Chemistry Reference
In-Depth Information
with each additional monomer (Hu et al. 2010a). The free energy of solvation (sol)
being defined as
∆
←→
protein
sol
protein
(12.16)
(gas)
(aq)
When we add a cosolvent osmolyte to the system, we obtain a free energy difference
for solvation in osmolyte solution,
∆
←→
protein
os
protein
(12.17)
(gas)
(os)
The difference is the transfer free energy from aqueous to osmolyte solution or
ΔΔ
G
tr
= Δ
G
os
- Δ
G
sol
.
We have found that we can obtain Δ
G
sol
to a precision of about a quarter of a kcal/
mol and can detect slopes in ΔΔ
G
tr
on the order of 10s of cal/mol for entire peptides
as a function of conformation. We have results that demonstrate no calculational
difficulties from pentapeptides (Hu et al. 2010b) to decapeptides.
With this level of precision, what remains in accuracy is therefore the underly-
ing atomic model choice (Brooks, Karplus, and Pettitt 1988). Using our λ- replica
exchange, free energy method, one computed model peptide backbone unit transfer
free energy to trimethylamine N-oxide (TMAO) solution of -54 cal/mol/monomer
(Figure 12.4c) compares quite favorably with -43 cal/mol/monomer determined
experimentally (Auton and Bolen 2004).
While the actual Δ
G
is reflect the idiosyncrasies of the choice of model, ΔΔ
G
is
measurably better behaved in this scheme. In Figure 12.4, we show the decomposi-
tion of ΔΔ
G
into (a) vdW, (b) electrostatics, and (c) total for a series of Gly
2-5
peptides.
While computational estimates of free energy are clearly important for a variety of
reasons, precise computer simulation estimates are cumbersome at best and more
likely tiresome for any given system. The use of solutions to analytical theoreti-
cal techniques to consider free energy changes in solution has a long history from
continuum methods (Gouy 1910; Chapman 1913) to the more modern ideas, which
include explicit solvent correlations (Andersen and Chandler 1972).
However, experiment also shows that the solubility defined as precipitation (precip)
or liquid-liquid separation (sep) decreases with the addition of each monomer (Auton
and Bolen 2005). These are not the processes above but refer to the phase transitions
between the solvent phase and the precipitate or liquid phase-separated system,
∆
G
←→
protein
precip
protein
(12.18)
(sol)
(precip)
∆
←→
protein
sep
protein
(12.19)
(sol)
(sep)
Thus, even though oligo glycine has a lower free energy of solvation or favorable
thermodynamic interaction with water with the addition of each monomer, the solu-
bility limit lowers; and therefore it phase separates as the concentration increases.
