The concept of proof in the light of mathematical work

ZDM – Mathematics Education - Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and...     

Characterizing protein glycosylation sites through higher‐energy C‐trap dissociation

Assigning glycosylation sites of glycoproteins and their microheterogeneity is still a very challenging analytical task despite the rapid advancements in mass spectrometry. It is shown here that glycopeptide ions can be fragmented efficiently using the higher‐energy C‐trap dissociation (HCD) feature of a linear ion trap orbitrap hybrid mass spectrometer (LTQ Orbitrap). An attractive aspect of this dissociation option is the generation of distinct Y1 ions (peptide+GlcNAc), thus allowing unequivocal assignment of N‐glycosylation sites of glycoproteins. The combination of the very informative collision‐induced dissociation spectra acquired in the linear ion trap with the distinct features of HCD offers very useful information aiding in the characterization of the glycosylation sites of glycoproteins. The HCD activation energy needed to obtain optimum Y1 ions was studied in terms of glycan structure and charge state, and size and structure of the peptide backbone. The latter appeared to be primarily dictating the needed HCD energy. The distinct Y1 ion formation in HCD facilitated an easy assignment of such an ion and its subsequent isolation and dissociation through multiple‐stage tandem mass spectrometry. The resulting MS³ spectrum of the Y1 ion facilitates database searching and de novo sequencing thus prompting the subsequent identification of the peptide backbone and associated glycosylation sites. Moreover, fragment ions formed by HCD are detected in the Orbitrap, thus overcoming the 1/3 cut‐off limitation that is commonly associated with ion trap mass spectrometers. As a result, in addition to the Y1 ion, the common glycan oxonium ions are also detected. The high mass accuracy offered by the LTQ Orbitrap mass spectrometer is also an attractive feature that allows a confident assignment of protein glycosylation sites and the microheterogeneity of such sites. Copyright © 2010 John Wiley & Sons, Ltd.     

Improving confidence in detection and characterization of protein N-glycosylation sites and microheterogeneity

Protein glycosylation is one of the most common post-translational modifications, estimated to occur in over 50% of human proteins. Mass spectrometry (MS)-based approaches involving different fragmentation mechanisms have been frequently used to detect and characterize protein N-linked glycosylations. In addition to the popular Collision-Induced Dissociation (CID), high-energy C-trap dissociation (HCD) fragmentation, which is a feature of a linear ion trap orbitrap hybrid mass spectrometer (LTQ Orbitrap), has been recently used for the fragmentation of tryptic N-linked glycopeptides in glycoprotein analysis. The oxonium ions observed with high mass accuracy in the HCD spectrum of glycopeptides can be combined with characteristic fragmentation patterns in the CID spectrum resulting from consecutive glycosidic bond cleavages, to improve the detection and characterization of N-linked glycopeptides. As a means of automating this process, we describe here GlypID 2.0, a software tool that implements several algorithmic approaches to utilize MS information including accurate precursor mass and spectral patterns from both HCD and CID spectra, thus allowing for an unequivocal and accurate characterization of N-linked glycosylation sites of proteins.     

Mixed fluoroamine complexes of chromium(III)

Summary Mixed difluoro(diamine)(diamme)chromium(III) complexes have been synthesized with ethylenediamine (en), 1,3 propanediamine(tn) and 1,2-cyclohexanediamine(chxn):trans-[CrF₂(aa)(bb)]Br (aa=en, bb=tn; aa=tn, bb= chxn) andcis-[CrF₂(aa)(bb)]Br (aa=en, bb=chxn). The corresponding fluoroaqua(diamine) (diamine)chromium(III) complexes have been prepared by acid hydrolysis as perchlorate or iodide salts. All have been characterized by chemical analysis, electronic and i.r. spectra and conductivity measurements.     

Ion-selective electrodes for anionic surfactants using a cyclam derivative as ionophore

