The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and dym type

An extension of the algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of $N$-component systems of nonlinear evolution equations. This class includes, among others, equations from the Dym and shallow water equation hierarchies. The main goal of the paper is to give explicit theta-functional solutions of these nonlinear PDE's, which are associated to nonlinear subvarieties of hyperelliptic Jacobians. The main results of the present paper are twofold. First, we exhibit some of the special features of integrable PDE's that admit piecewise smooth weak solutions, which make them different from equations whose solutions are globally meromorphic, such as the KdV equation. Second, we blend the techniques of algebraic geometry and weak solutions of PDE's to gain further insight into, and explicit formulas for, piecewise-smooth finite-gap solutions.Comment: 31 pages, no figures, to appear in Commun. Math. Phy

Fr-TM-align: a new protein structural alignment method based on fragment alignments and the TM-score

©2008 Pandit and Skolnick; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is available from: http://www.biomedcentral.com/1471-2105/9/531doi:10.1186/1471-2105-9-531Background: Protein tertiary structure comparisons are employed in various fields of contemporary structural biology. Most structure comparison methods involve generation of an initial seed alignment, which is extended and/or refined to provide the best structural superposition between a pair of protein structures as assessed by a structure comparison metric. One such metric, the TM-score, was recently introduced to provide a combined structure quality measure of the coordinate root mean square deviation between a pair of structures and coverage. Using the TM-score, the TM-align structure alignment algorithm was developed that was often found to have better accuracy and coverage than the most commonly used structural alignment programs; however, there were a number of situations when this was not true. Results: To further improve structure alignment quality, the Fr-TM-align algorithm has been developed where aligned fragment pairs are used to generate the initial seed alignments that are then refined using dynamic programming to maximize the TM-score. For the assessment of the structural alignment quality from Fr-TM-align in comparison to other programs such as CE and TMalign, we examined various alignment quality assessment scores such as PSI and TM-score. The assessment showed that the structural alignment quality from Fr-TM-align is better in comparison to both CE and TM-align. On average, the structural alignments generated using Fr-TM-align have a higher TM-score (~9%) and coverage (~7%) in comparison to those generated by TM-align. Fr- TM-align uses an exhaustive procedure to generate initial seed alignments. Hence, the algorithm is computationally more expensive than TM-align. Conclusion: Fr-TM-align, a new algorithm that employs fragment alignment and assembly provides better structural alignments in comparison to TM-align. The source code and executables of Fr- TM-align are freely downloadable at: http://cssb.biology.gatech.edu/skolnick/files/FrTMalign/

Multiple structure alignment and consensus identification for proteins

<p>Abstract</p> <p>Background</p> <p>An algorithm is presented to compute a multiple structure alignment for a set of proteins and to generate a consensus (pseudo) protein which captures common substructures present in the given proteins. The algorithm represents each protein as a sequence of triples of coordinates of the alpha-carbon atoms along the backbone. It then computes iteratively a sequence of transformation matrices (i.e., translations and rotations) to align the proteins in space and generate the consensus. The algorithm is a heuristic in that it computes an approximation to the optimal alignment that minimizes the sum of the pairwise distances between the consensus and the transformed proteins.</p> <p>Results</p> <p>Experimental results show that the algorithm converges quite rapidly and generates consensus structures that are visually similar to the input proteins. A comparison with other coordinate-based alignment algorithms (MAMMOTH and MATT) shows that the proposed algorithm is competitive in terms of speed and the sizes of the conserved regions discovered in an extensive benchmark dataset derived from the HOMSTRAD and SABmark databases.</p> <p>The algorithm has been implemented in C++ and can be downloaded from the project's web page. Alternatively, the algorithm can be used via a web server which makes it possible to align protein structures by uploading files from local disk or by downloading protein data from the RCSB Protein Data Bank.</p> <p>Conclusions</p> <p>An algorithm is presented to compute a multiple structure alignment for a set of proteins, together with their consensus structure. Experimental results show its effectiveness in terms of the quality of the alignment and computational cost.</p

Effects of dietary phytoestrogens on plasma testosterone and triiodothyronine (T3) levels in male goat kids

