Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances

Third-order 2N-storage Runge-Kutta schemes with error control

A family of four-stage third-order explicit Runge-Kutta schemes is derived that requires only two storage locations and has desirable stability characteristics. Error control is achieved by embedding a second-order scheme within the four-stage procedure. Certain schemes are identified that are as efficient and accurate as conventional embedded schemes of comparable order and require fewer storage locations

Fourth-order 2N-storage Runge-Kutta schemes

A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes

Antioxidant Enzyme Genes and Oxidative DNA Damage Repair Genes: Potential Biomarkers for the Early Detection of Lung Cancer

Reactive oxygen species (ROS) are produced in cells by both endogenous and exogenous processes. Oxidative stress arises when the ROS are at high enough concentrations to overwhelm the cell's normal antioxidant defense mechanisms. The fact that DNA is modified by ROS has led to the suggestion that oxidative stress may be an important factor in the process of carcinogenesis. Mammalian cells contain three main antioxidant enzymes that function to maintain ROS at very low concentrations. Catalase (CAT) acts to scavenge hydrogen peroxide. Glutathione peroxidase (GPX) detoxifies hydrogen peroxide as well as lipid-derived organic hydroperoxides. Superoxide dismutase (SOD) converts the superoxide anion radical to hydrogen peroxide. Decreased expression of CAT, GPX and SOD in cancer cells would be expected to result in elevated levels of hydrogen peroxide and superoxide. A number of studies have shown that the activities of these enzymes are decreased in tumor cells compared to adjacent normal tissue. Downregulation of antioxidant gene expression results in consistently elevated levels of ROS, a state referred to as persistent oxidative stress. ROS cause several types of DNA damage, including base modification, strand breakage, and DNA-protein cross-links. One of the major oxidatively modified DNA bases in vivo is 8-hydroxy-2'-deoxyguanosine. This product, which is also referred to as 8-OH-dG or 7,8-dihydro-8-oxo-2'-deoxyguanosine, is mutation prone and results in a G:C to T:A transversion following DNA replication. Elevated levels of 8-OH-dG have been detected in cancers from several tissues (i.e., breast, lung and kidney). Human mutT homologue (hMTHl) prevents the formation of 8-OH-dG residues by dephosphorylating 8-oxo-dGTP to 8-oxo-dGMP, thereby preventing misincorporation of the oxidized free nucleotide into DNA. Overexpression of hMTHl mRNA has been detected in primary renal cell and breast carcinomas as well as in lung cancer cell lines. Human 8-oxoguamne DNA glycosylase (hOGGl)catalyzes the excision of 8-oxo-guanine (8-oxoG) and 2,6-diamino-4-hydroxy-5-formamido-pyrimidine (Fapy) from DNA. To date, no studies have shown hOGGl to be overexpressed in tumor tissues. However, expression of hOGGI has been shown to be upregulated in vitro in response to oxidative stress. Human mutY homologue (hMYH) has an enzymatic activity that removes an adenine base from an A:8-oxoG base pair. No studies have examined the expression of hMYH in tumor tissues. If persistent oxidative stress is a feature of cancer cells, then it is predicted that hMTHl, hOGGl and hMYH should be overexpressed in these cells. By measuring protein levels of CAT, GPX, SOD, hMTHl, hOGGl and hMYH in sputum samples from at-risk individuals (i.e., smokers), it should be possible to detect persistent oxidative stress in exfoliated cells from the lung. This may provide a new strategy for the early detection of lung cancer.Master of Public Healt

Overexpression of hMTH1 mRNA: a molecular marker of oxidative stress in lung cancer cells

AbstractHuman MutT homologue (hMTH1) mRNA was overexpressed in SV-40-transformed non-tumorigenic human bronchial epithelial cells (BEAS-2B cells) and in 11 out of 12 human lung cancer cell lines relative to normal human bronchial epithelial cells. Expression levels of hMTH1 mRNA were inversely proportional to cellular levels of 8-oxo-deoxyguanosine. Together, these results suggest that hMTH1 gene expression may represent a molecular marker of oxidative stress that could ultimately be used to elucidate the temporal relationships between oxidative stress, genomic instability and the development of lung cancer

