A formula for the determinant of a sum of matrices

We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.UQAM and LITPUniversité Paris 7 and LITP.     

Determination of (R)- and (S)-phenprocoumon in human plasma by enantioselective liquid chromatography/electrospray ionisation tandem mass spectrometry

Phenprocoumon is a commonly used oral anticoagulant of the coumarin type, and has found extensive clinical use in the treatment of thrombophlebitis, pulmonary embolism and atrial fibrillation. In the course of a clinical study to investigate the influence of genetic polymorphisms of the CYP2C9 enzyme on phenprocoumon metabolism, we developed a new enantioselective liquid chromatography/electrospray ionisation tandem mass spectrometry (LC/MS/MS) method to quantify (R)- and (S)-phenprocoumon in human plasma. HPLC separation of the enantiomers was achieved on a Chira-Grom-2 column under isocratic conditions using a water/acetonitrile/formic acid eluent. For detection and quantification a triple-quadrupole MS system was used in the selected reaction monitoring (SRM) mode. As an internal standard the structurally homologous compound warfarin was chosen. The detector response was linear with a correlation coefficient of 0.988-0.999 for (R)-phenprocoumon and 0.989-0.999 for (S)-phenprocoumon in the investigated concentration range between 62.5 and 1000 ng/mL (per enantiomer). The limit of detection (LOD) was 12.5 ng/mL.     

Synthesis of pyrimidines from 3-trifluoromethylsulfonyl-oxypropeniminium triflates and nitriles; molecular and crystal structure of the 1:1 and 1:2 Adducts of a 4-(2-diethylaminovinyl)pyrimidine with triflic acid

The 3-trifluoromethylsulfonyloxy-1-hexeniminium triflate 1 reacts with two equivalents of an aliphatic nitrile or of benzonitrile to give the 4-(2-diethylaminovinyl)pyrimidinediium bis(triflates) 4 , which can be deprotonated to give the monoprotonated or neutral pyrimidines 5 and 6 , respectively. When the related 1-phenyl-substituted iminium salt 7 is heated in acetonitrile at 140°, 1,5-cyclization of the cation leading to indane derivative 8 competes with formation of the pyrimidinium salt 9 . X-ray crystal structure determination reveals significant differences in the bond lengths of mono-and diprotonated 4-(2-diethylaminovinyl)pyrimidines 5a and 4a .     

Deprotonierte Dithiocarbaminsäureester als Thiolat-S-Donor-Liganden. Strukturen von Ph(H)NC(S)SMe,Co(PhNC(S)SMe)3 und Cu6(PhNC(S)SMe)6

Deprotonated Dithiocarbamic Acid Esters as Thiolate S-Donor Ligands. Structures of Ph(H)NC(S)SMe, Co(PhNC(S)SMe)₃, and Cu₆(PhNC(S)SMe)₆ The reaction of N-phenyl-S-methyldithiocarbamate, PhN(H)C(?S)SMe, ( 1 ) with cobalt(II) and copper(II) salts yields the monomeric compound Co^III(PhNC(S)SMe)₃ ( 2 ) and the hexameric compound Cu₆^I(PhNC(S)SMe)₆ ( 3 ). These complexes contain the negatively charged imino-thiolate ligand PhN?C(? S)SMe, which has been formed by deprotonation of 1 . The crystal structures of 1 – 3 have been determined. 1 forms centrosymmetrical dimers through N? H …? S bridge bonds, the conformation in the solid state and in solution is Z,E′. Co^III shows in 2 a trigonal-antiprismatic coordination, with the ligands acting as N,S-chelates. 3 contains an octahedral Cu₆-core with Cu …? Cu-distances ranging from 276.3(5) to 305.7(4) pm. Each copper center is trigonally coordinated to one nitrogen and two sulfur atoms of three different ligands. Crystal data: 1 , triclinic, space group P1 , a = 590.5(6), b = 869.0(1), c = 968.5(9) pm, α = 67.29(8), β = 78.44(8), γ = 81.64(9)°, Z = 2, 1 775 reflections, R(R_w) = 0.0317(0.032). 2 , orthorhombic, space group Pbca, a = 978.0(2), b = 1 842.9(4), c = 3 059.7(6) pm, Z = 8, 1 129 reflections, R(R_w) = 0.0997(0.0886). 3 , monoclinic, space group P2₁/c, a = 1 363.1(3), b = 1 342.8(3), c = 1 671.9(3) pm, β = 103.48°, Z = 2, 1 374 reflections, R(R_w) = 0.0708(0.0617).     

Mass spectrometry of steroid glucuronide conjugates. II-Electron impact fragmentation of 3-keto-4-en- and 3-keto-5alpha-steroid-17-O-beta glucuronides and 5alpha-steroid-3alpha,17beta-diol 3- and 17-glucuronides

The steroid glucuronide conjugates of 16,16,17-d(3)-testosterone, epitestosterone, nandrolone (19-nortestosterone), 16,16,17-d(3)-nortestosterone, methyltestosterone, metenolone, mesterolone, 5alpha-androstane-3alpha,17beta-diol, 2,2,3,4,4-d(5)-5alpha-androstane-3alpha,17beta-diol, 19-nor-5alpha-androstane-3alpha,17beta-diol, 2,2,4,4-d(4)-19-nor-5alpha-androstane-3alpha,17beta-diol and 1alpha-methyl-5alpha-androstane-3alpha/beta,17beta-diol were synthesized by means of the Koenigs-Knorr reaction. Selective 3- or 17-O-conjugation of bis-hydroxylated steroids was performed either by glucuronidation of the corresponding steroid ketole and subsequent reduction of the keto group or via a four-step synthesis starting from a mono-hydroxylated steroid including (a) protection of the hydroxy group, (b) reduction of the keto group, (c) conjugation reaction and (d) removal of protecting groups. The mass spectra and fragmentation patterns of all glucuronide conjugates were compared with those of the commercially available testosterone glucuronide and their characterization was performed by gas chromatography/mass spectrometry and nuclear magnetic resonance spectroscopy. For mass spectrometry the substances were derivatized to methyl esters followed by trimethylsilylation of hydroxy groups and to pertrimethylsilylated products using labelled and unlabelled trimethylsilylating agents. The resulting electron ionization mass spectra obtained by GC/MS quadrupole and ion trap instruments, full scan and selected reaction monitoring experiments are discussed, common and individual fragment ions are described and their origins are proposed.     

An improved method for the synthesis of cellulose membrane-bound peptides with free C termini is useful for PDZ domain binding studies

SPOT synthesis permits parallel synthesis and screening of thousands of cellulose membrane-bound peptides to study protein-protein interactions in a proteomic context. Recognition of C-terminal residues is one of the most common binding features of PDZ domains. Unfortunately, most solid support-bound peptide libraries lack a free C terminus due to C-terminal fixation on the solid support. To overcome this restriction, we developed a robust methodology based on our previous strategy for generating peptides with authentic C termini. To validate this improved method, we screened a human peptide library of 6223 C termini with the syntrophin PDZ domain. Furthermore, using the same library, new peptide ligands derived from membrane proteins and receptors were found for the ERBIN PDZ domain. Finally, we identified the protein kinase breakpoint cluster region, which is known as a negative regulator of cell proliferation and oncogenic transformation, as an ERBIN ligand.