476 research outputs found
Effects of Large-Scale Convection on p-mode Frequencies
We describe an approach for finding the eigenfrequencies of solar acoustic
modes (p modes) in a convective envelope in the WKB limit. This approximation
restricts us to examining the effects of fluid motions which are large compared
to the mode wavelength, but allows us to treat the three-dimensional mode as a
localized ray. The method of adiabatic switching is then used to investigate
the frequency shifts resulting from simple perturbations to a polytropic model
of the convection zone as well as from two basic models of a convective cell.
We find that although solely depth-dependent perturbations can give frequency
shifts which are first order in the strength of the perturbation, models of
convective cells generate downward frequency shifts which are second order in
the perturbation strength. These results may have implications for resolving
the differences between eigenfrequencies derived from solar models and those
found from helioseismic observations.Comment: 27 pages + 6 figures; accepted for publication in Ap
The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials
We present a general, asymptotical solution for the discretised harmonic
oscillator. The corresponding Schr\"odinger equation is canonically conjugate
to the Mathieu differential equation, the Schr\"odinger equation of the quantum
pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian
of an isolated Josephon junction or a superconducting single-electron
transistor (SSET), we obtain an asymptotical representation of Mathieu
functions. We solve the discretised harmonic oscillator by transforming the
infinite-dimensional matrix-eigenvalue problem into an infinite set of
algebraic equations which are later shown to be satisfied by the obtained
solution. The proposed ansatz defines a new class of generalised Hermite
polynomials which are explicit functions of the coupling parameter and tend to
ordinary Hermite polynomials in the limit of vanishing coupling constant. The
polynomials become orthogonal as parts of the eigenvectors of a Hermitian
matrix and, consequently, the exponential part of the solution can not be
excluded. We have conjectured the general structure of the solution, both with
respect to the quantum number and the order of the expansion. An explicit proof
is given for the three leading orders of the asymptotical solution and we
sketch a proof for the asymptotical convergence of eigenvectors with respect to
norm. From a more practical point of view, we can estimate the required effort
for improving the known solution and the accuracy of the eigenvectors. The
applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression
Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
Metropolis Monte Carlo simulation is a powerful tool for studying the
equilibrium properties of matter. In complex condensed-phase systems, however,
it is difficult to design Monte Carlo moves with high acceptance probabilities
that also rapidly sample uncorrelated configurations. Here, we introduce a new
class of moves based on nonequilibrium dynamics: candidate configurations are
generated through a finite-time process in which a system is actively driven
out of equilibrium, and accepted with criteria that preserve the equilibrium
distribution. The acceptance rule is similar to the Metropolis acceptance
probability, but related to the nonequilibrium work rather than the
instantaneous energy difference. Our method is applicable to sampling from both
a single thermodynamic state or a mixture of thermodynamic states, and allows
both coordinates and thermodynamic parameters to be driven in nonequilibrium
proposals. While generating finite-time switching trajectories incurs an
additional cost, driving some degrees of freedom while allowing others to
evolve naturally can lead to large enhancements in acceptance probabilities,
greatly reducing structural correlation times. Using nonequilibrium driven
processes vastly expands the repertoire of useful Monte Carlo proposals in
simulations of dense solvated systems
Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS
GROMACS is a widely used package for biomolecular simulation, and over the
last two decades it has evolved from small-scale efficiency to advanced
heterogeneous acceleration and multi-level parallelism targeting some of the
largest supercomputers in the world. Here, we describe some of the ways we have
been able to realize this through the use of parallelization on all levels,
combined with a constant focus on absolute performance. Release 4.6 of GROMACS
uses SIMD acceleration on a wide range of architectures, GPU offloading
acceleration, and both OpenMP and MPI parallelism within and between nodes,
respectively. The recent work on acceleration made it necessary to revisit the
fundamental algorithms of molecular simulation, including the concept of
neighborsearching, and we discuss the present and future challenges we see for
exascale simulation - in particular a very fine-grained task parallelism. We
also discuss the software management, code peer review and continuous
integration testing required for a project of this complexity.Comment: EASC 2014 conference proceedin
From Heisenberg matrix mechanics to EBK quantization: theory and first applications
Despite the seminal connection between classical multiply-periodic motion and
Heisenberg matrix mechanics and the massive amount of work done on the
associated problem of semiclassical (EBK) quantization of bound states, we show
that there are, nevertheless, a number of previously unexploited aspects of
this relationship that bear on the quantum-classical correspondence. In
particular, we emphasize a quantum variational principle that implies the
classical variational principle for invariant tori. We also expose the more
indirect connection between commutation relations and quantization of action
variables. With the help of several standard models with one or two degrees of
freedom, we then illustrate how the methods of Heisenberg matrix mechanics
described in this paper may be used to obtain quantum solutions with a modest
increase in effort compared to semiclassical calculations. We also describe and
apply a method for obtaining leading quantum corrections to EBK results.
Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.
Genome-wide study of association and interaction with maternal cytomegalovirus infection suggests new schizophrenia loci.
Genetic and environmental components as well as their interaction contribute to the risk of schizophrenia, making it highly relevant to include environmental factors in genetic studies of schizophrenia. This study comprises genome-wide association (GWA) and follow-up analyses of all individuals born in Denmark since 1981 and diagnosed with schizophrenia as well as controls from the same birth cohort. Furthermore, we present the first genome-wide interaction survey of single nucleotide polymorphisms (SNPs) and maternal cytomegalovirus (CMV) infection. The GWA analysis included 888 cases and 882 controls, and the follow-up investigation of the top GWA results was performed in independent Danish (1396 cases and 1803 controls) and German-Dutch (1169 cases, 3714 controls) samples. The SNPs most strongly associated in the single-marker analysis of the combined Danish samples were rs4757144 in ARNTL (P=3.78 × 10(-6)) and rs8057927 in CDH13 (P=1.39 × 10(-5)). Both genes have previously been linked to schizophrenia or other psychiatric disorders. The strongest associated SNP in the combined analysis, including Danish and German-Dutch samples, was rs12922317 in RUNDC2A (P=9.04 × 10(-7)). A region-based analysis summarizing independent signals in segments of 100 kb identified a new region-based genome-wide significant locus overlapping the gene ZEB1 (P=7.0 × 10(-7)). This signal was replicated in the follow-up analysis (P=2.3 × 10(-2)). Significant interaction with maternal CMV infection was found for rs7902091 (P(SNP × CMV)=7.3 × 10(-7)) in CTNNA3, a gene not previously implicated in schizophrenia, stressing the importance of including environmental factors in genetic studies
Rare loss of function variants in candidate genes and risk of colorectal cancer
Although ~ 25% of colorectal cancer or polyp (CRC/P) cases show familial aggregation, current germline genetic testing identifies a causal genotype in the 16 major genes associated with high penetrance CRC/P in only 20% of these cases. As there are likely other genes underlying heritable CRC/P, we evaluated the association of variation at novel loci with CRC/P. We evaluated 158 a priori selected candidate genes by comparing the number of rare potentially disruptive variants (PDVs) found in 84 CRC/P cases without an identified CRC/P risk-associated variant and 2440 controls. We repeated this analysis using an additional 73 CRC/P cases. We also compared the frequency of PDVs in select genes among CRC/P cases with two publicly available data sets. We found a significant enrichment of PDVs in cases vs. controls: 20% of cases vs. 11.5% of controls with ≥ 1 PDV (OR = 1.9, p = 0.01) in the original set of cases. Among the second cohort of CRC/P cases, 18% had a PDV, significantly different from 11.5% (p = 0.02). Logistic regression, adjusting for ancestry and multiple testing, indicated association between CRC/P and PDVs in NTHL1 (p = 0.0001), BRCA2 (p = 0.01) and BRIP1 (p = 0.04). However, there was no significant difference in the frequency of PDVs at each of these genes between all 157 CRC/P cases and two publicly available data sets. These results suggest an increased presence of PDVs in CRC/P cases and support further investigation of the association of NTHL1, BRCA2 and BRIP1 variation with CRC/P
A spatio-temporal mining approach towards summarizing and analyzing protein folding trajectories
Understanding the protein folding mechanism remains a grand challenge in structural biology. In the past several years, computational theories in molecular dynamics have been employed to shed light on the folding process. Coupled with high computing power and large scale storage, researchers now can computationally simulate the protein folding process in atomistic details at femtosecond temporal resolution. Such simulation often produces a large number of folding trajectories, each consisting of a series of 3D conformations of the protein under study. As a result, effectively managing and analyzing such trajectories is becoming increasingly important. In this article, we present a spatio-temporal mining approach to analyze protein folding trajectories. It exploits the simplicity of contact maps, while also integrating 3D structural information in the analysis. It characterizes the dynamic folding process by first identifying spatio-temporal association patterns in contact maps, then studying how such patterns evolve along a folding trajectory. We demonstrate that such patterns can be leveraged to summarize folding trajectories, and to facilitate the detection and ordering of important folding events along a folding path. We also show that such patterns can be used to identify a consensus partial folding pathway across multiple folding trajectories. Furthermore, we argue that such patterns can capture both local and global structural topology in a 3D protein conformation, thereby facilitating effective structural comparison amongst conformations. We apply this approach to analyze the folding trajectories of two small synthetic proteins-BBA5 and GSGS (or Beta3S). We show that this approach is promising towards addressing the above issues, namely, folding trajectory summarization, folding events detection and ordering, and consensus partial folding pathway identification across trajectories
Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations
Accelerated molecular dynamics (aMD) has been shown to enhance conformational space sampling relative to classical molecular dynamics; however, the exponential reweighting of aMD trajectories, which is necessary for the calculation of free energies relating to the classical system, is oftentimes problematic, especially for systems larger than small poly peptides. Here, we propose a method of accelerating only the degrees of freedom most pertinent to sampling, thereby reducing the total acceleration added to the system and improving the convergence of calculated ensemble averages, which we term selective aMD. Its application is highlighted in two biomolecular cases. First, the model system alanine dipeptide is simulated with classical MD, all-dihedral aMD, and selective aMD, and these results are compared to the infinite sampling limit as calculated with metadynamics. We show that both forms of aMD enhance the convergence of the underlying free energy landscape by 5-fold relative to classical MD; however, selective aMD can produce improved statistics over all-dihedral aMD due to the improved reweighting. Then we focus on the pharmaceutically relevant case of computing the free energy of the decoupling of oseltamivir in the active site of neuraminidase. Results show that selective aMD greatly reduces the cost of this alchemical free energy transformation, whereas all-dihedral aMD produces unreliable free energy estimates
Conformational Preferences of a 14-Residue Fibrillogenic Peptide from Acetylcholinesteraseâ€
A 14-residue fragment from near the C-terminus of the enzyme acetylcholinesterase (AChE) is believed to have a neurotoxic/neurotrophic effect acting via an unknown pathway. While the peptide is α-helical in the full-length enzyme, the structure and association mechanism of the fragment are unknown. Using multiple molecular dynamics simulations, starting from a tetrameric complex of the association domain of AChE and systematicall disassembled subsets that include the peptide fragment, we show that the fragment is incapable of retaining its helicity in solution. Extensive replica exchange Monte Carlo folding and unfolding simulations in implicit solvent with capped and uncappted termini failed to converge to any consistent cluster of structures, suggesting that the fragment remains largely unstructured in solution under the conditions considered. Furthermore, extended molecular dynamics simulations of two steric zipper models show that the peptide is likely to form a zipper with antiparallel sheets and that peptides with mutations known to prevent fibril formation likely do so by interfering with this packing. The results demonstrate how the local environment of a peptide can stabilize a particular conformation
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