Protein model refinement using an optimized physics-based all-atom force field

Abstract

One of the greatest challenges in protein structure prediction is the refinement of low-resolution predicted models to high-resolution structures that are close to the native state. Although contemporary structure prediction methods can assemble the correct topology for a large fraction of protein domains, such approximate models are often not of the resolution required for many important applications, including studies of reaction mechanisms and virtual ligand screening. Thus, the development of a method that could bring those structures closer to the native state is of great importance. We recently optimized the relative weights of the components of the Amber ff03 potential on a large set of decoy structures to create a funnel-shaped energy landscape with the native structure at the global minimum. Such an energy function might be able to drive proteins toward their native structure. In this work, for a test set of 47 proteins, with 100 decoy structures per protein that have a range of structural similarities to the native state, we demonstrate that our optimized potential can drive protein models closer to their native structure. Comparing the lowest-energy structure from each trajectory with the starting decoy, structural improvement is seen for 70% of the models on average. The ability to do such systematic structural refinements by using a physics-based all-atom potential represents a promising approach to high-resolution structure prediction.

Fig. 1.

For all refinement trajectories, results of decoy structure refinement within each trajectory (100 decoys per protein, 39 proteins). (A and B) TM-score (A) and C^α rmsd (B) to the native structure of the lowest-energy decoy after refinement versus decoy's initial TM-score (A) or C^α rmsd (B). (C) Fraction of decoys that refined by more than a given C^α rmsd threshold (for 0.2-, 0.5-, 1.0-, 1.5-, and 2.0-Å rmsd thresholds) with respect to their initial native similarity. (D) Fraction of decoys that refined to (or remained within) the accuracy of 2-Å (black) and 3-Å (gray) C^α rmsd to the native state with respect to their initial native similarity. Fractions of decoys were calculated in 1-Å bins.

Fig. 2.

Results of decoy structure refinement within each trajectory (100 decoys per protein, 39 proteins) for different structural elements. (A–C and A′–C′) C^α rmsd to the native structure of the lowest-energy decoy after refinement versus the decoy's initial C^α rmsd, for helical (A), β-sheet (B), and loop (C) regions when all the native secondary structure elements of a given type are superimposed together onto the corresponding decoy regions, and for helices (A′), β-sheets (B′), and loops (C′) when individual secondary structure elements from the native are superimposed onto related decoy regions. (A″–C″) Comparison of fractions of the native secondary structure in the refined (lowest-energy decoy from each trajectory) and the initial decoy, for helical (A″), β-sheet (B″), and loop (C″) regions. (D–F) Refinement of packing of buried side chains. (D) χ1 rmsd (degrees) to the native structure of the lowest-energy decoy after refinement with respect to χ1 rmsd of the initial structure. (E and F) Fraction of the lowest-energy decoys that improved their χ1 rmsd by more than (E) or below (F) a given threshold with respect to χ1 rmsd of the initial structure. Fractions of decoys were calculated in 10° bins.

Fig. 3.

Examples of refinement for 1b07A (A) and 1a0b (B). Models (yellow) are superimposed onto the native structure (blue).

Fig. 4.

Results of the refinement of decoy structures over the entire ensemble of decoys above a given native similarity threshold (each circle represents one protein; the 20 testing proteins with energy–TM-score correlation coefficient larger than 0.5 for the bottom of the energy–TM-score cloud are used). (A and B) TM-score (A) and C^α rmsd (B) to the native structure of the best-of-five lowest-energy decoys after refinement with respect to the TM-score of the best initial structure within a given native similarity bin; e.g., for a threshold of 3 Å, for each protein we consider all the decoys with initial rmsd in the range 3–8 Å, and we compare the lowest initial rmsd in this range against the rmsd of the best-of-five lowest-energy decoy after refinement that had initial structure within this range. The analysis is repeated for each native similarity bin, i.e. 0.8–0.2, 0.7–0.2, …, 0.4–0.2 for TM-score, and 2–8, 3–8, …, 7–8 Å, for rmsd (this explains why there are more than 20 circles in the figure).