A three-dimensional potential of mean force to improve backbone and sidechain hydrogen bond geometry in Xplor-NIH protein structure determination

Abstract

We introduce a new hydrogen bonding potential of mean force generated from high-quality crystal structures for use in Xplor-NIH structure calculations. This term applies to hydrogen bonds involving both backbone and sidechain atoms. When used in structure refinement calculations of 10 example protein systems with experimental distance, dihedral and residual dipolar coupling restraints, we demonstrate that the new term has superior performance to the previously developed hydrogen bonding potential of mean force used in Xplor-NIH.

Keywords: hydrogen bond; potential of mean force; protein; structure determination.

Figure 1

Definition of hydrogen bond geometry with the abbreviations D for donor atom, H for proton, A for acceptor, and AA for acceptor antecedent

Figure 2

Surfaces of constant HBPot energy for the Class V hydrogen bonds (involving glutamic acid and aspartic acid sidechain oxygens) at three different values of energy for w_HBPot = 1. Units for r are Å, while θ and ϕ are in degrees

Figure 3

Panels (a)–(c) depict isosurfaces of 2D cross‐sections of the Class VI HBPot energy surface (involving glutamine and asparagine sidechain oxygens) at three values of r. Each gray dot corresponds to an input data point from the Top8000 database within the indicated value of r ± 0.1 Å. Contours are drawn at energy intervals of 0.1, with the maximum contour plotted for an energy of 0.2, such that the minimum energy contours are drawn for values of −0.7, −0.7, and −0.9 in (a), (b), and (c), respectively

Figure 4

2D contour plots of constant density through the 3D HBPot surfaces at ϕ = 130°. Panels (a)–(c) depict the Class I helix backbone–backbone, Class II non‐helix backbone–backbone, and Class VI sidechain glutamine/asparagine surfaces, respectively. The dashed curve corresponds to Equation (1), the HBDA target relationship between r and θ. Each gray dot corresponds to an instance of hydrogen bonding geometry from the Top8000 database if the corresponding value of ϕ has a value of 130 ± 4°. Contours are drawn at energy intervals of 0.1 with the maximum contour plotted for an energy of 0.2, such that the minimum energy contours are drawn for −0.7, −0.8, and −0.9 in panels (a), (b), and (c), respectively

Figure 5

The effect of the hydrogen bonding energy terms on the nonexperimental covalent, nonbonded, and dihedral‐angle terms. Black bars report values for the case of no explicit hydrogen bonding term, while red and cyan report results for the HBDB and HBPot terms, respectively. Panels (a), (b), and (c) depict root mean square deviation from ideal values of the bond, bond angle, and improper dihedral‐angle covalent energy terms. Panel (d) depicts the number of nonbonded clashes, as reported by Xplor‐NIH. Panel (e) reports the TorsionDB potential of mean force energy including an explicit hydrogen bonding term normalized by the TorsionDB energy observed when no hydrogen bonding term is used. In each panel, a smaller value indicates structures which are more consistent with the Xplor‐NIH force field, and the spread in value among the 20 lowest energy structures is indicated by the thin black error bars

Figure 6

The effect of the hydrogen bonding energy terms on the agreement of experimental restraints with back‐calculated values for 10 proteins. Panels (a) and (b) depict root mean square deviation agreement for distance and dihedral restraints, respectively. Agreement of RDC data calculated from structures is shown in panels (c) and (d). Panel (c) shows the RDC R‐factor for the calculation with the RDC term included in the structure calculation, while Panel (d) shows the R‐factor for calculations run without this term. In all panels, a smaller value indicates better agreement with experiment, and the spread in value among the 20 lowest energy structures is indicated by the thin black error bars

Figure 7

Backbone positional RMSD between regularized mean structures calculated with no hydrogen bonding term, using the HBDB term, and using the HBPot term for 10 proteins. The black/red bars represent the difference between structures computed with no hydrogen bonding term and those computed including the HBDB term. The black/cyan bars represent the differences between structures computed with no hydrogen bonding term with those computed including the HBPot term. The red/cyan bars represent the differences between structures calculated including HBDB or HBPot terms

Figure 8

Positional RMSD between structures calculated from NMR data compared with the corresponding crystal structures for GB1, ubiquitin, KH3, and EIN. Spread in fit among the 20 lowest energy structures is indicated by the thin black error bars. Panel (a) depicts the backbone atomic accuracy, while Panel (b) shows the sidechain accuracy measured after fitting backbone atomic coordinates

Figure 9

The number of hydrogen bonds reported by HBDB, VMD, and HBPot are shown in panels (a), (b), and (c), respectively, for the cases of no explicit hydrogen bond term, the use of the HBDB term, and the use of the HBPot term. The VMD and HBDB numbers report only on number of backbone–backbone hydrogen bonds. The blue bars represent the number of hydrogen bonds measured from the protonated reference structures for the four examples for which there are crystal structures

Figure 10

Hydrogen bond energies report the efficacy of the hydrogen bond energy terms. Panels (a), (b), and (c) report the HBDB, HBPot, and HBDA energy terms for the 10 protein example cases with either the HBDB or HBPot energy term, normalized by the energy corresponding to the calculations with no explicit hydrogen bonding energy. In each panel a horizontal line indicates signed unity, the normalized energy corresponding to using no hydrogen bonding term. Because a smaller (more negative or less positive) value indicates a better fit to the potential of mean force or (in the case of HBDA) empirical formula, bars below/above the line represent better/worse fits for the depicted energy term. For each bar, deviations in energy between the lowest 20 calculated structures are denoted by the thin black error bars