Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Intrinsic regional differences in androgen receptors and dihydrotestosterone metabolism in human preadipocytes

Androgens play an important role in regulating the central obesity that is a strong risk factor for cardiovascular disease and insulin resistance. This study confirms that androgen receptors are present in subcultured human preadipocytes, with androgen receptor gene expression and saturable specific dihydrotestosterone binding, dissociation constant 1.02 - 2.56 nM and maximal binding capacity 30.8 - 55.7 fmol/mg protein. There was an intrinsic regional difference in androgen receptor complement, with more androgen receptors in visceral than in subcutaneous preadipocytes. Dihydrotestosterone was metabolised by human preadipocytes, with more androstanediol produced by subcutaneous than visceral preadipocytes. While dihydrotestosterone metabolism was insufficient to explain the regional variation in androgen binding, both of these differences would reduce the androgen responsiveness of the subcutaneous preadipocytes compared with visceral preadipocytes. There were no gender differences in androgen binding or metabolism. While the direct effects of androgens on human PAS remain uncertain, these regional differences suggest that AR-mediated regulation of certain PA functions influences adipose tissue distribution.

Implementing the quantum random walk

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains quantum, '' this algorithm could serve as an important benchmarking protocol for ion trap quantum computers.

Copper transfer from the Cu(I) chaperone, CopZ, to the repressor, Zn(II)CopY: Metal coordination environments and protein interactions

Extracellular copper regulates the DNA binding activity of the CopY repressor of Enterococcus hirae and thereby controls expression of the copper homeostatic genes encoded by the cop operon. CopY has a CxCxxxxCxC metal binding motif. CopZ, a copper chaperone belonging to a family of metallochaperones characterized by a MxCxxC metal binding motif, transfers copper to CopY. The copper binding stoichiometries of CopZ and CopY were determined by in vitro metal reconstitutions. The stoichiometries were found to be one copper(l) per CopZ and two copper(l) per CopY monomer. X-ray absorption studies suggested a mixture of two- and three-coordinate copper in Cu(1)CopZ, but a purely three-coordinate copper coordination with a Cu-Cu interaction for Cu(1)(2)CopY. The latter coordination is consistent with the formation of a compact binuclear Cu(l)-thiolate core in the CxCxxxxCxC binding motif of CopY. Displacement of zinc, by copper. from CopY was monitored with 2,4-pyridylazoresorcinol. Two copper(l) ions were required to release the single zinc(II) ion bound per CopY monomer. The specificity of copper transfer between CopZ and CopY was dependent on electrostatic interactions. Relative copper binding affinities of the proteins were investigated using the chelator, diethyldithiocarbamic acid (DDC). These data suggest that CopY has a higher affinity for copper than CopZ. However, this affinity difference is not the sole factor in the copper exchange: a charge-based interaction between the two proteins is required for the transfer reaction to proceed. Gain-of-function mutation of a CopZ homologue demonstrated the necessity of four lysine residues on the chaperone for the interaction with CopY. Taken together, these results suggest a mechanism for copper exchange between CopZ and CopY.

Negative ion electrospray mass spectra of caerulein peptides: an aid to structural determination

MS/MS data derived from the [M-H](-) ions of desulfated caerulein peptides provide (i) sequencing information from a combination of alpha, beta and gamma backbone cleavages, and (ii) identification of specific amino acid side chains by side-chain cleavages [e.g. Ser (-CH2O), Thr (-CH3CHO) and Asp (-H2O)] (fragmentations having no counterparts in positive ion spectra). In addition, delta and/or gamma backbone cleavage ions from Asp residues identify the position of these residues in the peptide. In contrast, neither delta nor gamma cleavage ions are observed from either the Gln2 residue nor from Phe residues. Full structural information can be obtained from a consideration of the positive and negative ion MS/MS data in concert. Copyright (C) 2002 John Wiley Sons, Ltd.

