New insights into the interdependence between amino acid stereochemistry and protein structure

Abstract

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.

Figure 1

Stick representation of Leu (left) and Ile (right) dipeptide mimetics. The backbone dihedral angles, ϕ and ψ, and the side-chain dihedral angles χ₁ and χ₂ are highlighted, with positive angles indicated by the arrows. The methyl hydrogen atoms were added using the REDUCE program (56). The C_α atoms of the central, proceeding (i + 1), and trailing (i − 1) amino acids are labeled. Carbon, nitrogen, oxygen, and hydrogen atoms are shaded pink, blue, oxygen, and white, respectively. To see this figure in color, go online.

Figure 2

Observed probability distributions for the backbone dihedral angles P(ϕ,ψ) (top) and side-chain dihedral angles P(χ₁, χ₂) (bottom) binned in 5° × 5° increments for Leu (left) and Ile (right) from protein crystal structures in the culled Dunbrack database. (a–d) The sums of the probability distributions over all ϕ and ψ in a and b, or over all χ₁ and χ₂, in c and d equal one. In c and d, the probability values within each of the nine χ₁ and χ₂ boxes are labeled.

Figure 3

Calculated probability distributions of the sterically allowed side-chain dihedral-angle combinations χ₁ and χ₂ (5° × 5° bins) from the steric plus stereochemical constraint model (in b, d, f, h, and j) after averaging over all Ile configurations with the ϕ and ψ backbone dihedral angles given in a, c, e, g, and i, respectively. Panel a shows the distribution of ϕ and ψ from the culled Dunbrack database. Panel c indicates that the dipeptide mimetics derived from the culled Dunbrack database have ϕ and ψ set to the canonical α-helix values, ϕ = −60° and ψ = −45°. Panels e, g, and i represent uniform sampling of ϕ and ψ values in the shaded regions that coincide roughly with the α-helix, β-sheet, and α-helix plus β-sheet regions of the Ramachandran plot outer limits (dashed line) for τ = 115°. Note that sterically allowed conformations can occur outside the Ramachandran outer limits because we are not including clashes between backbone atoms. To see this figure in color, go online.

Figure 4

Calculated probability distributions P(χ₁,χ₂) of the sterically allowed side-chain dihedral-angle combinations χ₁ and χ₂ using the hard-sphere plus stereochemical constraint model for Ile dipeptides extracted from protein crystal structures in the culled Dunbrack database, after setting them to particular values of the backbone dihedral angles ϕ and ψ indicated in each panel. The sum of the P(χ₁, χ₂) distributions over all χ₁ and χ₂ equals one in each panel separately. To see this figure in color, go online.

Figure 5

Calculated probability distributions P(ϕ, ψ) based on the sterically allowed combinations of Ile side-chain dihedral angles in boxes 1–9 (Fig. 2 d) in each panel. The Ramachandran plot inner (red) and outer (blue) limits for τ = 115° are indicated. The sums of the distributions P(ϕ, ψ) over all ϕ and ψ equal one for each panel separately. To see this figure in color, go online.

Figure 6

(a–c) Calculated probability distribution P(χ₁, χ₂) of the sterically allowed combinations of χ₁ and χ₂ for (a) Ile dipeptides extracted from protein crystal structures in the culled Dunbrack database with backbone dihedral angles for all residues rotated to ϕ = −60° and ψ = −45° (same as Fig. 3c); (b) 8970 randomly generated Ile dipeptide mimetics with the backbone dihedral angles rotated to ϕ = −60° and ψ = −45°, bond lengths, bond angles, and dihedral angles ω (from residues i and i + 1) chosen randomly from Gaussian distributions with the same mean, SD, and multivariate correlations as found in the culled Dunbrack database; and (c) 8970 randomly generated Ile dipeptide mimetics with backbone dihedral angles set to ϕ = −60° and ψ = −45° and bond lengths, bond angles, and ω-dihedral angles chosen randomly from Gaussian distributions with only means and SDs that match the culled Dunbrack database. Panels d–f show the correlation coefficients between the 12 bond lengths, 15 bond angles, and two backbone ω-dihedral angles from the Ile dipeptide mimetics employed to calculate the probability distributions P(χ₁, χ₂) in a–c, respectively. The axes labels in d–f index the bond lengths, bond angles, and dihedral angles as shown in Table 1. To see this figure in color, go online.

Figure 7

(a–j) Calculated probability distributions of the sterically allowed side-chain dihedral-angle combinations χ₁ and χ₂ (5°×5° bins) from the steric plus stereochemical constraint model (in b, d, f, h, and j) after averaging over all Leu configurations with ϕ and ψ backbone dihedral angles given in a, c, e, g, and i, respectively. See Fig. 3 for additional information. To see this figure in color, go online.