The cyclam derivative 1,4,8,11-tetra(n-octyl)-1,4,8,11-tetraazacyclotetradecane (L) has been used as carrier for the preparation of PVC-based membrane ion-selective electrodes for anionic surfactants. Different membranes were prepared using L as ionophore, tetra-n-octylammonium bromide (TOAB) as cationic additive and dibutyl phthalate (DBP) or o-nitrophenyl octyl ether (NPOE) as plasticizers. The final used electrode contained a membrane of the following composition: 56% DBP, 3.4% ionophore, 3.8% TOAB and 36.8% PVC. This electrode displays a Nernstian slope of -60.0+/-0.9 mV/decade in a 2.0 x 10(-3) to 7.9 x 10(-6) mol dm(-3) concentration range and a limit of detection of 4.0 x 10(-6) mol dm(-3). The electrode can be used for 144 days without showing significant changes in the value of slope or working range. The electrode shows a selective response to dodecyl sulfate (DS-) and a poor response to common inorganic cations and anions. The selective sequence found was DS->ClO4->HCO3->SCN->NO3- approximately CH3COO- approximately I->Cl->Br->IO3- approximately NO2- approximately SO3(2-)>HPO4(2-)>C2O4(2-)>SO4(2-), i.e. basically following the Hoffmeister series except for the hydrophilic anion bicarbonate. Most of the potentiometric coefficients determined are relatively low indicating that common anions would not interfere in the DS- determination. A complete study of the response of the electrode to a family of surfactant was also carried out. The electrode showed a clear anionic response to DS- and to Na-LAS and a much poorer response to other anionic surfactants and to non-ionic surfactants. Also the electrode shows certain non-linear cationic response in the presence of cationic and zwitterionic surfactants. The electrode was used for the determination of anionic surfactants in several mixtures, and the results obtained were compared to those found using a commercially available sensor.     

Rapid and efficient glycoprotein identification through microwave-assisted enzymatic digestion

Identification of protein glycosylation sites is analytically challenging due to the diverse glycan structures associated with a glycoprotein. Mass spectrometry (MS)-based identification and characterization of glycoproteins has been achieved predominantly with the bottom-up approach, which typically involves the enzymatic cleavage of proteins to peptides prior to LC/MS or LC/MS/MS analysis. However, the process can be challenging due to the structural variations and steric hindrance imposed by the attached glycans. Alternatives to conventional heating protocols, that increase the rate of enzymatic cleavage of glycoproteins, may aid in addressing these challenges. An enzymatic digestion of a glycoprotein can be accelerated and made more efficient through microwave-assisted digestion. In this paper, a systematic study was conducted to explore the efficiency of microwave-assisted enzymatic (trypsin) digestion (MAED) of glycoproteins as compared with the conventional method. In addition, the optimum experimental parameters for the digestion such as temperature, reaction time, and microwave radiation power were investigated. It was determined that efficient tryptic digestion of glycoproteins was attained in 15 min, allowing comparable if not better sequence coverage through LC/MS/MS analysis. Optimum tryptic cleavage was achieved at 45°C irrespective of the size and complexity of the glycoprotein. Moreover, MAED allowed the detection and identification of more peptides and subsequently higher sequence coverage for all model glycoprotein. MAED also did not appear to prompt a loss or partial cleavage of the glycan moieties attached to the peptide backbones.     

Schwinger's method for the massive Casimir effect

We apply a method recently proposed by Schwinger to the massive scalar field to calculate the Casimir effect. The method is applied with two different regularization schemes: Schwinger's original one by means of Poisson formula and another one by means of analytical continuation.     

Influence on friction behavior of micro-texturing under lubricated non-conformal contact

Laser surface texturing (LST) is a well-known surface engineering process used to create arranged dimples on surface using a material ablation process. In this process, a well arranged micro-dimple can produce significant improvements of engineering components in aspects such as load carrying capacity, wear resistance, wetting characteristics and reduction of friction coefficient. In the present work, we investigated the effect of multi-dimple LST steel surfaces on tribological properties under non-conforming contact. The multi-dimple textured surfaces with some specific formula arrays were fabricated by laser ablation process on steel disc by combining patterns of circles and triangles, and circles and squares, having different dimple densities to optimize the surface texturing effect on tribological performance. The tribological test of multi-dimple textured surface was performed by a ball-on-flat unidirectional tribometer in lubricated condition, and the results compared with that of a single-dimple and untextured (polished and ground) surfaces. The results indicate that the surface with multi-dimple textured patterns had better friction performance than the untextured and single-dimple textured surfaces. The beneficial effect of multi-dimple textured patterns was associated with transition of lubrication from boundary to mixed lubrication regime.     

Preparation and Characterization of Mn Doped ZnO Nanorods

Physics of the Solid State - Mn doped ZnO nanorods were prepared by chemical precipitation method. The micro-structural and structural properties of the nanorods were calculated from the X-ray...     

Holonomy Groups Coming from F-Theory Compactification

We study holonomy groups coming from F-theory compactifications. We focus mainly on SO(8) as 12−4=8 and subgroups SU(4), Spin(7), G ₂ and SU(3) suitable for descent from F-theory, M-theory and Superstring theories. We consider the relation of these groups with the octonions, which is striking and reinforces their role in higher dimensions and dualities. These holonomy groups are related in various mathematical forms, which we exhibit.