Tarski's theorem on intuitionistic logic,for polyhedra

In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space ${\mathbb{R}}^n$ with $n?1$ suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot detect topological dimension in the Heyting algebra of all open sets of a Euclidean space. By contrast, we consider the lattice of open subpolyhedra of a given compact polyhedron $P?{\mathbb{R}}^n$, prove that it is a locally finite Heyting subalgebra of the (non-locally-finite) algebra of all open sets of P, and show that intuitionistic logic is able to capture the topological dimension of P through the bounded-depth axiom schemata. Further, we show that intuitionistic logic is precisely the logic of formulæ valid in all Heyting algebras arising from polyhedra in this manner. Thus, our main theorem reconciles through polyhedral geometry two classical results: topological completeness in the style of Tarski, and Ja?kowski's theorem that intuitionistic logic enjoys the finite model property. Several questions of interest remain open. E.g., what is the intermediate logic of all closed triangulable manifolds?     

Microwave-assisted synthesis of 3-aryl-pyrimido[5,4-e][1,2,4]triazine-5,7(1H,6H)-dione libraries: derivatives of toxoflavin

The parallel synthesis of a library of toxoflavin derivatives is described. The microwave-assisted approach involves the de novo generation of the heterocyclic scaffold and allows for facile introduction of a variety of fragments.     

Proficiency testing in analytical chemistry, microbiology, and laboratory medicine – working group discussions on current status, problems, and future directions

Working group (WG) discussions on proficiency testing (PT) held at the joint Eurachem/ EQALM workshop, Borås, Sweden, 24–26 September 2000 are summarized. The discussions focused on aspects of PT and accreditation (WG 1), general aspects of PT in analytical chemistry (WG 2), microbiology (WG 3), and laboratory medicine (WG 4), incorporation of measurement uncertainty into PT schemes (WG 5), international harmonization of PT schemes (WG 6), and the role of PT in the international structure of chemical measurement (WG 7). Current status, problems and future directions are identified. Each WG contained a majority of participants experienced in the subject being covered by that WG, and a few participants with different expertise. This was done to promote cross-fertilization of ideas between sectors, a key objective of the workshop. The WG issues reflected the content of the keynote lectures and some issues were covered from different perspectives by more than one group.     

Coordination complexes of iron(III) with 3-hydroxy-2(1H)-pyridinone, 2,3-dihydroxybenzoic acid and 3,4-dihydroxybenzoic acid: preparation and characterization in the solid state

Summary The synthesis and study of a number of new iron(III) complexes of the ligands 3-hydroxy-2(1H)-pyridinone (3,2-opoH), 2,3-dihydroxybenzoic acid (2,3-dhbH₃) and 3,4-dihydroxybenzoic acid (3,4-dhbH₃) are described. These complexes have the formulae [Fe(3,2-opo)₂Cl]·PrⁿOH, K[Fe(2,3-dhbH)₂(H₂O)₂], [Fe(2,3-dhb)(H₂O)₂], K[Fe-(3,4-dhbH)₂(H₂O)₂], [Fe(3,4-dhb)(H₂O)₂] and K₆[Fe(3,4-dhb)₃]·3H₂O. The complexes were characterized by elemental analyses. X-ray powder patterns, t.g.a./d.t.g. techniques, magnetic susceptibilities and spectroscopic (u.v.-vis., i.r. and variable-temperature ⁵⁷Fe-M?ssbauer) studies. Monomeric octahedral structures are assigned for the 1∶2 2,3-dhbH²⁻ complex and the 1:3 3,4-dhb³⁻ compound. Dinuclear and/or oligonuclear structures are tentatively proposed for the remaining complexes in the solid state. In [FeL(H₂O)₂] (L³⁻ = 2,3-dhb³⁻ or 3,4-dhb³⁻), iron(III) appears to be 5-coordinate. Both oxygens of 3,2-opo⁻ participate in coordination, while the dihydroxybenzoato ligands exhibit various coordination modes, depending mainly on the positions of the hydroxy groups, their anionic charge and the ligand∶metal molar ratio used.     

