Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure

GeNMR: a web server for rapid NMR-based protein structure determination

GeNMR (GEnerate NMR structures) is a web server for rapidly generating accurate 3D protein structures using sequence data, NOE-based distance restraints and/or NMR chemical shifts as input. GeNMR accepts distance restraints in XPLOR or CYANA format as well as chemical shift files in either SHIFTY or BMRB formats. The web server produces an ensemble of PDB coordinates for the protein within 15–25 min, depending on model complexity and completeness of experimental restraints. GeNMR uses a pipeline of several pre-existing programs and servers to calculate the actual protein structure. In particular, GeNMR combines genetic algorithms for structure optimization along with homology modeling, chemical shift threading, torsion angle and distance predictions from chemical shifts/NOEs as well as ROSETTA-based structure generation and simulated annealing with XPLOR-NIH to generate and/or refine protein coordinates. GeNMR greatly simplifies the task of protein structure determination as users do not have to install or become familiar with complex stand-alone programs or obscure format conversion utilities. Tests conducted on a sample of 90 proteins from the BioMagResBank indicate that GeNMR produces high-quality models for all protein queries, regardless of the type of NMR input data. GeNMR was developed to facilitate rapid, user-friendly structure determination of protein structures via NMR spectroscopy. GeNMR is accessible at http://www.genmr.ca

Site-specific perturbations of alpha-synuclein fibril structure by the Parkinson's disease associated mutations A53T and E46K.

PMCID: PMC3591419This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Parkinson's disease (PD) is pathologically characterized by the presence of Lewy bodies (LBs) in dopaminergic neurons of the substantia nigra. These intracellular inclusions are largely composed of misfolded α-synuclein (AS), a neuronal protein that is abundant in the vertebrate brain. Point mutations in AS are associated with rare, early-onset forms of PD, although aggregation of the wild-type (WT) protein is observed in the more common sporadic forms of the disease. Here, we employed multidimensional solid-state NMR experiments to assess A53T and E46K mutant fibrils, in comparison to our recent description of WT AS fibrils. We made de novo chemical shift assignments for the mutants, and used these chemical shifts to empirically determine secondary structures. We observe significant perturbations in secondary structure throughout the fibril core for the E46K fibril, while the A53T fibril exhibits more localized perturbations near the mutation site. Overall, these results demonstrate that the secondary structure of A53T has some small differences from the WT and the secondary structure of E46K has significant differences, which may alter the overall structural arrangement of the fibrils

BioMagResBank

The BioMagResBank (BMRB: www.bmrb.wisc.edu) is a repository for experimental and derived data gathered from nuclear magnetic resonance (NMR) spectroscopic studies of biological molecules. BMRB is a partner in the Worldwide Protein Data Bank (wwPDB). The BMRB archive consists of four main data depositories: (i) quantitative NMR spectral parameters for proteins, peptides, nucleic acids, carbohydrates and ligands or cofactors (assigned chemical shifts, coupling constants and peak lists) and derived data (relaxation parameters, residual dipolar couplings, hydrogen exchange rates, pKa values, etc.), (ii) databases for NMR restraints processed from original author depositions available from the Protein Data Bank, (iii) time-domain (raw) spectral data from NMR experiments used to assign spectral resonances and determine the structures of biological macromolecules and (iv) a database of one- and two-dimensional 1H and 13C one- and two-dimensional NMR spectra for over 250 metabolites. The BMRB website provides free access to all of these data. BMRB has tools for querying the archive and retrieving information and an ftp site (ftp.bmrb.wisc.edu) where data in the archive can be downloaded in bulk. Two BMRB mirror sites exist: one at the PDBj, Protein Research Institute, Osaka University, Osaka, Japan (bmrb.protein.osaka-u.ac.jp) and the other at CERM, University of Florence, Florence, Italy (bmrb.postgenomicnmr.net/). The site at Osaka also accepts and processes data depositions

How exactly did the Universe become neutral?

