Building native protein conformation from highly approximate backbone torsion angles

Abstract

Reconstructing a protein in three dimensions from its backbone torsion angles is an ongoing challenge because minor inaccuracies in these angles produce major errors in the structure. As a familiar example, a small change in an elbow angle causes a large displacement at the end of your arm, the longer the arm, the larger the displacement. Even accurate knowledge of the backbone torsions and is insufficient, owing to the small, but cumulative, deviations from ideality in backbone planarity, which, if ignored, also lead to major errors in the structure. Against this background, we conducted a computational experiment to assess whether protein conformation can be determined from highly approximate backbone torsion angles, the kind of information that is now obtained readily from NMR. Specifically, backbone torsion angles were taken from proteins of known structure and mapped into 60°؋ 60°grid squares, called mesostates. Side-chain atoms beyond the ␤-carbon were discarded. A mesostate representation of the protein backbone was then used to extract likely candidates from a fragment library of mesostate pentamers, followed by Monte Carlo-based fragment-assembly simulations to identify stable conformations compatible with the given mesostate sequence. Only three simple energy terms were used to gauge stability: molecular compaction, soft-sphere repulsion, and hydrogen bonding. For the six representative proteins described here, stable conformers can be partitioned into a remarkably small number of topologically distinct clusters. Among these, the native topology is found with high frequency and can be identified as the cluster with the most favorable energy.protein structure ͉ protein secondary structure ͉ protein fragment assembly ͉ Monte Carlo simulation P rotein molecules are known to undergo a reversible disorder order transition (1). In the classical view, the unfolded state is thought to be a structurally featureless ensemble that adopts its native structure spontaneously and uniquely under conditions that favor folding. For many small proteins of biophysical interest, this well studied folding reaction is apparently a two-state process. Accordingly, it can be represented by the equation: U(nfolded)^N(ative), with equilibrium constant, K eq ϭ N͞U, and free energy, ⌬G 0 ϭ ϪRT ln K eq , the free energy difference between the two populations. Central to this view, U is thought to be largely comprised of randomly coiled molecules, and N is thought to be largely comprised of uniquely structured molecules.Lately, we have been exploring the doubly divergent alternative view that the unfolded state is more organized (2) and the folded state is less homogeneous (3) than previously thought. If so, then both states can be treated productively as constrained thermodynamic ensembles. Numerous recent papers suggest that the unfolded population is not featureless, despite the fact that it does indeed exhibit random-coil statistics (4). Based on residual dipolar couplings from NMR, Shortle (5) and Shortle and Ackerman (6) have a...

A backbone-based theory of protein folding

“…In simulations, correct secondary structure assignments together with hydrogen bonding are sufficient to fold a collapsed backbone chain, devoid of side chains, to its native conformation (81,82,123). All of this suggests that the backbone plays the dominant role in protein folding.…”

“…The sidechain:backbone interactions in capping motifs that bracket helices are all within a few residues of the helix termini (78,79). Once established, these backbone elements determine the tertiary structure, an old idea (80) extended recently (75,81,82).…”

“…In other words, even one unsatisfied hydrogen bond is unlikely. This constraint alone is sufficient to limit a protein solution to a few native-like populations when conditions favor collapse (81,82).…”

Fragment‐HMM: A new approach to protein structure prediction

“…Therefore, it is impossible to cover the whole conformation space by a limited number of structural motifs. This drawback limits the accuracy of protein structure prediction (Holmesand and Tsai 2004;Gong et al 2005). …”

“…Shortle argued that these propensities are the results of local side-chain-backbone interactions and may restrict the denatured conformation ensemble to a relatively small subset of native-like conformations. Gong et al (2005) also investigated the protein structure-reconstructing problem from coarse-grained estimation of the native torsion angle. The only difference in these works lies at the definition of a Ramachandran basin: Gong et al (2005) partitioned both f and c angle intervals into six ranges, each range of 60°; thus, the Ramachandran map is partitioned into 36 basins uniformly.…”