Chemistry Reference
In-Depth Information
This traditional interpretation of the
m
-values, however, is based upon an unrealis-
tic assumption. Experiments suggest that denatured states make compact structures,
even in the presence of highly concentrated denaturants (Klein-Seetharaman et al.
2002). Therefore, the fully extended unfolded structures, which have been assumed
in the previous models do not reflect reality. In addition, size-exclusion chromatog-
raphy has cast doubts upon the correlation between the
m
-value and the expansion
in size of proteins upon denaturation (Wrabl and Shortle 1999). This suggests that
the SASA proportionality of the
m
-values may not be an accurate assumption. We
therefore need a better theory. FST can fill this gap (Shimizu and Boon 2004).
FST analysis of protein denaturation requires two sets of input data: the cosolvent-
induced equilibrium shift and the change of partial molar volume. The former can be
calculated from the
m
-value by (Shimizu and Boon 2004),
o
o
∂
∆
r
G
c
c
c
∂
∂
µ
∂
∆
r
G
3
1
3
3
m
=−
=
(11.9)
∂
c
∂
µ
3
1
T
pm
,
→
0
Tpm
,,
→
0
Tpm
,,
→
0
3
3
3
for infinitely dilute solutes. This converts the experimental
m
-values so they conform
to the language of FST. Equation 11.2 and Equation 11.4 can now be solved to yield
the excess coordination numbers.
Although
m
-values have been measured extensively for GuHCl and urea, the par-
tial molar volume change accompanying the denaturation process has rarely been
measured. GuHCl denaturation of hen egg lysozyme (
m
= 10.445 kJ/mol/M and
Δ
V
2
= -55 ml/mol) and tendamistat (
m
= 4.62 kJ/mol/M and Δ
V
2
= -41.2 ml/mol) are
the rare data available for the monomeric systems with two-state folding equilibria,
which report Δ
V
2
over a wide denaturant concentration range (Sasahara, Sakurai, and
Nitta 1999, 2001; Pappenberger et al. 2000). The concentration dependence of Δ
V
2
in
both cases has been reported to be negligible.
Traditionally, biophysicists have always been interested in obtaining the contri-
bution from the first solvation shell. This requires the estimation of Δ
V
E
for protein
denaturation. Unfortunately, it is difficult to determine the excluded volume for the
denatured state structures with sufficient accuracy. This is because the denatured
state consists of an enormous number of possible configurations. Therefore, an accu-
rate evaluation of excluded volume for such an ensemble is prohibitive at this stage
(Shimizu and Boon 2004). Therefore, we are forced to make a bold approxima-
tion by using an empirical model proposed by Chalikian and Filfil (2003) for this
purpose. Their model estimates the
V
E
for the denatured states from the molecular
weight of the protein and the degree of unfolding (α = 0 corresponds to the native
state, and α = 1 to the fully extended structure). The value of α for lysozyme has
been estimated to be similar to acid denaturation, namely α = 0.7-0.8. Therefore, we
use α = 0.75±0.05 for lysozyme (Chalikian and Filfil 2003; Shimizu and Boon 2004).
Figure 11.6 shows the FST-based analysis of GuHCl-denaturation of lysozyme. At
lower GuHCl concentration, the denaturant-induced equilibrium shift -∂Δ
r
G
o
/∂μ
3
is
determined predominantly by Δ
N
23
. As the concentration increases, the contribution
from the protein-water interaction becomes more important. Combining this with
Equation 11.2 and Equation 11.9, one can show that Δ
N
21
must have the opposite sign
