Kinetics of disassembly of a DNA-bound porphyrin supramolecular array

trans-Bis(N-methylpyridinium-4-yl)diphenylporphine forms extended, organized assemblies on DNA templates under appropriate conditions of concentration, ionic strength, and temperature. Addition of beta-cyclodextrin to these arrays leads to their disassembly as evidenced by changes in extinction, circular dichroism, and resonance light scattering spectra. The structure or flexibility of the polymer template has an effect on the rate of disassembly; the reaction is faster on a poly(dG-dC)(2) surface than on ct DNA. The kinetic profiles for the disassembly process can be fit with great precision with a two-kinetic parameter equation in which the rate constant is itself a function of time. The reaction rate, studied in the presence of excess beta-CD, shows a dependence on the mode of detection. A model is presented to account for these observations in which the arrays become increasingly reactive with time due to beta-CD attack at the interior of the porphyrin assemblies as well as the ends.     

Investigation of Cr(III) hydrolytic polymerisation products by capillary electrophoresis-inductively coupled plasma-mass spectrometry

The development of a new method for the determination of Cr(III) hydrolytic polymerisation products using capillary electrophoresis-inductively coupled plasma mass spectrometry (CE-ICP-MS) is described. The results indicate that CE-ICP-MS can be used to separate and detect monomeric and polymeric Cr(III) species. The various species migrate through the capillary at a rate proportional to their equilibrium distribution, which is dictated by the solution pH, metal ion concentration and ageing period. In general, the data suggest that the relative mobility follows the order trimer>dimer>monomer. The experimentally determined speciation shows a good qualitative agreement with that described in the literature. Independent confirmation of the presence of polymeric Cr(III) species was performed by ionspray mass spectrometry.     

Improving the stereoselectivity of bakers' yeast reductions by genetic engineering

[formula: see text] The stereoselectivities of bakers' yeast catalyzed reductions of beta-keto esters can be manipulated by genetic design. Strains in which two major beta-keto ester reductases are either knocked out or overexpressed have been constructed. The former approach results in whole cell biocatalysts with reversed stereoselectivity from unmodified bakers' yeast while the latter shows useful improvements in stereoselectivity. These results indicate that the "designer yeast" approach can provide useful biocatalysts for these transformations.     

Complex multiplication of exactly solvable Calabi–Yau varieties

We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi–Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi–Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.     

Regular Subgraphs in Graphs and Rooted Graphs and Definability in Monadic Second - Order Logic

We investigate the definability in monadic ∑₁¹ and monadic Π₁¹ of the problems REG_k, of whether there is a regular subgraph of degree k in some given graph, and XREG_k, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REG_k^k and XREG_k^k, respectively, for k ≥ 2 (all our graphs are undirected). Our motivation partly stems from the fact (which we prove here) that REG_k^k and XREG_k^k are logspace equivalent to CONN and REACH, respectively, for k ≥ 3, where CONN is the problem of whether a given graph is connected and REACH is the problem of whether a given graph has a path joining two given vertices. We use monadic first - order reductions, monadic ∑₁¹ games and a recent technique due to Fagin, Stockmeyer and Vardi to almost completely classify whether these problems are definable in monadic ∑₁¹ and monadic Π₁¹, and we compare the definability of these problems (in monadic ∑₁¹ and monadic Π₁¹ with their computational complexity (which varies from solvable using logspace to NP - complete).     

Reactions involving fluoride ion. Part 40. Amines as initiators of fluoride ion catalysed reactions

Tetrakis(dimethylamino)ethene (TDAE) and trimethylamine react with anhydrous unsaturated fluorocarbons to produce, ‘in situ’, powerful fluoride- ion sources. These are used to initiate carbon- carbon bond forming reactions eg. oligomerisation and polyfluoroalkylation, and many of these reactions occur efficiently in the absence of a solvent.     

Numerical sensitivity of trajectories across conformational energy hypersurfaces from geometry optimized molecular orbital calculations: AM1, MNDO,and MINDO/3

The monocyclic β-lactam [[4(S)-methyl-2-oxo-1-azetidinyl]thia]acetic acid was studied by the semiempirical molecular orbital methods AM1, MNDO, and MINDO/3. Using the reaction coordinate option in the program MOPAC on VAX and Cray X-MP computers, the potential energy curve was calculated for rotation of the C2-N1-S-C torsional angle in the conformationally flexible side chain while optimizing all other geometrical variables in the molecule. The trajectory taken during geometry optimization was found to be sensitive to the computer, the program version, the convergence criteria, and the degree of code optimization used in the calculation. In order to reduce the likelihood of spurious results, conformational or reaction energy hypersurfaces need to be calculated with the more precise SCF convergence and minimization criteria available in programs for MINDO/3, MNDO, and AM1 calculations. The nitrogen in the model β-lactam antibiotic is predicted to invert periodically as the dihedral angle to the exocyclic N-substituent sweeps through 360°.     

Mathematics for young people: The royal institution masterclasses

The Mathematical Intelligencer - We expected a fair number of participants to drop out as the course progressed. Indeed, we had raised the numbers to 48 anticipating this. In fact the average level...