We present a refined treatment of H, He I, and He II recombination in the early Universe. The difference from previous calculations is that we use multi-level atoms and evolve the population of each level with redshift by including all bound-bound and bound-free transitions. In this framework we follow several hundred atomic energy levels for H, He I, and He II combined. The main improvements of this method over previous recombination calculations are: (1) allowing excited atomic level populations to depart from an equilibrium distribution; (2) replacing the total recombination coefficient with recombination to and photoionization from each level directly at each redshift step; and (3) correct treatment of the He I atom, including the triplet and singlet states. We find that the ionization fraction x_e = n_e/n_H is approximately 10% smaller at redshifts <~800 than in previous calculations, due to the non-equilibrium of the excited states of H, which is caused by the strong but cool radiation field at those redshifts. In addition we find that He I recombination is delayed compared with previous calculations, and occurs only just before H recombination. These changes in turn can affect the predicted power spectrum of microwave anisotropies at the few percent level. Other improvements such as including molecular and ionic species of H, including complete heating and cooling terms for the evolution of the matter temperature, including collisional rates, and including feedback of the secondary spectral distortions on the radiation field, produce negligible change to x_e. The lower x_e at low z found in this work affects the abundances of H molecular and ionic species by 10-25%. However this difference is probably not larger than other uncertainties in the reaction rates.Comment: 24 pages, including 18 figures, using emulateapj.sty, to appear in ApJ, the code recfast can be obtained at http://www.astro.ubc.ca/people/scott/recfast.html (in FORTRAN) and http://cfa-www.harvard.edu/~sasselov/rec/ (in C

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde

HMDB: a knowledgebase for the human metabolome

The Human Metabolome Database (HMDB, http://www.hmdb.ca) is a richly annotated resource that is designed to address the broad needs of biochemists, clinical chemists, physicians, medical geneticists, nutritionists and members of the metabolomics community. Since its first release in 2007, the HMDB has been used to facilitate the research for nearly 100 published studies in metabolomics, clinical biochemistry and systems biology. The most recent release of HMDB (version 2.0) has been significantly expanded and enhanced over the previous release (version 1.0). In particular, the number of fully annotated metabolite entries has grown from 2180 to more than 6800 (a 300% increase), while the number of metabolites with biofluid or tissue concentration data has grown by a factor of five (from 883 to 4413). Similarly, the number of purified compounds with reference to NMR, LC-MS and GC-MS spectra has more than doubled (from 380 to more than 790 compounds). In addition to this significant expansion in database size, many new database searching tools and new data content has been added or enhanced. These include better algorithms for spectral searching and matching, more powerful chemical substructure searches, faster text searching software, as well as dedicated pathway searching tools and customized, clickable metabolic maps. Changes to the user-interface have also been implemented to accommodate future expansion and to make database navigation much easier. These improvements should make the HMDB much more useful to a much wider community of users

Star formation at very low metallicity. II: On the insignificance of metal-line cooling during the early stages of gravitational collapse

We study the influence of low levels of metal enrichment on the cooling and collapse of ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations. Our initial conditions represent protogalaxies forming within a fossil HII region -- a previously ionized HII region which has not yet had time to cool and recombine. Prior to cosmological reionization, such regions should be relatively common, since the characteristic lifetimes of the likely ionizing sources are significantly shorter than a Hubble time. We show that in these regions, H_2 is the dominant and most effective coolant, and that it is the amount of H_2 formed that determines whether or not the gas can collapse and form stars. At the low metallicities (Z < 10^{-3} Z_sun) thought to be associated with the transition from population III to early population II star formation, metal line cooling has an almost negligible effect on the evolution of low density gas, altering the density and temperature evolution of the gas by less than 1% compared to the metal-free case at densities below 1 cm^{-3} and temperatures above 2000 K. Although there is evidence that metal line cooling becomes more effective at higher density, we find no significant differences in behaviour from the metal-free case at any density below our sink particle creation threshold at n = 500 cm^{-3}. Increasing the metallicity also increases the importance of metal line cooling, but it does not significantly affect the dynamical evolution of the low density gas until Z = 0.1 Z_sun. This result holds regardless of whether or not an ultraviolet background is present.Comment: 38 pages, 8 figures, AASTex. Accepted by ApJ. Corrected typos and reference