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 (3.613/10) 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.
Table 1.
Hydrogen-bond analysis of the PDB as a function of nominal crystallographic resolution.
Table 2.
Structural Percentage of the PDB as a function of nominal crystallographic resolution.
Table 3.
Hydrogen-bond analyses for neutron-diffraction data for 26 proteins.
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 3.613/10-helix (φ = −62, ψ = −43) are indicated. Note that the helical pitch is nearly identical for the α- and 3.613/10-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 3.613/10-helix (φ = −62, ψ = −43) are indicated. Note that d is approximately the same for the α- and 3.613/10-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 3.613/10-helix (φ = −62, ψ = −43) are indicated. Note that n is approximately the same for the α- and 3.613/10-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 3.613/10-helix and the α-helix. However, the average ψ value was between the experimental 3.613/10-helix and a 310-helix.
Table 4.
Backbone Torsional Angles of High-resolution (1ejg, 0.54 Å) Structure of Crambin 7–18 Helix (Fig 11).
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).
Table 5.
Relative energies of the three helical structures of Ac-Ala-Ala-Ala-NHMe by MP2/6–311(1d,1p) quantum calculations in vacuo.
Table 6.
Location of the two energy mimima-like positions on the potential energy surfaces of Ac-Ala-Ala-Ala-NHMe based on methodology.
Table 7.
Calculated dipole moments [65] in Debye using a modified set of parameters for solvation energy (Parse) partial atomic charges [67] for various capped 12-residue oligoalanine helices as well as for crambin and its isolated helix compared with those using AMOEBA multipoles.
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-, 3.613/10-helix are marked with circles.