Folding simulations of a three-stranded antiparallel beta -sheet peptide

Abstract

Protein folding is a grand challenge of the postgenomic era. In this paper, 58 folding events sampled during 47 molecular dynamics trajectories for a total simulation time of more than 4 micros provide an atomic detail picture of the folding of a 20-residue synthetic peptide with a stable three-stranded antiparallel beta-sheet fold. The simulations successfully reproduce the NMR solution conformation, irrespective of the starting structure. The sampling of the conformational space is sufficient to determine the free energy surface and localize the minima and transition states. The statistically predominant folding pathway involves the formation of contacts between strands 2 and 3, starting with the side chains close to the turn, followed by association of the N-terminal strand onto the preformed 2-3 beta-hairpin. The folding mechanism presented here, formation of a beta-hairpin followed by consolidation, is in agreement with a computational study of the free energy surface of another synthetic three-stranded antiparallel beta-sheet by Bursulaya and Brooks [(1999) J. Am. Chem. Soc. 121, 9947-9951]. Hence, it might hold in general for antiparallel beta-sheets with short turns.

Figure 1

Time dependence of the fraction of native contacts Q. (A) 300-K simulation started from the folded conformation. (B) 360-K simulation started from the folded conformation. (C and D) 360-K simulations started from random conformations 2 and 39.

Figure 2

Ribbon representation of three snapshots from a 360-K trajectory started from random conformation 1 (Tr1) at (Top) 5.56 ns (Q = 0.19, rms deviation from the average NMR conformation of 6.2 Å), (Middle) 5.84 ns (Q = 0.38, rms deviation = 3.7 Å), and (Bottom) 9.71 ns (Q = 0.96, rms deviation = 2.0 Å). The secondary structure was assigned with the dssp program (28) and plotted with molscript (29). The regions of the sequence corresponding to the turns (Gly-6–Ser-7 and Gly-14-Ser-15) are colored in red.

Figure 3

(A) Time dependence of the fraction of native contacts Q for Tr1. (B) Projection into the Q₁₋₂Q₂₋₃ plane, (C) the Q_scQ_hb plane, and (D) the Q_distalQ_proximal plane for the same trajectory. The two folding events are shown with the black and green curves, and the two unfolding events are shown with the red and blue curves. (B–D) Each point corresponds to the average over 100 ps (10 conformations).

Figure 4

Same as in Fig. 3 for a 330-K trajectory started from the folded state.

Figure 5

Average effective energy (, Left) and free energy surface (ΔG, Right) at 360 K as a function of the fraction of native contacts between residues in strands 1 and 2 (Q₁₋₂), and between residues in strands 2 and 3 (Q₂₋₃). A total of 3.0 × 10⁵ conformations sampled during the 41 simulations at 360 K were used. To make it more clear, the plot of ΔG is rotated with respect to the one of <E> by 180° around an axis going through the center of the horizontal plane. <E> was evaluated by averaging the effective energy values of the conformations within a bin without minimizing them. ΔG was computed as −k_BTln(N_n,m/N_0,0), where N_n,m denotes the number of conformations with n contacts formed between strands 1 and 2 and m contacts between strands 2 and 3. The minimum and maximum values of N_n,m are 42 and 31,987, respectively. The error in ΔG is estimated by separating the 40 simulations started from random conformations into two sets of 20 simulations each. The average and maximal errors of <E> are 0.8 and 3.7 kcal/mol (bin with n = 8 and m = 4), respectively. The average and maximal errors of ΔG are 0.2 and 0.6 kcal/mol (n = 11, m = 11), respectively.

Figure 6

Same as in Fig. 5 for the four simulations at 330 K. A total of 0.77 × 10⁵ conformations were used. The minimum and maximum values of N_n,m are 19 and 4531, respectively. The average and maximal error of <E> are 1.9 and 7.5 kcal/mol (bin with n = 11 and m = 2), respectively. The average and maximal errors of ΔG are 0.6 and 1.8 kcal/mol (n = 0, m = 5), respectively.