On the sensitivity of the LU factorization

This paper gives sensitivity analyses by two approaches forL andU in the factorizationA=LU for general perturbations inA which are sufficiently small in norm. By the matrix-vector equation approach, we derive the condition numbers for theL andU factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting affect the sensitivity of the LU factorization. The material presented here is a part of the first author's PhD thesis under the supervision of the second author. This research was supported by NSERC of Canada Grant OGP0009236.     

DEMONSTRATION THAT PHOSPHORESCENT 6-BROMO-2-NAPHTHYL SULFATE CAN BE USED TO PROBE HEME ACCESSIBILITY IN HEME PROTEINS

The phosphorescence properties of 6-bromo-2-naphthyl sulfate (BNS) in aqueous solution were studied. The phosphorescence lifetime is several hundred microseconds and is self-quenched. Although a fluorescent photoproduct is formed from BNS, it does not interfere with the decay properties of triplet-state BNS and its utility as a probe of the accessibility of the heme group in heme proteins. Quenching of BNS phosphorescence does not occur for the non-heme protein lysozyme and apomyoglobin but occurs by a dynamic mechanism with a quenching constant of 1-2 x 10(9) M-1 s-1 for cytochrome c and myoglobin and with a quenching constant of 6.2 x 10(9) M-1 s-1 for protoporphyrin IX. The phosphorescence of an inclusion complex of 1-bromonaphthalene and beta-cyclodextrin is not quenched by heme-containing proteins. The temperature and viscosity dependencies of the rate with which BNS phosphorescence is quenched by microperoxidase-11 are consistent with unit quenching efficiency. These results indicate that quenching of BNS phosphorescence occurs only upon contact with the quencher, and the quenching constant can be used to assess the degree of accessibility of the heme group.     

A modular synthesis of annonaceous acetogenins

A synthesis of four Annonaceous acetogenins, asiminocin, asimicin, asimin, and bullanin, by a modular approach from seven fundamental subunits, A-G, is described. The approach employs a central core aldehyde segment, C, to which are appended an aliphatic terminus, A or B, a spacer subunit, D or E, and a butenolide terminus, F or G. Coupling of the A, B, D, and E segments to the core aldehyde unit is effected by highly diastereoselective additions of enantiopure allylic indium or tin reagents. The butenolide termini are attached to the ACD, BCE, or BCD intermediates by means of a Sonogashira coupling. The design of the core, spacer, and termini subunits is such that any of the C30, C10, or C4 natural acetogenins or stereoisomers thereof could be prepared. IC50 values for the four aforementioned acetogenins against H-116 human colon cancer cells were found to be in the 10(-3) to 10(-4) microM range. The IC90 activities were ca. 10(-3) microM for asimicin and asimin but only 0.1-1 microM for bullanin and asiminocin.     

Dendron to Central Core S1–S1 and S2–Sn (n>1) Energy Transfers in Artificial Special Pairs Containing Dendrimers with Limited Numbers of Conformations

Two dendrimers consisting of a cofacial free‐base bisporphyrin held by a biphenylene spacer and functionalized with 4‐benzeneoxomethane (5‐(4‐benzene)tri‐10,15,20‐(4‐n‐octylbenzene)zinc(II)porphyrin) using either five or six of the six available meso‐positions, have been synthesized and characterized as models for the antenna effect in Photosystems I and II. The presence of the short linkers, ‐CH₂O‐, and long C₈H₁₇ soluble side chains substantially reduces the number of conformers (foldamers) compared with classic dendrimers built with longer flexible chains. This simplification assists in their spectroscopic and photophysical analysis, notably with respect to fluorescence resonance energy transfer (FRET). Both steady‐state and time‐resolved spectroscopic measurements indicate that the cofacial free bases and the flanking zinc(II)–porphyrin antennas act as energy acceptor and donor, respectively, following excitation in either the Q or Soret bands of the dendrimers. The rate constants for singlet electronic energy transfer (k_EET) extracted from the S₁ and S₂ fluorescence lifetimes of the donor in the presence and absence of the acceptor are ≤ (0.1–0.3)×10⁹ and ～2×10⁹ s^?1 for S₁→S₁ (range from a bi‐exponential decay model) and about 1.5×10¹² s^?1 for S₂→S_n (n>1). Comparisons of these experimental data with those calculated from Förster theory using orientation factors and donor–acceptor distances extracted from computer modeling suggest that a highly restricted number of the many foldamers facilitate energy transfer. These foldamers have the lowest energy by molecular modeling and consist of one or at most two of the flanking zinc porphyrin antennas folded so they lie near the central artificial special pair core with the remaining antennas located almost parallel to and far from it.     

