Solvation Effect on the Equilibrium Constants

The three fundamental parameters K, h and Tj that determine the indirect cooperativity are essentially equilibrium constants, corresponding to three well-defined processes. In this section we explore the modification that we are required to make in these parameters when the same processes are carried out in a solvent. See, for example. Chapters 2 and 8 in Ben-Naim (1992). 

We begin with a general process leading from an initial (/) to a final (/) state 

By applying the general cyclic process of Fig. 9.1 to this process, we obtain the modified equilibrium constant 

We should also note that if the two binding sites are identical, then q as well as jj are the same, whether the ligand binds to the first or to the second site. Therefore, we have only one parameter h defined in Eq. (9.2.10). When a solvent is present, and q, and hence also h, might be modified differently for the first and for the second site. For the second site the process (9.2.7) is replaced by 

The specific processes discussed above are all special cases of the general process (9.2.1). In all of these cases we have seen the explicit modification of the equilibrium constant of the corresponding process. As indicated in Eq. (9.2.3), the general modification requires knowledge of the solvation Gibbs energies of all the components involved in the process. For macromolecules such as proteins or nucleic acid, none of these is known, however. Nevertheless, some specific solvation effects are examined in Sections 9.4 and 9.5. 

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