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coordination numbers. Here, I apply FST to the interpretation of protein folding and
stability, namely, to the conformational changes induced by the presence of cosolvents.
Protein molecules are denatured when denaturants, such as urea or guanidine
hydrochloride, are added to the solution. Even though such an effect of urea has
long been observed, reported, and exploited, a crucial question still remains unan-
swered: how do denaturants affect the stability of proteins? Numerous papers (focus-
ing mainly on urea) have been published to address this question (Timasheff 2002a).
They are based upon two different hypotheses as summarized below.
The first hypothesis states that the breaking of “water structure” by denaturants is
the cause of protein denaturation (Frank and Franks 1968): urea has been assumed
to play a role in reducing “the ability of the hydrocarbon solute to 'make structure'
of water surrounding it.” When the water structure is broken, the hydrophobic effect
is weakened, thereby leading to protein denaturation (Frank and Franks 1968).
The second hypothesis claims that the denaturants preferentially bind to the sur-
face of the proteins (Timasheff 2002a): the larger the surface area, the more denatur-
ant molecules are bound to each protein; the denatured state therefore becomes more
stable than the native state. Both of these proposals have been founded upon primi-
tive and antiquated models of solutions; the lattice theory of solution is the founda-
tion of the water structure breaker hypothesis (Frank and Franks 1968), whereas
the stoichiometric binding model of solvation is the basis of the preferential binding
hypothesis (Schellman 1987; Timasheff 2002a). Consequently, the weak theoretical
foundation had prompted much debate, not only over the validity of these hypoth-
eses, but also over the true meaning of these hypotheses at a molecular level.
Now the introduction of FST to the study of biomolecules has made it possible
to formulate this problem microscopically and to quantify how the binding of dena-
turants can lead to denaturation (Shimizu 2004; Shulgin and Ruckenstein 2005a,
2006b; Smith 2006a; Pierce et al. 2008; Jiao and Smith 2011). The theoretical formu-
lation has already been laid in the previous section. The goal here is to determine the
change in excess coordination numbers and their solvation shell contributions. What
we need for the calculation is the data on denaturant-induced equilibrium shifts and
partial molar volume changes. They can again be obtained from experimental data,
as will be discussed in the following sections.
11.4.2
m
-v
alue
a
nalysis
and
The
F
lucTuaTion
s
oluTion
T
heory
The effectiveness of protein denaturants has long been quantified via the
m
- value,
which is defined as the proportionality constant relating the molar denaturant concen-
tration to the change in free energy upon protein denaturation. In short, the larger the
m
-value, the more susceptible the protein is to denaturation (Myers, Pace, and Scholtz
1995). How then can the
m
-values be interpreted in terms of interactions between
the protein and solvent molecules? Myers et al. demonstrated that the
m
- values are
proportional to the change of solvent-accessible surface area (SASA), which accom-
panies protein denaturation (Myers, Pace, and Scholtz 1995), namely, the change
from its native structure to the fully extended unfolded structures. This means that
the
m
-value reflects the degree of expansion of a protein upon denaturation.
