A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Characterization of the DNA-binding domain of beta protein, a component of phage lambda Red-pathway by UV catalyzed cross-linking

beta protein, a key component of Red-pathway of phage lambda is necessary for its growth and general genetic recombination in recombination-deficient mutants of Escherichia coli. To facilitate studies on structure-function relationships, we overexpressed beta protein and purified it to homogeneity. A chemical cross-linking reagent, glutaraldehyde, was used to stabilize the physical association of beta protein in solution. A 67-kDa band, corresponding to homodimer, was identified after separation by SDS-polyacrylamide gel electrophoresis. Stoichiometric measurements indicated a site-size of 1 monomer of beta protein/5 nucleotide residues. Electrophoretic gel mobility shift assays suggested that beta protein formed stable nucleoprotein complexes with 36-mer, but not with 27- or 17-mer DNA. Interestingly, the interaction of beta protein with DNA and the stability of nucleoprotein complexes was dependent on the presence of MgCl2, and the binding was abolished by 250 mM NaCl. The K-d of beta protein binding to 36-mer DNA was on the order of 1.8 x 10(-6) M. Photochemical cross-linking of native beta protein or its fragments, generated by chymotrypsin, to 36-mer DNA was performed to identify its DNA-binding domain. Characterization of the cross-linked peptide disclosed that amino acids required for DNA-binding specificity resided within a 20-kDa peptide at the N-terminal end. These findings provide a basis for further understanding oi the structure and function of beta protein.

Heme biosynthesis by the malarial parasite - Import of delta-aminolevulinate dehydrase from the host red cell

The mouse and human malarial parasites, Plasmodium berghei and Plasmodium falciparum, respectively, synthesize heme de novo following the standard pathway observed in animals despite the availability of large amounts of heme, derived from red cell hemoglobin, which is stored as hemozoin pigment, The enzymes, delta-aminolevulinate dehydrase (ALAD), coproporphyrinogen oxidase, and ferrochelatase are present at strikingly high levels in the P, berghei infected mouse red cell in vivo, The isolated parasite has low levels of ALAD and the data clearly indicate it to be of red cell origin. The purified enzyme preparations from the uninfected red cell and the parasite are identical in kinetic properties, subunit molecular weight, cross-reaction with antibodies to the human enzyme, and N-terminal amino acid sequence. Immunogold electron microscopy of the infected culture indicates that the enzyme is present inside the parasite and, therefore, is not a contaminant, The parasite derives functional ALAD from the host and the enzyme binds specifically to isolated parasite membrane in vitro, suggestive of the involvement of a receptor in its translocation into the parasite, While, ALAD, coproporphyrinogen oxidase, and ferrochelatase from the parasite and the uninfected red cell supernatant have identical subunit molecular weights on SDS-polyacrylamide gel electrophoresis and show immunological cross-reaction with antibodies to the human enzymes, as revealed by Western analysis, the first enzyme of the pathway, namely, delta-aminolevulinate synthase (ALAS) in the parasite, unlike that of the red cell host, does not cross-react with antibodies to the human enzyme, However, ALAS enzyme activity in the parasite is higher than that of the infected red cell supernatant. We therefore conclude that the parasite, while making its own ALAS, imports ALAD and perhaps most of the other enzymes of the pathway from the host to synthesize heme de novo, and this would enable it to segregate this heme from the heme derived from red cell hemoglobin degradation, ALAS of the parasite and the receptor(s) involved in the translocation of the host enzymes into the parasite would be unique drug targets.

A thermal molecular migration in the solid-state - structures of isomeric 5-amino-4-(2,6-dichlorophenyl)-1-(2-nitrophenyl)-1h-1,2,3-triazole (yellow form i) and 4-(2,6-dichlorophenyl)-5-(2-nitroanilino)-2h-1,2,3-triazole (red form-ii), c14h9cl2n5o2

Yellow form (I): Mr= 350.09, monoclinic, P2Jn, Z--4, a=9.525(1), b=14.762(1), c= 11.268(1),/t, fl= 107.82 (1) o , V= 1508.3 A 3 , Din(flotation in aqueous KI)= 1.539 (2), D x= 1.541 (2) g cm -3, #(Cu Ka, 2 = 1.5418 A) = 40.58 cm -~, F(000) = 712, T= 293 K, R = 8.8% for 2054 significant refections. Red form (II): Mr= 350.09, triclinic, Pi, Z=2, a=9.796(2), b= 10.750 (2), c= 7.421 (1)A, a= 95.29 (2), fl= 0108-2701/84/111901-05501.50 70.18 (1), y = 92-.76 (2) °, V= 731.9 A 3, Din(flotation in KI) = 1.585 (3), D x = 1.588 (3) g cm -3, ~t(Cu Ka, 2 = 1.5418/~) = 40.58 cm -1, F(000) = 356, T=293 K, R = 5.8% for 1866 significant reflections. There are no unusual bond distances or angles. The triazole and two phenyl rings are planar. On the basis of packing considerations the possibility of intermolecular interactions playing a role in the reactivity of the starting material is ruled out.

