Singular perturbation analysis of spherical and cylindrical N waves

Using a singular perturbation analysis the nonplanar Burgers' equation is solved to yield the shock wave-displacement due to diffusion for spherical and cylindrical N waves, thus supplementing the earlier results of Lighthill for the plane N waves. Physics of Fluids is copyrighted by The American Institute of Physics.

Structural studies of analgesics and their interactions. II. The crystal structure of a 1:1 complex between antipyrine and salicyclic acid (salipyrine)

The complex crystallizes in the space group P21/c with four formula units in a unit cell of dimensions a= 12.747, b= 7.416, c= 17.894 A and/3= 90.2 °. The structure has been solved by the symbolic addition procedure using three-dimensional photographic data and refined to an R value of 0.079 for 2019 observed reflexions. The pyramidal nature of the two hetero nitrogen atoms in the antipyrine molecule is inter:nediate between that observed in free antipyrine and in some of its metal complexes. The molecule is more polar than that in crystals of free antipyrine but less so compared with that in metal complexes. In the salicylic acid molecule, the hydroxyl group forms an internal hydrogen bond with one of the oxygen atoms in the carboxyl group. The association between the salicylic acid and the antipyrine molecules is achieved through an intermolecular hydrogen bond with the other carboxyl oxygen atom in the salicylic acid molecule as the proton donor and the carboxyl oxygen atom of the antipyrine molecule as the acceptor.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

Two forms of methionyl-transfer RNA synthetase from Mycobacterium Smegmatis

Two methionyl-transfer RNA synthetases (A and B forms) have been isolated from Image . The homogeneous preparations of the enzymes showed 1500 fold increase in specific activity in aminoacylation of methionine specific tRNA. The A and B forms differed in their specificity of aminoacylation of tRNAmMet and tRNAfMet; enzyme B exhibited much higher specificity for tRNAfMet. The molecular activities of A and B enzymes for aminoacid and tRNA were identical. The turnover number for aminoacid was 27 fold greater than that for tRNA, while the Km values for tRNA were lower by a factor of 106 as compared to the aminoacid. Both the enzymes catalysed ATP-pyrophosphate exchange reaction to the same extent.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Conformational analysis of cyclo (l-cystine

Conformational analysis of cyclo(L-cystine) shows that the diketopiperazine ring has to exist only in the boat form. With this geometry, the molecule can adopt two distinct forms differing mainly in the chirality of the disulphide bridge. In both the P- and M-models, corresponding to dihedral angles of nearly + 90° and —90° respectively about the S-S bond, the molecule displays an approximate two-fold symmetry. According to our semi-empirical energy calculations, the minimum energy of the M-model is —9.2 kcal/mol, only 0.3 kcal/mol lower than that of the P-model. Because the difference between the two minima is so small, neither form is clearly superior to the other. However, the number of low energy conformations of the M-model in the allowed conformational space is significantly larger than that of the P-model by a ratio of 3 to 1, and therefore the former is likely to be thermodynamically favoured.

Conformational Choices for the Stereochemically Constrained gamma-Amino Acid Residue Gabapentin: Theoretical Studies and Correlation With Experimental Results

Gabapentin (1-aminomethylcyclohexaneacetic acid, Gpn) is an achiral, conformationally constrained gamma amino acid residue. A survey of available crystal structures of Gpn peptides reveals that the torsion angles about the C-gamma-C-beta (theta(1)) and C-beta-C-alpha(theta(2)) bonds are overwhelmingly limited to gauche, gauche (g(+)g(+)/g(-)g(-)) conformations. The Gpn residue forms C-7 and C-9 hydrogen bonds in which the donor and acceptor atoms come from the flanking peptide units. In combination with alpha amino acid residues alpha gamma and gamma alpha segments can adopt C-12 hydrogen bonded structures. The conformational choices available to the Gpn residue have been probed using energy calculations, adopting a grid search strategy. Ramachandran phi-psi maps have been constructed for fixed values of theta(1) and theta(2), corresponding to the gauche and trans conformations. The sterically allowed and energetically favorable regions of conformational space have been defined and experimental observations compared. C-7 and C-9 hydrogen bonded conformational families have been identified using a grid search approach in which theta(1) and theta(2) values are varied over a range of +/- 10 degrees about ideal values at 1 degrees intervals. The theoretical analysis together with experimental observations for 59 Gpn residues from 35 crystal structures permits definition of the limited range of conformational possibilities at this gamma amino acid residue. .

