Trp-cage: folding free energy landscape in explicit water

Abstract

Trp-cage is a 20-residue miniprotein, which is believed to be the fastest folder known so far. In this study, the folding free energy landscape of Trp-cage has been explored in explicit solvent by using an OPLSAA force field with periodic boundary condition. A highly parallel replica exchange molecular dynamics method is used for the conformation space sampling, with the help of a recently developed efficient molecular dynamics algorithm P3ME/RESPA (particle-particle particle-mesh Ewald/reference system propagator algorithm). A two-step folding mechanism is proposed that involves an intermediate state where two correctly formed partial hydrophobic cores are separated by an essential salt-bridge between residues Asp-9 and Arg-16 near the center of the peptide. This metastable intermediate state provides an explanation for the superfast folding process. The free energy landscape is found to be rugged at low temperatures, and then becomes smooth and funnel-like above 340 K. The lowest free energy structure at 300 K is only 1.50 A Calpha-RMSD (Calpha-rms deviation) from the NMR structures. The simulated nuclear Overhauser effect pair distances are in excellent agreement with the raw NMR data. The temperature dependence of the Trp-cage population, however, is found to be significantly different from experiment, with a much higher melting transition temperature above 400 K (experimental 315 K), indicating that the current force fields, parameterized at room temperature, need to be improved to correctly predict the temperature dependence.

Fig. 1.

Free energy contour maps at various temperatures vs. the two reaction coordinates, the Rg and the fraction of the native contacts (ρ). It shows the free energy landscape is rugged at lower temperatures and then becomes smooth at higher temperatures. There is an intermediate state I in addition to the folded state F at low temperatures such as 300 K. See text for more details.

Fig. 5.

The average fraction of the native contacts (Trp-cage population) as a function of the temperature. The error bars are estimated by block averaging (block size 200 ps). The experimental results (3) from NMR CSD and CD are shown in the Inset for comparison [converted from their unfolded population; the fluorescence data (4), not shown, are basically identical to CD]. Even though both the simulation and experiment show a monotonic decrease in the Trp-cage population with temperature, the melting transition temperature is found to be ≈440 K in simulation, which is much higher than the experimental transition temperature of 315 K, indicating that the temperature dependence of the force field has serious deficiency.

Fig. 2.

Comparison between the lowest free energy structure (a) and the native NMR structure (b). The key hydrophobic residues packing against the central Trp-6 residue (Tyr-3, Trp-6, Leu-7, Pro-12, Pro-17, Pro-18, and Pro-19) are shown in sticks following previous studies (3, 5, 6), and all other residues are shown in ribbons. The lowest free energy structure shows an overall C^α-RMSD of 1.50 Å from the native structure, with the major differences in the 3₁₀-helix region (residues 11–14) and residue Tyr-3, where the phenyl ring is not as closely packed to the Trp-6 as the native structure.

Fig. 3.

Comparison of simulated NOE pair distances (represented as diamonds with error bars) with the NMR data [represented as circles with distance ranges (3)]. The simulation data are shifted slightly in x axis to show error bars clearly. The error bars are estimated by block averaging (block size 200 ps). The 28 key long-range (i/(i + n) with n ≥ 5) NOE pairs are shown of the total 169 constraints. They are as follows: 1, HE^* Y3 and HB2 P18; 2, HA Y3 and HB2 P19; 3, HA Y3 and HD2 P19; 4, HA Y3 and HG^* P19; 5, HB2 Y3 and HG^* P19; 6, HD^* Y3 and HA P12; 7, HZ2 W6 and HA P12; 8, HH2 W6 and HG^* P12; 9, HH2 W6 and HA P12; 10, HH2 W6 and HD1 P12; 11, HD1 W6 and HB^* R16; 12, HE1 W6 and HN R16; 13, HE1 W6 and HB^* R16; 14, HE1 W6 and HA P17; 15, HZ2 W6 and HA P17; 16, HD1 W6 and HD^* R16; 17, HD1 W6 and HG^* R16; 18, HZ2 W6 and HD1 P18; 19, HZ2 W6 and HD2 P18; 20, HZ2 W6 and HB1 P18; 21, HZ2 W6 and HG1 P18; 22, HH2 W6 and HB1 P18; 23, HE1 W6 and HA P18; 24, HH2 W6 and HG1 P18; 25, HD1 W6 and HA P18; 26, HD1 W6 and HD2 P19; 27, HD2^* L7 and HD1 P12; 28, HB1 D9 and HB2 S14.

Fig. 4.

Comparison of the most popular structure in the intermediate state I (a) with the native NMR structure (b). The key hydrophobic core residues packing against Trp-6 (Tyr-3, Trp-6, Leu-7, Pro-12, Pro-17, Pro-18, and Pro-19) are shown in space-fill mode whereas the two charged residues Asp-9 and Arg-16 are represented as sticks. The intermediate state shows structures having two partially formed hydrophobic cores separated by a salt-bridge between Asp-9 and Arg-16 near the center of the molecule.