Ultrastructure and assembly of segmental long spacing collagen studied by atomic force microscopy

The in vitro formation of segmental long spacing (SLS) collagen as induced by the addition of ATP to acidified Type I collagen solutions has been examined with the atomic force microscope (AFM). AFM images obtained suggest that the assembly proceeds in a stepwise manner, through an intermediate stage of oligomers, which then associate laterally to form the so-called "SLS crystallites". Attempts to induce SLS formation by the addition of other polyanionic species to monomeric collagen solutions met with mixed success; ATP-gamma-S and GTP produced SLS crystallites, whereas inorganic phosphate and other polyanionic dyes did not. This indicates that the formation of SLS cannot simply be attributed to the negation of positive charges believed to be located on the end of the collagen monomer, but rather it is a complex function of the structure and charge of both the collagen monomer and polyanion.     

The one- and multi-sample problem for functional data with application to projective shape analysis

In this paper tests are derived for testing neighborhood hypotheses for the one- and multi-sample problem for functional data. Our methodology is used to generalize testing in projective shape analysis, which has traditionally involving data consisting of finite number of points, to the functional case. The one-sample test is applied to the problem of scene identification, in the context of the projective shape of a planar curve.     

LSPR Biosensor Signal Enhancement Using Nanoparticle-Antibody Conjugates

A method to amplify the wavelength shift observed from localized surface plasmon resonance (LSPR) bioassays is developed using gold nanoparticle-labeled antibodies. The technique, which involves detecting surface-bound analytes using gold nanoparticle conjugated antibodies, provides a way to enhance LSPR shifts for more sensitive detection of low-concentration analytes. Using the biotin and antibiotin binding pair as a model, we demonstrate up to a 400% amplification of the shift upon antibody binding to analyte. In addition, the antibody-nanoparticle conjugate improves the observed binding constant by 2 orders of magnitude, and the limit of detection by nearly 3 orders of magnitude. This amplification strategy provides a way to improve the sensitivity of plasmon-based bioassays, paving the way for single molecule-based detection and clinically relevant diagnostics.     

Syntheses of the opioid substructures 1,2,3,4,5,6-hexahydro-2,6-methano-3-benzazocine and 2,3,4,5-tetrahydro-1,5-methano-1H-2-benzazepine

Concise syntheses of 1,2,3,4,5,6-hexahydro-2,6-methano-3-benzazocine (12) and 2,3,4,5-tetrahydro-1,5-methano-1H-2-benzazepine (18) are described and involve an intramolecular Friedel-Crafts alkylation and an intramolecular Heck cyclization as their respective key ring-forming steps.     

One octarepeate expansion to the human prion protein alters both the Zn2+ and Cu2+ coordination environments within the octarepeate domain

The influence of a single octarepeat expansion on the Cu(II) and Zn(II) coordination environments within the octarepeat domain of the human prion protein is examined. Using X-ray absorption spectroscopy and diethyl pyrocarbonate labeling studies, we find that at low copper concentrations the "normal" octarepeat domain (four PHGGGWGQ repeats) coordinates Zn(II) in an (N/O)(6) coordination environment with two histidine residues and Cu(II) in a redox-inactive (N/O)(4) coordination environment using one imidazole residue. Expansion of the octarepeat region by one repeat (five PHGGGWGQ repeats) yields a three-histidine (N/O)(6) coordination environment for Zn(II) and a two-histidine (N/O)(4) coordination environment for Cu(II) at low copper concentrations. This Cu(II)[(N/O)(2)-histidine(2)] coordination motif is redox-active and capable of generating H(2)O(2) under reducing aerobic conditions.