Interaction of Cibacron Blue F3G-A and Procion Red HE-3B with sheep liver 5,10-methylenetetrahydrofolate reductase

Cibacron Blue F3G-A, a probe used to monitor nucleotide binding domains in enzymes, inhibited sheep liver 5, 10-methylenetetrahydrofolate reductase competitively with respect to 5-methyltetrahydrofolate and NADPH. The Ki values obtained by kinetic methods and the Kd value for the binding of the dye to the enzyme estimated by protein fluorescence quenching were in the range 0·9-1·2 μM. Another triazine dye, Procion Red HE-3B interacted with the enzyme in an essentially similar manner to that observed with Cibacron Blue F3G-A. These results as well as the interaction of the dye with the enzyme monitored by difference spectroscopy and intrinsic protein fluorescence quenching methods indicated that the dye was probably interacting at the active site of the enzyme by binding at a hydrophobic region.

Pozzolanic properties of rice husk ash, burnt clay and red mud

In this paper materials like rice husk ash, burnt clay and red mud are examined for their pozzolanic properties. Rice husk ash, obtained from various sources, is analysed by X-ray diffraction. Compressive strength properties of lime-pozzolana mortars with rice husk ash, burnt clay and red mud as pozzolana are studied. Influence of grinding of rice husk ash and intergrinding with lime are also investigated. Combination pozzolana with partial replacement of burnt clay and red mud by rice husk ash are examined for their pozzolanic properties. Long term strength behaviour of lime-pozzolana mortars is investigated to understand the durability of lime-pozzolana cements.

Additional binding sites in lysozyme. X-ray analysis of lysozyme complexes with bromophenol red and bromophenol blue

The binding sites in hen egg-white lysozyme for neutral bromophenol red (BPR) and ionized bromophenol blue (BPB) have been characterized at 2 Å resolution. In either case, the dye-bound enzyme is active against the polysaccharide, but not against the cell wall. Both binding sites are outside, but close to, the hexasaccharide binding cleft in the enzyme. The binding site of BPR made up of Arg5, Lys33, Phe34, Asn37, Phe38, Ala122, Trp123 and possibly Arg125, is dose to subsite F while that of BPB made up of Tyr20, Arg21, Asn93, Lys96, Lys97 and Ser100, is close to subsites A and B. The binding sites of the neutral dye and the ionized dye are thus spatially far apart. The peptide component of the bacterial cell wall probably interacts with these cells during enzyme action. Such interactions are perhaps necessary for appropriately positioning the enzyme molecule on the bacterial cell wall.

A Proof of Convergence of the B-RED and P-RED Algorithms for Random Early Detection

In [8], we recently presented two computationally efficient algorithms named B-RED and P-RED for random early detection. In this letter, we present the mathematical proof of convergence of these algorithms under general conditions to local minima.

Anaerobic DNA cleavage activity in red light and photocytotoxicity of (pyridine-2-thiol)cobalt(III) complexes of phenanthroline bases

Cobalt(III) complexes [Co(pnt)(B)(2)](NO3)(2) (1-3) of pyridine-2-thiol (pnt) and phenanthroline bases (B), viz. 1,10-phenanthroline (phen in 1), dipyrido[3,2-d: 2',3'-f]quinoxaline (dpq in 2) and dipyrido[3,2-a:2',3'-c] phenazine (dppz in 3), have been prepared, characterized and their photo-induced anaerobic DNA cleavage activity studied. The crystal structure of 1a as mixed ClO4- and PF6- salt of 1 shows a (CoN5S)-N-III coordination geometry in which the pnt and phen showed N,S- and N,N-donor binding modes, respectively. The complexes exhibit Co(III)/Co(II) redox couple near -0.3 V (vs. SCE) in 20% DMF-Tris-HCl buffer having 0.1 M TBAP. The complexes show binding propensity to calf thymus DNA giving K-b values within 2.2 x 10(4)-7.3 x 10(5) M-1. Thermal melting and viscosity data suggest DNA surface and/or groove binding of the complexes. The complexes show significant anaerobic DNA cleavage activity in red light under argon atmosphere possibly involving sulfide anion radical or thiyl radical species. The DNA cleavage reaction under aerobic medium in red light is found to involve both singlet oxygen and hydroxyl radical pathways. The dppz complex 3 shows non-specific BSA and lysozyme protein cleavage activity in UV-A light of 365 nm via both hydroxyl and singlet oxygen pathways. The dppz complex 3 exhibits photocytotoxicity in HeLa cervical cancer cells giving IC50 values of 767 nM and 19.38 mu M in UV-A light of 365 nm and in the dark, respectively. A significant reduction of the dark toxicity of the dppz base (IC50 = 8.34 mu M in dark) is observed on binding to the cobalt(III) center.

