Tackling Force-Field Bias in Protein Folding Simulations: Folding of Villin HP35 and Pin WW Domains in Explicit Water

Abstract

The ability to fold proteins on a computer has highlighted the fact that existing force fields tend to be biased toward a particular type of secondary structure. Consequently, force fields for folding simulations are often chosen according to the native structure, implying that they are not truly “transferable.” Here we show that, while the AMBER ff03 potential is known to favor helical structures, a simple correction to the backbone potential (ff03^∗) results in an unbiased energy function. We take as examples the 35-residue α-helical Villin HP35 and 37 residue β-sheet Pin WW domains, which had not previously been folded with the same force field. Starting from unfolded configurations, simulations of both proteins in Amber ff03^∗ in explicit solvent fold to within 2.0 Å RMSD of the experimental structures. This demonstrates that a simple backbone correction results in a more transferable force field, an important requirement if simulations are to be used to interpret folding mechanism.

Small proteins with microsecond folding times have generated a lot of interest in both simulation and experimental communities, because of their potential to bridge the gap between the accessible length- and timescales in these disciplines (1–5). The prototypical fast folders with α-helical and β-sheet structure are, respectively, the Villin headpiece domain HP35 (6–12) and the pin WW domain (13–17) which have been successfully folded with all-atom simulations. However, current energy functions, or “force fields,” are known to be biased toward particular secondary structures (18,19). Thus, folding simulations often employ force fields according to the native structure of the protein in question: Villin has been folded with the AMBER 94GS (20,21), AMBER ff03 (1,8,22), and CHARMM 27 (2,23,24) force fields, which have different degrees of α-helical bias (18). In contrast, the all-β Pin WW domain has been folded in implicit solvent using the AMBER ff96 force field (3), which prefers β-structure. Indeed, a 10-μs simulation of the FIP35 variant of the Pin WW domain with the CHARMM 27 force field, starting from an unfolded state, resulted in only helical structures (25), which were subsequently shown to be lower in free energy than the native state in this potential (26).

This difficulty is a central problem in force-field development if the goal is to find a “transferable” force field: i.e., one depending only on protein sequence (27). This search has motivated backbone modifications in the AMBER 99SB force field (28), which has shown promising results for unfolded Villin and the Trp cage (29,30), but has not been extensively used in folding simulations. Building on work by others (20), one of us has optimized the AMBER ff03 (8) force field against helix-coil experimental data near 300 K, reducing the overall helical propensity in the resulting (ff03^∗) energy function (19). Here, we demonstrate the transferability of this optimization by folding Villin HP35 and a variant of the Pin WW domain in molecular dynamics simulations starting from only unfolded configurations.

To facilitate faster sampling of folding events in the simulations, we selected variants of each protein with the highest folding rate near 300 K (where the force field is optimal (19)): a double norleucine mutant of Villin from Kubelka et al. (10) with a folding time of 0.7 μs at 300 K; and a Pin WW variant 17 of Liu et al. (31), which folds in 19 μs at 313 K. We have run replica exchange molecular dynamics (REMD) simulations of these two proteins, starting from unfolded configurations drawn from a simulation at 800 K, all having backbone root mean-square deviation (RMSD) at least 0.8 nm from the experimental structures, PDB entries 2F4K(17) and 2F21(10) for Villin and WW domains, respectively. REMD simulations were run with 32 replicas spanning the temperatures 300–457 K for Pin WW and 40 replicas spanning 278–595 K for Villin. The lengths of the simulations for the individual replicas were 1.27 μs and 1.37 μs for the Villin and WW domains, respectively. Further simulation details are available as Supporting Material.

