these quantities. We use a shorthand notation whenever possible. For instance, we shall use 2(1) rather than the more detailed notation 2(U 0, 0, 0) as we have done in previous sections. Thus the intrinsic binding constants and the corresponding Helmholtz energy changes for binding the zth ligand are 

With these definitions, we can write the binding isotherm for this model as 

If we denote by Ki the thermodynamic equilibrium constant for binding the zth ligand as in section 2.9.1, we obtain the relation between the two sets of quantities  

In order to obtain relations between the various AT/, we introduce the following correlation functions. The correlation functions between / ligands on a polymer where there are exactly i ligands on i specific sites are 

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