Density functional theory and QT atoms-in-molecules study on the hydration of CuI and AgI ions and sulfides

The hydrates of Cu+, Ag+, CuS-, AgS-, Cu2S, and Ag2S were investigated with density functional theory (DFT), solvent field, and atoms-in-molecules (QTAIM) calculations. We found that covalent bonding of the first-shell water molecules to the metals plays a significant role in the total solvation energy. Molecular graphs were obtained and the bonding characterized by analysis of the electron density and its laplacian at bond critical points. Long-range electrostatic interactions between solute and the bulk solvent, quantified by solvent-field calculations, are more important for hydrated anions CuS- and AgS- than for Cu+ and Ag+ as well as for the neutral species Cu2S and Ag2S. Computed enthalpies of formation for hydrated Cu+ and Ag+ correlated well with experimentally determined values and allowed us to characterize the structures of several hydrates studied in the gas phase. We found that the stability of the hydrates is leveled in the water solvent field. The reactions of dissociation and substitution of metal sulfides in the gas phase and in solution were compared. A decrease in the of energy of the reactions in going from the gas phase to solution is explained on the basis of the higher coordination of metal atoms in the first hydration shell.     

Relationship of stereochemical and skeletal diversity of small molecules to cellular measurement space

Systematic and quantitative measurements of the roles of stereochemistry and skeleton-dependent conformational restriction were made using multidimensional screening. We first used diversity-oriented synthesis to synthesize the same number (122) of [10.4.0] bicyclic products (B) and their corresponding monocyclic precursors (M). We measured the ability of these compounds to modulate a broad swath of biology using 40 parallel cell-based assays. We analyzed the results using statistical methods that revealed illuminating relationships between stereochemistry, ring number, and assay outcomes. Conformational restriction by ring-closing metathesis increased the specificity of responses among active compounds and was the dominant factor in global activity patterns. Hierarchical clustering also revealed that stereochemistry was a second dominant factor; whereas the stereochemistry of macrocyclic appendages was a determinant for bicyclic compounds, the stereochemistry of the carbohydrates was a determinant for the monocyclic compounds of global activity patterns. These studies illustrate a quantitative method for measuring stereochemical and skeletal diversity of small molecules and their cellular consequences.     

Dioxygen reactivity of copper and heme-copper complexes possessing an imidazole-phenol cross-link

Recent spectroscopic, kinetics, and structural studies on cytochrome c oxidases (CcOs) suggest that the histidine-tyrosine cross-link at the heme a3-CuB binuclear active site plays a key role in the reductive O2-cleavage process. In this report, we describe dioxygen reactivity of copper and heme/Cu assemblies in which the imidazole-phenol moieties are employed as a part of copper ligand LN4OH (2-{4-[2-(bis-pyridin-2-ylmethyl-amino)-ethyl]-imidazol-1-yl}-4,6-di -tert-butyl-phenol). Stopped-flow kinetic studies reveal that low-temperature oxygenation of [CuI(LN4OH)]+ (1) leads to rapid formation of a copper-superoxo species [CuII(LN4OH)(O2-)]+ (1a), which further reacts with 1 to form the 2:1 Cu:O2 adduct, peroxo complex [{CuII(LN4OH)}2(O2(2-))]2+ (1b). Complex 1b is also short-lived, and a dimer Cu(II)-phenolate complex [CuII(LN4O-)]2(2+) (1c) eventually forms as a final product in the later stage of the oxygenation reaction. Dioxygen reactivities of 1 and its anisole analogue [CuI(LN4OMe)]+ (2) in the presence of a heme complex (F8)FeII (3) (F8 = tetrakis(2,6,-difluorotetraphenyl)-porphyrinate) are also described. Spectroscopic investigations including UV-vis, 1H and 2H NMR, EPR, and resonance Raman spectroscopies along with spectrophotometric titration reveal that low-temperature oxygenation of 1/3 leads to formation of a heme-peroxo-copper species [(F8)FeIII-(O2(2-))-CuII(LN4OH)]+ (4), nu(O-O) = 813 cm(-1). Complex 4 is an S = 2 spin system with strong antiferromagnetic coupling between high-spin iron(III) and copper(II) through a bridging peroxide ligand. A very similar complex [(F8)FeIII-(O2(2-))-CuII(LN4OMe)]+ (5) (nu(O-O) = 815 cm(-1)) can be generated by utilizing the anisole compound 2, which indicates that the cross-linked phenol moiety in 4 does not interact with the bridging peroxo group between heme and copper. This investigation thus reveals that a stable heme-peroxo-copper species can be generated even in the presence of an imidazole-phenol group (i.e., possible electron/proton donor source) in close proximity. Future studies are needed to probe key factors that can trigger the reductive O-O cleavage in CcO model compounds.     

