Transcendental Numbers

The numbers e and π are transcendental numbers, meaning each of them are not the root of any polynomial with rational coefficients. We prove that e and π are transcendental numbers. The original proofs use the Fundamental Theorem of Symmetric Polynomials and Stirling’s Formula, which we develop and prove. Since π is not algebraic, neither is √π, which answers the ancient question of whether one can square a circle. The proof that π is transcendental is a beautiful example of how higher level mathematics can be used to answer ancient questions

Zinc absorption in adult humans: the effect of protein sources added to liquid test meals

The influence of different protein sources on Zn absorption was evaluated in healthy adults by radioisotopic labelling of single meals, followed by whole-body retention measurements 14 d after intake. Semi-synthetic liquid diets were used for the evaluation of different animal-protein sources and dephytinized soyabean-protein isolate ( ··01 g phytic acid/kg). Zn absorption was measured in the same subjects from identical test meals containing no added protein. No statistically significant differences were found in the Zn absorption from test meals containing bovine whey, casein or egg albumen when compared with test meals without added protein. Bovine serum albumin (BSA) and soyabean-protein isolate (< ··01 g phytic acid/kg) significantly reduced the mean absorption of Zn from 45-49% (no added protein) to 38·0 (SD 10·9) (BSA, P < ··05) and 33·9 (SD 12·6)% (soyabean-protein isolate < ··01 g phytic acid/kg, P < ··01). These results demonstrate that Zn absorption is inhibited by certain protein sources, such as BSA and dephytinized soyabean-protein isolate, while other proteins have little or no effec

Tryptic phosphopeptides from whole casein. I. Preparation and analysis by fast protein liquid chromatography

Tryptic phosphopeptides were obtained from whole bovine casein by chromatography on the anion exchange resin QAE-Sephadex A 25. Salt gradient elution of the column allowed separation of non-phosphorylated peptides from phosphorylated species. The preparations obtained contained at least seven distinct phosphopeptides of which the following casein fragments were identified: αs1(43-58):2P, αs1(59-79): 5P, αs2(46-70): 4P, β(1-28): 4P, β(2-28): 4P, and β(33-48): 1P. Fast protein liquid chromatography (FPLC) on Mono Q HR 5/5 resin showed that the phosphopeptides were eluted in the same order as from the QAE-Sephadex resin. However, on the analytical column HR 5/5 the fragments αs1(59-79): 5P and β(2-28): 4P, having the same net charge under the conditions of chromatography, co-eluted, whereas they were at least partly separated on the preparative column HR 16/10. Following enzymic dephosphorylation, the peptides eluted at lower salt strength in the gradient. FPLC on Mono Q resin thus permitted dephosphorylation to be monitored and intermediates between the parent species and the fully dephosphorylated peptide to be identifie

Tryptic phosphopeptides from whole casein. II. Physicochemical properties related to the solubilization of calcium

Casein phosphopeptides (GPP) were produced by tryptic hydrolysis of sodium caseinate and further purified by precipitation and chromatography on QAE-Sephadex A-25. Their physico-chemical properties were compared with the properties of an enzymically dephosphorylated equivalent preparation (DPP). Binding of Ca2+ to the peptides was measured using a Ca selective electrode and was found to increase with pH and to show 1/1 stoicheiometry Ca/Porg in CPP at pH 6·5 a.nd 7·6. Klotz plots indicated equivalent binding sites at these two pH values, but some heterogeneity was seen at pH 3·5. In contrast, DPP did not bind significant amounts of Ca2+. CPP effectively inhibited the formation of insoluble calcium phosphates at different Ca/P ratios. The effective CPP concentration was 10 mg/1 and complete stability of calcium phosphate solutions was obtained at about 100 mg/1. This stabilizing effect was dependent on the presence of organic

Cryogenic Facilities at 1.9 K for the Reception of the Superconducting Wires and Cables of the LHC Dipoles Magnets

CERN's LHC project has moved to an implementation phase. The fabrication of 1600 high-field superconducting magnets operating at 1.9 K will require about 6400 km of Nb-Ti cables. A cryogenic test facility has therefore been set up in order, on the one hand, to verify the quality of individual wires and, on the other hand, to control the critical current of the assembled cables. The facility is composed of a helium liquefier, a transfer line, a dewar and pumps. The paper describes the fully automatic operation of this installation and the different test cycles applied to these wires and cables

Case Report: Don’t chew the fufu: a case report of suspected drug body stuffing

Background: Intrabody concealment of illicit substances is a common practice in the trafficking chain. Body packing is a technique used in drug trafficking that consists of deliberately ingesting many drug pellets. Body stuffing consists of precipitously swallowing packets of substances, which are smaller and more fragile than body-packing pellets, for concealment from law-enforcement officers in anticipation of impending search or arrest. Therefore, body stuffing is particularly dangerous due to the rupture risk of the loosely wrapped drug packets, which could lead to substance intoxication or even death. Case presentation:  This article reports the case of a young man who was taken by law enforcement authorities to our Emergency Department for investigation of suspected body stuffing. Although the patient denied the facts, the initial reading of the computed tomography (CT) scan confirmed the presence of multiple images compatible with drug pellets, which were mostly in the stomach. The pellet findings were more consistent with body packing than body stuffing as initially suspected by the police. However, upon admission to our secured inpatient ward for clinical surveillance of pellet evacuation, the patient denied again having ingested such pellets, and declared that he only ate ‘fufu’. Fufu is a traditional food of central and western Africa consisting of a starchy preparation compacted by hand into small balls. Fufu balls are usually swallowed without chewing to allow a sensation of stomach fullness throughout the day. Considering the fufu intake history, a careful reassessment of the imaging confirmed the presence of food content. Conclusions: This case study offers an example of suspected intrabody concealment of illicit substances, which turned out to be false positive due to fufu. It illustrates the importance of a history of food intake that could bias the interpretation of CT scan images.</ns3:p

Controlled assembly of SNAP-PNA-fluorophore systems on DNA templates to produce fluorescence resonance energy transfer

The SNAP protein is a widely used self-labeling tag that can be used for tracking protein localization and trafficking in living systems. A model system providing controlled alignment of SNAP-tag units can provide a new way to study clustering of fusion proteins. In this work, fluorescent SNAP-PNA conjugates were controllably assembled on DNA frameworks forming dimers, trimers, and tetramers. Modification of peptide nucleic acid (PNA) with the O6-benzyl guanine (BG) group allowed the generation of site-selective covalent links between PNA and the SNAP protein. The modified BG-PNAs were labeled with fluorescent Atto dyes and subsequently chemo-selectively conjugated to SNAP protein. Efficient assembly into dimer and oligomer forms was verified via size exclusion chromatography (SEC), electrophoresis (SDS-PAGE), and fluorescence spectroscopy. DNA directed assembly of homo- and hetero-dimers of SNAP-PNA constructs induced homo- and hetero-FRET, respectively. Longer DNA scaffolds controllably aligned similar fluorescent SNAP-PNA constructs into higher oligomers exhibiting homo-FRET. The combined SEC and homo-FRET studies indicated the 1:1 and saturated assemblies of SNAP-PNA-fluorophore:DNA formed preferentially in this system. This suggested a kinetic/stoichiometric model of assembly rather than binomially distributed products. These BG-PNA-fluorophore building blocks allow facile introduction of fluorophores and/or assembly directing moieties onto any protein containing SNAP. Template directed assembly of PNA modified SNAP proteins may be used to investigate clustering behavior both with and without fluorescent labels which may find use in the study of assembly processes in cells