Melarsoprol cyclodextrin inclusion complexes as promising oral candidates for the treatment of human African trypanosomiasis

Human African trypanosomiasis (HAT), or sleeping sickness, results from infection with the protozoan parasites <i>Trypanosoma brucei</i> (<i>T.b.</i>) <i>gambiense</i> or <i>T.b.rhodesiense</i> and is invariably fatal if untreated. There are 60 million people at risk from the disease throughout sub-Saharan Africa. The infection progresses from the haemolymphatic stage where parasites invade the blood, lymphatics and peripheral organs, to the late encephalitic stage where they enter the central nervous system (CNS) to cause serious neurological disease. The trivalent arsenical drug melarsoprol (Arsobal) is the only currently available treatment for CNS-stage <i>T.b.rhodesiense</i> infection. However, it must be administered intravenously due to the presence of propylene glycol solvent and is associated with numerous adverse reactions. A severe post-treatment reactive encephalopathy occurs in about 10% of treated patients, half of whom die. Thus melarsoprol kills 5% of all patients receiving it. Cyclodextrins have been used to improve the solubility and reduce the toxicity of a wide variety of drugs. We therefore investigated two melarsoprol cyclodextrin inclusion complexes; melarsoprol hydroxypropyl-͎-cyclodextrin and melarsoprol randomly-methylated-β-cyclodextrin. We found that these compounds retain trypanocidal properties <i>in vitro</i> and cure CNS-stage murine infections when delivered orally, once per day for 7-days, at a dosage of 0.05 mmol/kg. No overt signs of toxicity were detected. Parasite load within the brain was rapidly reduced following treatment onset and magnetic resonance imaging showed restoration of normal blood-brain barrier integrity on completion of chemotherapy. These findings strongly suggest that complexed melarsoprol could be employed as an oral treatment for CNS-stage HAT, delivering considerable improvements over current parenteral chemotherapy

Recombination and its impact on the genome of the haplodiploid parasitoid wasp Nasonia

Homologous meiotic recombination occurs in most sexually reproducing organisms, yet its evolutionary advantages are elusive. Previous research explored recombination in the honeybee, a eusocial hymenopteran with an exceptionally high genome-wide recombination rate. A comparable study in a non-social member of the Hymenoptera that would disentangle the impact of sociality from Hymenoptera-specific features such as haplodiploidy on the evolution of the high genome-wide recombination rate in social Hymenoptera is missing. Utilizing single-nucleotide polymorphisms (SNPs) between two Nasonia parasitoid wasp genomes, we developed a SNP genotyping microarray to infer a high-density linkage map for Nasonia. The map comprises 1,255 markers with an average distance of 0.3 cM. The mapped markers enabled us to arrange 265 scaffolds of the Nasonia genome assembly 1.0 on the linkage map, representing 63.6% of the assembled N. vitripennis genome. We estimated a genome-wide recombination rate of 1.4-1.5 cM/Mb for Nasonia, which is less than one tenth of the rate reported for the honeybee. The local recombination rate in Nasonia is positively correlated with the distance to the center of the linkage groups, GC content, and the proportion of simple repeats. In contrast to the honeybee genome, gene density in the parasitoid wasp genome is positively associated with the recombination rate; regions of low recombination are characterized by fewer genes with larger introns and by a greater distance between genes. Finally, we found that genes in regions of the genome with a low recombination frequency tend to have a higher ratio of non-synonymous to synonymous substitutions, likely due to the accumulation of slightly deleterious non-synonymous substitutions. These findings are consistent with the hypothesis that recombination reduces interference between linked sites and thereby facilitates adaptive evolution and the purging of deleterious mutations. Our results imply that the genomes of haplodiploid and of diploid higher eukaryotes do not differ systematically in their recombination rates and associated parameters.Publisher PDFPeer reviewe