Quantum graph of Sierpinski gasket type: Computational experiment

A continuous model of the Sierpinski gasket (SG) is suggested. The Laplace operator on the SG is defined. An effective computational algorithm for solving the scattering problem is suggested. The self-similarity of the graph of transmission coefficient via the wave number k is observed. A violation of symmetry of the SG is considered. The results are compared with the discrete SG model. In memoriam V. A. Geyler     

Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

Sexual attraction in the silkworm moth: structure of the pheromone-binding-protein-bombykol complex

BACKGROUND: Insects use volatile organic molecules to communicate messages with remarkable sensitivity and specificity. In one of the most studied systems, female silkworm moths (Bombyx mori) attract male mates with the pheromone bombykol, a volatile 16-carbon alcohol. In the male moth's antennae, a pheromone-binding protein conveys bombykol to a membrane-bound receptor on a nerve cell. The structure of the pheromone-binding protein, its binding and recognition of bombykol, and its full role in signal transduction are not known. RESULTS: The three-dimensional structure of the B. mori pheromone-binding protein with bound bombykol has been determined by X-ray diffraction at 1.8 A resolution. CONCLUSIONS: The pheromone binding protein of B. mori has six helices, and bombykol binds in a completely enclosed hydrophobic cavity formed by four antiparallel helices. Bombykol is bound in this cavity through numerous hydrophobic interactions, and sequence alignments suggest critical residues for specific pheromone binding.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.     

Bioactive steroidal glycosides from the marine sponge Erylus lendenfeldi

Bioassay-guided fractionation of the methanol extract of Erylus lendenfeldi using engineered strains of budding yeast (Saccharomyces cerevisiae) has resulted in the isolation of the known compound eryloside A (1) and two new compounds, erylosides K (2) and L (3). The structures were established based mainly on 1D and 2D NMR data. The absolute stereochemistry of eryloside A, which had never been fully characterized, was determined using the modified Mosher's method. The absolute stereochemistry of eryloside K was determined by comparison with tetrahydroeryloside A. Compounds 1-3 exhibited selective cytotoxicity against a yeast strain (Δrad50) deficient in double strand break (DSB) repair.     

Stability of nuclear matter against neutral pion condensation

The global stability of the uniform ground state of nuclear matter is tested relative to a π⁰-condensed state characterized by static spin-(isospin-) waves. Strong nuclear correlations are introduced into the trial wave functions for each phase, thereby permitting models of the realistic two-nucleon force to be employed. In low cluster-order comparison, the uniform phases of symmetrical nuclear matter and neutron matter are emphatically favored over the entire density range considered.     

Scanning tunneling microscopy and surface simulation of zinc-blende GaN(001) intrinsic 4x reconstruction: linear gallium tetramers?

Scanning tunneling microscopy images confirm electron diffraction studies that the zinc-blende GaN(001)-4x reconstruction consists of rows aligned along [110] with a spacing along [110] of 4a. Dual-bias imaging shows a 180 degree shift of the corrugation maximum position between the profiles of empty and occupied states, in agreement with surface simulations based on the 4 x 1 linear tetramer model of Neugebauer et al. [Phys. Rev. Lett. 80, 3097 (1998)]. Electronic structure calculations predict a surface band gap of 1.1 eV, close to the measured value of 1.14 eV and the previously predicted value (1.2 eV). Despite the successes of this model, high-resolution images reveal an unexpected 3x periodicity (not seen in diffraction) along the [110] row direction, indicating the need for a 4 x 3 model, and putting into question the existence of linear Ga tetramers.