Folding mechanisms of individual beta-hairpins in a Go model of Pin1 WW domain by all-atom molecular dynamics simulations

Abstract

This paper examines the folding mechanism of an individual beta-hairpin in the presence of other hairpins by using an off-lattice model of a small triple-stranded antiparallel beta-sheet protein, Pin1 WW domain. The turn zipper model and the hydrophobic collapse model originally developed for a single beta-hairpin in literature is confirmed to be useful in describing beta-hairpins in model Pin1 WW domain. We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second, but the formation process are significantly dependent on temperature. More specifically, beta1-beta2 hairpin folds via the turn zipper model at a low temperature and the hydrophobic collapse model at a high temperature, while the folding of beta2-beta3 hairpin follows the turn zipper model at both temperatures. The change in folding mechanisms is interpreted by the interplay between contact stability (enthalpy) and loop lengths (entropy), the effect of which is temperature dependent.

Figure 1

(a) A cartoon display of the native structure of Pin1 WW domain (K6 to G39) ) along with several key residues (S16 and S19 in green, and W11, N236, T29, and A31 in red). Drawn with software VMD (Ref. 57). (b) Two-dimensional presentation of the Pin1 WW domain. In addition to the secondary-structure elements, the main-chain H-bonds and side-chain H-bonds are illustrated by the black and gray dashed lines, respectively. Each H-bond is indicated by an arrow from a hydrogen donor to the associated hydrogen accepter. Ten main-chain H-bonds (H1-H6, H8-H11) and a side-chain H7 are labeled. The hydrophobic core 1 (L7, W11, Y24, and P37) and core 2 (R14, Y23, and F25) are specifically highlighted with a black dashed-line border and a red solid-line border, respectively. (c) The contact map of the global-minimum-energy structure of the model protein. A residue is in contact with another residue if there is at least one square-well atomic contact between them. Square symbols denote β1-β2 contacts; diamonds, β2-β3 contacts; triangles, β1-β3 contacts; the filled squares indicate contacts between loop 1 residues and other residues; the filled diamonds refer to contacts between loop 2 residues and other ones; and other contacts are labeled with crosses. The total number of native residue-residue contacts (∣i−j∣⩾3) is 65.

Figure 2

The average fractions of native contacts over all 135 trajectories (including 102 folded and 33 unfolded trajectories) as a function of reduced time at T^*=3.0. The fraction for the total contacts (Q) is shown in thick black line. The fractions of the native contacts between β1 and β2 (blue), between β2 and β3 (red), within loop 1 and between loop 1 and other residues (olive), and within loop 2 and between loop 2 and other residues (magenta) are also given.

Figure 3

Structural snapshots at the marked reduced times for two typical folded trajectories at T^*=3.0. (a) path I and (b) path II. Several key residues (S16 and S19 in green, and W11, N26, T29, and A31 in red) are shown.

Figure 4

Probabilities of native residue-residue contacts at various stages of folding according to the Q values. Results for the folded trajectories via path I (22 trajectories) and path II (80 trajectories) are shown in the upper and lower triangles, respectively. The reduced folding temperature T^* is 3.0.

Figure 5

Probabilities of 11 H-bonds at various folding stages according to the Q values of the 102 folded trajectories via (a) path I or (b) path II at T^*=3.0. The H-bond indices are defined in Fig. 1b. The secondary-structure regions are also labeled in Fig. 5a. The circles indicate the key H-bonds (H6 in loop 1 and H7 in loop 2) that would be initiated at first in the folding process. Lines serve as guides for the eye and are broken to separate the region of β1-β2 hairpin from the region of β2-β3 hairpin: Q=0.0–0.1 (×), Q=0.1–0.2 (▷), Q=0.2–0.3 (◼), Q=0.3–0.4 (◁), Q=0.4–0.5 (○), and Q=0.5–0.5 (+).

Figure 6

Probability distribution of the absolute value of the reduced energy (−E∕ε) at the transition temperature T^*=3.60. C, coil state; F, folded state.

Figure 7

Probabilities of native residue-residue contacts at various folding stages according to the Q values for the equilibrium folding trajectories via path I (in the upper triangle) and unfolding trajectories via the reverse of path I (in the lower triangle) at the proximate transition temperature T^*=3.6.

Figure 8

Typical snapshots showing the key step in Pin1 WW domain through path I. (a) At low temperature (T^*=3.0), folding of β1-β2 and β2-β3 hairpins are initiated from loop 1 and loop 2, respectively, and the zipping directions are indicated by the arrows. (b) At the transition temperature (T^*=3.6), the folding of β1-β2 hairpin is initiated from the contact between W11 and N26, and the directions of the sheet formation are also indicated by the arrows. Several key residues (S16 and S19 in green, and W11, N26, T29, and A31 in red) are shown.