Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Electromagnetic fields inside a lossy, multilayered spherical head phantom excited by MRI coils: models and methods

The precise evaluation of electromagnetic field (EMF) distributions inside biological samples is becoming an increasingly important design requirement for high field MRI systems. In evaluating the induced fields caused by magnetic field gradients and RF transmitter coils, a multilayered dielectric spherical head model is proposed to provide a better understanding of electromagnetic interactions when compared to a traditional homogeneous head phantom. This paper presents Debye potential (DP) and Dyadic Green's function (DGF)-based solutions of the EMFs inside a head-sized, stratified sphere with similar radial conductivity and permittivity profiles as a human head. The DP approach is formulated for the symmetric case in which the source is a circular loop carrying a harmonic-formed current over a wide frequency range. The DGF method is developed for generic cases in which the source may be any kind of RF coil whose current distribution can be evaluated using the method of moments. The calculated EMFs can then be used to deduce MRI imaging parameters. The proposed methods, while not representing the full complexity of a head model, offer advantages in rapid prototyping as the computation times are much lower than a full finite difference time domain calculation using a complex head model. Test examples demonstrate the capability of the proposed models/methods. It is anticipated that this model will be of particular value for high field MRI applications, especially the rapid evaluation of RF resonator (surface and volume coils) and high performance gradient set designs.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

Novel one-dimensional structures and solution behaviour of copper(II) bromide and chloride complexes of a new pentapyridyldiamine ligand

Copper(II) bromide and chloride complexes of the new heptadentate ligand 2,6-bis(bis(2-pyridylmethyl)amino)methylpyridine (L) have been prepared. For the bromide complexes, chains of novel, approximately C-2-symmetric, chiral [Cu-2(L)Br-2](2+) 'wedge-shaped' tectons are found. The links between the dicopper tectons and the overall chirality and packing of the chains are dictated by the bromide ion content, not the counter anion. In contrast, the chloride complexes exhibit linked asymmetric [Cu-2(L)Cl-3](+) tectons with distinct N3CuCl2 and N4CuCl2 centres in the solid. The overall structures of the dicopper bromide and chloride units persist in solution irrespective of the halide. The redox chemistry of the various species is also described.

NMR imaging of the diffusion of water at 310 K into semi-IPNs of PEM and Poly(HEMA-co-THFMA)

Magnetic resonance imaging has been used to monitor the diffusion of water at 310 K into a series of semi-IPNs of poly(ethyl methacrylate), PEM, and copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA. The diffusion was found to be well described by a Fickian kinetic model in the early stages of the water sorption process, and the diffusion coefficients were found to be slightly smaller than those for the copolymers of HEMA and THFMA, P(HEMA-co-THFMA), containing the same mole fraction of HEMA in the matrix. A second stage sorption process was identified in the later stage of water sorption by the PEM/PTHFMA semi-IPN and for the systems containing a P(HEMA-co-THFMA) component with a mole fraction HEMA of 0.6 or less. This was characterized by the presence of Water near the surface of the cylinders with a longer NMR T-2 relaxation time, which would be characteristic of mobile water, such as water present in large pores or surface fissures. The presence of the drug chlorhexidine in the polymer matrixes at a concentration of 5.625 wt % was found not to modify the properties significantly, but the diffusion coefficients for the water sorption were systematically smaller when the drug was present.

