Multi-strand β-sheet of Alzheimer Aβ(1-40) folds to β-strip helix: Implication for protofilament formation

X-ray fiber diffraction experiments on Alzheimer Aβ(1–40) fibrils formed in an assembly process thought to simulate a portion of the pathophysiological process in Alzheimer's disease, indicated protofilaments with tilted β-strands rather than strands oriented perpendicular to the fibril axis as is usually interpreted from cross-β patterns. The protofilament width and tilt angle determined by these experiments were used to predict a β-strip helix model–a β-helix-like structure in which multiple identical polypeptide molecules assemble in-register to form a helical sheet structure such that the outer strands 1 and m join with a register shift t–with m = 11 and t = 22. Starting from untwisted β-sheets comprising 10, 11, and 12 strands, multiple explicit solvent molecular dynamics (MD) simulations were performed to determine whether the sheets form β-strip helices matching the dimensions of the experimentally measured protofilament. In the simulations, the predicted 11-strand sheets curled up to form a closed β-strip helix-like structure with dimensions matching experimental values, whereas the 10- and 12-strand sheets did not form a closed helical structure. The 12-strand structure did, however, show similarity to a cross-β structure determined by a solid-state NMR experiment. The 11-strand β-strip helix resembles a trans-membrane β-barrel which could explain the ability of small oligomers of Aβ(1–40) to form toxic ion channels. A further consequence of opposite sides of the 11-strand strip coming together at a register shift of 22 is end-to-end joins between neighboring β-strip helices, resulting in a protofilament that keeps growing in both directions. Communicated by Ramaswamy H. Sarma

Haptic-assisted interactive molecular docking incorporating receptor flexibility

Haptic-assisted interactive docking tools immerse the user in an environment where intuition and knowledge can be used to help guide the docking process. Here we present such a tool where the user “holds” a rigid ligand via a haptic device through which they feel interaction forces with a flexible receptor biomolecule. To ensure forces transmitted through the haptic device are smooth and stable, they must be updated at a rate greater than 500 Hz. Due to this time constraint, the majority of haptic docking tools do not attempt to model the conformational changes that would occur when molecules interact during binding. Our haptic-assisted docking tool, “Haptimol Flexidock”, models a receptor’s conformational response to forces of interaction with a ligand whilst maintaining the required haptic refresh rate. In order to model receptor flexibility we use the method of linear response for which we determine the variance-covariance matrix of atomic fluctuations from the trajectory of an explicit-solvent Molecular Dynamics simulation of the ligand-free receptor molecule. Key to satisfying the time constraint is an eigenvector decomposition of the variance-covariance matrix which enables a good approximation to the conformational response of the receptor to be calculated rapidly. This exploits a feature of protein dynamics whereby most fluctuation occurs within a relatively small subspace. The method is demonstrated on Glutamine Binding Protein in interaction with glutamine, and Maltose Binding Protein in interaction with maltose. For both proteins, the movement that occurs when the ligand is docked near to its binding site matches the experimentally determined movement well. It is thought that this tool will be particularly useful for structure-based drug design

The role of the half-turn in determining structures of Alzheimer’s Aβ wild-type and mutants

Half-turns are shown to be the main determinants of many experimental Alzheimer’s Aβ fibril structures. Fibril structures contain three half-turn types, βαRβ, βαLβ and βεβ which each result in a ∼90° bend in a β-strand. It is shown that only these half-turns enable cross-β stacking and thus the right-angle fold seen in fibrils is an intrinsic feature of cross-β. Encoding a strand as a conformational sequence in β, αR, αL and ε(βL), pairwise combination rules for consecutive half-turns are used to decode this sequence to give the backbone path. This reveals how structures would be dramatically affected by a deletion. Using a wild-type Aβ(42) fibril structure and the pairwise combination rules, the Osaka deletion is predicted to result in exposure of surfaces that are mutually shielding from the solvent. Molecular dynamics simulations on an 11-mer β-sheet of Alzheimer’s Aβ(40) of the Dutch (E22Q), Iowa (D23N), Arctic (E22G), and Osaka (E22Δ) mutants, show the crucial role glycine plays in the positioning of βαRβ half-turns. Their “in-phase” positions along the sequence in the wild-type, Dutch mutant and Iowa mutant means that the half-folds all fold to the same side creating the same closed structure. Their out-of-phase positions in Arctic and Osaka mutants creates a flatter structure in the former and an S-shape structure in the latter which, as predicted, exposes surfaces on the inside in the closed wild-type to the outside. This is consistent with the gain of interaction model and indicates how domain swapping might explain the Osaka mutant’s unique properties

High quality rendering of protein dynamics in space filling mode

Producing high quality depictions of molecular structures has been an area of academic interest for years, with visualisation tools such as UCSF Chimera, Yasara and PyMol providing a huge number of different rendering modes and lighting effects. However, no visualisation program supports per-pixel lighting effects with shadows whilst rendering a molecular trajectory in space filling mode. In this paper, a new approach to rendering high quality visualisations of molecular trajectories is presented. To enhance depth, ambient occlusion is included within the render. Shadows are also included to help the user perceive relative motions of parts of the protein as they move based on their trajectories. Our approach requires a regular grid to be constructed every time the molecular structure deforms allowing per-pixel lighting effects and ambient occlusion to be rendered every frame, at interactive refresh rates. Two different regular grids are investigated, a fixed grid and a memory efficient compact grid. The algorithms used allow trajectories of proteins comprising of up to 300,000 atoms in size to be rendered at ninety frames per second on a desktop computer using the GPU for general purpose computations. Regular grid construction was found to only take up a small proportion of the total time to render a frame. It was found that despite being slower to construct, the memory efficient compact grid outperformed the theoretically faster fixed grid when the protein being rendered is large, owing to its more efficient memory access patterns. The techniques described could be implemented in other molecular rendering software

Multidimensional replica-exchange method for free-energy calculations

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.Comment: 13 pages, (ReVTeX), 9 figures. J. Chem. Phys. 113 (2000), in pres

Protein Electron Transfer Reorganization Energy Spectrum from Normal Mode Analysis. 2. Application to Ru-Modified Cytochrome c

In an accompanying paper (part 1) we presented a model (NMRES) that describes the coupling of protein fluctuations to electron transfer. The NMRES model, employing normal mode analysis that incorporates Tanford-Kirkwood reaction field energies, relates each normal mode to a mode-specific reorganization energy (λ k prot ), ultimately yielding a protein λ spectrum. In this paper we have successfully applied the NMRES model and analyzed intramolecular electron transfer in Ru-modified cytochrome c (at His33). The NMRES estimate for the total protein λ was found to be 15.6 kcal/mol, while the bulk solvent contribution was found to be 7.2 kcal/mol. Of this 15.6 kcal/mol, the high-frequency inner sphere protein modes contributed 3.2 kcal/mol (λ in prot ), while the remaining 12.4 kcal/mol (λ out prot ) arose from the low-frequency outer sphere protein modes, the focus of this paper. Out of about 600 "soft" low-frequency modes, 60% contributed very little, while the remaining 40% contributed more or less equally. There were no special soft modes in terms of contribution to λ out prot , structurally or energetically. In other words, although not all the soft modes contributed, those that did shared the coupling more or less equally, implying that minor changes in the dynamic structure will not alter the total λ significantly. This could be the reason that the experimental λ on Ru-modified (at various His sites) cytochrome c is found to be almost invariant

Hydration Effect on Low-Frequency Protein Dynamics Observed in Simulated Neutron Scattering Spectra

Hydration effects on protein dynamics were investigated by comparing the frequency dependence of the calculated neutron scattering spectra between full and minimal hydration states at temperatures between 100 and 300 K. The protein boson peak is observed in the frequency range 1–4 meV at 100 K in both states. The peak frequency in the minimal hydration state shifts to lower than that in the full hydration state. Protein motions with a frequency higher than 4 meV were shown to undergo almost harmonic motion in both states at all temperatures simulated, whereas those with a frequency lower than 1 meV dominate the total fluctuations above 220 K and contribute to the origin of the glass-like transition. At 300 K, the boson peak becomes buried in the quasielastic contributions in the full hydration state but is still observed in the minimal hydration state. The boson peak is observed when protein dynamics are trapped within a local minimum of its energy surface. Protein motions, which contribute to the boson peak, are distributed throughout the whole protein. The fine structure of the dynamics structure factor is expected to be detected by the experiment if a high resolution instrument (<∼20 μeV) is developed in the near future

カスケード型超並列シミュレーションによるタンパク質構造遷移のパスウェイ探索

要旨あり生体高分子の揺らぎとダイナミクス－シミュレーションと実験の統計解析－研究詳

Spontaneous Quaternary and Tertiary T-R Transitions of Human Hemoglobin in Molecular Dynamics Simulation

We present molecular dynamics simulations of unliganded human hemoglobin (Hb) A under physiological conditions, starting from the R, R2, and T state. The simulations were carried out with protonated and deprotonated HC3 histidines His(β)146, and they sum up to a total length of 5.6µs. We observe spontaneous and reproducible T→R quaternary transitions of the Hb tetramer and tertiary transitions of the α and β subunits, as detected from principal component projections, from an RMSD measure, and from rigid body rotation analysis. The simulations reveal a marked asymmetry between the α and β subunits. Using the mutual information as correlation measure, we find that the β subunits are substantially more strongly linked to the quaternary transition than the α subunits. In addition, the tertiary populations of the α and β subunits differ substantially, with the β subunits showing a tendency towards R, and the α subunits showing a tendency towards T. Based on the simulation results, we present a transition pathway for coupled quaternary and tertiary transitions between the R and T conformations of Hb