Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

The Relationship between Population Structure and Aluminum Tolerance in Cultivated Sorghum

Background: Acid soils comprise up to 50% of the world's arable lands and in these areas aluminum (Al) toxicity impairs root growth, strongly limiting crop yield. Food security is thereby compromised in many developing countries located in tropical and subtropical regions worldwide. In sorghum, SbMATE, an Al-activated citrate transporter, underlies the Alt(SB) locus on chromosome 3 and confers Al tolerance via Al-activated root citrate release. Methodology: Population structure was studied in 254 sorghum accessions representative of the diversity present in cultivated sorghums. Al tolerance was assessed as the degree of root growth inhibition in nutrient solution containing Al. A genetic analysis based on markers flanking Alt(SB) and SbMATE expression was undertaken to assess a possible role for Alt(SB) in Al tolerant accessions. In addition, the mode of gene action was estimated concerning the Al tolerance trait. Comparisons between models that include population structure were applied to assess the importance of each subpopulation to Al tolerance. Conclusion/Significance: Six subpopulations were revealed featuring specific racial and geographic origins. Al tolerance was found to be rather rare and present primarily in guinea and to lesser extent in caudatum subpopulations. Alt(SB) was found to play a role in Al tolerance in most of the Al tolerant accessions. A striking variation was observed in the mode of gene action for the Al tolerance trait, which ranged from almost complete recessivity to near complete dominance, with a higher frequency of partially recessive sources of Al tolerance. A possible interpretation of our results concerning the origin and evolution of Al tolerance in cultivated sorghum is discussed. This study demonstrates the importance of deeply exploring the crop diversity reservoir both for a comprehensive view of the dynamics underlying the distribution and function of Al tolerance genes and to design efficient molecular breeding strategies aimed at enhancing Al tolerance.

A Simple and Fast Method for the Production and Characterization of Methylic and Ethylic Biodiesels from Tucum Oil via an Alkaline Route

A simple, fast, and complete route for the production of methylic and ethylic biodiesel from tucum oil is described. Aliquots of the oil obtained directly from pressed tucum (pulp and almonds) were treated with potassium methoxide or ethoxide at 40 degrees C for 40 min. The biodiesel form was removed from the reactor and washed with 0.1 M HCl aqueous solution. A simple distillation at 100 degrees C was carried out in order to remove water and alcohol species from the biodiesel. The oxidative stability index was obtained for the tucum oil as well as the methylic and ethylic biodiesel at 6.13, 2.90, and 2.80 h, for storage times higher than 8 days. Quality control of the original oil and of the methylic and ethylic biodiesels, such as the amount of glycerin produced during the transesterification process, was accomplished by the TLC, GC-MS, and FT-IR techniques. The results obtained in this study indicate a potential biofuel production by simple treatment of tucum, an important Amazonian fruit.

Determination and Molecular Analysis of the Complete Genome Sequence of Two Wild-Type Rabies Viruses Isolated from a Haematophagous Bat and a Frugivorous Bat in Brazil

The complete genome sequences of two Brazilian wild-type rabies viruses (RABV), a BR-DR1 isolate from a haematophagous bat (Desmodus rotundus) and a BR-AL1 isolate from a frugivorous bat (Artibeus lituratus), were determined. The genomes of the BR-DR1 and RR-AL1 had 11,923 and 11,922 nt, respectively, and both encoded the five standard genes of rhabdoviruses. The complete nucleotide sequence identity between the BR-DR1 and BR-AL1 isolates was 97%. The BR-DR1 and BR-AL1 isolates had some conserved functional sites revealed by the fixed isolates, whereas both isolates had unique amino acid substitutions in the antigenic region IV of the nucleocapsid gene. Therefore, it is speculated that both isolates were nearly identical in virologic character. According to our phylogenetic analysis based on the complete genomes, both isolates belonged to genotype 1, and to the previously defined ""vampire bat-related RABV lineage"" which consisted of mainly D. rotundus- and A. lituratus- isolates; however, a branch pattern with high bootstrap values suggested that BR-DR1 was more closely related to the 9001FRA isolate, which was collected from a dog bitten by a bat in French Guiana, than to BR-AL1. This result suggests that the vampire bat-related RABV lineage includes Brazilian vampire bat and Brazilian frugivorous bat RABV and is further divided into Brazilian vampire bat and Brazilian frugivorous bat RABV sub-lineages. The phylogenetic analysis based on the complete genomes was valuable in discriminating among very closely related isolates.

Laser Phototherapy for Stevens-Johnson Syndrome: A Case Report

Background and Objective: Stevens-Johnson syndrome (SJS) is a life-threatening dermatosis characterized by epidermal sloughing and stomatitis. We report the case of a 7-year-old boy in whom laser phototherapy (LPT) was highly effective in reversing the effects of an initial episode of SJS that had apparently developed in association with treatment with phenobarbital for a seizure disorder. The patient was first seen in the intensive care unit (ICU) of our institution with fever, cutaneous lesions on his extremities, trunk, face, and neck; mucosal involvement of his genitalia and eyes (conjunctivitis); ulcerative intraoral lesions; and swollen, crusted, and bleeding lips. He reported severe pain at the sites of his intraoral and skin lesions and was unable to eat, speak, swallow, or open his mouth. Materials and Methods: Trying to prevent and minimize secondary infections, gastric problems, pain, and other complications, the patient was given clindamycin, ranitidine, dipyrone, diphenhydramine (Benadryl) drops, and morphine. In addition, he was instructed to use bicarbonate solution and Ketoconazole (Xylogel) in the oral cavity. Because of the lack of progress of the patient, the LPT was selected. Results: At 5 days after the initial session of LPT, the patient was able to eat gelatin, and on the following day, the number and severity of his intraoral lesions and his labial crusting and swelling had diminished. By 6 days after his initial session of LPT, most of the patient's intraoral lesions had disappeared, and the few that remained were painless; the patient was able to eat solid food by himself and was removed from the ICU. Ten sessions of LPT were conducted in the hospital. The patient underwent three further and consecutive sessions at the School of Dentistry, when complete healing of his oral lesions was observed. Conclusion: The outcome in this case suggests that LPT may be a new adjuvant modality for SJS complications.

Relationship between maxillary and mandibular base lengths and dental crowding in patients with complete Class II malocclusions

Objective: To verify the relationship between maxillary and mandibular effective lengths and dental crowding in patients with Class II malocclusions. Materials and Methods: The sample comprised 80 orthodontic patients with complete Class II malocclusions in the permanent dentition (47 male, 33 female) who were divided into two groups according to the amount of mandibular tooth-arch size discrepancy. The maxillary and mandibular effective lengths (Co-A and Co-Gn) and tooth-arch size discrepancies were measured on the initial cephalograms and dental casts, respectively. Intergroup comparisons of apical base lengths were performed with independent t-tests. Correlation between base length and dental crowding was examined by means of Pearson's correlation coefficient (P < .05). Results: Patients with Class II malocclusion and moderate to severe crowding had significantly smaller maxillary and mandibular effective lengths than subjects with the same malocclusion and slight mandibular crowding. A weak inverse correlation was also found between maxillary and mandibular effective lengths and the severity of dental crowding. Conclusion: Decreased maxillary and mandibular effective lengths constitute an important factor associated with dental crowding in patients with complete Class II malocclusion. (Angle Orthod. 2011;81:217-221.)

An oligonucleotide primer set for PCR amplification of the complete honey bee mitochondrial genome

Mitochondrial DNA markers have been widely used to address population and evolutionary questions in the honey bee Apis mellifera. Most of the polymorphic markers are restricted to few mitochondrial regions. Here we describe a set of 24 oligonucleotides that allow PCR amplification of the entire mitochondrial genome of the honey bee A. mellifera in 12 amplicons. These fragments have important applications for the study of mitochondrial genes in different subspecies of A. mellifera and as heterospecific probes to characterize mitochondrial genomes in other bee species.

Complete Genome Sequence of Mycoplasma suis and Insights into Its Biology and Adaption to an Erythrocyte Niche

Mycoplasma suis, the causative agent of porcine infectious anemia, has never been cultured in vitro and mechanisms by which it causes disease are poorly understood. Thus, the objective herein was to use whole genome sequencing and analysis of M. suis to define pathogenicity mechanisms and biochemical pathways. M. suis was harvested from the blood of an experimentally infected pig. Following DNA extraction and construction of a paired end library, whole-genome sequencing was performed using GS-FLX (454) and Titanium chemistry. Reads on paired-end constructs were assembled using GS De Novo Assembler and gaps closed by primer walking; assembly was validated by PFGE. Glimmer and Manatee Annotation Engine were used to predict and annotate protein-coding sequences (CDS). The M. suis genome consists of a single, 742,431 bp chromosome with low G+C content of 31.1%. A total of 844 CDS, 3 single copies, unlinked rRNA genes and 32 tRNAs were identified. Gene homologies and GC skew graph show that M. suis has a typical Mollicutes oriC. The predicted metabolic pathway is concise, showing evidence of adaptation to blood environment. M. suis is a glycolytic species, obtaining energy through sugars fermentation and ATP-synthase. The pentose-phosphate pathway, metabolism of cofactors and vitamins, pyruvate dehydrogenase and NAD(+) kinase are missing. Thus, ribose, NADH, NADPH and coenzyme A are possibly essential for its growth. M. suis can generate purines from hypoxanthine, which is secreted by RBCs, and cytidine nucleotides from uracil. Toxins orthologs were not identified. We suggest that M. suis may cause disease by scavenging and competing for host nutrients, leading to decreased life-span of RBCs. In summary, genome analysis shows that M. suis is dependent on host cell metabolism and this characteristic is likely to be linked to its pathogenicity. The prediction of essential nutrients will aid the development of in vitro cultivation systems.

Complete Genome Viral Phylogenies Suggests the Concerted Evolution of Regulatory Cores and Accessory Satellites

We consider the concerted evolution of viral genomes in four families of DNA viruses. Given the high rate of horizontal gene transfer among viruses and their hosts, it is an open question as to how representative particular genes are of the evolutionary history of the complete genome. To address the concerted evolution of viral genes, we compared genomic evolution across four distinct, extant viral families. For all four viral families we constructed DNA-dependent DNA polymerase-based (DdDp) phylogenies and in addition, whole genome sequence, as quantitative descriptions of inter-genome relationships. We found that the history of the polymerase gene was highly predictive of the history of the genome as a whole, which we explain in terms of repeated, co-divergence events of the core DdDp gene accompanied by a number of satellite, accessory genetic loci. We also found that the rate of gene gain in baculovirus and poxviruses proceeds significantly more quickly than the rate of gene loss and that there is convergent acquisition of satellite functions promoting contextual adaptation when distinct viral families infect related hosts. The congruence of the genome and polymerase trees suggests that a large set of viral genes, including polymerase, derive from a phylogenetically conserved core of genes of host origin, secondarily reinforced by gene acquisition from common hosts or co-infecting viruses within the host. A single viral genome can be thought of as a mutualistic network, with the core genes acting as an effective host and the satellite genes as effective symbionts. Larger virus genomes show a greater departure from linkage equilibrium between core and satellites functions.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture-the Adaptive Culture Heuristic (ACH)-on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(1/4) so that the number of agents must increase with the fourth power of the problem size, N proportional to F(4), to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F(6) which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

Determination of the molecular weight of proteins in solution from a single small-angle X-ray scattering measurement on a relative scale

This paper describes a new and simple method to determine the molecular weight of proteins in dilute solution, with an error smaller than similar to 10%, by using the experimental data of a single small-angle X-ray scattering (SAXS) curve measured on a relative scale. This procedure does not require the measurement of SAXS intensity on an absolute scale and does not involve a comparison with another SAXS curve determined from a known standard protein. The proposed procedure can be applied to monodisperse systems of proteins in dilute solution, either in monomeric or multimeric state, and it has been successfully tested on SAXS data experimentally determined for proteins with known molecular weights. It is shown here that the molecular weights determined by this procedure deviate from the known values by less than 10% in each case and the average error for the test set of 21 proteins was 5.3%. Importantly, this method allows for an unambiguous determination of the multimeric state of proteins with known molecular weights.

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

A Component of the Xanthomonadaceae Type IV Secretion System Combines a VirB7 Motif with a N0 Domain Found in Outer Membrane Transport Proteins

Type IV secretion systems (T4SS) are used by Gram-negative bacteria to translocate protein and DNA substrates across the cell envelope and into target cells. Translocation across the outer membrane is achieved via a ringed tetradecameric outer membrane complex made up of a small VirB7 lipoprotein (normally 30 to 45 residues in the mature form) and the C-terminal domains of the VirB9 and VirB10 subunits. Several species from the genera of Xanthomonas phytopathogens possess an uncharacterized type IV secretion system with some distinguishing features, one of which is an unusually large VirB7 subunit (118 residues in the mature form). Here, we report the NMR and 1.0 angstrom X-ray structures of the VirB7 subunit from Xanthomonas citri subsp. citri (VirB7(XAC2622)) and its interaction with VirB9. NMR solution studies show that residues 27-41 of the disordered flexible N-terminal region of VirB7(XAC2622) interact specifically with the VirB9 C-terminal domain, resulting in a significant reduction in the conformational freedom of both regions. VirB7(XAC2622) has a unique C-terminal domain whose topology is strikingly similar to that of N0 domains found in proteins from different systems involved in transport across the bacterial outer membrane. We show that VirB7(XAC2622) oligomerizes through interactions involving conserved residues in the N0 domain and residues 42-49 within the flexible N-terminal region and that these homotropic interactions can persist in the presence of heterotropic interactions with VirB9. Finally, we propose that VirB(7XAC2622) oligomerization is compatible with the core complex structure in a manner such that the N0 domains form an extra layer on the perimeter of the tetradecameric ring.

Solution structure of the human signaling protein RACK1

Background: The adaptor protein RACK1 (receptor of activated kinase 1) was originally identified as an anchoring protein for protein kinase C. RACK1 is a 36 kDa protein, and is composed of seven WD repeats which mediate its protein-protein interactions. RACK1 is ubiquitously expressed and has been implicated in diverse cellular processes involving: protein translation regulation, neuropathological processes, cellular stress, and tissue development. Results: In this study we performed a biophysical analysis of human RACK1 with the aim of obtaining low resolution structural information. Small angle X-ray scattering (SAXS) experiments demonstrated that human RACK1 is globular and monomeric in solution and its low resolution structure is strikingly similar to that of an homology model previously calculated by us and to the crystallographic structure of RACK1 isoform A from Arabidopsis thaliana. Both sedimentation velocity and sedimentation equilibrium analytical ultracentrifugation techniques showed that RACK1 is predominantly a monomer of around 37 kDa in solution, but also presents small amounts of oligomeric species. Moreover, hydrodynamic data suggested that RACK1 has a slightly asymmetric shape. The interaction of RACK1 and Ki1/57 was tested by sedimentation equilibrium. The results suggested that the association between RACK1 and Ki-1/57(122-413) follows a stoichiometry of 1:1. The binding constant (KB) observed for RACK1-Ki-1/57(122-413) interaction was of around (1.5 +/- 0.2) x 10(6) M(-1) and resulted in a dissociation constant (KD) of (0.7 +/- 0.1) x 10(-6) M. Moreover, the fluorescence data also suggests that the interaction may occur in a cooperative fashion. Conclusion: Our SAXS and analytical ultracentrifugation experiments indicated that RACK1 is predominantly a monomer in solution. RACK1 and Ki-1/57(122-413) interact strongly under the tested conditions.