Rearrangement of 2-quinolyl- and 1-isoquinolylcarbenes to naphthylnitrenes

2-Quinolylcarbene 23 and 1-isoquinolylcarbene 33 are generated by flash vacuum thermolysis (FVT) of the corresponding triazolo[1,5-a]quinoline and triazolo[5,1-a]isoquinoline 19 and 29, as well as 2-(5-tetrazolyl)quinoline and 1-(5-tetrazolyl)isoquinoline 20 and 30, respectively. These carbenes rearrange to 1- and 2-naphthylnitrene 21 and 31, respectively, and the nitrenes are also generated by FVT of 1- and 2-naphthyl azides 18 and 28. The products of FVT of both the nitrene and carbene precursors are the 2- and 3-cyanoindenes 26 and 27 together with the nitrene dimers, viz. azonaphthalenes 25 and 35, and the H-abstraction products, aminonaphthalenes 24 and 34. All the azide, triazole, and tetrazole precursors yield 3-cyanoindene 26 as the principal ring contraction product under conditions of low FVT temperature (340-400 degreesC) and high pressure (1 Torr N-2 as carrier gas for the purpose of collisional deactivation). This ring contraction reaction is strongly subject to chemical activation, which caused extensive isomerization of 3-cyanoindene to 2-cyanoindene under conditions of low pressure (10(-3) Torr). 2-Cyanoindene is calculated to be ca. 1.7 kcal/mol below 3-cyanoindene in energy; accordingly, high-temperature FVT of these cyanoindenes always gives mixtures of the two compounds with the 2-cyano isomer dominating. Photolysis of trizolo[1,5-a]quinoline 19 and triazolo[5,1-a]isoquinoline 29 in Ar matrixes causes partial ring opening to the corresponding 2-diazomethylquinoline 19' and 1-diazomethylisoquinoline 29'. The photolysis of the former gives rise to a small amount of the cyclic ketenimine 22, the intermediate connecting 2-quinolylcarbene and 1-naphthylnitrene.

Synthesis in the plakortone series: Plakortone E

A Pd(II)-mediated hydroxycyclisation-carbonylation-lactonisation sequence has operated efficiently with racemic enediol (8) to furnish (four) separable diastereomers of the bicyclic lactone system assigned to the sponge-derived, bioactive plakortone E. All four are cis ring-fused, and one is identical, on the basis of H-1 and C-13 NMR spectroscopic comparisons, with plakortone E, thus confirming its constitution and relative stereochemistry about the bicyclic lactone core. This synthetic approach, when applied to stereoisomer (13), will establish the absolute stereochemistry of plakortone E, likely to be that shown for (14).

Rugulotrosins A and B: Two new antibacterial metabolites from an Australian isolate of a penicillium sp.

Two new antibacterial agents, rugulotrosin A (1) and B (2), were obtained from cultures of a Penicillium sp. isolated from soil samples acquired near Sussex Inlet, New South Wales, Australia. Rugulotrosin A (1) is a chiral symmetric dimer, and its relative stereostructure was determined by spectroscopic and X-ray crystallographic analysis. Rugulotrosin B (2) is a chiral asymmetric dimer isomeric with 1. Its structure was determined by spectroscopic analysis with comparison to the co-metabolite 1 and previously reported fungal metabolites. Both rugulotrosins A and B displayed significant antibacterial activity against Bacillus subtilis, while rugulotrosin A was also strongly active against Enterococcus faecalis and B. cereus.

Ncr1p, the yeast ortholog of mammalian niemann pick C1 protein, is dispensable for endocytic transport

The Niemann Pick C1 protein localizes to late endosomes and plays a key role in the intracellular transport of cholesterol in mammalian cells. Cholesterol and other lipids accumulate in a lysosomal or late endosomal compartment in cells lacking normal NPC1 function. Other than accumulation of lipids, defects in lysosomal retroendocytosis, sorting of a multifunctional receptor and endosomal movement have also been detected in NPC1 mutant cells. Ncr1p is an ortholog of NPC1 in the budding yeast Saccharomyces cerevisiae. In this study, we show that Ncr1p is a vacuolar membrane protein that transits through the biosynthetic vacuolar protein sorting pathway, and that it can be solubilized by Triton X-100 at 4 degreesC. Using well-established assays, we demonstrate that the absence of Ncr1p had no effect on fluid phase and receptor- mediated endocytosis, biosynthetic delivery to the vacuole, retrograde transport from endosome to Golgi and ubiquitin- and nonubiquitin-dependent multivesicular body sorting. We conclude that Ncr1p does not have an essential role in known endocytic transport pathways in yeast.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Active site mutations and substrate inhibition in human sulfotransferase 1A1 and 1A3

Human SULT1A1 is primarily responsible for sulfonation of xenobiotics, including the activation of promutagens, and it has been implicated in several forms of cancer. Human SULT1A3 has been shown to be the major sulfotransferase that sulfonates dopamine. These two enzymes shares 93% amino acid sequence identity and have distinct but overlapping substrate preferences. The resolution of the crystal structures of these two enzymes has enabled us to elucidate the mechanisms controlling their substrate preferences and inhibition. The presence of two p-nitrophenol (pNP) molecules in the crystal structure of SULT1A1 was postulated to explain cooperativity at low and inhibition at high substrate concentrations, respectively. In SULT1A1, substrate inhibition occurs with pNP as the substrate but not with dopamine. For SULT1A3, substrate inhibition is found for dopamine but not with pNP. We investigated how substrate inhibition occurs in these two enzymes using molecular modeling, site-directed mutagenesis, and kinetic analysis. The results show that residue Phe-247 of SULT1A1, which interacts with both p-nitrophenol molecules in the active site, is important for substrate inhibition. Mutation of phenylalanine to leucine at this position in SULT1A1 results in substrate inhibition by dopamine. We also propose, based on modeling and kinetic studies, that substrate inhibition by dopamine in SULT1A3 is caused by binding of two dopamine molecules in the active site. © 2004 by The American Society for Biochemistry and Molecular Biology, Inc.

Three distinct molecular surfaces in ephrin-A5 are essential for a functional interaction with EphA3

Eph receptor tyrosine kinases (Ephs) function as molecular relays that interact with cell surface-bound ephrin ligands to direct the position of migrating cells. Structural studies revealed that, through two distinct contact surfaces on opposite sites of each protein, Eph and ephrin binding domains assemble into symmetric, circular heterotetramers. However, Eph signal initiation requires the assembly of higher order oligomers, suggesting additional points of contact. By screening a random library of EphA3 binding-compromised ephrin-A5 mutants, we have now determined ephrin-A5 residues that are essential for the assembly of high affinity EphA3 signaling complexes. In addition to the two interfaces predicted from the crystal structure of the homologous EphB2 center dot ephrin-B2 complex, we identified a cluster of 10 residues on the ephrin-A5 E alpha-helix, the E-F loop, the underlying H beta-strand, as well as the nearby B - C loop, which define a distinct third surface required for oligomerization and activation of EphA3 signaling. Together with a corresponding third surface region identified recently outside of the minimal ephrin binding domain of EphA3, our findings provide experimental evidence for the essential contribution of three distinct protein-interaction interfaces to assemble functional EphA3 signaling complexes.

Different behavior of nitrenes and carbenes on photolysis and thermolysis: Formation of azirine, ylidic cumulene, and cyclic ketenimine and the rearrangement of 6-phenanthridylcarbene to 9-phenanthrylnitrene

Flash vacuum thermolysis (FVT) of 9-azidophenanthrene 8, 6-(5-tetrazolyl)phenanthridine 18, and [1,2,3]triazolo[1,5-f]phenanthridine 19 yields 9-cyanofluorene 12 as the principal product and 4-cyanofluorene as a minor product. In all cases, when the product is condensed at or below 77 K, the seven-membered ring ketenimine 24 is detectable by IR spectroscopy (1932 cm(-1)) up to 200 K. Photolysis of Ar matrix isolated 8 at lambda = 308 or 313 nm generates at first the azirine 26, rapidly followed by the ylidic cumulene 27. The latter reverts to azirine 26 at lambda > 405 nm, and the azirine reverts to the ylidic cumulene at 313 nm. Nitrene 9 is observed by ESR spectroscopy following FVT of either azide 8, tetrazole 18, or triazole 19 with Ar matrix isolation of the products. Nitrene 9 and carbene 21 are observed by ESR spectroscopy in the Ar matrix photolyses of azide 8 and triazole 19, respectively.