Dominant Folding Pathways of a WW Domain

We investigate the folding mechanism of the WW domain Fip35 using a realistic atomistic force field by applying the Dominant Reaction Pathways (DRP) approach. We find evidence for the existence of two folding pathways, which differ by the order of formation of the two hairpins. This result is consistent with the analysis of the experimental data on the folding kinetics of WW domains and with the results obtained from large-scale molecular dynamics (MD) simulations of this system. Free-energy calculations performed in two coarse-grained models support the robustness of our results and suggest that the qualitative structure of the dominant paths are mostly shaped by the native interactions. Computing a folding trajectory in atomistic detail only required about one hour on 48 CPU’s. The gain in computational efficiency opens the door to a systematic investigation of the folding pathways of a large number of globular proteins.

💡 Research Summary

This paper investigates the folding mechanism of the WW domain mutant Fip35 using a realistic atomistic force field combined with the Dominant Reaction Pathways (DRP) approach. Traditional molecular dynamics (MD) simulations are limited by the long timescales required for protein folding, making it difficult to capture complete folding events for even modestly sized proteins. To overcome this limitation, the authors employ DRP, a theoretical framework that identifies the most probable transition pathways by minimizing the Onsager‑Machlup action associated with overdamped Langevin dynamics.

The atomistic simulations are performed with the AMBER ff99SB force field in an implicit solvent using the Generalized Born model as implemented in GROMACS 4.5.2. To explore the high‑dimensional path space efficiently, the authors generate a large ensemble of trial trajectories using a ratchet‑and‑pawl molecular dynamics (rMD) algorithm. In rMD, a collective variable z measures the distance between the instantaneous contact map and the native contact map; a time‑dependent bias potential penalizes increases in z, thereby encouraging monotonic formation of native contacts without imposing explicit forces on specific residues. Each trial trajectory is subsequently scored using the exact DRP probability functional (Eq. 3), allowing the selection of the dominant pathways.

Analysis of the scored trajectories reveals two distinct dominant folding routes. In the first route, hairpin 1 folds completely before hairpin 2 begins to form; in the second route, the order is reversed. The relative statistical weight of these pathways depends on temperature and on the specific denatured configuration used as the starting point. Coarse‑grained free‑energy calculations performed with two models—one containing only native (Go‑type) interactions and another that also includes non‑native quasi‑chemical and electrostatic terms—show that the qualitative shape of the dominant pathways is largely dictated by native contacts. At higher temperatures the second pathway (hairpin 2 first) becomes more prevalent, indicating a modest temperature dependence of pathway selection. Moreover, the coarse‑grained simulations suggest that non‑native interactions have little influence on the transition region, supporting the atomistic findings.

The authors also examine the impact of the initial denatured ensemble. By generating multiple random denatured structures and applying the DRP protocol, they find that trajectories starting from conformations already biased toward one hairpin tend to follow the corresponding folding route. This demonstrates that the folding mechanism is correlated with the structural features of the initial state.

A key practical outcome of the study is the computational efficiency of the DRP method. Using 48 CPU cores, a single atomistic folding trajectory can be obtained in roughly one hour, a dramatic speed‑up compared with conventional MD, which would require microseconds to milliseconds of simulation time for the same system. This efficiency opens the possibility of systematic, high‑throughput investigations of folding pathways across a wide range of globular proteins.

In summary, the paper provides strong evidence that the WW domain Fip35 folds predominantly through two pathways distinguished by the order of hairpin formation. The relative importance of these pathways varies with temperature and initial conditions, while non‑native interactions play a minor role in shaping the transition. The DRP approach, validated against coarse‑grained models and consistent with previous experimental and MD studies, emerges as a powerful tool for probing protein folding at atomic resolution with feasible computational resources.