Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Cloning, expression, purification, crystallization and preliminary X-ray crystallographic study of the putative SAICAR synthetase (PH0239) from Pyrococcus horikoshii OT3

The study of proteins involved in de novo biosynthesis of purine nucleotides is central in the development of antibiotics and anticancer drugs. In view of this, a protein from the hyperthermophile Pyrococcus horikoshii OT3 was isolated, purified and crystallized using the microbatch method. Its primary structure was found to be similar to that of SAICAR synthetase, which catalyses the seventh step of de novo purine biosynthesis. A diffraction-quality crystal was obtained using Hampton Research Crystal Screen II condition No. 34, consisting of 0.05 M cadmium sulfate hydrate, 0.1 M HEPES buffer pH 7.5 and 1.0 M sodium acetate trihydrate, with 40%(v/v) 1,4-butanediol as an additive. The crystal belonged to space group P3(1), with unit-cell parameters a = b = 95.62, c = 149.13 angstrom. Assuming the presence of a hexamer in the asymmetric unit resulted in a Matthews coefficient (V-M) of 2.3 angstrom(3) Da(-1), corresponding to a solvent content of about 46%. A detailed study of this protein will yield insights into structural stability at high temperatures and should be highly relevant to the development of antibiotics and anticancer drugs targeting the biosynthesis of purine nucleotides.

High-yield bacterial expression and structural characterization of recombinant human insulin-like growth factor binding protein-2

The diverse biological activities of the insulin-like growth factors (IGF-1 and IGF-2) are mediated by the IGF-1 receptor (IGF-1R). These actions are modulated by a family of six IGF-binding proteins (ICFBP-1-6; 22-31 kDa) that via high affinity binding to the IGFs (K-D similar to 300-700 pM) both protect the IGFs in the circulation and attenuate IGF action by blocking their receptor access In recent years, IGFBPs have been implicated in a variety of cancers However, the structural basis of their interaction with IGFs and/or other proteins is not completely understood A critical challenge in the structural characterization of full-length IGFBPs has been the difficulty in expressing these proteins at levels suitable for NMR/X-ray crystallography analysis Here we describe the high-yield expression of full-length recombinant human IGFBP-2 (rhIGFBP-2) in Eschericha coli Using a single step purification protocol, rhIGFBP-2 was obtained with >95% purity and structurally characterized using NMR spectroscopy. The protein was found to exist as a monomer at the high concentrations required for structural studies and to exist in a single conformation exhibiting a unique intra-molecular disulfide-bonding pattern The protein retained full biologic activity. This study represents the first high-yield expression of wild-type recombinant human IGFBP-2 in E coli and first structural characterization of a full-length IGFBP (C) 2010 Elsevier Inc. All rights reserved

Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P-(1)(X,R,t)) and the product (p((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent, As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

A convenient and high-yield synthesis for pyridinium and metal hexafluorocomplexes of vanadium, chromium, iron and cobalt

Pyridinium poly(hydrogen fluoride) reacts with the oxide of vanadium(V) and chlorides of chromium(III), iron (III) and Co(II) at room temperature forming the pyridinium salts of hexafluoro vanadate(V), hexafluorochromate(III), hexafluoroferrate(III) and hexafluorocobaltate(II) in near quantitative yields (80%). These pyridinium salts are the precursors for the preparation of the alkali metal hexafluorometallates by metathetic reactions in acetonitrile medium with the corresponding metal chlorides. The prepared salts have been identified by their infrared spectral data and elemental analysis.

A Convenient High-Yield Room-Temerature Synthesis of Mixed Tri(Amino) Silanes by Transmination of Tris(Dicyclohexylamino) Silane And-Their Characterization

Tris(dicyclohexylamino)silane. (DCA)3SiH. is prepared by the reaction of trichlorosilane with dicyclohexylamine. This is found to undergo transamination reactions with other secondary amines (R2NH). such as pyrrolidine, piperidine, hexamethyleneimine. morpholine. N-methylpiperazine and diethylamine to yield mixed tri(amino)silanes of the formula (DCA)(R2N)2SiH in quantitative yields. These new derivatives are found to be moisture sensitive and hydrolyze to yield their respective amines, hydrogen and silica. They are found to be stable in an inert atmosphere. They have been characterized by IR, NMR (H-1, Si-29), mass spectroscopy and CHN analysis. N-15 NMR for one of the compounds has been done.

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

High Yield Room Temperature Synthesis And Spectral Studies Of Tri(Amino)Silanes: (R2n)3SIH

Tri(amino)silanes were prepared by the condensation of trichlorosilane with secondary amines in 1:6 molar ratio. Reactions of trichlorosilane with pyrrolidine, piperidine, hexamethyleneimine, morpholine, N-methylpiperazine and diethylamine afford the tri(amino)silanes in nearly quantitative yields. Their physical and spectroscopic properties are discussed. All these compounds are highly sensitive to moisture and hydrolyse to silica and the respective amine with the evolution of hydrogen. The compounds have been characterised by IR, 1H NMR, [1H]29Si NMR spectroscopic methods and CHN elemental analysis.

Cross-polarization from the dipolar reservoir under the mismatched Hartmann-Hahn condition

Cross-polarization from the dipolar reservoir for a range of mismatched Hartmann-Hahn conditions has been considered. Experiment, in general, agrees with the dispersive Lorentzian behavior expected on the basis of quasi-equilibrium theory. It is observed that inclusion of additional mechanisms of polarization transfer lead to an improvment of the fit of the experimental results. The utility of extending the technique to the case of ordered long chain molecules, such as liquid crystals, for the measurement of the local dipolar field is also presented. (C) 2002 Elsevier Science (USA).

Shear banding in a yield stress bearing Langmuir monolayer

We examine the shear-thinning behaviour of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs, showing coexistence of the fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile, which is linear at low shear rates, becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behaviour like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation.