Counting integral ideals in a number field

Let K   be an algebraic number field. We discuss the problem of counting the number of integral ideals below a given norm and obtain effective error estimates. The approach is elementary and follows a classical line of argument of Dedekind and Weber. The novelty here is that explicit error estimates can be obtained by fine tuning this classical argument without too much difficulty. The error estimate is sufficiently strong to give the analytic continuation of the Dedekind zeta function to the left of the line R(s)=1$\mathfrak{R}(s)=1$ as well as explicit bounds for the residue of the zeta function at s=1$s=1$.     

Resting and active states of the ERK2:HePTP complex

The MAP kinase ERK2 (ERK2, extracellular signal-regulated kinase 2) is regulated by numerous phosphatases that tightly control its activity. For example, the hematopoietic tyrosine phosphatase (HePTP) negatively regulates T cell activation in lymphocytes via ERK2 dephosphorylation. However, only very limited structural information is available for these biologically important complexes. Here, we use small-angle X-ray scattering combined with EROS ensemble refinement to characterize the structures of the resting and active states of ERK2:HePTP complexes. Our data show that the resting state ERK2:HePTP complex adopts a highly extended, dynamic conformation that becomes compact and ordered in the active state complex. This work experimentally demonstrates that these complexes undergo significant dynamic structural changes in solution and provides the first structural insight into an active state MAPK complex.     

Direct evidence for tautomerization of the uracil moiety within the Pb2+/uridine-5'-monophosphate complex: a combined tandem mass spectrometry and IRMPD study

The structure of the [Pb(UMP)-H](+) (UMP = uridine-5'-monophosphate) complex was studied in the gas phase by combining electrospray ionization (ESI), tandem mass spectrometry, and mid-infrared multiple photon dissociation (IRMPD) spectroscopy. The results obtained show that Pb(2+) ions interact not only with the deprotonated phosphate group but also with a carbonyl group of the nucleobase moiety by folding of the mononucleotide, resulting in macrochelates that are not likely to be present in solution. Comparison between the IRMPD and DFT-computed spectra suggests that the ESI-generated complex likely corresponds to a mixture of several structures, and establishes the enolic tautomers as the most abundant species for the [Pb(UMP)-H](+) ion, while the very weak IRMPD signal observed at ～1763 cm(-1) points to a minor population of oxo forms. Our data also suggest that losing the nucleobase residue under CID conditions does not necessarily mean a lack of interaction between the metal and the nucleobase moiety, as commonly reported in the literature for large oligonucleotides.     

High-pressure investigation of Li2MnSiO4 and Li2CoSiO4 electrode materials for lithium-ion batteries

In this work, the high-pressure behavior of Pmn2(1)-Li(2)MnSiO(4) and Pbn2(1)-Li(2)CoSiO(4) is followed by in situ X-ray diffraction at room temperature. Bulk moduli are 81 and 95 GPa for Pmn2(1)-Li(2)MnSiO(4) and Pbn2(1)-Li(2)CoSiO(4), respectively. Regardless of the moderate values of the bulk moduli, there is no evidence of any phase transformation up to a pressure of 15 GPa. Pmn2(1)-Li(2)MnSiO(4) shows an unusual expansion of the a lattice parameter upon compression. A density functional theory investigation yields lattice parameter variations and bulk moduli in good agreement with experiments. The calculated data indicate that expansion of the a lattice parameter is inherent to the crystal structure and independent of the nature of the transition-metal atom (M). The absence of pressure-driven phase transformation is likely associated with the incapability of the Li(2)MSiO(4) composition to adopt denser structures while avoiding large electrostatic repulsions.     

Co2+ binding cysteine and selenocysteine: a DFT study

In this paper we report structural and energetic data for cysteine and selenocysteine in the gas phase and the effect of Co(2+) complexation on their properties. Different conformers are analyzed at the DFT/B3LYP level of both bound and unbound species. Geometries, vibrational frequencies, and natural population analysis are reported and used to understand the activity of these species. In particular, we have focused our attention on the role of sulfur and selenium in the metal binding process and on the resulting deprotonation of the thiol and seleniol functions. From the present calculations we are able to explain, both from electronic structure and thermochemical point of views, a metal-induced thiol deprotonation as observed in gas-phase experiments. A similar process is expected in the case of selenocysteine. In fact, cobalt was found to have a preferential affinity with respect to thiolate and selenolate functions. This can be related to the observation that only S and Se are able-in thiolate and selenolate states-to make a partial charge transfer to the cobalt thus forming very stable complexes. Globally, very similar results are found when substituting S with Se, and a very small difference in cobalt binding affinity is found, thus justifying the use of this substitution in X-ray absorption experiments done on biomolecules containing cysteine metal binding pockets.     

Synthesis of Dienedioic and Tetraenedioic Acids by Oxidative Coupling of Unsaturated Carboxylic Acid Dienediolates by 1,2-Diiodoethane

Acyclic and cyclic unsaturated carboxylic acids 1 to 4 are most easily converted to unsaturated dicarboxylic acids 5 to 8 by oxidative coupling of their diene- or triene-diolates by 1,2-diiodoethane. This procedure improves formerly reported oxidations by iodine or silver salts.     

Synthesis of trans-(3S,4S)-dibenzyloxycyclopentanone

The 1-cyano-1-thiophenylcyclopentone derivative $\text{1}$, obtained from (R,R)-(+)-tartaric acid, has been converted into a number of derivatives including the important $\text{trans}$-(3S,4S)-dibenzyloxycyclopentanone $\text{2}$ in 45% overall yield.