NC_αC deviation of the CDL values from crystal structures as a function of resolution of the analysis. At each of five resolutions ranging from 1.0–3.0 Å, the NC_αC RMSDs from the CDL were calculated for 50 nonredundant structures. The distributions of RMSDs at each resolution are shown. The thickness of the black line indicates the standard error of the mean, and the thickness of the gray line indicates the standard deviation. Figure created with gnuplot.

CDL NC_αC values match ultrahigh-resolution structures best. Deviations of predicted angles from the experimental ones for atomic-resolution ribonuclease (PDB code 1rge; Sevcik et al., 1996) with various methods are shown: EH single ideal values (blue), molecular mechanics (green), and the CDL (red). Results are shown in a histogram-like manner using 1° bins and frequency polygons. Of these three methods, the CDL matches best, followed by molecular mechanics, then single ideal values. Figure created with gnuplot.

Protein backbone conformations of non-Gly residues. This Ramachandran plot is colored by empirical observation density in atomic-resolution proteins. Labels indicate regions of particular interest (Karplus, 1996; Lovell et al., 2003; Hollingsworth et al., 2009). Coloring uses a logarithmic function to allow lower- and higher-population regions to be seen simultaneously. Observation density was calculated using kernel regressions (see Experimental Procedures). Unlabeled versions of this plot and another for only Gly residues are available as supplementary material (Figures S12 and S13). Figure created with Inkscape.

Conformation-dependent variation in bond lengths is partially masked by experimental uncertainty. Ramachandran plots are shown for average lengths and standard deviations of the C=O bond (left panels) and the C-N bond (right panels) using colors as in Figure 3. These bonds are involved in the partial double-bond character of the peptide bond, so the expectation is for them to be anticorrelated as electron density shifts between them. Some such anticorrelation is visible as a Ψ-dependent effect in averages (shown in the top panels) but it is not as clear as trends seen in bond angles, possibly because the standard deviations (shown in the bottom panels) are near the level of experimental uncertainty.

NC_αC distributions are well-defined and distinct. Shown are observations from selected 10° × 10° bins in each of four conformations: α (gray), β (green), P_II (blue), and a region left of δ at (−125°, −5°) (red). The Y-axis range is set to visualize the distributions in non-α bins. Histograms were calculated using 1° bins and plotted as frequency polygons. Distributions are visibly separate and thus conformation-dependent. Inset: The same plot, with the Y-axis range set to display the full height of the α distribution. If not broken out by conformation, the non-α bins would be indistinguishable from tails of the α distribution. Figure created with gnuplot and Inkscape.

Evolution of the ideal values for backbone geometry used in the single-value paradigm. A central residue (residue 0) is shown with atoms from residues −1 and +1 that contribute to its two adjacent peptide units. For each of the seven bond angles associated with residue 0, three ideal values from earlier work are shown from oldest (top) to most recent (bottom). They are from Corey and Donohue (1950), Engh and Huber (1991), and Engh and Huber (2001). Most refinement and modeling programs use one of the Engh and Huber sets or a slight variation on them. Rotatable bonds defining the backbone torsion angles Φ and Ψ are indicated. Figure created with Inkscape.

Conformation-dependent variation in bond angles of general residues as a function of the Φ,Ψ of the central residue. A Ramachandran plot is shown for each backbone bond angle in the two peptide units surrounding the central residue of the tripeptide. The seven unique peptide bond angles are associated with either residue −1, 0, or +1 based on which residue contributes at least two atoms to the angle. Φ and Ψ in each plot, however, refer to the central residue, 0. Within each plot, colors indicate averages ranging from the global minimum (blue) to the global maximum (red) as calculated using kernel regressions (see Experimental Procedures). The global minima and maxima are provided in each plot. Figure created with Matlab.

Structural basis for geometry variations of selected conformations. Four Ala residues with adjacent peptides are shown, built using EH values and with dots showing van der Waals overlap between atoms: blue (wide contact), green (close contact), yellow (small overlap), and red (bad overlap). Clockwise from top left: tip of the Lα/Lδ region; left of the δ region; a prePro-Pro dipeptide in the α region; and the II′ region. Arrows indicate angles that open or close substantially relative to EH values. Note that all of these distortions serve to alleviate atomic clashes. The overlaps were calculated by MolProbity (Davis et al., 2007) and are shown in Coot (Emsley and Cowtan, 2004).

Energy minimization behaves better using experimental geometry as opposed to the rigid-geometry approximation. (A) Shown are 100 trials minimized with experimental (squares) and with EH (triangles) geometries. They are plotted as Rosetta energy versus the C_α RMSD from the crystal structure (as calculated by Rosetta). Figure created with gnuplot. (B) Shown are C_α shifts between the crystal structure chain A and a structure selected from the cluster center using experimental (dashed line) or EH (solid thick line) geometry, C_α shifts for chain B vs chain A from the same crystal (solid thin line), and a schematic of the secondary structure (using spirals for helices and arrows for β-strands). The crystal structure chain B reflects the differences in the same protein in two environments. Overlays were created using the McLachlan algorithm (McLachlan, 1982) as implemented in ProFit by iteratively overlaying structures using a subset of C_α atoms with a maximum per-atom RMSD of 0.1 Å until convergence was reached. The secondary structure is taken from PDBsum (Laskowski et al., 2005). Figure created with gnuplot and Inkscape.