<p>Abstract</p> <p>Background</p> <p>Exposure to xenoestrogens in humans and animals has gained increasing attention due to the effects of these compounds on reproduction. The present study was undertaken to investigate the influence of low-dose dietary phytoestrogen exposure, i.e. a mixture of genistein, daidzein, biochanin A and formononetin, on the establishment of testosterone production during puberty in male goat kids.</p> <p>Methods</p> <p>Goat kids at the age of 3 months received either a standard diet or a diet supplemented with phytoestrogens (3 - 4 mg/kg/day) for ~3 months. Plasma testosterone and total and free triiodothyronine (T₃) concentrations were determined weekly. Testicular levels of testosterone and cAMP were measured at the end of the experiment. Repeated measurement analysis of variance using the MIXED procedure on the generated averages, according to the Statistical Analysis System program package (Release 6.12, 1996, SAS Institute Inc., Cary, NC, USA) was carried out.</p> <p>Results</p> <p>No significant difference in plasma testosterone concentration between the groups was detected during the first 7 weeks. However, at the age of 5 months (i.e. October 1, week 8) phytoestrogen-treated animals showed significantly higher testosterone concentrations than control animals (37.5 nmol/l vs 19.1 nmol/l). This elevation was preceded by a rise in plasma total T₃that occurred on September 17 (week 6). A slightly higher concentration of free T₃was detected in the phytoestrogen group at the same time point, but it was not until October 8 and 15 (week 9 and 10) that a significant difference was found between the groups. At the termination of the experiment, testicular cAMP levels were significantly lower in goats fed a phytoestrogen-supplemented diet. Phytoestrogen-fed animals also had lower plasma and testicular testosterone concentrations, but these differences were not statistically significant.</p> <p>Conclusion</p> <p>Our findings suggest that phytoestrogens can stimulate testosterone synthesis during puberty in male goats by increasing the secretion of T₃; a hormone known to stimulate Leydig cell steroidogenesis. It is possible that feedback signalling underlies the tendency towards decreased steroid production at the end of the experiment.</p

The regulatory subunit of PKA-I remains partially structured and undergoes β-aggregation upon thermal denaturation

Background: The regulatory subunit (R) of cAMP-dependent protein kinase (PKA) is a modular flexible protein that responds with large conformational changes to the binding of the effector cAMP. Considering its highly dynamic nature, the protein is rather stable. We studied the thermal denaturation of full-length RIα and a truncated RIα(92-381) that contains the tandem cyclic nucleotide binding (CNB) domains A and B. Methodology/Principal Findings: As revealed by circular dichroism (CD) and differential scanning calorimetry, both RIα proteins contain significant residual structure in the heat-denatured state. As evidenced by CD, the predominantly α-helical spectrum at 25°C with double negative peaks at 209 and 222 nm changes to a spectrum with a single negative peak at 212-216 nm, characteristic of β-structure. A similar α→β transition occurs at higher temperature in the presence of cAMP. Thioflavin T fluorescence and atomic force microscopy studies support the notion that the structural transition is associated with cross-β-intermolecular aggregation and formation of non-fibrillar oligomers. Conclusions/Significance: Thermal denaturation of RIα leads to partial loss of native packing with exposure of aggregation-prone motifs, such as the B' helices in the phosphate-binding cassettes of both CNB domains. The topology of the β-sandwiches in these domains favors inter-molecular β-aggregation, which is suppressed in the ligand-bound states of RIα under physiological conditions. Moreover, our results reveal that the CNB domains persist as structural cores through heat-denaturation. © 2011 Dao et al

Sn-Beta zeolites with borate salts catalyse the epimerization of carbohydrates via an intramolecular carbon shift

Carbohydrate epimerization is an essential technology for the widespread production of rare sugars. In contrast to other enzymes, most epimerases are only active on sugars substituted with phosphate or nucleotide groups, thus drastically restricting their use. Here we show that Sn-Beta zeolite in the presence of sodium tetraborate catalyses the selective epimerization of aldoses in aqueous media. Specifically, a 5 wt% aldose (for example, glucose, xylose or arabinose) solution with a 4:1 aldose:sodium tetraborate molar ratio reacted with catalytic amounts of Sn-Beta yields near-equilibrium epimerization product distributions. The reaction proceeds by way of a 1,2 carbon shift wherein the bond between C-2 and C-3 is cleaved and a new bond between C-1 and C-3 is formed, with C-1 moving to the C-2 position with an inverted configuration. This work provides a general method of performing carbohydrate epimerizations that surmounts the main disadvantages of current enzymatic and inorganic processes.National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Award DMR-0819762)DuPont MIT Alliance (Graduate Research Fellowship)National Institutes of Health (U.S.) (Grant EB-001960)National Institutes of Health (U.S.) (Grant EB-002026)National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374

Solution structure of a repeated unit of the ABA-1 nematode polyprotein allergen of ascaris reveals a novel fold and two discrete lipid-binding sites

