Evaluation of the solvation properties in osmolyte solution requires knowledge of the chemical activities of osmolytes. In uncovering the basis for the observed behavior of osmolytes in solution we first compare the experimental behavior of most protecting osmolytes [represented by Eq. (26.3) along with Table 26.1] with the result of Kirkwood—Buff theory [Eq. (26.28)]. Equation (26.3) can be reformulated to yield where the apparent hydrated volume of the osmolyte Vapp = 1 /c1 replaces the constant c1. Comparison with Eq. (26.28) shows that the apparent hydrated volume equals the difference between osmolyte hydration G^O and osmolyte self-solvation GOO. This means that most osmolytes have a concentration-independent difference G^O — GOO, as pointed out elsewhere (Rosgen et al., 2005). Consequently, any change in preference of the osmolyte for water is balanced by the same change in preference for other osmolyte molecules, and vice versa. Such concentration-independent solvation behavior might be a prerequisite for a compound to be useful as an osmolyte (Rosgen et al., 2005). Compounds such as alcohols, which strongly change their solvation preferences as their concentration increases, are normally not used as osmolytes in living organisms.
Next, we derive expressions for G^O, G^-^, and GOO. These three unknowns are contained in Eqs. (26.28) through (26.30). Solving these equations results in (Rosgen et al., 2007)
for osmolyte hydration (which equals solvation of water by osmolyte for symmetry reasons),
for osmolyte self-solvation, and
for water self-hydration. The term RTk is of the order of 1 ml/mol for aqueous solutions (Lide, 2004) and can therefore be neglected relative to the other contributions, which are shown in Fig. 26.3. Solvation in urea solution (black lines) is very similar for all three kinds of water and osmolyte self-solvation, and their mutual interaction. The small difference among GWW, GW°, and G°° results in the nearly ideal behavior of urea solutions (Rosgen et al, 2004a, 2005, 2007). This can be seen from Eq. (26.28), in which only the ideal term 1/cO remains if the solvation differences are zero. Sorbitol (gray lines in Fig. 26.3) has a much larger spread in its solvation properties. GWW, GW°, and G°° are distinctly different. However, GW° and G°° are nearly parallel, which leads to the first-order behavior mentioned earlier.
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