Physical-chemical determinants of turn conformations in globular proteins

Abstract

Globular proteins are assemblies of alpha-helices and beta-strands, interconnected by reverse turns and longer loops. Most short turns can be classified readily into a limited repertoire of discrete backbone conformations, but the physical-chemical determinants of these distinct conformational basins remain an open question. We investigated this question by exhaustive analysis of all backbone conformations accessible to short chain segments bracketed by either an alpha-helix or a beta-strand (i.e., alpha-segment-alpha, beta-segment-beta, alpha-segment-beta, and beta-segment-alpha) in a nine-state model. We find that each of these four secondary structure environments imposes its own unique steric and hydrogen-bonding constraints on the intervening segment, resulting in a limited repertoire of conformations. In greater detail, an exhaustive set of conformations was generated for short backbone segments having reverse-turn chain topology and bracketed between elements of secondary structure. This set was filtered, and only clash-free, hydrogen-bond-satisfied conformers having reverse-turn topology were retained. The filtered set includes authentic turn conformations, observed in proteins of known structure, but little else. In particular, over 99% of the alternative conformations failed to satisfy at least one criterion and were excluded from the filtered set. Furthermore, almost all of the remaining alternative conformations have close tolerances that would be too tight to accommodate side chains longer than a single beta-carbon. These results provide a molecular explanation for the observation that reverse turns between elements of regular secondary can be classified into a small number of discrete conformations.

Figure 1.

Fragments that link elements of secondary structure. Two- and three-residue fragments were extracted from the Protein Coil Library (Fitzkee et al. 2005b), a repository of all non-α-helix and non-β-sheet residues culled from the PISCES server (Wang and Dunbrack Jr. 2003). This fragment data set was supplemented by all one-residue links. (A) Histogram of all non-α-helix and non-β-sheet fragment lengths. One-, two-, and three-residue fragments are the most abundant (shaded bars). (B) Histogram of observed crossing angles between secondary-structure elements. Crossing angles between elements linked by one-, two-, and three-residue fragments (shaded bars) have angles in the range of 110° to 180°, reversing the overall chain direction.

Figure 2.

Turn conformations populate a limited set of discrete conformations. Backbone ϕ,ψ angles of fragments are contoured, revealing discrete conformational basins. The four rows correspond to the four microenvironments, and panels in each row are plots of the observed conformations of one-, two-, and three-residue fragments: (row 1, A–C) helix–helix; (row 2, D–F) helix–strand; (row 3, G–I) strand–helix; and (row 4, J–L) strand–strand. Every fragment length (one-, two-, or three-residue) in each microenvironment (α–α, α–β, β–α, and β–β) is identified by an arbitrarily assigned color (red, blue, or yellow) that is maintained in successive panels of that turn type. Contour levels are measured by the vertical bars associated with these 12 (3 fragment lengths × 4 microenvironments) possible categories. It is apparent that only a small number of discrete conformations (28 in all, listed in Table 1) are observed in the 24 backbone ϕ,ψ pairs (one for each panel in the figure) for these 12 categories, and their conformations are particular to each secondary-structure microenvironment.

Figure 3.

Three examples illustrating topological, steric, and hydrogen-bonding restrictions imposed by bracketing elements of secondary structure. Atoms that violate steric or hydrogen-bond restrictions are depicted as space-filling spheres, overlaid on a ball-and-stick representation of the structure, with ribbon diagrams marking helices and strands. (A) In a one-residue fragment, the same backbone conformation (ϕ,ψ = −120°, 90°) reverses the chain direction when situated between two α-helices (left) but not when situated between two β-strands (right). (B) In a two-residue fragment, the same backbone conformation (ϕ₁,ψ₁ = −90°, −30°; ϕ₂,ψ₂ = –80°, 130°) is sterically allowed in a strand–helix pair (left) but causes a steric clash between two β-carbons in a helix–helix pair (right). (C) In a three-residue fragment, the same backbone conformation (ϕ₁,ψ₁ = −75°, 5°; ϕ₂,ψ₂ = 65°, 40°; ϕ₃,ψ₃ = –100°, 80°) is fully hydrogen-bonded when situated between a helix–helix pair (left) but not when situated between a strand–helix pair (right).

Figure 4.

Simulated turns binned by crossing angle and acceptance ratio. (A) Crossing angles and acceptance ratios were subdivided into 10 bins (dashed lines). Effective turns reverse the chain direction (i.e., high crossing angles) and have backbone conformations that engender clash-free, hydrogen-bond–satisfied structures (i.e., high acceptance ratios); such conformers fall into low-numbered bins. Values from simulations of authentic turns (red ×'s) fall exclusively into bin 2, indicating that these structures satisfy topological, steric, and hydrogen-bonding restrictions. (B) A population histogram showing the fraction of simulated conformations in each bin. Simulations of alternative conformations (unfilled bars) are distributed across multiple, higher-numbered bins; most fall into bin 10, indicating either crossing angles that fail to reverse the chain direction or structures with steric violations and/or unsatisfied hydrogen bonds. In contrast, simulations using representative backbone torsion angles gleaned from proteins of known structure (Fig. 2) fall exclusively into bin 2 (red bar).

Scheme 1.

Figure 5.

False positives have tight tolerances. Alternative conformers simulated using the nine-state model result in 14 false positives that satisfy authentic turn criteria (Table 2), but most of these cases are disfavored owing to C_β atoms with close tolerances, too tight to accommodate residues other than glycine or alanine. Accordingly, sparsely populated conformations in Fig. 2 can be rationalized by an incompatibility with bulky side chains. C_β atoms in question are depicted as space-filling spheres, overlaid on a ball-and-stick representation of the structure, with ribbon diagrams marking helices and strands. (A) A three-residue fragment (ϕ₁,ψ₁ = 60°, 30°; ϕ₂,ψ₂ = 60°, 30°; ϕ₃,ψ₃ = −80°, 80°) that brings C_β atoms into van der Waals contact. (B) A three-residue fragment (ϕ₁,ψ₁ = 60°, 30°; ϕ₂,ψ₂ = −80°, 160°; ϕ₃,ψ₃ = −80°, 160°) that brings C_β atoms into close proximity.