A proteome-wide CDK/CRK-specific kinase inhibitor promotes tumor cell death in the absence of cell cycle progression

The identification of molecular determinants of tumor cell survival is an important objective in cancer research. Here, we describe a small-molecule kinase inhibitor (RGB-286147), which, besides inhibiting tumor cell cycle progression, exhibits potent cytotoxic activity toward noncycling tumor cells, but not nontransformed quiescent fibroblasts. Extensive yeast three-hybrid (Y3H)-based proteome/kinome scanning with chemical dimerizers revealed CDK1/2/3/5/7/9 and the less well-characterized CDK-related kinases (CRKs) p42/CCRK, PCTK1/3, and PFTK1 as its predominant targets. Thus, RGB-286147 is a proteome-wide CDK/CRK-specific kinase inhibitor whose further study could yield new insight into molecular determinants of tumor cell survival. Our results also suggest that the [1, 3, 6]-tri-substituted-pyrazolo[3,4-d]-pyrimidine-4-one kinase inhibitor scaffold is a promising template for the rational design of kinase inhibitors with potential applications to disease indications other than cancer, such as neurodegeneration, cardiac hypertrophic growth, and AIDS.     

Ruthenium complexes of easily accessible tridentate ligands based on the 2-aryl-4,6-bis(2-pyridyl)-s-triazine motif: absorption spectra, luminescence properties, and redox behavior

A family of tridendate ligands 1 a-e, based on the 2-aryl-4,6-di(2-pyridyl)-s-triazine motif, was prepared along with their hetero- and homoleptic Ru(II) complexes 2 a-e ([Ru(tpy)(1 a-e)](2+); tpy=2,2':6',2"-terpyridine) and 3 a-e ([(Ru(1 a-e)(2)](2+)), respectively. The ligands and their complexes were characterized by (1)H NMR spectroscopy, ES-MS, and elemental analysis. Single-crystal X-ray analysis of 2 a and 2 e demonstrated that the triazine core is nearly coplanar with the non-coordinating ring, with dihedral angles of 1.2 and 18.6 degrees, respectively. The redox behavior and electronic absorption and luminescence properties (both at room temperature in liquid acetonitrile and at 77 K in butyronitrile rigid matrix) were investigated. Each species undergoes one oxidation process centered on the metal ion, and several (three for 2 a-e and four for 3 a-e) reduction processes centered on the ligand orbitals. All compounds exhibit intense absorption bands in the UV region, assigned to spin-allowed ligand-centered (LC) transitions, and moderately intense spin-allowed metal-to-ligand charge-transfer (MLCT) absorption bands in the visible region. The compounds exhibit relatively intense emissions, originating from triplet MLCT levels, both at 77 K and at room temperature. The incorporation of triazine rings and the near planarity of the noncoordinating ring increase the luminescence lifetimes of the complexes by lowering the energy of the (3)MLCT state and creating a large energy gap to the dd state.     

Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997