Stationary and oscillatory fronts in a two-component genetic regulatory network model

We investigate a two-component gene network model, originally used to describe the spatiotemporal patterning of the gene products in early Drosophila development. By considering a particular mode of interaction between the two gene products, denoted proteins A and B, we find both stable stationary and time-oscillatory fronts can occur in the reaction-diffusion system. We reduce the system by replacing B with its spatial average (shadow system) and assume an abrupt “on-and-off” switch for the genes. In doing so, explicit formula are obtained for all steady-state solutions and their linear eigenvalues. Using the diffusion of A,D_a, and the basal production rate, r, as bifurcation parameters, we explore ranges in which a monotone, stationary front is stable, and show it can lose stability through a Hopf bifurcation, giving rise to oscillatory fronts. We also discuss the existence and stability of steady-state and time-oscillatory solutions with multiple extrema. An intuitive explanation for the occurrence of stable stationary and oscillatory front solutions is provided based on the behavior of A in the absence of B and the opposite regulation between A and B. Such behavior is also interpreted in terms of the biological parameters in the model, including those governing the connection of the gene network.     

Determination of polybrominated diphenyl ethers in environmental standard reference materials

Standard reference materials (SRMs) are valuable tools in developing and validating analytical methods to improve quality assurance standards. The National Institute of Standards and Technology (NIST) has a long history of providing environmental SRMs with certified concentrations of organic and inorganic contaminants. Here we report on new certified and reference concentrations for 27 polybrominated diphenyl ether (PBDE) congeners in seven different SRMs: cod-liver oil, whale blubber, fish tissue (two materials), mussel tissue and sediment (two materials). PBDEs were measured in these SRMs, with the lowest concentrations measured in mussel tissue (SRM 1974b) and the highest in sediment collected from the New York/New Jersey Waterway (SRM 1944). Comparing the relative PBDE congener concentrations within the samples, we found the biota SRMs contained primarily tetrabrominated and pentabrominated diphenyl ethers, whereas the sediment SRMs contained primarily decabromodiphenyl ether (BDE 209). The cod-liver oil (SRM 1588b) and whale blubber (SRM 1945) materials were also found to contain measurable concentrations of two methoxylated PBDEs (MeO-BDEs). Certified and reference concentrations are reported for 12 PBDE congeners measured in the biota SRMs and reference values are available for two MeO-BDEs. Results from a sediment interlaboratory comparison PBDE exercise are available for the two sediment SRMs (1941b and 1944).     

Molecular structure of Hf(BH4)4 investigated by quantum mechanical calculations and gas-phase electron diffraction

The structure of the gaseous hafnium tetrakis(tetrahydroborate) molecule, Hf(BH4)4, has been investigated by detailed quantum mechanical calculations and by analysis of its gas electron-diffraction (GED) pattern. The ground-state geometry possesses T symmetry with all of the triply-bridged BH4 groups twisted equally about the Hf...B-H axes. Salient structural parameters (ra distances, r angles) deduced from the GED pattern by the SARACEN method were: r(Hf...B) 231.4(2), r(Hf-Hb) 221.5(7), r(B-Hb) 127.6(5), r(B-Ht) 121(1) pm, Hf...B-Hb 69.4(3), Hb-B-Hb 108.4(4), Hb-B-Ht 110.6(3), B...Hf...B-Hb 166(1) degrees. A notable feature is the large magnitude of the Hf...B and Hf-Hb anharmonicity parameters, attributed to the fluxional hydrogen atom exchange process. The properties are compared with those of related tetrahydroborates..     

Generalized phase diversity for wave-front sensing

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.     

Simultaneous determination of estrogenic and androgenic hormones in water by isotope dilution gas chromatography-tandem mass spectrometry

A rapid gas chromatography-tandem mass spectrometry (GC-MS/MS) analytical method was developed for the simultaneous analysis of 7 estrogenic hormones (17α-estradiol, 17β-estradiol, estrone, mestranol, 17α-ethynylestradiol, levonorgestrel, estriol) and 5 androgenic hormones (testosterone, androsterone, etiocholanolone, dihydrotestosterone, androstenedione) in aqueous matrices. This method is unique in its inclusion of all 12 of these estrogens and androgens and is of particular value due to its very short chromatographic run time of 15 min. The use of isotope dilution for all analytes ensures the accurate quantification, accounting for analytical variabilities that may be introduced during sample processing and instrumental analysis. Direct isotopically labelled analogues were used for 8 of the 12 hormones and satisfactory isotope standards were identified for the remaining 4 hormones. Method detection levels (MDLs) were determined to describe analyte concentrations sufficient to provide a signal with 99% certainty of detection. The established MDLs for most analytes were 1-5 ngL(-1) in a variety of aqueous matrices. However, slightly higher MDLs were observed for etiocholanolone, androstenedione, testosterone, levonorgestrel and dihydrotestosterone in some aqueous matrices. Sample matrices were observed to have only a minor impact on MDLs and the method validation confirmed satisfactory method stability over intra-day and inter-day analyses of surface water and tertiary treated effluent samples.     

Allylic C-H activations using Cu(II) 2-quinoxalinol salen and tert-butyl hydroperoxide

Using a Cu(II) 2-quinoxalinol salen complex as the catalyst and tert-butyl hydroperoxide (TBHP) as the oxidant, allylic activations of olefin substrates can be converted to the corresponding enones or 1,4-enediones. Excellent yields can be achieved (up to 99%) within a very short reaction time and with great tolerance for additional functional groups. Possible mechanistic pathways have been characterized using Raman spectroscopy, cyclic voltammetry, and theoretical calculations.     

Biosynthesis of hydroxydiphenylacetylene by regiospecific monooxygenation

Bacterial monooxygenase enzymes catalyze a regiospecific single-step hydroxylation of diphenylacetylene to yield meta- and para-hydroxydiphenylacetylene.     

Counting singular plane curves via Hilbert schemes

We give a method of counting the number of curves with a given type of singularity in a suitably ample linear series on a smooth surface using punctual Hilbert schemes. The types of singularities for which our results suffice include the topological type with local equation x^a+y^b with ?a?3b. We work out the example of curves with the analytic type of singularity with local equation x²+yⁿ for 1<n<9.