Chemistry Reference
In-Depth Information
understand the protein behavior (Cohn and Edsall 1943; Arakawa and Timasheff 1984,
1985b, 1987; Timasheff and Arakawa 1988; Arakawa, Bhat, and Timasheff 1990; Qu,
Bolen, and Bolen 1998; Bolen 2004; Pace et al. 2004).
The goal of the present part is to establish a relation between: (1) the preferential
solvation (or hydration) of a protein, and (2) the protein solubility in an aqueous
mixed solvent. The relation obtained will be used to predict the protein solubility in
an aqueous solvent in terms of the preferential binding parameter.
The preferential binding parameter Γ
2
(
m
)
can be measured experimentally using
various methods, such as sedimentation (Kuntz Jr. and Kauzmann 1974), dialysis
equilibrium (Timasheff 1998a), vapor pressure osmometry (Cohn and Edsall 1943),
and so forth, and was determined for numerous systems (Casassa and Eisenberg
1964; Wyman 1964; Kuntz Jr. and Kauzmann 1974; Arakawa and Timasheff 1984,
1985b, 1987; Timasheff and Arakawa 1988; Arakawa, Bhat, and Timasheff 1990;
Timasheff 1992, 1993, 1998a; Zhang et al. 1996; Record, Zhang, and Anderson
1998; Courtenay, Capp, and Record 2001; Anderson, Courtenay, and Record 2002;
Felitsky and Record 2004).
The results obtained will be presented as follows: (1) a relation between the pro-
tein solubility and the preferential binding parameter in a binary solvent will be
established; (2) the established relation will be used to derive criteria for the effect
of cosolvents (salting-in or salting-out), and (3) the experimental data for the prefer-
ential binding parameter Γ
2
(
m
)
will be used to predict the protein solubility and the
results obtained will be compared with available experimental data.
Previously (Shulgin and Ruckenstein 2005a), the following expression for the
preferential binding parameter Γ
2
(
c
)
was derived on the basis of the Kirkwood-Buff
theory of ternary solutions,
(
)
++
)
−
( )
++
(
∞
∞
cc
JV JV
ccJc
−
cc
cVV
ccJc
+
13
21
1
112
31
3
1
2
Γ
23
()
c
=
+
(10.45)
(
)
(
)
1
1
11
3
1
1
11
3
where
V
i
∞
is the partial molar volume of component
i
,
V
2
∞
is the partial molar volume of a
protein at infinite dilution in a mixed solvent,
∂
ln γ
1
J
=
lim
11
∂
x
x
→
0
2
1
x
2
∂
ln γ
2
J
=
lim
21
∂
x
x
→
0
2
1
x
2
x
i
is the mole fraction of component
i
, and γ
i
is the activity coefficient of component
i
at a mole fraction scale. It should be noted that the quantities Γ
2
(
c
)
,
V
2
∞
, and
J
21
of
Equation 10.45 depend on the nature of the protein, while all the other ones are related to
the properties of the protein-free mixed solvent.
