Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

Abstract

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.

FIGURE 1

(A) A cartoon display of the global-minimum-energy structure of an all-atom off-lattice model of Pin1 WW domain (Lys⁶ to Gly³⁹). Three β-strands, two loop regions and coil regions, the hydrophobic Core 1 (Leu⁷, Trp¹¹, Tyr²⁴, Pro³⁷), and Core 2 (Arg¹⁴, Tyr²³, Phe²⁵) are specifically indicated. Drawn with VMD (65). (B) Two-dimensional presentation of the Pin1 WW domain. In addition to the secondary-structure elements, the two conserved Trp residues are highlighted by squares. Ten main-chain H-bonds and four side-chain H-bonds are also shown by the dark dashed lines and the light dashed lines, respectively, and each H-bond is indicated by an arrow from a hydrogen donor to the associated hydrogen accepter. Core 1 is highlighted with a dashed-line border, while Core 2, with a solid-line border. (C) The contact map of the native structure. 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; crosses, contacts among Core 1 residues; pluses, contacts among Core 2 residues; the solid squares indicate contacts between loop 1 residues and other residues; the solid diamonds refer to contacts between loop 2 residues and other ones; and other contacts are labeled with circles. The total number of native residue-residue contacts (|i−j| ≥ 2) is 91. The number of nonlocal native contacts (|i−j| > 2) is 65.

FIGURE 2

(A) Reduced heat capacity (C_v* = C_v/k_B) as a function of reduced temperature (T* = k_BT/ɛ). The folding transition temperature is near T* = 3.60. (B) Probability distribution of energy at the transition temperature T* = 3.59. The results were obtained from the weighted histogram method.

FIGURE 3

Free energy profiles as a function of reduced energy (A) at low temperatures; (B) at approximately the folding transition temperature; (C) at high temperatures. The positions of the transition states and native states change with temperature, as indicated by the dashed lines. U, unfolded state; TS, transition state; F, folded state.

FIGURE 4

Probability distribution of the number of native contacts between β1 and β2 residues and that between β2 and β3 residues. A total of 5,130,000 configurations of eight trajectories at T* = 3.6 were collected for statistics.

FIGURE 5

A folding trajectory at T* = 3.6. (A) The reduced energy (E/ɛ), the fraction of native contacts between residues (Q), and the RMSD of Pin1 WW domain are plotted as a function of reduced time (t*). (B) A series of snapshots at the marked reduced times which are in a folding regime indicated by the dashed lines in panel A. The snapshots are displayed with the same symbols as those in Fig. 1 A.

FIGURE 6

Average main-chain-heavy-atom RMSD (solid line) and all-heavy-atom RMSD (dashed line) of the transition-state structures from the native structure for each residue.

FIGURE 7

Ten snapshots in the transition-state ensemble at T* = 3.6.

FIGURE 8

The simulated φ-values (just native contacts involved) and (containing total contacts) of each residue. The experimental from side-chain mutation and from main-chain mutation (A-to-E mutation) both measured by Gruebele group (26,27) are also shown. The secondary-structure elements are indicated above the diagram.

FIGURE 9

Probability distribution of the numbers of native β1-β2 and β2-β3 contacts at T* = 2.7. Seventy-seven trajectories were run, and 2000 configurations for each trajectory were collected for statistics.

FIGURE 10

A schematic presentation of the two folding pathways at approximately the transition temperature and at a low temperature.