Prescribed Gauss curvature problem on singular surfaces

We study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface \(\Sigma \) admitting conical singularities of orders \(\alpha _i\)’s at points \(p_i\)’s. In particular, we are concerned with the case where the prescribed Gaussian curvature is sign-changing. Such a geometrical problem reduces to solving a singular Liouville equation. By employing a min–max scheme jointly with a finite dimensional reduction method, we deduce new perturbative results providing existence when the quantity \(\chi (\Sigma )+\sum _i \alpha _i\) approaches a positive even integer, where \(\chi (\Sigma )\) is the Euler characteristic of the surface \(\Sigma \).     

X-ray absorption study of Cu,Zn SOD under high pressure

Abstract

We have investigated Cu, Zn Superoxide Dismutase (Cu, Zn SOD) metal sites at high pressure using X-ray absorption. XAS (X-ray Absorption Spectroscopy) gives information on local structure and it is particularly suited to metal site investigation. To the best of our knowledge, this is the first time that protein conformational states have been investigated using the high pressure XAS technique. Cu, Zn SOD catalyses the dismutation of toxic oxygen radicals produced in cells; this reaction occurs at the copper metal site. Structural changes around the copper, induced by pressure, can be directly related to protein substates. Their characterisation is thus important in the understanding of protein activity.

The high-pressure device was a Paris-Edinburgh large volume cell.

Experiments were performed on lyophilised Cu, Zn SOD between 0 and 48 kbar at the copper and zinc K-edges. The two metal local atomic environments have a different behaviour as pressure increases: copper exhibits a more flexible environment; on the contrary, zinc shows small structural modifications. We have identified a state, formed between 3 and 8 kbar, which is stable up to 48 kbar.     

Development of an Accurate Mass Retention Time Database for Untargeted Metabolomic Analysis and Its Application to Plasma and Urine Pediatric Samples

Liquid-chromatography coupled to high resolution mass spectrometry (LC-HRMS) is currently the method of choice for untargeted metabolomic analysis. The availability of established protocols to achieve a high confidence identification of metabolites is crucial. The aim of this work is to describe the workflow that we have applied to build an Accurate Mass Retention Time (AMRT) database using a commercial metabolite library of standards. LC-HRMS analysis was carried out using a Vanquish Horizon UHPLC system coupled to a Q-Exactive Plus Hybrid Quadrupole-Orbitrap Mass Spectrometer (Thermo Fisher Scientific, Milan, Italy). The fragmentation spectra, obtained with 12 collision energies, were acquired for each metabolite, in both polarities, through flow injection analysis. Several chromatographic conditions were tested to obtain a protocol that yielded stable retention times. The adopted chromatographic protocol included a gradient separation using a reversed phase (Waters Acquity BEH C18) and a HILIC (Waters Acquity BEH Amide) column. An AMRT database of 518 compounds was obtained and tested on real plasma and urine samples analyzed in data-dependent acquisition mode. Our AMRT library allowed a level 1 identification, according to the Metabolomics Standards Initiative, of 132 and 124 metabolites in human pediatric plasma and urine samples, respectively. This library represents a starting point for future metabolomic studies in pediatric settings.     

Centrally symmetric polytopes with many faces

We present explicit constructions of centrally symmetric polytopes with many faces: (1) we construct a d-dimensional centrally symmetric polytope P with about 3 ^d/4 ≈ (1.316) ^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, (2) for an integer k ≥ 2, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < δ _k < 1 at least (1 ? (δ _k ) ^d )( _k ^N ) k-subsets of the set of vertices span faces of P, and (3) for an integer k ≥ 2 and α > 0, we construct a centrally symmetric polytope Q with an arbitrarily large number of vertices N and of dimension d = k ^1+o(1) such that at least $(1 - k^{ - \alpha } )(_k^N )$ k-subsets of the set of vertices span faces of Q.     

A Dogma in Doubt: Hydrolysis of Equatorial Ligands of PtIV Complexes under Physiological Conditions

Due to their high kinetic inertness and consequently reduced side reactions with biomolecules, Pt^IV complexes are considered to define the future of anticancer platinum drugs. The aqueous stability of a series of biscarboxylato Pt^IV complexes was studied under physiologically relevant conditions. Unexpectedly and in contrast to the current chemical understanding, especially oxaliplatin and satraplatin complexes underwent fast hydrolysis in equatorial position (even in cell culture medium and serum). Notably, the resulting hydrolysis products strongly differ in their reduction kinetics, a crucial parameter for the activation of Pt^IV drugs, which also changes the anticancer potential of the compounds in cell culture. The discovery that intact Pt^IV complexes can hydrolyze at equatorial position contradicts the dogma on the general kinetic inertness of Pt^IV compounds and needs to be considered in the screening and design for novel platinum‐based anticancer drugs.     

Unique assemblies of alternating positively and negatively charged layers, directed by hydrogen bonds, ionic interactions, and π-stacking in the crystal structures of complexes between mellitic acid (benzenehexacarboxylic acid) and five planar aromatic bases

Benzenehexacarboxylic acid, mellitic acid (MA), has been used as a core motif to study possible radial self-assembly using complementary aromatic bases. By mixing water solutions of the components, crystals of the salts of MA with 4-aminopyridine (AP), 4-dimethylamino-pyridine (DM), 2,2-bipyridine (DP), o-phenanthroline (PL), and melamine (ML) have been obtained. The MA^–n ions have assembled in either extended sheets for MA^–2 or extended ribbons for MA^–4 by direct hydrogen bonding between MA and MA and additionally through mediation of hydrogen bonds to water molecules that distribute the negative charges throughout the MA sheet or ribbon. Most of the O atoms in carboxyl groups in the MA ions in the five complexes have been rotated significantly out of the plane of the central benzene ring. There are multiple base molecules, two or four, for each mellitic acid ion in the five complexes. Most of the NH⁺ moieties in all five bases make direct NH⁺ O–C hydrogen bonds with MA^–n . The planar base ions are generally arranged in stacks in which the components range from being parallel, with interplanar separations of 3.5 Å, to having a considerable tilt with respect to each other with nearest interplanar separation of atoms greater than 3.9 Å. These geometric characteristics are reflected in the color of the crystals. The three-dimensional networking makes some of the crystals very hard. Cell dimensions: 1, C₃₂H₃₀N₈O₁₂ 2H₂O, C2/c, a =13.764(2) Å, b =18.053(3) Å, c =14.876(4) Å, =105.99(2)° 2, C₂₆H₂₆N₄O₁₂ 3H₂O, P2₁/n, a =15.891(1) Å, b =10.444(1) Å, c =18.242(1) Å, =97.00(1); 3, C₆₄H₄₄N₈O₂₄ 7H2O, P2₁/c, a =23.016(4) Å, b =15.241(2) Å, c =19.124(2) Å, =100.60(1)° 4, C₃₆H₂₂N₄O₁₂, P2₁/n, a =14.581(1) Å, b =10.472(1) Å, c =20.607(2) Å, =106.43(1); 5, C₁₈H₁₈N₁₂O₁₂ 2H₂O, , a =8.257(2) Å, b =8.986(2) Å, c =9.383(1) Å, =98.60(1)°, =96.38(2)°, =117.07(1)°.     

Swollen and collapsed lyotropic lamellar rheology

We have investigated linear rheological properties and the structure-flow relationship of the swollen (Lam(1)) and collapsed (Lam(2)) lamellar phases, formed on didodecyldimethylammonium bromide (DDAB)/lecithin/water ternary system at 25 degrees C. Both lamellar phases behaved like Bingham fluids and showed remarkable yield stresses. At rest the Lam(1) phase, which is characterized by densely packed vesicles whose sizes increase as the water content decreases in accordance to evolution of (2)H NMR spectral profiles of D(2)O, resulted in a strong elastic gel-like response. On the other hand, the Lam(2) phase, formed at high surfactant concentrations, showed a weak-gel viscoelasticity and (2)H NMR spectral patterns which are typical of planar bilayered structures. The increase of the quadrupole splitting as the water content decreases was assumed as a strong evidence of size increasing of the lamellar domains. We have demonstrated that by using dynamic rheology and the derived relaxation time spectra, along with (2)H NMR spectra of D(2)O, it is possible to differentiate between equilibrium lamellar structures occurring in a broad interval of total surfactant concentration. In addition, a shear-thickening regime, observed at intermediate shear-rate values, highlighted the onset of out-equilibrium lamellar structures which were present both on Lam(1) and Lam(2) phases.