Building native protein conformation from highly approximate backbone torsion angles

Abstract

Reconstructing a protein in three dimensions from its backbone torsion angles is an ongoing challenge because minor inaccuracies in these angles produce major errors in the structure. As a familiar example, a small change in an elbow angle causes a large displacement at the end of your arm, the longer the arm, the larger the displacement. Even accurate knowledge of the backbone torsions and Psi is insufficient, owing to the small, but cumulative, deviations from ideality in backbone planarity, which, if ignored, also lead to major errors in the structure. Against this background, we conducted a computational experiment to assess whether protein conformation can be determined from highly approximate backbone torsion angles, the kind of information that is now obtained readily from NMR. Specifically, backbone torsion angles were taken from proteins of known structure and mapped into 60 degrees x 60 degrees grid squares, called mesostates. Side-chain atoms beyond the beta -carbon were discarded. A mesostate representation of the protein backbone was then used to extract likely candidates from a fragment library of mesostate pentamers, followed by Monte Carlo-based fragment-assembly simulations to identify stable conformations compatible with the given mesostate sequence. Only three simple energy terms were used to gauge stability: molecular compaction, soft-sphere repulsion, and hydrogen bonding. For the six representative proteins described here, stable conformers can be partitioned into a remarkably small number of topologically distinct clusters. Among these, the native topology is found with high frequency and can be identified as the cluster with the most favorable energy.

Fig. 1.

Backbone φ,Ψ-space for a dipeptide was subdivided into 36 alphabetically labeled, 60° × 60° grid squares, called mesostates. A residue's mesostate is a very coarse-grained representation of its backbone conformation (ref. and Table 1).

Fig. 2.

Flowchart of individual steps (fragment searching and replacement, structure generation, evaluation, and clustering) as described in Methods.

Fig. 3.

Two functions of the radius of gyration (Rg) vs. protein length (N), used as confinement potentials in Methods. Functions were calculated as best-fit curves to the observed Rg for 337 nonhomologous, x-ray elucidated proteins (○), using the Flory relationship (52), Rg = R_oN^ν, as the functional form of the curve. The best-fit curve (solid line) has ν = 0.34, as expected for a self-avoiding polymer in poor solvent. A relaxed function (dashed line) with ν = 0.40 was used in the initial relaxation stage of the simulation.

Fig. 4.

Stereoviews showing the most stable conformation (red) from simulations superimposed on its corresponding native conformation (green): Protein Data Bank ID codes 2GB1 (A), 1UBQ (B), 1C9OA (C), 1IFB (D), 1VII (E), and 1R69 (F).

Fig. 5.

Simulation energy (red) vs. rmsd from the native structure for 500 conformers in the six simulated ensembles: Protein Data Bank ID codes 2GB1 (A), 1UBQ (B), 1C9OA (C), 1IFB (D), 1VII (E), and 1R69 (F). Notably, the native clump has the lowest energy. Importantly, the energy is dominated by the hydrogen-bond score (green) that tracks with the total simulation energy almost exactly.