Atomistic Simulation Approach to a Continuum Description of Self-Assembled β-Sheet Filaments

Abstract

We investigated the supramolecular structure and continuum mechanical properties of a beta-sheet nanofiber comprised of a self-assembling peptide ac-[RARADADA]2-am using computer simulations. The supramolecular structure was determined by constructing candidate filaments with dimensions compatible with those observed in atomic force microscopy and selecting the most stable ones after running molecular dynamics simulations on each of them. Four structures with different backbone hydrogen-bonding patterns were identified to be similarly stable. We then quantified the continuum mechanical properties of these identified structures by running three independent simulations: thermal motion analysis, normal mode analysis, and steered molecular dynamics. Within the range of deformations investigated, the filament showed linear elasticity in transverse directions with an estimated persistence length of 1.2-4.8 microm. Although side-chain interactions govern the propensity and energetics of filament self-assembly, we found that backbone hydrogen-bonding interactions are the primary determinant of filament elasticity, as demonstrated by its effective thickness, which is smaller than that estimated by atomic force microscopy or from the molecular geometry, as well as by the similar bending stiffness of a model filament without charged side chains. The generality of our approach suggests that it should be applicable to developing continuum elastic ribbon models of other beta-sheet filaments and amyloid fibrils.

Nanomechanics and intermolecular forces of amyloid revealed by four-dimensional electron microscopy

“…This is confirmed when we use a coarse-grained model for the stiffness of the sheet-sheet interface (18), Y intersheet = k intersheet =h, where k intersheet is the intersheet bond stiffness and h is an intersheet spacing of 10.4 Å, to calculate k intersheet = 0.07 N/m. The spring constant k hydrophobic has an expected range of between 0.04 and 0.1 N/m, varying from hydrophilic to hydrophobic (8,31,32). Not surprisingly, given that the sequence of the amyloid-crystalforming peptide (VQIVYK) is only weakly hydrophobic (average sequence hydrophobicity, +0.24), our measured k intersheet = 0.07 N/m falls at the midpoint of these values.…”

“…By accurately measuring the movement ðΔxÞ of the reflection (initially occurring at an equilibrium separation, x e ) upon initiation of the ultrafast temperature jump, we determine the relative expansion, or strain, e = Δx=x e . Atomistic simulations predict that the stretching elasticity of amyloid is linear for strains up to only e ∼ 0:1%, i.e., 10 −3 (8). The exquisite sensitivity and high spatiotemporal resolution of four-dimensional (4D) electron microscopy (9, 10) enables us to measure such minute deformations and directly probe, at the atomic level, the stiffness of the intermolecular forces stabilizing amyloid.…”

Elastic deformation and failure in protein filament bundles: Atomistic simulations and coarse-grained modeling

“…While it has not been experimentally determined whether RAD16-II β-sheets have parallel or antiparallel alignment, previous simulations have shown that the antiparallel structure has significantly lower energy [13]. To make antiparallel β-sheets, we assigned dihedral angles consistent with a β-sheet to the peptide backbone, and positioned one peptide every 4.8 Å.…”

“…Each β-sheet has a hydrophobic surface of alanine side chains while charged arginine and aspartic acid side chains form the opposing hydrophilic surface. An antiparallel β-sheet is thought to be favored, as it has a lower energy than a parallel formation, which would juxtapose like charges [13]. At concentrations on the order of 0.1%, RAD16-II forms a macroscopic gel.…”

“…These observations suggest that the stiffness of AFP gels is not limited primarily by slippage between filament bundles, which cross-linking should restrict, but by the stiffness of the filament bundles themselves. While β-sheet filaments have a high elastic modulus on the order of 10 GPa in tension [13], filament bundles may have little resistance to bending if slipping occurs between filaments. Such slippage reportedly occurs in bundles of carbon nanotubes [29], but this phenomenon had not yet been postulated for bundled amyloid filaments such as RAD16-II.…”