The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g.     

A Crossed Immunoelectrophoretic Technique for the Detection of the Down's Syndrome Protein

Abstract

The sera of seventy-one women and twenty-six men of various ages were examined by a two dimensional (crossed) immunoelectrophoresis technique which was modified to detect a protein (the Down's Syndrome protein) originally found in the sera of mothers of trisomy 21 children. The sensitivity of the method is reported to be 0.1 to 1.0 mg/L. Modifications included use of a Tris-Tricine buffer, high voltage in the second dimension, and relatively low antibody concentration to allow easy detection of the Down's Syndrome (DS) protein.

Of twenty-eight mothers and twelve fathers of trisomy 21 children, eighteen mothers and five fathers were positive, while of forty-three women and fourteen men having unaffected or no children, only seven women and two men were positive for the DS protein.

Since the presence of the Down's Syndrome protein may indicate a propensity for giving birth to a trisomy 21 affected child, this crossed immunoelectrophoretic technique may be used as a screening procedure for the DS protein and, therefore, as a tool in genetic counseling.     

Simple and Convenient Synthesis of 21‐Thioalkylether Derivatives of Methyl 16‐Prednisolone Carboxylates

The antedrug approach for corticosteroids has been described as a fundamentally sound approach for the development of safer anti‐inflammatory and anti‐asthmatic therapy. However, the derivatization of prednisolone and its congeners have been considered to be major pitfalls, because their syntheses are complicated by the presence of numerous carboxylate esters and hydroxyl functions in the steroid nucleus. A simple and direct synthesis of 21‐thioalkylether derivatives of methyl 16‐prednisolonecarboxylates is described. The 21‐mesylate of the methyl 16‐prednisolonecarboxylate and 9‐fluoro‐17‐dehydro methyl 16‐prednisolonecarboxylate were reacted with Na‐thioalkoxides to furnish the desired thioethers in good yields. A previously published method for the methanolysis of 16‐cyanoprednisolone to methylcarboxylate has been reexamined, and the conditions are explained clearly. The reaction conditions for all these reactions were critical.     

Algebraic topological methods for the supercritical Q-curvature problem

We study the problem of existence of conformal metrics with prescribed Q-curvature on closed four-dimensional Riemannian manifolds. This problem has a variational structure, and in the case of interest here, it is noncompact in the sense that accumulations points of some noncompact flow lines of a pseudogradient of the associated Euler–Lagrange functional, the so-called true critical points at infinity of the associated variational problem, occur. Using the characterization of the critical points at infinity of the associated variational problem which is established in [42], combined with some arguments from Morse theory, some algebraic topological methods, and some tools from dynamical system originating from Conley's isolated invariant sets and isolated blocks theory, we derive a new kind of existence results under an algebraic topological hypothesis involving the topology of the underling manifold, stable and unstable manifolds of some of the critical points at infinity of the associated Euler–Lagrange functional.     

Software tools for green and sustainable chemistry

In this review, we consider green chemistry metrics, related software tools, and the opportunities and challenges for their use in research laboratories. We provide an overview of state-of-the-art software designed both to aid researchers in planning and conducting chemical experiments and to assess sustainability of individual reactions and synthetic routes. The increasing digitalisation of research means that there is great opportunity for more extensive use of computational tools by synthetic chemists and for closer integration of green chemistry principles into the routine work of chemical laboratories. We discuss the scope for using software tools in the laboratory and assisting synthetic chemists in the adoption of green and sustainable chemistry approaches that are suitable for their specific purposes.     

Decay rate with coordinate-dependent diffusion coefficients

Using a master equation for the reduced density matrix of open quantum system, the influence of coordinate-dependent microscopical diffusion coefficients on the decay rate from a potential well is studied. For different temperatures, frictions, heights of barrier and ratios of stiffnesses of the potential in the minimum and on the top of the barrier, the quasistationary decay rates are obtained with the sets of coordinate-dependent and -independent microscopical diffusion coefficients, and coordinate-dependent phenomenological diffusion coefficients.     

Mass spectrometry of peptides and proteins using digestion by a grape cysteine protease at pH 3

Cysteine protease from grapevine (Vitis vinifera) belongs to those resistant proteins, which survive the process of vinification and can therefore be detected as wine components. Its amino acid sequence shows a homology to other members of the papain family, but the enzyme has only partially been explored so far. In order to get more biochemical information with the help of mass spectrometry (MS), wine proteins were collected by ultrafiltration and separated by gel permeation chromatography. The purified enzyme surprisingly displayed a high molecular mass value of around 200 kDa, indicating a possible oligomeric status and aggregation, as it entered only negligibly the separating 10% gel during polyacrylamide gel electrophoresis. The isoelectric point (pI) value of 3.6 was determined by chromatofocusing. Matrix‐assisted laser desorption/ionization (MALDI)‐MS was employed to evaluate the cleavage specificity and usefulness of the isolated cysteine protease in protein and peptide research. A potential applicability could be anticipated from the efficient digestion performance in volatile ammonium formate buffers at pH 3. Common peptides were digested and the resulting products analyzed by MS/MS sequencing. Then, mixtures of protein standards and extracted barley nuclear proteins were processed in the same way. Grape cysteine protease is nonspecific but shows a certain preference for Arg, Lys, and also Leu residues. Compared with papain, it seems not to require fully the presence of a large hydrophobic residue adjacent to that at the cleavage site. The enzyme is suitable for protein research as it produces peptides of a reasonable length in acidic pH.     

肠道病毒71型外壳蛋白VP1在大肠杆菌中的表达

将扩增得到的肠道病毒71型外壳蛋白VP1基因克隆到测序载体pGEM-T,测序验证该序列为目的片段后,将目的基因克隆到原核表达载体pGEX-5x-1中,转化大肠杆菌BL21,IPTG诱导表达,产物经SDS-PAGE分析和Western blot验证。结果表明,在经IPTG诱导的BL21中检测到分子量与预期大小相符的大约60 kDa的融合蛋白。利用表达产物作为抗原,对EV71感染病人阳性血清的检测初步证实,重组蛋白VP1可以作为检测EV71感染的检测用抗原。