Chemistry Reference
In-Depth Information
where the subscript 2 on the final ensemble averages indicate the average number
of cosolvent or solvent molecules in the local vicinity of the solute. The value of the
preferential binding parameter is therefore a measure of changes in the local distribu-
tion of the cosolvent and water surrounding the protein solute. Positive values occur
when the cosolvent/solvent ratio in the vicinity of the protein exceeds that of the bulk
solvent (
m
3
), and vice versa. This includes both direct binding of the cosolvent to the
protein, together with any possible changes in the cosolvent and solvent distributions
at larger distances from the protein surface. In Section 1.3.8 and Chapter 11, the
preferential binding parameter will be used to rationalize the thermodynamics of
cosolvent-induced protein denaturation. Other measures of preferential interactions,
in a variety of semiopen ensembles, have been used to help rationalize cosolvent
effects on biomolecules, and are summarized by Smith (Smith 2006a).
A third illustration of the use of FST for open systems involves the effects of
cosolvents or additives on the solubility of a solute in a solvent. If one follows the
solute solubility curve, at a fixed temperature and pressure, then the chemical poten-
tial of the solute at saturation remains constant as it is in equilibrium with the solid
solute. Hence, the effect of an additive on the molar solute solubility (
S
2
) can be
expressed in terms of derivatives of this curve taken at constant
T
,
p
, and μ
2
. Using
these constraints in Equation 1.43 and taking the appropriate derivatives, one imme-
diately finds (Smith and Mazo 2008)
∂
ln
S
−
+−
G
G
NN
2
23
21
=
(1.88)
∂
ρ
1
3
33
13
Tp
,,
µ
2
for any concentration of solute, solvent, and additive. We note, however, that other
expressions in closed ensembles have also been used (see Chapters 9 and 10).
1.3.6 e
lecTrolyTe
s
oluTions
The application of FST to electrolyte solutions has received considerable interest.
It is generally assumed that the average number of cations surrounding an anion in
solution must be such that charge neutrality is obeyed for the local region (Kusalik
and Patey 1987). The resulting relationships are known as the
electroneutrality con-
ditions
and can be written in terms of the KBIs as follows:
zzGz
+
ρ
+
ρ
G
=
0
+
+
+++
−
−+−
zzGz
+
ρ
+
ρ
G
=
0
−
−
−−−
+
++−
(1.89)
z
ρ
Gz
+
ρ
G
=
0
+
+++
i
−− −
i
ν
z
+
ν
z
=
0
++
−−
for a salt (
M
z z
νν
+
−
) that generates a total of ν ions containing ν
+
and ν
-
cations and
anions in solution with charges of
z
+
and
z
-
, respectively, and where the index
i
refers
+
−
