Smooth statistical torsion angle potential derived from a large conformational database via adaptive kernel density estimation improves the quality of NMR protein structures

Abstract

Statistical potentials that embody torsion angle probability densities in databases of high-quality X-ray protein structures supplement the incomplete structural information of experimental nuclear magnetic resonance (NMR) datasets. By biasing the conformational search during the course of structure calculation toward highly populated regions in the database, the resulting protein structures display better validation criteria and accuracy. Here, a new statistical torsion angle potential is developed using adaptive kernel density estimation to extract probability densities from a large database of more than 10⁶ quality-filtered amino acid residues. Incorporated into the Xplor-NIH software package, the new implementation clearly outperforms an older potential, widely used in NMR structure elucidation, in that it exhibits simultaneously smoother and sharper energy surfaces, and results in protein structures with improved conformation, nonbonded atomic interactions, and accuracy.

Figure 1

Representative energy surfaces of the DELPHIC and torsionDBPot statistical torsion angle potentials in Xplor-NIH. (A and B) Contour plots of the His (χ₁, χ₂) energy term in the DELPHIC potential and torsionDBPot, respectively. (C and D) Single isoenergetic surfaces of the Val (ϕ, ψ, χ₁) energy term in the DELPHIC potential and torsionDBPot, respectively. Panels A and B were generated with Matplotlib, C and D with Mayavi. All units are in degrees.

Figure 2

MolProbity validation. Each barplot displays a Molprobity validation statistic for structure ensembles of different proteins, with bars representing the mean ± standard deviation computed from 20 structures. Structure calculations without any statistical torsion angle potential (black), with the DELPHIC potential (gray), and with the new torsionDBPot potential (white) are included. Abbreviated protein names are used; for full names see Table II. The clashscore (panel D) and the MolProbity score (panel E) are costs: the lower the better. Barplots in this and all other figures were generated with Matplotlib.

Figure 3

WHAT IF validation. Each barplot displays a WHAT IF validation statistic for structure ensembles of different proteins, with bars representing the mean ± standard deviation computed from 20 structures. Structure calculations without any statistical torsion angle potential (black), with the DELPHIC potential (gray), and with the new torsionDBPot potential (white) are included. Abbreviated protein names are used; for full names see Table II. Each statistic is a score: the larger the better. Packing quality (panel C) refers to the 2nd generation packing quality.

Figure 4

Fit to experimental data. Each barplot displays a figure of merit for the fit to a given experimental NMR observable of structure ensembles of different proteins, with bars representing the mean ± standard deviation computed from 20 structures (note that error bars associated with very small standard deviations may seem missing). Structure calculations without any statistical torsion angle potential (black), with the DELPHIC potential (gray), and with the new torsionDBPot potential (white) are included. Abbreviated protein names are used; for full names see Table II. Large torsion angle RMS deviations for ubiquitin (panel B, asterisk) stem from unrealistically narrow bounds in the publicly released restraints (PDB ID: 1D3Z). Each RDC R-factor (panel C) is an unweighted average over different alignment media and nuclei pairs (when applicable).