Polyvanadate-stimulated NADH oxidation by plasma membranes-The need for a mixture of deca and meta forms of vanadate

Polyvanadate solutions obtained by extracting vanadium pentoxide with dilute alkali over a period of several hours contained increasing amounts of decavanadate as characterized by NMR and ir spectra. Those solutions having a metavanadate:decavanadate ratio in the range of 1-5 showed maximum stimulation of NADH oxidation by rat liver plasma membranes. Reduction of decavanadate, but not metavanadate, was obtained only in the presence of the plasma membrane enzyme system. High simulation of activity of NADH oxidation was obtained with a mixture of the two forms of vanadate and this further increased on lowering the pH. Addition of increasing concentrations of decavanadate to metavanadate and vice versa increased the stimulatory activity, reaching a maximum when the metavanadate:decavanadate ratio was in the range of 1-5. Increased stimulatory activity can also be obtained by reaching these ratios by conversion of decavanadate to metavanadate by alkaline phosphate degradation, and of metavanadate to decavanadate by acidification. These studies show for the first time that both deca and meta forms of vanadate present in polyvanadate solutions are needed for maximum activity of NADH oxidation.

A Note on Minimal Reed-Muller Canonical Forms of Switching Functions

A nonexhaustive procedure for obtaining minimal Reed-Muller canonical (RMC) forms of switching functions is presented. This procedure is a modification of a procedure presented earlier in the literature and enables derivation of an upper bound on the number of RMC forms to be derived to choose a minimal one. It is shown that the task of obtaining minimal RMC forms is simplified in the case of symmetric functions and self-dual functions.

Preparation and x-ray characterization of four new crystal forms of Jacalin, a lectin from Artocarpus integrifolia

Four new crystal forms of the anti-T lectin from jackfruit (Artocarpus integrifolia) have been prepared and characterized. Three of them, two monoclinic (P21, A = 59·4 Å, B = 83·3 Å, C = 63·5 Å, β = 107·7°; C2, A = 106·1,Å, B = 53·9 Å, C = 128·0 Å, β = 95·0 Å) and one orthorhombic (C2221, A = 98·1 Å, B = 67·3 Å, C = 95·1 Å) were grown with 2-methylpentan-2,4-diol (MPD) as the precipitant while the fourth, an hexagonal from (P6122, A = b = 129·6 Å, C = 157·9 Å), was obtained in the presence of methyl-ga-Image -galactopyranoside with polyethylene glycol 4000 as the precipitant. The reported relative molecular mass (Mr) of the lectin was found to be inconsistent with the solvent content of the crystals estimated using measured densities. The Mr was redetermined using size-exclusion chromatography in the presence of methyl-α-Image -galactopyranoside and Ferguson-plot analysis of mobilities in polyacrylamide gel electrophoresis. The redetermined Mr (66,000) is consistent with the measured crystal densities. The orthorhombic and the hexagonal forms, which have one half molecule and one molecule, respectively, in the asymmetric unit, are suitable for high-resolution X-ray analysis.

Metal-Nucleotide Interactions: Crystal Structures of Alkali (Li+, Na+, K+) and Alkaline Earth (Ca2+, Mg2+) Metal Complexes of Adenosine 2'-Monophosphate

