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experiments. Answer 3 has shown that the basic hypothesis of the OSA is flawed. It
has also clarified what it means to be excluded using a rigorous approach based upon
radial distribution functions (Shimizu 2004).
The subsequent resolution of the debate regarding OSA has since brought a
wealth of breakthroughs, which will be elaborated upon one by one in the remainder
of this chapter.
11.3
PROTEIN HYDRATION AND ITS MICROSCOPIC MEANING
11.3.1 m
olecular
c
rowding
: T
he
d
ominance
oF
o
smolyTe
e
xclusion
in
o
smoTic
s
Tress
We have seen that FST has finally brought a molecular understanding of biomolecu-
lar solvation in the presence of cosolvents. It has paved a way toward an experimen-
tal determination of the excess coordination numbers. Now, the practical question
is: how can we estimate the change of hydration that accompanies a biomolecular
process? FST provides a clear answer to this question through partial molar volume
measurements, commonly called
volumetric analysis
(Shimizu 2004).
FST provides a clear theoretical framework for the solvation of biomolecules in
pure water. In the absence of osmolytes, the change in partial molar volume of a pro-
tein, provided by Equation 11.4, reduces to (Ben-Naim 1992; Shimizu 2004; Shulgin
and Ruckenstein 2005a; Pierce et al. 2008)
∆
VVN
2
=
∆
(11.5)
1
21
This means that the excess coordination number can directly be obtained from the
partial molar volume measurements.
The excess coordination number obtained via FST consists of two contributions
(Shimizu 2004; Chalikian 2011). The first contribution is the excluded volume,
namely, the contribution from the region into which the solvent molecules cannot
penetrate. The second is the contribution due to the change of water distribution in
the solvation shell. If one is interested in the latter, then the excluded volume contri-
bution should be subtracted out. Admittedly, the estimation of the excluded volume
at present is a rough estimation at best; it nevertheless has provided some useful
insight into biomolecular hydration (Chalikian 2003, 2011). Therefore, I employ the
method proposed by Chalikian and coworkers in the estimation of the excluded vol-
ume
V
E
. This requires the calculation of the following two factors: the first is the
inaccessibility of solvent molecules to biomolecules to intrinsic (core) volume
V
I
; and
the second is thermal volume (volume inaccessible due to thermal motion)
V
T
. The
former is calculated from the van der Waals volumes of the molecule, the second is
estimated from the solvent-accessible surface area. The contribution of the above
two to the excess coordination number is -
c
i
V
E
= -
c
i
(
V
I
+
V
T
). Thus, we obtain the
solvation-shell contribution to the excess hydration number,
∆∆
NNcV V
21
′ =
+
1
(
∆∆
+
)
(11.6)
21
I
T
