Protein structural ensembles are revealed by redefining X-ray electron density noise

Abstract

To increase the power of X-ray crystallography to determine not only the structures but also the motions of biomolecules, we developed methods to address two classic crystallographic problems: putting electron density maps on the absolute scale of e(-)/Å(3) and calculating the noise at every point in the map. We find that noise varies with position and is often six to eight times lower than thresholds currently used in model building. Analyzing the rescaled electron density maps from 485 representative proteins revealed unmodeled conformations above the estimated noise for 45% of side chains and a previously hidden, low-occupancy inhibitor of HIV capsid protein. Comparing the electron density maps in the free and nucleotide-bound structures of three human protein kinases suggested that substrate binding perturbs distinct intrinsic allosteric networks that link the active site to surfaces that recognize regulatory proteins. These results illustrate general approaches to identify and analyze alternative conformations, low-occupancy small molecules, solvent distributions, communication pathways, and protein motions.

Keywords: Ringer; electron number density; molecular motions; protein dynamics; refinement against perturbed input data.

Fig. 1.

END and RAPID maps define the absolute scale and noise level of electron density and expose a hidden ligand. (A) Histogram of END values corresponding to standard modeling threshold (1 σ above the mean; gray) in 485 high-resolution (≤1.7 Å) structures. Mean values for |Fo-Fc| RAPID maps represent errors from the model (red), and mean values for σ(F_obs) RAPID maps represent experimental error (rose). (B) The 1 σ threshold overestimates noise by six-to eightfold. Ratio of the 1 σ value to the average value of the noise due to model errors determined by the RAPID procedure for 685 representative structures in the Protein Data Bank. (C) Standard σ-weighted map contoured at 1 σ (blue mesh) shows weak, uninterpretable electron density features in the CAP-1 binding site of HIV capsid protein. (D–F) Electron density for END (orange mesh; 0.5 e⁻/ų) and RAPID (gray solid; 0.5 e⁻/ų) maps shows where CAP-1 binds to the HIV capsid protein. The lowest occupancy protein conformation (10%) resembles the original model. The ligand was built in two conformations (at 50% and 40% occupancy). Shifts in His62 and Gln63 accommodate ligand binding.

Fig. 2.

END and RAPID maps reveal signal for unmodeled, low-population side-chain conformations. (A) Histogram of unmodeled, secondary χ1 electron density peaks from Ringer plots above the noise (red) and above 0.4 e⁻/ų (blue). (B) The discovery rate, calculated as the ratio of the number χ1 secondary electron density peaks (normalized by the total number of χ1 side-chains) to alanine primary electron density peaks (normalized by the total number of alanines), plotted vs. the lower electron density cutoff (e⁻/ų) in END maps of 485 1.0- to 1.7-Å resolution structures. Values above 0.4 e⁻/ų enrich for alternative, low-occupancy structural features. (C) Unmodeled conformations were detected by identifying electron density correlations in dihedral space. Peaks in the electron density (gray mesh; 0.4 e⁻/ų) above the noise (red solid; 0.4 e⁻/ų) were identified by sampling χ1 (pink ring) and χ2 (purple ring) at idealized heavy-atom bond lengths from the χ1 secondary peak (orange sphere). (D) Correlated unmodeled χ1 and χ2 peaks for side-chains unbranched at χ1 in 485 high-resolution structures. 3D histogram of correlated secondary χ1 Ringer peaks and primary χ2 Ringer peaks built from the unmodeled secondary χ1 peaks for 31,086 side-chains unbranched at χ1. The nonrandom, low-energy, checkerboard distribution suggests that unmodeled side-chain conformations are common. (E) For alanine residues in 485 high-resolution structures, histogram of χ1 and pseudo-χ2 Ringer peaks above the RAPID noise. The columns of peaks at χ1 = 60°, 180°, and 240° suggest that the hydrogens are staggered, the noise peaks are distributed randomly around the pseudo-χ2, and there is no missing source of noise that swamps the hydrogen signals. The strong cross-peaks in the left, right, and front corners come from the backbone amide hydrogen. (F) For alanines in the set of 485 structures, the histogram of χ1 and pseudo-χ2 Ringer peaks above 0.4 e⁻/ų. The suppression of features compared with E provides confidence that the END maps were on a similar scale and the 0.4 e⁻/ų threshold effectively enriches for alternative conformations of longer side-chains.

Fig. 3.

ATP perturbs different allosteric networks in human protein kinases (A) DAPK, (B) CDK2, and (C) CK2α, but causes localized ensemble shifts in (D) EphA3. Residues with Ringer ccs < 0.85 (spheres) between free and ATP-bound (orange surface) electron density maps indicate shifts in the side-chain ensembles or rotamer flips. Side-chains that cluster within 4 Å of the nucleotide (red) show allosteric networks connected to the active site. Other clusters are shown in different colors. The surfaces show atoms in the regulatory protein that are within 4 Å of the kinase. Representative Ringer plots for key residues from the nucleotide-free (blue line) and bound (red line) END maps for (E) DAPK and (F) CDK2. Ringer plots for the apo (blue fill) and bound (red fill) RAPID maps are shown, as well, to indicate the distribution of noise. Residues illustrate the coupled ensemble shifts in the allosteric pathways for each protein in response to Mg²⁺-ATP binding, as well as the corresponding residue in the other protein as a control. The perturbations connect the kinase active site to distinct regulatory surfaces.