Crystal structures of lithium, sodium, potassium, calcium and magnesium salts of adenosine 2'-monophosphate (2'-AMP) have been obtained at atomic resolution by X-ray crystallographic methods. 2'-AMP.Li belongs to the monoclinic space group P21 with a = 7.472(3)Å, b = 26.853(6) Å, c = 9.184(1)Å, b = 113.36(1)Å and Z= 4. 2'-AMP.Na and 2'-AMP.K crystallize in the trigonal space groups P31 and P3121 with a = 8.762(1)Å, c = 34.630(5)Å, Z= 6 and a = 8.931(4), Åc = 34.852(9)Å and Z= 6 respectively while 2'-AMP.Ca and 2'-AMP.Mg belong to space groups P6522 and P21 with cell parameters a = 9.487(2), c = 74.622(13), Z = 12 and a = 4.973(1), b = 10.023(2), c = 16.506(2), beta = 91.1(0) and Z = 2 respectively. All the structures were solved by direct methods and refined by full matrix least-squares to final R factors of 0.033, 0.028, 0.075, 0.069 and 0.030 for 2'-AMP.Li, 2'-AMP.Na, 2'- AMP.K, 2'-AMP.Ca and 2'-AMP.Mg, respectively. The neutral adenine bases in all the structures are in syn conformation stabilized by the O5'-N3 intramolecular hydrogen bond as in free acid and ammonium complex reported earlier. In striking contrast, the adenine base is in the anti geometry (cCN = -156.4(2)°) in 2'-AMP.Mg. Ribose moieties adopt C2'-endo puckering in 2'-AMP.Li and 2'-AMP.Ca, C2'-endo-C3'-exo twist puckering in 2'-AMP.Na and 2'-AMP.K and a C3'-endo-C2'-exo twist puckering in 2'-AMP.Mg structure. The conformation about the exocyclic C4'-C5' bond is the commonly observed gauche-gauche (g+) in all the structures except the gauche- trans (g-) conformation observed in 2'-AMP.Mg structure. Lithium ions coordinate with water, ribose and phosphate oxygens at distances 1.88 to 1.99Å. Na+ ions and K+ ions interact with phosphate and ribose oxygens directly and with N7 indirectly through a water oxygen. A distinct feature of 2'-AMP.Na and 2'-AMP.K structures is the involvement of ribose O4' in metal coordination. The calcium ion situated on a two-fold axis coordinates directly with three oxygens OW1, OW2 and O2 and their symmetry mates at distances 2.18 to 2.42Å forming an octahedron. A classic example of an exception to the existence of the O5'-N3 intramolecular hydorgen bond is the 2'-AMP.Mg strucure. Magnesium ion forms an octahedral coordination with three water and three phosphate oxygens at distances ranging from 2.02 to 2.11Å. A noteworthy feature of its coordination is the indirect link with N3 through OW3 oxygen resulting in macrochelation between the base and the phosphate group. Greater affnity of metal clays towards 5' compared to 2' and 3' nucleotides (J. Lawless, E. Edelson, and L. Manring, Am. Chem. Soc. Northwest Region Meeting, Seattle. 1978) due to macrochelation infered from solution studies (S. S. Massoud, H. Sigel, Eur. J. Biochem. 179, 451-458 (1989)) and interligand hydrogen bonding induced by metals postulated from metal-nucleotide structures in solid state (V. Swaminathan and M. Sundaralingam, CRC. Crit. Rev. Biochem. 6, 245-336 (1979)) are borne out by our structures also. The stacking patterns of adenine bases of both 2'-AMP.Na and 2'-AMP.K structures resemble the 2'-AMP.NH4 structure reported in the previous article. 2'-AMP.Li, 2'-AMP.Ca and 2'-AMP.Mg structures display base-ribose O4' stacking. An overview of interaction of monovalent and divalent cations with 2' and 5'-nucleotides has been presented.

Trifurcated (four-center) hydrogen bond in solid state crystal structure of 5'-amino-5'-deoxyadenosine p-toluenesulfonate

The crystal structure of 5'-amino-5'-deoxyadenosine (5'-Am.dA) p-toluenesulfonate has been determined by X-ray crystallographic methods. It belongs to the orthorhombic space group P2(1)2(1)2(1) with a = 7.754(3)Angstrom, b = 8.065(1)Angstrom and c = 32.481(2)Angstrom. This nucleoside side shows a syn conformation about the glycosyl bond and C2'-endo-C3'-exo puckering for the ribose sugar. The orientation of N5' atom is gauche-trans about the exocyclic C4'-C5' bond. The amino nitrogen N5' forms a trifurcated hydrogen bond with N3, O9T and O4' atoms. Adenine bases form A.A.A triplets through hydrogen bonding between N6, N7 and N1 atoms of symmetry related nucleoside molecules.

Functional characterization of the precursor and spliced forms of RecA protein of Mycobacterium tuberculosis

The recA locus of pathogenic mycobacteria differs from that of nonpathogenic species because it contains large intervening sequences nested in the RecA homology region that are excised by an unusual protein-splicing reaction. In vivo assays indicated that Mycobacterium tuberculosis recA partially complemented Escherichia coli recA mutants for recombination and mutagenesis. Further, splicing of the 85 kDa precursor to 38 kDa MtRecA protein was necessary for the display of its activity, in vivo. To gain insights into the molecular basis for partial and lack of complementation by MtRecA and 85 kDa proteins, respectively, we purified both of them to homogeneity. MtRecA protein, but not the 85 kDa form, bound stoichiometrically to single-stranded DNA in the presence of ATP. MtRecA protein was cross-linked to 8-azidoadenosine 5'-triphosphate with reduced efficiency, and kinetic analysis of ATPase activity suggested that it is due to decreased affinity for ATP. In contrast, the 85 kDa form was unable to bind ATP, in the presence or absence of ssDNA and, consequently, was entirely devoid of ATPase activity. Molecular modeling studies suggested that the decreased affinity of MtRecA protein for ATP and the reduced efficiency of its hydrolysis might be due to the widening of the cleft which alters the hydrogen bonds and the contact area between the enzyme and the substrate and changes in the disposition of the amino acid residues around the magnesium ion and the gamma-phosphate. The formation of joint molecules promoted by MtRecA protein was stimulated by SSB when the former was added first. The probability of an association between the lack and partial levels of biological activity of RecA protein(s) to that of illegitimate recombination in pathogenic mycobacteria is considered.

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.