Parasitic nematode worms cause serious health problems in humans and other animals. They can induce allergic-type immune responses, which can be harmful but may at the same time protect against the infections. Allergens are proteins that trigger allergic reactions and these parasites produce a type that is confined to nematodes, the nematode polyprotein allergens (NPAs). These are synthesized as large precursor proteins comprising repeating units of similar amino acid sequence that are subsequently cleaved into multiple copies of the allergen protein. NPAs bind small lipids such as fatty acids and retinol (Vitamin A) and probably transport these sensitive and insoluble compounds between the tissues of the worms. Nematodes cannot synthesize these lipids, so NPAs may also be crucial for extracting nutrients from their hosts. They may also be involved in altering immune responses by controlling the lipids by which the immune and inflammatory cells communicate. We describe the molecular structure of one unit of an NPA, the well-known ABA-1 allergen of Ascaris and find its structure to be of a type not previously found for lipid-binding proteins, and we describe the unusual sites where lipids bind within this structur

Serum amyloid A primes microglia for ATP-dependent interleukin-1\u3b2 release

Acute-phase response is a systemic reaction to environmental/inflammatory insults and involves production of acute-phase proteins, including serum amyloid A (SAA). Interleukin-1\u3b2 (IL-1\u3b2), a master regulator of neuroinflammation produced by activated inflammatory cells of the myeloid lineage, in particular microglia, plays a key role in the pathogenesis of acute and chronic diseases of the peripheral nervous system and CNS. IL-1\u3b2 release is promoted by ATP acting at the purinergic P2X7 receptor (P2X7R) in cells primed with toll-like receptor (TLR) ligands

Long-term results after Boston brace treatment in late-onset juvenile and adolescent idiopathic scoliosis

<p>Abstract</p> <p>Background</p> <p>It is recommended that research in patients with idiopathic scoliosis should focus on short- and long-term patient-centred outcome. The aim of the present study was to evaluate outcome in patients with late-onset juvenile or adolescent idiopathic scoliosis 16 years or more after Boston brace treatment.</p> <p>Methods</p> <p>272 (78%) of 360 patients, 251 (92%) women, responded to follow-up examination at a mean of 24.7 (range 16 - 32) years after Boston brace treatment. Fifty-eight (21%) patients had late-onset juvenile and 214 had adolescent idiopathic scoliosis. All patients had clinical and radiological examination and answered a standardised questionnaire including work status, demographics, General Function Score (GFS) (100 - worst possible) and Oswestry Disability Index (ODI) (100 - worst possible), EuroQol (EQ-5D) (1 - best possible), EQ-VAS (100 - best possible), and Scoliosis Research Society - 22 (SRS - 22) (5 - best possible).</p> <p>Results</p> <p>The mean age at follow-up was 40.4 (31-48) years. The prebrace major curve was in average 33.2 (20 - 57)°. At weaning and at the last follow-up the corresponding values were 28.3 (1 - 58)° and 32.5 (7 - 80)°, respectively. Curve development was similar in patients with late-onset juvenile and adolescent start. The prebrace curve increased > 5° in 31% and decreased > 5° in 26%. Twenty-five patients had surgery. Those who did not attend follow-up (n = 88) had a lower mean curve at weaning: 25.4 (6-53)°. Work status was 76% full-time and 10% part-time. Eighty-seven percent had delivered a baby, 50% had pain in pregnancy. The mean (SD) GFS was 7.4 (10.8), ODI 9.3 (11.0), EQ-5D 0.82 (0.2), EQ-VAS 77.6 (17.8), SRS-22: pain 4.1 (0.8), mental health 4.1 (0.6), self-image 3.7 (0.7), function 4.0 (0.6), satisfaction with treatment 3.7 (1.0). Surgical patients had significantly reduced scores for SRS-physical function and self-image, and patients with curves ≥ 45° had reduced self-image.</p> <p>Conclusion</p> <p>Long-term results were satisfactory in most braced patients and similar in late-onset juvenile and idiopathic adolescent scoliosis.</p

Estimation of In Vivo Water Content of the Stratum Corneum from Electrical Measurements

In vivo water content in the epidermal stratum corneum can be estimated by means of low frequency susceptance measurements. In the in vitro calibration necessary to find the in vivo water content, the stratum corneum will have a uniform distribution of water across its thickness. However, in vivo stratum corneum has an increasing water concentration profile from the outermost towards the innermost parts. This paper will investigate the possibility of estimating the equilibrium water content in the in vivo stratum corneum non-invasively from electrical susceptance measurements. Given a known shape of the water concentration profile in the in vivo stratum corneum and the dependence of susceptance on the water content, it is possible to calculate the water content in vivo based on analytically derived expressions for the water concentration profile. A correspondence between in vivo and in vitro water content needed for this purpose is also established