Kaspar Schott’s “encyclopedia of all mathematical sciences”

In 1661, Kaspar Schott published his comprehensive textbook “Cursus mathematicus” in Würzburg for the first time, his “Encyclopedia of all mathematical sciences”. It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred authors, among them Protestants like Michael Stifel and Johannes Kepler, but also Catholics like Nicolaus Copernicus. The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra

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

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]

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

Guidelines for delineation of lymphatic clinical target volumes for high conformal radiotherapy: head and neck region

The success of radiotherapy depends on the accurate delineation of the clinical target volume. The delineation of the lymph node regions has most impact, especially for tumors in the head and neck region. The purpose of this article was the development an atlas for the delineation of the clinical target volume for patients, who should receive radiotherapy for a tumor of the head and neck region. Literature was reviewed for localisations of the adjacent lymph node regions and their lymph drain in dependence of the tumor entity. On this basis the lymph node regions were contoured on transversal CT slices. The probability for involvement was reviewed and a recommendation for the delineation of the CTV was generated

Protein Domain of Unknown Function 3233 is a Translocation Domain of Autotransporter Secretory Mechanism in Gamma proteobacteria

Vibrio cholerae, the enteropathogenic gram negative bacteria is one of the main causative agents of waterborne diseases like cholera. About 1/3rd of the organism's genome is uncharacterised with many protein coding genes lacking structure and functional information. These proteins form significant fraction of the genome and are crucial in understanding the organism's complete functional makeup. In this study we report the general structure and function of a family of hypothetical proteins, Domain of Unknown Function 3233 (DUF3233), which are conserved across gram negative gammaproteobacteria (especially in Vibrio sp. and similar bacteria). Profile and HMM based sequence search methods were used to screen homologues of DUF3233. The I-TASSER fold recognition method was used to build a three dimensional structural model of the domain. The structure resembles the transmembrane beta-barrel with an axial N-terminal helix and twelve antiparallel beta-strands. Using a combination of amphipathy and discrimination analysis we analysed the potential transmembrane beta-barrel forming properties of DUF3233. Sequence, structure and phylogenetic analysis of DUF3233 indicates that this gram negative bacterial hypothetical protein resembles the beta-barrel translocation unit of autotransporter Va secretory mechanism with a gene organisation that differs from the conventional Va system

Generalised ballooning theory of two-dimensional tokamak modes

In this work, using solutions from a local gyrokinetic flux-tube code combined with higher order ballooning theory, a new analytical approach is developed to reconstruct the global linear mode structure with associated global mode frequency. In addition to the isolated mode (IM), which usually peaks on the outboard mid-plane, the higher order ballooning theory has also captured other types of less unstable global modes: (a) the weakly asymmetric ballooning theory (WABT) predicts a mixed mode (MM) that undergoes a small poloidal shift away from the outboard mid-plane, (b) a relatively more stable general mode (GM) balloons on the top (or bottom) of the tokamak plasma. In this paper, an analytic approach is developed to combine these disconnected analytical limits into a single generalised ballooning theory. This is used to investigate how an IM behaves under the effect of sheared toroidal flow. For small values of flow an IM initially converts into a MM where the results of WABT are recaptured, and eventually, as the flow increases, the mode asymptotically becomes a GM on the top (or bottom) of the plasma. This may be an ingredient in models for understanding why in some experimental scenarios, instead of large edge localised modes (ELMs), small ELMs are observed. Finally, our theory can have other important consequences, especially for calculations involving Reynolds stress driven intrinsic rotation through the radial asymmetry in the global mode structures. Understanding the intrinsic rotation is significant because external torque in a plasma the size of ITER is expected to be relatively low

Eukaryote-wide sequence analysis of mitochondrial β-barrel outer membrane proteins

<p>Abstract</p> <p>Background</p> <p>The outer membranes of mitochondria are thought to be homologous to the outer membranes of Gram negative bacteria, which contain 100's of distinct families of <it>β</it>-barrel membrane proteins (BOMPs) often forming channels for transport of nutrients or drugs. However, only four families of mitochondrial BOMPs (MBOMPs) have been confirmed to date. Although estimates as high as 100 have been made in the past, the number of yet undiscovered MBOMPs is an open question. Fortunately, the recent discovery of a membrane integration signal (the <it>β</it>-signal) for MBOMPs gave us an opportunity to look for undiscovered MBOMPs.</p> <p>Results</p> <p>We present the results of a comprehensive survey of eukaryotic protein sequences intended to identify new MBOMPs. Our search employs recent results on <it>β</it>-signals as well as structural information and a novel BOMP predictor trained on both bacterial and mitochondrial BOMPs. Our principal finding is circumstantial evidence suggesting that few MBOMPs remain to be discovered, if one assumes that, like known MBOMPs, novel MBOMPs will be monomeric and <it>β</it>-signal dependent. In addition to this, our analysis of MBOMP homologs reveals some exceptions to the current model of the <it>β</it>-signal, but confirms its consistent presence in the C-terminal region of MBOMP proteins. We also report a <it>β</it>-signal independent search for MBOMPs against the yeast and Arabidopsis proteomes. We find no good candidates MBOMPs in yeast but the Arabidopsis results are less conclusive.</p> <p>Conclusions</p> <p>Our results suggest there are no remaining MBOMPs left to discover in yeast; and if one assumes all MBOMPs are <it>β</it>-signal dependent, few MBOMP families remain undiscovered in any sequenced organism.</p

Structure of a Burkholderia pseudomallei Trimeric Autotransporter Adhesin Head

Pathogenic bacteria adhere to the host cell surface using a family of outer membrane proteins called Trimeric Autotransporter Adhesins (TAAs). Although TAAs are highly divergent in sequence and domain structure, they are all conceptually comprised of a C-terminal membrane anchoring domain and an N-terminal passenger domain. Passenger domains consist of a secretion sequence, a head region that facilitates binding to the host cell surface, and a stalk region.Pathogenic species of Burkholderia contain an overabundance of TAAs, some of which have been shown to elicit an immune response in the host. To understand the structural basis for host cell adhesion, we solved a 1.35 A resolution crystal structure of a BpaA TAA head domain from Burkholderia pseudomallei, the pathogen that causes melioidosis. The structure reveals a novel fold of an intricately intertwined trimer. The BpaA head is composed of structural elements that have been observed in other TAA head structures as well as several elements of previously unknown structure predicted from low sequence homology between TAAs. These elements are typically up to 40 amino acids long and are not domains, but rather modular structural elements that may be duplicated or omitted through evolution, creating molecular diversity among TAAs.The modular nature of BpaA, as demonstrated by its head domain crystal structure, and of TAAs in general provides insights into evolution of pathogen-host adhesion and may provide an avenue for diagnostics

<i>De novo</i> design of a four-fold symmetric TIM-barrel protein with atomic-level accuracy

Despite efforts for over 25 years, de novo protein design has not succeeded in achieving the TIM-barrel fold. Here we describe the computational design of 4-fold symmetrical (β/α)(8)-barrels guided by geometrical and chemical principles. Experimental characterization of 33 designs revealed the importance of sidechain-backbone hydrogen bonding for defining the strand register between repeat units. The X-ray crystal structure of a designed thermostable 184-residue protein is nearly identical with the designed TIM-barrel model. PSI-BLAST searches do not identify sequence similarities to known TIM-barrel proteins, and sensitive profile-profile searches indicate that the design sequence is distant from other naturally occurring TIM-barrel superfamilies, suggesting that Nature has only sampled a subset of the sequence space available to the TIM-barrel fold. The ability to de novo design TIM-barrels opens new possibilities for custom-made enzymes