Fig. 1 Populated high-energy passes for transitions between ϕ < 0° and ϕ > 0° conformations. (A) A standard geometry (13) alanine dipeptide with ϕ,ψ = 0°,+90°. The positive rotation direction for the ϕ and ψ torsion angles (magenta), the standard values for the five backbone bond angles not involving Cβ (black), and the O−1…C clash (red dashes with distance) are indicated. (B) An alanine dipeptide, as in (A), but with ϕ,ψ = 0°,−90°. The H+1…Cβ approach (orange dashes with distance) also shown, matches the “normal” close approach limit of 2.4 Å for these atoms (14) and causes the ψ ~ −90° transition track to be somewhat more unfavorable than the ψ ~ +90° track [~7 versus ~5 kcal/mol as seen in (D)]. (C) O−1…C distances as a function of φ for standard geometry alanine dipeptides. The expected normal (2.8 Å) and extreme (2.7 Å) approach limits (14) are indicated; red dashed lines at ϕ = ±53° mark where the normal approach limit is crossed. (D) A Ramachandran plot with energy contours for the alanine dipeptide calculated using an adaptive force biasing algorithm (5) displayed in steps of 2 kcal/mol (pink). Also shown (small black dots) are 616,212 non-glycine residues from representative ≤1.5 Å resolution structures; of these, 16,613 (or ~3%) have ϕ > 0°. Reliable (large circles) and unreliable (large triangles) observations between −35° < ϕ < +35° and +110° < ϕ < +160° are highlighted. The best-fit lines for reliable residues between −35° < φ < +35° are shown for both the ψ = +90° and ψ = −90° passes (green).
Fig. 2 Electron density evidence for four residues adopting conformations in the −35° < ϕ < +35° range. Each panel shows a residue with its 2FO − FC electron density, its backbone bond angle values (black), its φ,ψ angles (inset box), and its O−1…C approach (green line with distance). (A) His261 from PDB entry 4N1I [1.0 Å resolution; contoured at 6.2 × root mean square electron density (ρrms)]. (B) Ser115 from PDB entry 2DDX (0.86 Å resolution; contoured at 7.0 × ρrms). (C) Asp249 from PDB entry 4AYO (0.85 Å resolution; contoured at 7.0 × ρrms). (D) Ile152 from PDB entry 3NOQ (1.0 Å resolution; contoured at 5.5 × ρrms).
Fig. 3 Systematic deformations of geometry associated with transition through the high-energy ϕ ~ 0° passes. (A) Observed average O−1…C distance (large purple dots and error bars) plotted as a function of ϕ (see table S4 for details), along with each data point (blue triangles), and the O−1…C distance predicted by standard geometry (black curve), by the empirically defined φ-dependent geometry functions (green curve), and by the AMBER FF99SB force field (orange curve). Red dashed lines at ϕ = ± 53° are as in Fig. 1B. (B) Average backbone bond angles (black dots with error bars) as a function of ϕ (see table S4 for details) along with cosine functions fit to the data (green curves; see table S3 for the equations). All error bars are SEM.
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/9/e1501188/DC1
Fig. S1. Electron density evidence for a reliable residue adopting a conformation in the +110° < ϕ < +160° range.
Fig. S2. ϕ,ψ angles describing the local conformational context of the mountain pass residues.
Fig. S3. Four diverse examples showing the contexts of residues adopting a ϕ ~ 0° conformation.
Fig. S4. How the average bond angle variations obtained by treating the ψ ≤ 0° and ψ ≥ 0° transitions separately compare with each other and with those based on the combined data.
Fig. S5. AMBER minimizations of alanine dipeptides distort bond angles to alleviate the O−1 … C steric clash in ϕ ~ 0 conformations.
Table S1. Complete list of analyzed ϕ ~ 0 mountain pass residues.
Table S2. Frequency of amino acid types in the mountain pass transition region.
Table S3. Equations governing ϕ-dependent changes in geometry during transition through the mountain pass.
Table S4. Further details of data plotted in Fig. 3 including the ranges for and numbers of observations in each ϕ bin and the average distances and angles.
Movie S1. An alanine dipeptide animation generated according to the “general” model of the ψ ~ +90° conformational transition described in this paper.
References (34, 35)
Additional Files
Supplementary Materials
This PDF file includes:
- Fig. S1. Electron density evidence for a reliable residue adopting a conformation in the +110° < ϕ < +160° range.
- Fig. S2. ϕ,ψ angles describing the local conformational context of the mountain pass residues.
- Fig. S3. Four diverse examples showing the contexts of residues adopting a ϕ ~ 0° conformation.
- Fig. S4. How the average bond angle variations obtained by treating the ψ ≤ 0° and ψ ≥ 0° transitions separately compare with each other and with those based on the combined data.
- Fig. S5. AMBER minimizations of alanine dipeptides distort bond angles to alleviate the O−1 … C steric clash in ϕ ~ 0 conformations.
- Table S1. Complete list of analyzed ϕ ~ 0 mountain pass residues.
- Table S2. Frequency of amino acid types in the mountain pass transition region.
- Table S3. Equations governing ϕ-dependent changes in geometry during transition through the mountain pass.
- Table S4. Further details of data plotted in Fig. 3 including the ranges for and numbers of observations in each ϕ bin and the average distances and angles.
- References (34, 35)
- Legend for movie S1
Other Supplementary Material for this manuscript includes the following:
- Movie S1 (.mov format). An alanine dipeptide animation generated according to the “general” model of the ψ ~ +90° conformational transition described in this paper.
Files in this Data Supplement:
