The Coulomb phase shift revisited

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular momentum $l$ and other regimes. We employ the uniform approximation. The use of our expressions in low energy scattering of charged particles is discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl

An open problem in complex analytic geometry arising in harmonic analysis

In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential equations. The problem is discussed in a self-contained elementary way and some results towards its resolution are presented. A conjecture concerning the structure of appearing affine fibrations is formulated.Comment: 8 page

Super-KMS functionals for graded-local conformal nets

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare

Compressive genomics for protein databases

Motivation: The exponential growth of protein sequence databases has increasingly made the fundamental question of searching for homologs a computational bottleneck. The amount of unique data, however, is not growing nearly as fast; we can exploit this fact to greatly accelerate homology search. Acceleration of programs in the popular PSI/DELTA-BLAST family of tools will not only speed-up homology search directly but also the huge collection of other current programs that primarily interact with large protein databases via precisely these tools. Results: We introduce a suite of homology search tools, powered by compressively accelerated protein BLAST (CaBLASTP), which are significantly faster than and comparably accurate with all known state-of-the-art tools, including HHblits, DELTA-BLAST and PSI-BLAST. Further, our tools are implemented in a manner that allows direct substitution into existing analysis pipelines. The key idea is that we introduce a local similarity-based compression scheme that allows us to operate directly on the compressed data. Importantly, CaBLASTP’s runtime scales almost linearly in the amount of unique data, as opposed to current BLASTP variants, which scale linearly in the size of the full protein database being searched. Our compressive algorithms will speed-up many tasks, such as protein structure prediction and orthology mapping, which rely heavily on homology search. Availability: CaBLASTP is available under the GNU Public License at http://cablastp.csail.mit.edu/ Contact: [email protected]

The Phyre2 web portal for protein modeling, prediction and analysis

Phyre2 is a suite of tools available on the web to predict and analyze protein structure, function and mutations. The focus of Phyre2 is to provide biologists with a simple and intuitive interface to state-of-the-art protein bioinformatics tools. Phyre2 replaces Phyre, the original version of the server for which we previously published a paper in Nature Protocols. In this updated protocol, we describe Phyre2, which uses advanced remote homology detection methods to build 3D models, predict ligand binding sites and analyze the effect of amino acid variants (e.g., nonsynonymous SNPs (nsSNPs)) for a user's protein sequence. Users are guided through results by a simple interface at a level of detail they determine. This protocol will guide users from submitting a protein sequence to interpreting the secondary and tertiary structure of their models, their domain composition and model quality. A range of additional available tools is described to find a protein structure in a genome, to submit large number of sequences at once and to automatically run weekly searches for proteins that are difficult to model. The server is available at http://www.sbg.bio.ic.ac.uk/phyre2. A typical structure prediction will be returned between 30 min and 2 h after submission

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

TMFoldRec: a statistical potential-based transmembrane protein fold recognition tool.

BACKGROUND: Transmembrane proteins (TMPs) are the key components of signal transduction, cell-cell adhesion and energy and material transport into and out from the cells. For the deep understanding of these processes, structure determination of transmembrane proteins is indispensable. However, due to technical difficulties, only a few transmembrane protein structures have been determined experimentally. Large-scale genomic sequencing provides increasing amounts of sequence information on the proteins and whole proteomes of living organisms resulting in the challenge of bioinformatics; how the structural information should be gained from a sequence. RESULTS: Here, we present a novel method, TMFoldRec, for fold prediction of membrane segments in transmembrane proteins. TMFoldRec based on statistical potentials was tested on a benchmark set containing 124 TMP chains from the PDBTM database. Using a 10-fold jackknife method, the native folds were correctly identified in 77 % of the cases. This accuracy overcomes the state-of-the-art methods. In addition, a key feature of TMFoldRec algorithm is the ability to estimate the reliability of the prediction and to decide with an accuracy of 70 %, whether the obtained, lowest energy structure is the native one. CONCLUSION: These results imply that the membrane embedded parts of TMPs dictate the TM structures rather than the soluble parts. Moreover, predictions with reliability scores make in this way our algorithm applicable for proteome-wide analyses. AVAILABILITY: The program is available upon request for academic use

Evolution of outer membrane beta-barrels from an ancestral beta beta hairpin.

Outer membrane β-barrels (OMBBs) are the major class of outer membrane proteins from Gram-negative bacteria, mitochondria, and plastids. Their transmembrane domains consist of 8–24 β-strands forming a closed, barrel-shaped β-sheet around a central pore. Despite their obvious structural regularity, evidence for an origin by duplication or for a common ancestry has not been found. We use three complementary approaches to show that all OMBBs from Gram-negative bacteria evolved from a single, ancestral ββ hairpin. First, we link almost all families of known single-chain bacterial OMBBs with each other through transitive profile searches. Second, we identify a clear repeat signature in the sequences of many OMBBs in which the repeating sequence unit coincides with the structural ββ hairpin repeat. Third, we show that the observed sequence similarity between OMBB hairpins cannot be explained by structural or membrane constraints on their sequences. The third approach addresses a longstanding problem in protein evolution: how to distinguish between a very remotely homologous relationship and the opposing scenario of “sequence convergence.” The origin of a diverse group of proteins from a single hairpin module supports the hypothesis that, around the time of transition from the RNA to the protein world, proteins arose by amplification and recombination of short peptide modules that had previously evolved as cofactors of RNAs

Psychosocial Predictors of Non-Adherence and Treatment Failure in a Large Scale Multi-National Trial of Antiretroviral Therapy for HIV: Data from the ACTG A5175/PEARLS Trial

Background: PEARLS, a large scale trial of antiretroviral therapy (ART) for HIV (n = 1,571, 9 countries, 4 continents), found that a once-daily protease inhibitor (PI) based regimen (ATV+DDI+FTC), but not a once-daily non-nucleoside reverse transcriptase inhibitor/nucleoside reverse transcriptase inhibitor (NNRTI/NRTI) regimen (EFV+FTC/TDF), had inferior efficacy compared to a standard of care twice-daily NNRTI/NRTI regimen (EFV+3TC/ZDV). The present study examined non-adherence in PEARLS. Methods: Outcomes: non-adherence assessed by pill count and by self-report, and time to treatment failure. Longitudinal predictors: regimen, quality of life (general health perceptions = QOL-health, mental health = QOL-mental health), social support, substance use, binge drinking, and sexual behaviors. “Life-Steps” adherence counseling was provided. Results: In both pill-count and self-report multivariable models, both once-a-day regimens had lower levels of non-adherence than the twice-a-day standard of care regimen; although these associations attenuated with time in the self-report model. In both multivariable models, hard-drug use was associated with non-adherence, living in Africa and better QOL-health were associated with less non-adherence. According to pill-count, unprotected sex was associated with non-adherence. According to self-report, soft-drug use was associated with non-adherence and living in Asia was associated with less non-adherence. Both pill-count (HR = 1.55, 95% CI: 1.15, 2.09, p<.01) and self-report (HR = 1.13, 95% CI: 1.08, 1.13, p<.01) non-adherence were significant predictors of treatment failure over 72 weeks. In multivariable models (including pill-count or self-report nonadherence), worse QOL-health, age group (younger), and region were also significant predictors of treatment failure. Conclusion: In the context of a large, multi-national, multi-continent, clinical trial there were variations in adherence over time, with more simplified regimens generally being associated with better adherence. Additionally, variables such as QOL-health, regimen, drug-use, and region play a role. Self-report and pill-count adherence, as well as additional psychosocial variables, such QOL-health, age, and region, were, in turn, associated with treatment failure