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c -1 ∂ln K /∂ln a 1
1
-∆ G 23
2000
0
-2000
FIGURE 11.7 Cosolvent-induced equilibrium shift in the heat denaturation. A comparison
between c 1 -1 ∂ ln K /∂ ln a 1 (black) and -Δ G 23 (meshed) of Equation 11.10. The contribution from
the protein-cosolvent interaction changes (meshed) dominate. (Data from S. Shimizu, 2011,
Molecular Origin of the Cosolvent-Induced Changes in the Thermal Stability of Proteins,
Chemical Physics Letters, 514, 156.)
the protein-cosolvent Kirkwood-Buff (KB) integral change, Δ G 23 , and that the
contribution from protein hydration, Δ G 21 , is negligible. The only exception is
α-chymotripsinogen A in the presence of ribose, which is a weak osmolyte. In all
the other cases, Δ G 21 is negligibly small compared to Δ G 23 for both denaturants and
stabilizers alike. This, again, simplifies Equation 11.10 to Equation 11.7; the latter is
the fundamental equation for the molecular crowding theory, which has been derived
originally via a second virial approximation (Davis-Searles et al. 2001). Indeed, the
molecular crowding theory is a special case of FST, as has repeatedly been demon-
strated (Shimizu and Boon 2004; Shimizu and Matubayasi 2006; Shimizu 2011).
What is even more powerful is that the molecular crowding approximation
(Equation 11.7) is even reasonably valid for chemical denaturation by urea and guani-
dinium ions. The protein-cosolvent interaction thus seems to be a driving force for a
wider range of biochemical processes, including protein-ligand interaction, cosolvent-
induced denaturation, and the cosolvent-induced modulation of thermal denaturation.
11.6
PROTEIN-WATER AND PROTEIN-COSOLVENT INTERACTIONS
11.6.1 T heory
The focus of our discussion so far has been the following: how do cosolvent molecules
modulate biochemical reactions? Any biochemical reaction, by definition, involves
more than two states—such as free and bound states, or unfolded and folded states.
This chapter so far has focused upon the differences in solute-solvent interactions
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