Production, purification, and biochemical characterization of two beta-glucosidases from Sclerotinia sclerotiorum

The filamentous fungus Sclerotinia sclerotiorum produces beta-glucosidases in liquid culture with a variety of carbon sources, including cellulose (filter paper), xylan, barley straw, oat meal, and xylose. Analysis by native polyacrylamide gel electrophoresis (PAGE) followed by an activity staining with the specific chromogenic substrate, 5-bromo 4-chloro 3-indolyl beta-1,4 glucoside (X-glu) showed that two extracellular beta-glucosidases, designated as beta-glu1 and beta-glu2, were in the filter paper culture filtrate. Only one enzyme designated as beta-glu x was revealed by the same method in the xylose culture filtrate. Beta-glu1 and beta-glu2 were purified to homogeneity. The purification procedure consist of a common step of anion-exchange chromatography on DEAE-Sepharose CL6B, both high-performance liquid chromatography (HPLC) anion-exchange and gel filtration columns for beta-glu1 and only HPLC gel filtration for beta-glu2. Beta-glu1 has a molecular mass of 196 kDa and 96.5 kDa, as estimated by gel filtration and sodium dodecyl sulfate (SDS)-PAGE, respectively, suggesting that the native enzyme may consist of two identical subunits. The same analysis showed that beta-glu2 is a monomeric protein with an apparent molecular mass of about 76.5 kDa. Beta-glu1 and beta-glu2 hydrolyses PNPGlc and cellobiose, with apparent Km values respectively for PNPGlc and cellobiose of 0.1 and 1.9 mM for beta-glu1 and 2.8 and 8 mM for beta-glu2. Both enzymes exhibit the same temperature and pH optima for PNPGlc hydrolysis (60 degrees C and pH 5.0). beta-glu1 was stable over a pH range of 3-8 and kept 50% of its activity after 30 min of heating at 60 degrees C without substrate. It was further characterized by studying the effect of some cations and various reagents on its activity.     

Experimental and theoretical study of the coordination of 1,2,4-triazolato, tetrazolato, and pentazolato ligands to the [K(18-crown-6)]+ fragment

Treatment of 3,5-diisopropyltriazole, 3,5-diphenyltriazole, 3,5-di-3-pyridyltriazole, phenyltetrazole, pyrrolidinyltetrazole, or tert-butyltetrazole with equimolar quantities of potassium hydride and 18-crown-6 in tetrahydrofuran at ambient temperature led to slow hydrogen evolution and formation of (3,5-diisopropyl-1,2,4-triazolato)(18-crown-6)potassium (88%), (3,5-diphenyl-1,2,4-triazolato)(tetrahydrofuran)(18-crown-6)potassium (87%), (3,5-di-3-pyridyl-1,2,4-triazolato)(18-crown-6)potassium (81%), (phenyltetrazolato)(18-crown-6)potassium (94%), (pyrrolidinyltetrazolato)(18-crown-6)potassium (90%), and (tert-butyltetrazolato)(18-crown-6)potassium (94%) as colorless crystalline solids. (1,2,4-Triazolato)(18-crown-6)potassium was isolated as a hemi-hydrate in 81% yield upon treatment of 1,2,4-triazole with potassium metal in tetrahydrofuran. The X-ray crystal structures of these new complexes were determined, and the solid-state structures consist of the nitrogen heterocycles bonded to the (18-crown-6)potassium cationic fragments with eta2-bonding interactions. In addition, (3,5-diphenyl-1,2,4-triazolato)(tetrahydrofuran)(18-crown-6)potassium has one coordinated tetrahydrofuran ligand on the same face as the 3,5-diphenyl-1,2,4-triazolato ligand, while (3,5-di-3-pyridyl-1,2,4-triazolato)(18-crown-6)potassium forms a polymeric solid through coordination of the distal 3-pyridyl nitrogen atoms to the potassium ion on the face opposite the 1,2,4-triazolato ligand. The solid-state structures of the new complexes show variable asymmetry in the potassium-nitrogen distances within the eta2-interactions and also show variable bending of the heterocyclic C2N3 and CN4 cores toward the best plane of the 18-crown-6 ligand oxygen atoms. Molecular orbital and natural bond order calculations were carried out at the B3LYP/6-311G(d,p) level of theory on the model complex, (phenyltetrazolato)(18-crown-6)potassium, and demonstrate that the asymmetric potassium-nitrogen distances and bending of the CN4 core toward the 18-crown-6 ligand are due to hydrogen bond-like interactions between filled nitrogen-based orbitals and carbon-hydrogen sigma orbitals on the 18-crown-6 ligands. Calculations carried out on the model pentazolato complex (pentazolato)(18-crown-6)potassium predict a structure in which the pentazolato ligand N5 core is bent by 45 degrees toward the best plane of the 18-crown-6 oxygen atoms. Such bending is induced by the formation of intramolecular nitrogen-hydrogen-carbon hydrogen bonds. Examination of the solid-state structures of the new complexes reveals many intramolecular and intermolecular nitrogen-hydrogen distances of < or =3.0 A which support the presence of nitrogen-hydrogen-carbon hydrogen bonds.     

On Toeplitz operators with quasihomogeneous symbols

In this paper, we give some basic results concerning Toeplitz operators whose symbol is of the form e^{i p θ}ϕ, where ϕ is a radial function, then use these results to characterize all Toeplitz operators which commute with them.Received: 12 June 2004; revised: 27 January 2005     

On a class of matrices generated by certain generalized permutation matrices and applications

ABSTRACT

In this paper, we study a particular class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. As applications, we first present a technique from which we can get closed formulas for the roots of many families of polynomial equations with degree between 5 and 10, inclusive. Then, we describe a tool that shows how to find solutions to Fermat's last theorem and Beal's conjecture over the square integer matrices of any dimension. Finally, simple generalizations of some of the concepts in number theory to integer square matrices are presented.     

A high resolution spatially adaptive vortex method for separating flows. Part I: Two-dimensional domains

A grid-free high-resolution spatially-adaptive vortex method for two-dimensional incompressible flow in bounded domains is presented. The computational algorithm is based on operator splitting in which convection and diffusion are handled separately every time step. In the convection step, computational elements are convected with velocities obtained by fast approximations of the Biot–Savart superposition with second-order Runge–Kutta time integration scheme. Diffusion is performed using the smooth redistribution method that employs a Gaussian basis function for vorticity in the interior. Near solid walls, the core functions are modified to conserve circulation. The no-slip boundary condition is enforced by creating of a vortex sheet that is redistributed to neighboring elements using the redistribution method. The proposed method enables accurate and smooth recovery of the vorticity and does not require explicit use of vortex images or occasional re-meshing. Algorithms for reduction in computational cost by accurately removing elements in overcrowded regions and for spatial adaptivity that allows for variable core sizes and variable element spacing are presented. Computations of flow around an impulsively started cylinder for Reynolds number values of 1000, 3000, and 9500 are preformed to investigate various aspects of the proposed method.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Complexation Studies of a Calix[4](aza)crown and Crystal Structure of its Magnesium Complex

A systematic study of extraction properties and complexation behaviour of the calix[4](aza)crown 1 towards alkaline earth (Mg²⁺, Ca²⁺,Sr²⁺, Ba²⁺) and transition metal (Co²⁺, Ni²⁺, Cu²⁺,Zn²⁺) cations is presented. The binding behaviour of 1 was also investigated by ¹H-NMR and the crystal structure of the 1:1 complex with Mg²⁺ isdescribed.