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. 2001 Dec 18;98(26):14931-6.
doi: 10.1073/pnas.201543998.

The free energy landscape for beta hairpin folding in explicit water

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The free energy landscape for beta hairpin folding in explicit water

R Zhou et al. Proc Natl Acad Sci U S A. .

Abstract

The folding free energy landscape of the C-terminal beta hairpin of protein G has been explored in this study with explicit solvent under periodic boundary condition and OPLSAA force field. A highly parallel replica exchange method that combines molecular dynamics trajectories with a temperature exchange Monte Carlo process is used for sampling with the help of a new efficient algorithm P3ME/RESPA. The simulation results show that the hydrophobic core and the beta strand hydrogen bond form at roughly the same time. The free energy landscape with respect to various reaction coordinates is found to be rugged at low temperatures and becomes a smooth funnel-like landscape at about 360 K. In contrast to some very recent studies, no significant helical content has been found in our simulation at all temperatures studied. The beta hairpin population and hydrogen-bond probability are in reasonable agreement with the experiment at biological temperature, but both decay more slowly than the experiment with temperature.

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Figures

Figure 1
Figure 1
Free energy contour map versus the number of β sheet H bonds Nformula image and the hydrophobic core radius gyration Rgcore. A hydrogen bond is counted if the distance between two heavy atoms (N and O in this case) is less than 3.5 Å and the angle N—H⋅⋅⋅O is larger than 150.0°. The contours are spaced at intervals of 0.5 RT. We used RT instead of kcal/mol for energy intervals across various temperatures, because it might be easier to quantify the barriers at different temperatures.
Figure 2
Figure 2
(a) Temperature dependence of the probability of forming individual native hydrogen bonds. The thick solid line shows the average probability overall all native hydrogen bonds. (b) The average fraction of native contacts (population of β hairpin) as a function of temperature. The population of β sheet decreases monotonically but decays too slowly with temperature. The experimental results (solid line) (4) and simulation results from Klimov and Thirumalai (dashed line) (16) are shown (Inset).
Figure 3
Figure 3
Free energy contour map versus (a) the principal components PC1 and PC2 (Upper) and (b) the fraction of native contact ρ and the radius gyration of the entire peptide Rg (Lower) at 310 K. The contours are spaced at intervals of 0.5 RT. The contour maps at various other temperatures are published as supporting information on the PNAS web site.
Figure 4
Figure 4
Representative structures from the local minima of the free energy contour map versus (a) the principal components PC1 and PC2 (Fig. 3 a and b) the fraction of native contacts and the radius of gyration of the entire peptide (Fig. 3b).
Figure 5
Figure 5
Free energy as a function of first principal coordinates PC1 (Left) and the overall rmsd from the native structure (Right) for various temperatures. Curves are shifted up from each other by 3 RT.

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