Binding Helmholtz Energies on First and Second Site, Cooperativity

Binding Helmholtz Energies on First and Second Site, Cooperativity 

We define the process of binding on the first site as the process of bringing G from a fixed position in the vacuum onto a specific site of an empty polymer (see also definitions in section 2.8). Symbolically the process is 

Note that since we are considering a structureless ligand, the partition function of the ligand at a fixed position in the vacuum is unity. The result (3.2.24) is, however, also valid if we include internal partition functions of G but assume that the internal degrees of freedom are unchanged in the process (3.2.33). The result (3.2.34) is formally the same as for the solvation Helmholtz energy of a solute G. (This topic is discussed in Chapter 6.) 

The average in (3.2.34) is taken with the distribution of the two states L and H of the empty polymer, given in Eq. (3.2.2). Here we introduce the subscript (0, 0) to stress the condition that both sites are empty to distinguish this average from the conditional average defined below. 

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