Gas Electron Diffraction and its Influence on the Solution of the Phase Problem in Crystal Structure Determination

We studied, and performed research for our Ph.D. degrees in the area of gas electron diffraction. Our mentor was Lawrence Brockway. a pioneer in this subject. At that time, research in gas electron diffraction was in its early stages of development. In 1941, the distinguished Peter Debye wrote a theoretical paper concerning gas electron diffraction which challenged ones capability to develop the necessary experimental equipment and to further advance the theoretical developments so as to greatly extend the science of gas electron diffraction. We carried these thoughts in mind when we joined the Naval Research Laboratory, where the opportunity to design and produce excellent equipment was readily available. In the course of pursuing this research area, one of the findings was the existence of non-negativity as a condition for the results of a diffraction experiment for gaseous substances. When we became interested in the field of crystal structure determination, the familiarity with non-negativity which was needed in the study of gases, led to a search for the necessary and sufficient condition for a Fourier series to be non-negative. The search was successful and has played an important part in crystal structure determination. Some early applications to complicated structures are described.     

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.     

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)°.     

Weakening Additivity in Adjoining Closures

In this paper, we weaken the conditions for the existence of adjoint closure operators, going beyond the standard requirement of additivity/co-additivity. We consider the notion of join-uniform (lower) closure operators, introduced in computer science, in order to model perfect lossless compression in transformations acting on complete lattices. Starting from Janowitz’s characterization of residuated closure operators, we show that join-uniformity perfectly weakens additivity in the construction of adjoint closures, and this is indeed the weakest property for this to hold. We conclude by characterizing the set of all join-uniform lower closure operators as fix-points of a function defined on the set of all lower closures of a complete lattice.     

Configurationally stable propeller-like triarylphosphine and triarylphosphine oxide

Configurationally stable, propeller-like triarylphosphine and triarylphosphine oxide can be synthesized; a chiral scaffold based on Lissoclinum-cyclopeptides linked via three peptide bonds with a triphenylphosphine and triphenylphosphine oxide moiety, respectively, prevents effectively epimerization at the chiral phosphorus atom.