To circumvent discontinuities in the trajectories from exchanges, we obtain continuous trajectories by following each replica through temperature space. We identify the folded state as being within 0.25 nm RMSD from the experimental coordinates. A single folding event is obtained for each protein and the corresponding continuous trajectories are shown in Fig. 1, A and B. The Villin replica folds within the first 50 ns and thereafter fluctuates about its folded state. Although the RMSD from experiment is as low as 1–1.5 Å, fluctuations of up to 4 Å from the folded state are seen, due to transient undocking and melting of the short N-terminal helix. Partly, this may be due to the larger native state fluctuations in the higher temperature replicas. We have also benchmarked the folded state dynamics with a 0.2-μs run at 300 K starting from folded (Fig. 1). Notably, the REMD folding simulations reach a similar RMSD to that of the folded state simulation. In addition, the folded state simulations also show large transient fluctuations in RMSD associated with N-terminal helix melting, consistent with previous experiments and simulations on folded Villin (32,33). For the WW domain, there is a longer waiting time before folding occurs, with the protein eventually folding to within 2.0 Å of the experimental structure after ∼1.25 μs. According to existing criteria, this domain may be considered folded (3). In contrast to Villin, the folding simulation of WW never reaches the same RMSD from the experimental structure as the simulation initiated from the folded state (Fig. 1), because the strand 2:3 interaction is one residue out of register—most likely due to inadequate sampling.

Figure 1.

Molecular dynamics trajectories of protein folding. Continuous folding trajectories are shown for (A) Villin and (B) the WW domain. The blue traces at right show the backbone RMSD for a 0.2-μs simulation starting from folded; the initial and folded structures are also shown along with the trajectory. For Pin WW, only the structured region from residues 7–30 is included in the RMSD. Folded structures from the simulations (green) overlaid with the experimental structures (silver) are shown for (C) Villin and (D) Pin WW, respectively.

Although our folding trajectories cannot be assigned to a single temperature, we analyze the folding mechanism qualitatively. For example, whereas the experimental Pin WW and Villin Φ-values (34) are temperature-dependent, the regions with the highest Φ-values are similar at all temperatures (11,13,14). In Fig. 2, we present transition paths—the segments of trajectory connecting unfolded and folded states. We represent local structure formation using a fraction of native contacts for each residue, Q_res (definition in Supporting Material), and we compute the secondary structure over the trajectory using the DSSP (35) algorithm (Fig. 2).

Figure 2.

Transition-path region of the folding trajectories. For (A) Villin and (B) Pin WW transition paths, we show (upper panels) local contact formation, Q_res; (center panels) secondary structure formation; and (lower panels) backbone RMSD from experimental structures. To the right of the upper panels is the color scale for Q_res, while to the right of the center panels is the secondary structure of the experimental structure. (Color scale for secondary structure: blue, helix; red, sheet; and green, turn.)

For Villin, there is an initial reduction of RMSD associated with forming helix 3 followed shortly by 1, with a longer waiting period to form helix 2. It is hard to compare this trajectory with experiment because the experimental Φ-values for this protein are very low and must be interpreted with caution due to the low folding barrier. There is some evidence both for structure formation at the N-terminus (11) and in the turn between helices 2 and 3 (12). The observed mechanism for Pin WW is more clearly consistent with experimental Φ-values, which suggest that the first hairpin is formed in the transition state (13,14). Secondary structure and contact formation occur simultaneously, which would also be consistent with similar backbone and side-chain Φ-values (13,14). The amount of nonnative structure seen in both simulations is small, suggestive of an unfrustrated energy landscape for fast-folding proteins (36); in fact, substantial nativelike structure is seen in the unfolded WW domain before folding. Our simulations provide a wealth of information on the unfolded state: in the Supporting Material, we show the radius of gyration and secondary structure as a function of temperature. A detailed unfolded state analysis will be published separately.

Accurate molecular simulations can potentially play an important role in interpreting folding experiments, but the observed mechanism could obviously be distorted by force-field bias (consider hierarchical versus nucleation-condensation scenarios) (37). We believe that the force-field improvements demonstrated here constitute an important step toward more accurate, predictive folding simulations.