On single laws for varieties of quasigroups associated with extended cycle systems

It has been previously shown by Lindner and Rodger that quasigroups associated with 2-perfect extended m-cycle systems can be equationally defined if and only if m is an element of {3, 5, 7}. In this paper we present a single identity for each such m which is equivalent to the identities given for these varieties.

Projections from the substantia nigra pars reticulata to the motor thalamus of the rat: Single axon reconstructions and immunohistochemical study

This is a study in the rat of the distribution of specific neurotransmitters in neurones projecting from the substantia nigra reticulata (SNR) to the ventrolateral (VL) and ventromedial (VM) thalamic nuclei. Individual axons projecting from the SNR to these thalamic nuclei have also been reconstructed following small injection of the anterograde tracer dextran biotin into the the SNR. Analysis of reconstructions revealed two populations of SNR neurones projecting onto the VL and VM thalamic nuclei. One group projects directly onto the VM and VL, and the other projects to the VM/VL and to the parafascicular nucleus. In another set of experiments Fluoro-Gold was injected into the VL/VM to label SNR projection neurones retrogradely, and immunohistochemistry was performed to determine the distribution of choline acetyltransferase (ChAT), vesicular acetylcholine transporter (VAChT), gamma -aminobutyric acid (GABA), and glutamate in Fluoro-Gold-labelled SNR projection neurones. Most SNR-VL/VM thalamic projection neurones were immunoreactive to acetylcholine or glutamate, whereas only 25% of the projection neurones were found to be immunoreactive to GABA. (C) 2001 Wiley-Liss, Inc.

A single nucleotide polymorphism in the 5' untranslated region of RAD51 and risk of cancer among BRCA1/2 mutation carriers

RAD51 colocalizes with both BRCA1 and BRCA2, and genetic variants in RAD51 would be candidate BRCA1/2 modifiers. We searched for RAD51 polymorphisms by sequencing 20 individuals. We compared the polymorphism allele frequencies between female BRCA1/2 mutation carriers with and without breast or ovarian cancer and between population-based ovarian cancer cases with BRCA1/2 mutations to cases and controls without mutations. We discovered two single nucleotide polymorphisms (SNPs) at positions 135 g-->c and 172 g-->t of the 5' untranslated region. In an initial group of BRCA1/2 mutation carriers, 14 (21%) of 67 breast cancer cases carried a c allele at RAD51:135 g-->c, whereas 8 (7%) of 119 women without breast cancer carried this allele. In a second set of 466 mutation carriers from three centers, the association of RAD51:135 g-->c with breast cancer risk was not confirmed. Analyses restricted to the 216 BRCA2 mutation carriers, however, showed a statistically significant association of the 135 c allele with the risk of breast cancer (adjusted odds ratio, 3.2; 95% confidence limit, 1.4-40). BRCA1/2 mutation carriers with ovarian cancer were only about one half as likely to carry the RAD51:135 g-->c SNP. Analysis of the RAD51:135 g-->c SNP in 738 subjects from an Israeli ovarian cancer case-control study was consistent with a lower risk of ovarian cancer among BRCA1/2 mutation carriers with the c allele. We have identified a RAD51 5' untranslated region SNP that may be associated with an increased risk of breast cancer and a lower risk of ovarian cancer among BRCA2 mutation carriers. The biochemical basis of this risk modifier is currently unknown.

Theory of pseudomodes in quantum optical processes

This paper deals with non-Markovian behavior in atomic systems coupled to a structured reservoir of quantum electromagnetic field modes, with particular relevance to atoms interacting with the field in high-Q cavities or photonic band-gap materials. In cases such as the former, we show that the pseudomode theory for single-quantum reservoir excitations can be obtained by applying the Fano diagonalization method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two, and many discrete quasimodes are made. For a simple photonic band-gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.

Macrocycles mimic the extended peptide conformation recognized by aspartic, serine, cysteine and metallo proteases

It has been previously demonstrated that aspartic, serine, metallo and cysteine proteases bind to their inhibitors and substrate analogues in a single conformation, the saw-tooth or extended beta-strand. Consequently a generic approach to the development of protease inhibitors is the use of constraints that conformationally restrict putative inhibitor molecules to an extended form. In this way the inhibitor is pre-organized for binding to a protease and does not need to rearrange its structure. One constraining device that has proven to be effective for such pre-organization is macrocyclization. This article illustrates the general principle that macrocycles, especially those composed of 3-4 amino acids and usually 13-17 ring atoms, can effectively mimic the extended conformation of short peptide sequences. Such structure-stabilising macrocycles are stable to degradation by proteases, valuable components of potent protease inhibitors, and in many cases they are also bioavailable.

Solution structures by H-1 NMR of the novel cyclic trypsin inhibitor SFTI-1 from sunflower seeds and an acyclic permutant

SFTI-1 is a recently discovered cyclic peptide trypsin inhibitor from sunflower seeds comprising 14 amino acid residues. It is the most potent known Bowman-Birk inhibitor and the only naturally occurring cyclic one. The solution structure of SFTI-1 has been determined by H-1-NMR spectroscopy and compared with a synthetic acyclic permutant. The solution structures of both are remarkably similar. The lowest energy structures from each family of 20 structures of cyclic and acyclic SFTI-1 have an rmsd over the backbone and heavy atoms of 0.29 Angstrom and 0.66 Angstrom, respectively. The structures consist of two short antiparallel beta -strands joined by an extended loop containing the active site at one end. Cyclic SFTI-1 also has a hairpin turn completing the cycle. Both molecules contain particularly stable arrangements of cross-linking hydrogen bonds between the beta -strands and a single disulfide bridge, making them rigid and well defined in solution. These stable arrangements allow both the cyclic and acyclic variants of SFTI-1 to inhibit trypsin with very high potencies (0.5 nM and 12.1 nM, respectively). The cyclic nature of SFTI-1 appears to have evolved to provide higher trypsin inhibition as well as higher stability. The solution structures are similar to the crystal structure of the cyclic inhibitor in complex with trypsin. The lack of a major conformational change upon binding suggests that the structure of SFTI-1 is rigid and already pre-organized for maximal binding due to minimization of entropic losses compared to a more flexible ligand. These properties make SFTI-1 an ideal platform for the design of small peptidic pharmaceuticals or pesticides. (C) 2001 Academic Press.

Multiple bifurcations in atom optics

We report the observation of multiple bifurcations in a nonlinear Hamiltionian system: laser-cooled atoms in a standing wave with single-frequency intensity modulation. We provide clear evidence of the occurrence of bifurcations by analyzing the atomic momentum distributions.

Dynamical tunnelling of ultracold atoms

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling(1,2) between two regions of classically stable motion. An archetype of such nonclassical motion is tunnelling through an energy barrier. In the 1980s, a new process, 'dynamical' tunnelling(1-3), was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom(4-6). Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted(4) dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose-Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180 degrees out of phase with the initial state.

Single-electron measurements with a micromechanical resonator

A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge.