Theoretical Studies on the Origin of β-sheet Twisting

Abstract

Right-handed twisting is a fundamental structural feature of β-pleated sheets in globular proteins which is critical for their geometry and function. The origin of this twisting is poorly understood and has represented a challenge for theoretical chemistry for almost 30 years. Density functional theory using the B3LYP exchange-correlation functional and the split-valence 6-31G** basis set has been utilized to investigate the structure and conformational transitions of single and double-stranded antiparallel β-sheet models to determine the driving force for the right-handed twisting. Right-handed twisting is found to be an intrinsic property of a peptide main chain because of the difference in rotational potentials around N(sp2)−Cα(sp3) and C(sp2)−Cα(sp3) bonds. The difference arises from a tendency of the single Cα(sp3)−C(sp2) bonds to eclipse the lone pair of atoms N(sp2), which results in decreasing absolute values of dihedral angles φ but not ψ. This tendency is suppressed by hydrogen bonding between adjacent CO and NH groups within single β-strands, and released only when these bonds are disrupted by the interstrand CO···HN hydrogen bonding. The results obtained constitute the following paradigm of the origin of β-sheet twist: although right-handed twisting of β-sheets in globular proteins is an inherent property of the peptide backbone within single β-strands, it is unleashed by the interstrand hydrogen bonding in multistranded β-sheets. The observed pleating, right-handed twisting, skewed mutual orientation of β-strands, and intrinsic conformational variability of double-stranded antiparallel β-sheet motifs in globular proteins are explained from the first principles.

Design of nanostructured biological materials through self-assembly of peptides and proteins

“…Further pursuits will focus on controlling the uniformity of the self-assembled nanostructures, a critical criterion for applications in nanotechnology. The right-handed twist of the peptide backbone [31] in β-strand conformation leads to the formation of left-handed helical ribbons of regular pitch at the nanometer scale ( Figure 4). The molecular structure of these nanofibers is difficult to obtain, because they are not amenable to highresolution X-ray diffraction nor solution NMR.…”

A simple and realistic model system for studying hydrogen bonds in β-sheets

“…One can see that the chains twist right-handedly, as has been known for a long time for ␤-sheets. 10,42 A single Ala chain also twists slightly. The Gly chains do not twistneither the parallel nor the antiparallel chains.…”

“…[3][4][5][6] Previous theoretical investigations of ␤-sheets fall in two categories: Quantum mechanical studies have concentrated on small molecules whose structure was assumed to resemble the ␤-sheet structure to a certain degree. [7][8][9][10][11][12][13][14] The other strategy has been to analyze larger and realistic ␤-sheet structures in proteins with force field methods. 7,15 Thus there is either a payoff in method accuracy or in number of atoms in the model.…”

β‐Strand twisting/bending in soluble and transmembrane β‐barrel structures

“…In 1996, Wang et al reinforced the idea that the driving force for the right‐handed twist involves inter‐strand interactions because the free energy difference between twisted and nontwisted conformations of a single strand is very small . In 2000, Shamovsky et al used calculations based on density functional theory to show that a right‐handed twist of β‐strands is an inherent property of the peptide backbone within single β‐strands and that twisting is enhanced by inter‐strand hydrogen bonding (β‐bridge) in multi‐stranded β‐sheets . In 2002, Ho and Curmi showed that the intra‐strand O⋯C β steric clash constrains the angle psi to <116°, resulting in a bias toward a right‐handed twist .…”