β-hairpin forms by rolling up from C-terminal: topological guidance of early folding dynamics

Abstract

That protein folding is a non-random, guided process has been known even prior to Levinthal's paradox; yet, guided searches, attendant mechanisms and their relation to primary sequence remain obscure. Using extensive molecular dynamics simulations of a β-hairpin with key sequence features similar to those of >13,000 β-hairpins in full proteins, we provide significant insights on the entire pre-folding dynamics at single-residue levels and describe a single, highly coordinated roll-up folding mechanism, with clearly identifiable stages, directing structural progression toward native state. Additional simulations of single-site mutants illustrate the role of three key residues in facilitating this roll-up mechanism. Given the many β-hairpins in full proteins with similar residue arrangements and since β-hairpins are believed to act as nucleation sites in early-stage folding dynamics of full proteins, the topologically guided mechanism seen here may represent one of Nature's strategies for reducing early-stage folding complexity.

Figure 1. Dynamics of formation of residue-level turn structures and native turn in chignolin.

a) Folded chignolin, showing the native turn (NT) at the central turn region (emerald green) and the amino- and carboxyl-terminal strands (N-strand and C-strand, respectively; lime green). b) Four examples (coloured, solid structures) taken from the more than 13,000 β-hairpins which can be found in full proteins and which show features similar to chignolin (gray, transparent structures). c) Probability of residue-level turn structure formation when NT has not formed. NT is considered to form when the Cα-Cα distance between the corner residues Pro4 and Gly7, d_PG,Cα, is less than 0.7 nm. The corresponding probabilities when NT has formed are shown in the inset. Probabilities higher than 1% are indicated by open symbols. In both cases, the residues in the N-strand (Gly1-Asp3) never form turns. d) Sample trajectory, showing the root-mean-squared-distance, RMSD, as described previously (top panels), the radius of gyration R_g (middle panels), and the occurrences of turns (bottom panels), as identified using DSSP, in NT and the C-strand residues. While RMSD and R_g reflect the fluctuations in the overall structural features, the turn occurrences show more coordinated evolution. e) Turn propagation from the C-strand to the NT region in the “roll-up mechanism”. The probability of turn conformation is plotted as a function of time lapsed from a specific, pre-determined starting conformation, in this case conformations with turns at Thr8 and Trp9. The dark line marks the boundary of the C-strand from the NT region, Gly7-Pro4. Typical examples of backbone structures in the roll-up process are also shown.

Figure 2. Effect of single-site mutations on conformational features.

a-b) Ramachandran plots of the dihedral angles of (a) Tyr2 (in non-mutated chignolin) and (b) Ala2 (in chignolin-Y2A). Interactions between Tyr2 side chain and Pro4 ring forces Tyr2 to assume an extended conformation with magnitudes of backbone dihedral angles Φ and Ψ both close to ±180°. In the absence of side-chain interactions a helical conformation emerges at (Φ,Ψ) ~ (−80°,−20°). c–d) Probability density distribution of the distance between Gly1 and Pro4 Cα-atoms in (c) chignolin and (d) chignolin-Y2A. The distance remains relatively constant at ~0.96 nm in chignolin, corresponding to extended conformation for the N-strand. In contrast, without the side-chain interactions the N-strand can also assume a bent conformation, as indicated by the second peak at ~0.76 nm. e–f) Frequency of the occurrence of turn structure in each residue in (e) chignolin and (f) chignolin-P4A. Rigidity of Pro4 limits turn formation to the NT region and the C-strand of chignolin, whereas replacement of Pro4 with Ala allows turn formation also in the N-strand (Gly1-Asp3). g) Typical structure with turns at Thr8 and Trp9. The formation of turn structures at Thr8 and Trp9 is facilitated by interactions between Pro4 and Trp9. h) Lack of consistent turn propagation in the absence of Pro4-Trp9 interactions. In the same manner as in Figure 1e, the probability of turn conformation for the ten residues in chignolin-W9A is plotted as a function of lapsed time, again for given conformations with turns at Thr8 and Ala9 as starting point.