Quasi-Shuffle Products

Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be viewed as a generalization of the shuffle product III. We extend this commutative algebra structure to a Hopf algebra (U, *, ); in the case where A is the set of positive integers and the operation on A is addition, this gives the Hopf algebra of quasi-symmetric functions. If rational coefficients are allowed, the quasi-shuffle product is in fact no more general than the shuffle product; we give an isomorphism exp of the shuffle Hopf algebra (U, III, ) onto (U, *, ) the set L of Lyndon words on A and their images { exp(w) w L} freely generate the algebra (U, *). We also consider the graded dual of (U, *, ). We define a deformation *_q of * that coincides with * when q = 1 and is isomorphic to the concatenation product when q is not a root of unity. Finally, we discuss various examples, particularly the algebra of quasi-symmetric functions (dual to the noncommutative symmetric functions) and the algebra of Euler sums.     

Novel microscopic mechanism of intermixing during growth on soft metallic substrates

Generic computer simulations using empiric interatomic potentials suggest a new, collective mechanism that could be responsible for mixing at heteroepitaxial interfaces. Even if single adsorbate atoms diffuse by hopping on the substrate surface and do not mix at the terraces, two-dimensional islands formed by nucleation may become unstable above a certain critical size and explode upwards forming clusters of several atomic layers. This process is accompanied by strong distortions of the underlying atomic layers, and on soft materials it can result in surface etching and incorporation of substrate atoms into the islands.     

Changes in ADC caused by tensile loading of rabbit achilles tendon: evidence for water transport

Water diffusion measurements were performed on rabbit Achilles tendons during static tensile loading and tendons in an unloaded state. The apparent diffusion coefficient (ADC) was measured along two directions: parallel and perpendicular to the long axis of the tendon. Tendons were studied after being prepared in two ways: (a) after being stored frozen in phosphate-buffered saline (PBS) and (b) freshly isolated. Statistically significant directional anisotropy was observed in the ADC in all tendons. The ADC was significantly greater in the direction parallel to the long axis of the tendon than in the perpendicular direction. The anisotropy is attributed to the greater restrictions seen by the water molecules in the perpendicular direction and is consistent with the known geometry of the tendon. Storage in PBS caused tendons to swell. This increased the ADC measured along both directions and reduced the anisotropy. The existence of anisotropy in the ADC was not related to the orientation of the specimen in the magnet. The ADC increased along both directions following the application of a 5-N tensile load; the increase was greatest along the perpendicular axis of the tendon. In order to determine whether load-related changes in the ADC reflected changes in interfibrilar spacing, we used electron microscopy to measure load-related changes in fibril spacing. Load-related changes in fiber spacing could not account for the observed changes in the ADC. The increase in ADC caused by loading was attributed to the extrusion of tendon water into a bulk phase along the outside surface of the tendon. In PBS-stored samples, enough fluid was extruded that it could be visualized. The transient response of the ADC to a 5-N tensile load was also studied. The absolute ADC in both directions increased with loading and recovered to baseline upon unloading. The transient changes in ADC, for both loading and unloading, had a mean time constant of approximately 15 min. The magnitude of the load-induced transient ADC changes was comparable to that seen in the static-loading experiments.     

Detection efficiency calculations using Geant4 for a broad-energy germanium gamma spectrometer

In assistance of radionuclide measurements at Canada’s Comprehensive Nuclear-Test-Ban Treaty (CTBT) laboratory, a Geant4 Monte Carlo application has been developed in simulating a broad-energy germanium detector and calculating detection efficiencies. The detector model was optimized in a reliable and non-biased manner through simultaneous tuning on gap distance and detector dimension, and was validated over various realistic measurement scenarios. All work is based on a series of experiments which covers the typical energy range of gamma radiation in environmental analysis, and considers the variety of the CTBT sample type, dimension and distance-to-detector. In all cases, the predicted efficiencies are consistent with the empirical ones within 5%, with a typical deviation of 3% in majority.     

Probing the oxyferrous and catalytically active ferryl states of Amphitrite ornata dehaloperoxidase by cryoreduction and EPR/ENDOR spectroscopy. Detection of compound I

