We are dealing with a specific binding reaction of an osmolyte to a protein, with stoichiometry n:
As long as we consider just the protein and ignore (or are not aware of) the participation of the ligand, we can just copy Eq. (26.42) to obtain the m value for this reaction f dln(cN0„/cma = m = a(Gpw ~ Gpo)cq 4
In that case, however, the binding of the ligand is included in the preferential interaction A(GPW — Gpo). To unravel these contributions, we first have a quick look at preferential interaction. There are many kinds of preferential interaction parameters (Anderson et al., 2002; Shulgin and Ruckenstein, 2006). The one that is useful for our case is (Schurr et al., 2005)
G°(P!0) = — (GPW — GP°)c° = — XW^W — X' (26.50)
where the excess or deficit in number of waters and osmolyte around the protein is X W = GPWcW and X ° = GP°c°, respectively. To distinguish between general solvation of the protein and events at the binding site, we reserve the symbol m for general solvation and the symbols X W and X ° for the binding site. Equation (26.49) then becomes
We use prime 0 to distinguish the m' value in this equation from the m value in Eq. (26.49), which does not consider the specific binding separately. aX ° equals the stoichiometry n. All terms containing the factor cO in this equation vanish in the region of dilute osmolyte, and @lna°/9lnc° becomes 1. The only term that is significant under such conditions is the aX° term. Thus, the term aX W should also be counted as solvation and we get
The solvation term m"/RT is insignificant at low cO, and thus the binding equilibrium reacts to the presence of osmolyte solely by specific binding. At molar concentrations of cO the solvation term becomes significant and will therefore influence the binding equilibrium.
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