High-resolution crystal structures of protein helices reconciled with three-centered hydrogen bonds and multipole electrostatics

Abstract

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.6(13) α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.6(13/10)-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding.

Fig 1. Hydrogen-bonding alternatives; linear H-bond assumed by the Pauling/Donohue groups; three-centered hydrogen bonds to carbonyl oxygens that dominate crystal structures of small organic molecules [6].

Fig 2. Schematic stick-figure diagrams of α-helix (top left and middle) and 3₁₀-helix (bottom left and right) helices.

Fig 3. Reproduction of Fig 1 from Némethy et al. [9] showing an intermediate N-helix (3.6_13/10) with the helical parameters of the classical α-helix and bifurcated amide H-bonds (used with permission).

Fig 4. The appearance of electron density as a function of the nominal resolution of the experimental crystallographic data, (adapted from similar figure for the N-terminal fragment (Lys1—Val2—Phe3) of triclinic lysozyme (PDB: 2vb1) from Wlodawer et al. [33] for which permission to reproduce by the journal was not granted).

Fig 5. Left: Distribution of helical backbone torsion angles (Φ, Ψ) for 1.0–1.5 Å nominal resolution of 3,462 protein structures from the PDB.

Right: Conversion of density of high-resolution helices to a relative energy scale by Boltzmann-weighting the distribution.

Fig 6. Average values of Φ (Phi) and Ψ (Psi) torsion angles of helical residues in PDB binned by nominal crystallographic resolution.

This compensatory change in Φ, Ψ is due to a “crankshaft” motion [39] of the amide bond that maintains the relative positions of the α-carbons of the peptide backbone despite significant deviations in Φ, Ψ torsions.

Fig 7. Definition of helical parameters with an oligopeptide helix backbone (nitrogens in blue).

Left: Helix winding (Ω) is the angle between two adjacent Cα vectors (n = residues-per-turn/360). Right: Helix pitch (p) is the rise-per-residue, or vertical distance between Ω adjacent residues, projected on the helical axis.

Fig 8. Contours and 3D surface helical pitch (n d) overlaid on 2D φ, ψ plot.

Positions of classic α-helix (φ = −57, ψ = −47), 3₁₀-helix (φ = −49, ψ = −26), and experimental Némethy-, N- or 3.6_13/10-helix (φ = −62, ψ = −43) are indicated. Note that the helical pitch is nearly identical for the α- and 3.6_13/10-helices—they lie on a contour of essentially equal value.

Fig 9. Contours and 3D surface showing rise-per-residue (d in Å) overlaid on 2D φ,ψ plot.

Positions of classic α-helix (φ = −57, ψ = −47), 3₁₀-helix (φ = −49, ψ = −26), and Némethy-, N- or 3.6_13/10-helix (φ = −62, ψ = −43) are indicated. Note that d is approximately the same for the α- and 3.6_13/10-helices.

Fig 10. Contours and 3D surface showing number of residues-per-turn (n) overlaid on 2D φ, ψ plot.

Positions of classic α-helix (φ = −57, ψ = −47), 3₁₀-helix (φ = −49, ψ = −26), and experimental Némethy-, N- or 3.6_13/10-helix (φ = −62, ψ = −43) are indicated. Note that n is approximately the same for the α- and 3.6_13/10-helices.

Fig 11. Helix 8–18 from the crambin crystal structure [PDB:1ejg], viewed from above the N-terminus.

The average φ value along the helix was between the experimental Némethy-, N- or 3.6_13/10-helix and the α-helix. However, the average ψ value was between the experimental 3.6_13/10-helix and a 3₁₀-helix.

Fig 12. Transition of oligoalanine from its starting α-helical conformation to intermediate states that includes near α-, 3₁₀- and polyglycine conformations.

Fig 13. Ramachandran plot of backbone torsional angles from the AMOEBA BIO09 MD simulation of 12-residue oligoalanine.

Fig 14. The Φ, Ψ angles distribution of the data filtered with H-bond distance (<4 Å) and Φ, Ψ angles range (-100 -> 0, -70 -> 0).

The median of Φ, Ψ angles was Φ-72.8, Ψ-33.4.

Fig 15. Distance distribution of observed H-bonds filtered by H-bond distance (<4 Å) and Φ, Ψ angles range (-100 -> 0, -70 -> 0).

The medians of i+3 and i+4 distances were 2.97 Å and 2.28 Å, respectively.

Fig 16. Orthogonal views of ball-and-stick model of “dynamic” helix of 12-residue capped oligoalanine with two three-centered hydrogen bonds indicated (red dots).

Fig 17. Potential surfaces for torsional force-fields surfaces surrounding helical conformations for A. AMBER99sb, B. AMOEBABIO09, C. CHARMM22, D. OPLS-AA, and E. OPLS-AAL versus F. QM—MP2/6-311(1d,1p) basis set.

Fig 18. The potential surface near helical torsional angles for Ac-Ala-Ala-Ala-NMe as calculated by QM.

The red line traces the transition between the two energy minima-like conformers without an activation energy barrier.

Fig 19. The whole (top) and expanded (lower) Ramachandran plots of 12-residue oligo-Ala (left sides) and oligo-Aib (right sides) from AMOEBA replica-exchange MD simulation.

The 3₁₀-region in Aib is heavily occupied while in alanine it’s almost absent.

Fig 20. The hydrogen-bonding matrix of 12-residue capped oligo-Ala (left) and oligo-Aib (right) from AMOEBA replica-exchange MD simulation.

The acceptor+1(i->i+2) and acceptor+2(i->i+3), indicating 3₁₀ helix) in oligo-Aib is more heavily occupied than in oligo-Ala.

Fig 21. Contour plots of oligo-Ala dipole moment.

The dipole moment magnitudes of the classic α-helix, 3₁₀-helix and Nemethy-, N-, 3.6_13/10-helix are marked with circles.