Dehaloperoxidase (DHP) from Amphitrite ornata is a heme protein that can function both as a hemoglobin and as a peroxidase. This report describes the use of 77 K cryoreduction EPR/ENDOR techniques to study both functions of DHP. Cryoreduced oxyferrous [Fe(II)-O(2)] DHP exhibits two EPR signals characteristic of a peroxoferric [Fe(III)-O(2)(2-)] heme species, reflecting the presence of conformational substates in the oxyferrous precursor. (1)H ENDOR spectroscopy of the cryogenerated substates shows that H-bonding interactions between His N(ε)H and heme-bound O(2) in these conformers are similar to those in the β-chain of oxyferrous hemoglobin A (HbA) and oxyferrous myoglobin, respectively. Decay of cryogenerated peroxoferric heme DHP intermediates upon annealing at temperatures above 180 K is accompanied by the appearance of a new paramagnetic species with an axial EPR signal with g(⊥) = 3.75 and g(∥) = 1.96, characteristic of an S = 3/2 spin state. This species is assigned to Compound I (Cpd I), in which a porphyrin π-cation radical is ferromagnetically coupled with an S = 1 ferryl [Fe(IV)═O] ion. This species was also trapped by rapid freeze-quench of the ambient-temperature reaction mixture of ferric [Fe(III)] DHP and H(2)O(2). However, in the latter case Cpd I is reduced very rapidly by a nearby tyrosine to form Cpd ES [(Fe(IV)═O)(porphyrin)/Tyr(?)]. Addition of the substrate analogue 2,4,6-trifluorophenol (F(3)PhOH) suppresses formation of the Cpd I intermediate during annealing of cryoreduced oxyferrous DHP at 190 K but has no effect on the spectroscopic properties of the remaining cryoreduced oxyferrous DHP intermediates and kinetics of their decay. These observations indicate that substrate (i) binds to oxyferrous DHP outside of the distal pocket and (ii) can reduce Cpd I to Cpd II [Fe(IV)═O]. These assumptions are also supported by the observation that F(3)PhOH has only a small effect on the EPR properties of radiolytically cryooxidized and cryoreduced ferrous [Fe(II)] DHP. EPR spectra of cryoreduced ferrous DHP disclose the multiconformational nature of the ferrous DHP precursor. The observation and characterization of Cpds I, II, and ES in the absence and in the presence of F(3)PhOH provides definitive evidence of a mechanism involving consecutive one-electron steps and clarifies the role of all intermediates formed during turnover.     

A helical flow, circular microreactor for separating and enriching "smart" polymer-antibody capture reagents

We report a mechanistic study of how flow and recirculation in a microreactor can be used to optimize the capture and release of stimuli-responsive polymer-protein reagents on stimuli-responsive polymer-grafted channel surfaces. Poly(N-isopropylacrylamide) (PNIPAAm) was grafted to polydimethylsiloxane (PDMS) channel walls, creating switchable surfaces where PNIPAAm-protein conjugates would adhere at temperatures above the lower critical solution temperature (LCST) and released below the LCST. A PNIPAAm-streptavidin conjugate that can capture biotinylated antibody-antigen targets was first characterized. The conjugate's immobilization and release were limited by mass transport to and from the functionalized PNIPAAm surface. Transport and adsorption efficiencies were dependent on the aggregate size of the PNIPAAm-streptavidin conjugate above the LCST and also were dependent on whether the conjugates were heated in the presence of the stimuli-responsive surface or pre-aggregated and then flowed across the surface. As conjugate size increased, through the addition of non-conjugated PNIPAAm, recirculation and mixing were shown to markedly improve conjugate immobilization compared to diffusion alone. Under optimized conditions of flow and reagent concentrations, approximately 60% of the streptavidin conjugate bolus could be captured at the surface and subsequently successfully released. The kinetic release profile sharpness was also strongly improved with recirculation and helical mixing. Finally, the concentration of protein-polymer conjugates could be achieved by continuous conjugate flow into the heated recirculator, allowing nearly linear enrichment of the conjugate reagent from larger volumes. This capability was shown with anti-p24 HIV monoclonal antibody reagents that were enriched over 5-fold using this protocol. These studies provide insight into the mechanism of smart polymer-protein conjugate capture and release in grafted channels and show the potential of this purification and enrichment module for processing diagnostic samples.     

Synthesis of zinc trisubstituted hydrazido complexes and ortho-metalation of 4-(dimethylamino)pyridine

The zinc hydrazide complexes [EtZn(N(SiMe(3))NMe(2))](2), [EtZn(N(Me)NMe(2))](4), and Zn(3)Et(4)(N(Et)NMe(2))(2) were synthesized by allowing excess hydrazine, HN(R)NMe(2), to react with diethyl zinc. The product of the reaction between ZnEt(2) and HN(i-Pr)NMe(2)ortho-metalated 4-(dimethylamino)pyridine (DMAP) at room temperature, producing the complex Zn[(NC(5)H(3)-p-NMe(2))ZnEt(N(i-Pr)NMe(2))](2). At elevated temperatures, Zn(3)Et(4)(N(Et)NMe(2))(2) also ortho-metalated DMAP, but [EtZn(N(Me)NMe(2))](4) did not. Single-crystal X-ray diffraction studies revealed that the hydrazide ligands in [EtZn(N(SiMe(3))NMe(2))](2) act as bridging mono-hapto amide ligands, and in Zn(3)Et(4)(N(Et)NMe(2))(2) and Zn[(NC(5)H(3)-p-NMe(2))ZnEt(N(i-Pr)NMe(2))](2) the hydrazide ligands are di-hapto.     

Tunable coupling in circuit quantum electrodynamics using a superconducting charge qubit with a V-shaped energy level diagram

We introduce a new type of superconducting charge qubit that has a V-shaped energy spectrum and uses quantum interference to provide independently tunable qubit energy and coherent coupling to a superconducting cavity. Dynamic access to the strong coupling regime is demonstrated by tuning the coupling strength from less than 200 kHz to greater than 40 MHz. This tunable coupling can be used to protect the qubit from cavity-induced relaxation and avoid unwanted qubit-qubit interactions in a multiqubit system.