DNA cleavage in red light promoted by copper(II) complexes of -amino acids and photoactive phenanthroline bases

Ternary copper(II) complexes [Cu(L-trp)(B)(H2O)](NO3) ( 1–3) and [Cu(L-phe)(B)(H2O)](NO3) ( 4–6) of L-tryptophan (L-trp) and L-phenylalanine (L-phe) having phenanthroline bases (B), viz. 1,10-phenanthroline (phen, 1 and 4), dipyrido[3,2-d:2,3-f]quinoxaline (dpq, 2 and 5) and dipyrido[3,2-a:2,3-c]phenazine (dppz, 3 and 6), were prepared and characterized by physico-chemical techniques. Complexes 3 and 6 were structurally characterized by X-ray crystallography and show the presence of a square pyramidal (4 + 1) CuN3O2 coordination geometry in which the N,O-donor amino acid (L-trp or L-phe) and N,N-donor phenanthroline base bind at the equatorial plane with an aqua ligand coordinated at the elongated axial site. Complex 3 shows significant distortion from the square pyramidal geometry and a strong intramolecular – stacking interaction between the pendant indole ring of L-trp and the planar dppz aromatic moiety. All the complexes display good binding propensity to the calf thymus DNA giving an order: 3, 6 (dppz) > 2, 5 (dpq) > 1, 4 (phen). The binding constant (Kb) values are in the range of 2.1 × 104–1.1 × 106 mol-1 with the binding site size (s) values of 0.17–0.63. The phen and dpq complexes are minor groove binders while the dppz analogues bind at the DNA major groove. Theoretical DNA docking studies on 2 and 3 show the close proximity of two photosensitizers, viz. the indole moiety of L-trp and the quinoxaline/phenazine of the dpq/dppz bases, to the complementary DNA strands. Complexes 2 and 3 show oxidative DNA double strand breaks (dsb) of supercoiled (SC) DNA forming a significant quantity of linear DNA along with the nicked circular (NC) form on photoexposure to UV-A light of 365 nm and red light of 647.1 nm (Ar–Kr laser). Complexes 1, 5 and 6 show only single strand breaks (ssb) forming NC DNA. The red light induced DNA cleavage involves metal-assisted photosensitization of L-trp and dpq/dppz base resulting in the formation of a reactive singlet oxygen (1O2) species.

Infra-red spectra of crystalline chloroacetates of Cu, Ca, Sr, Ba and Pb

The infra-red spectra of Cu, Ca, Sr, Ba and Pb chloroacetates were studied in order to investigate the effect of co-ordination on the vibration spectra of the ligand. The shifts of the symmetric and antisymmetric COO− vibrational frequencies indicate a bridged structure as the most probable one for the complexes investigated. No linear relationship between the shifts of the COO− stretching frequencies and E/r (where E is the electron excitation energy and r the ionic radius) was observed. No systematic mass effect on these COO− frequencies also could be established.

Infra-red and raman spectra of BaCl2.2H2O and BaCl2.2D2O

The infra-red and Raman spectra of ordinary and deuterated barium chloride dihydrate have been studied to throw light on the intramolecular hydrogen bonds in these two crystals. The frequencies of the stretching, bending and librational modes observed in infra-red and Raman spectra exclude the possibility of at least one of the OH.... Cl hydrogen bonds, contrary to the results of NMR and neutron diffraction studies.

Raman and infra-red spectra of crystalline ammonium sulphamate

Raman spectrum of a single crystal of ammonium sulphamate has been recorded for the two different orientations using λ 2537 resonance radiation of the mercury as the exciter. Thirty-four Raman lines have been observed of which eight belong to the lattice oscillations. Weak hydrogen bonding of NH2 group in the crystal was predicted. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc, using Carl Zeiss UR10 IR spectrometer. Thirty-five absorption maxima could be identified.

Raman and infra-red spectra of crystalline potassium sulphamate

Raman spectrum of a single crystal of potassium sulphamate has been recorded for the first time using λ 2536 radiation of mercury as the exciter. Thirty-three Raman lines have been observed of which nine belong to the lattice oscillations. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc using Carl Zeiss UR 10 IR spectrometer. Thirty-six absorption maxima could be identified of which twenty-five have been recorded for the first time. The analysis clearly shows that the N-H bond in the crystalline potassium sulphamate is not hydrogen-bonded to any appreciable extent.

Hydrogen bonding in thiolbenzoic acid. Infra-red, ultra-violet, n.m.r. and cryoscopic studies

Dimerization of thiolbenzoic acid has been studied by infra-red, ultra-violet and n.m.r. spectroscopy and cryoscopy. The results indicate that the tendency to form S - H. O hydrogen bonds is not appreciable.