Levels of consensus and majority and minority influence

Three experiments are reported which examine the effects of consensus information on majority and minority influence. In all experiments two levels of consensus difference were examined; large (82% versus 18%) and small (52% versus 48%). Experiment 1 showed that a majority source had more influence than a minority source, irrespective of consensus level. Experiment 2 examined the cause of this effect by presenting only the source label ('majority' versus 'minority'), only the consensus information (percentages) or both. The superior influence of the majority was again found when either (a) both source label and consensus information were given (replicating Experiment 1) and (b) only consensus information was given, but not when (c) only the source label was given. The results showed majority influence was due to the consensus information indicating more than 50% of the population supported that position. Experiment 3 also manipulated message quality (strong versus weak arguments) to identify whether systematic processing had occurred. Message quality only had an impact with the minority of 18%. These studies show that consensus information has different effects' for majority and minority influence. For majority influence, having over 50% support is sufficient to cause compliance while for a minority there are advantages to being numerically small, in terms of leading to detailed processing of its message. Copyright (C) 2002 John Wiley Sons, Ltd.

Diversity and change in Australia's rangelands: a post-productivist transition with a difference?

Australia's rangelands are experiencing a post-productivist transition at a tempo comparable to Western Europe's, but in contexts that ensure marked divergence in impulses, actors, processes and outcomes. In Australia's most marginal lands, a flimsy mode of pastoral occupance is being displaced by renewed indigenous occupance, conservation and tourism, with significant changes in land ownership, property rights, investment sources and power relations, but also with structural problems arising from fugitive income streams. The sharp delineation between structurally coherent commodity-oriented regions and emerging amenity-oriented regions can provisionally be mapped at a national scale. A comparison of Australia with Western Europe indicates that three distinct but interconnected driving forces are propelling the rural transition, namely: agricultural overcapacity; the emergence of amenity-oriented uses; and changing societal values.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Mixed gas equilibrium adsorption on zeolites and energetic heterogeneity of adsorption volume

A model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions is proposed in this paper. The model is based on statistical thermodynamics, and it is able to describe molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained in the framework of this approach has upper and lower limits, which define a permissible range in which all possible solutions will be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, while the other corresponds to a maximum ordered molecular structure. Comparison of the nearly ideal O-2-N-2-zeolite NaX system at ambient temperature with the system Of O-2-N-2-zeolite CaX at 144 K has shown that a decrease of temperature leads to a molecular rearrangement in the cavity volume, which results from the difference in the fluid-solid interactions. The model is able to describe this behavior and therefore allows predicting mixture adsorption more accurately compared to those assuming energetic uniformity of the adsorption volume. Another feature of the model is its ability to correctly describe the negative deviations from Raoult's law exhibited by the O-2-N-2-CaX system at 144 K. Analysis of the highly nonideal CO2-C2H6-zeolite NaX system has shown that the spatial molecular rearrangement in separate cavities is induced by not only the ion-quadrupole interaction of the CO2 molecule but also the significant difference in molecular size and the difference between the intermolecular interactions of molecules of the same species and those of molecules of different species. This leads to the highly ordered structure of this system.

Surface diffusion of strong adsorbing vapours on porous carbon

Surface diffusion of strongly adsorbing hydrocarbon vapours on activated carbon was measured by using a constant molar flow method (D.D. Do, Dynamics of a semi-batch adsorber with constant molar supply rate: a method for studying adsorption rate of pure gas, Chem. Eng. Sci. 50 (1995) 549), where pure adsorbate is introduced into a semi-batch adsorber at a constant molar flow rate. The surface diffusivity was determined from the analysis of pressure response versus time, using a linear mathematical model developed earlier. To apply the linear theory over the non-linear range of the adsorption isotherm, we implement a differential increment method on the system which is initially equilibrated with some pre-determined loading. By conducting the experiments at different initial loadings, the surface diffusivity can be extracted as a function of loading. Propane, n-butane, n-hexane, benzene, and ethanol were used as diffusing adsorbate on a commercial activated carbon. It is found that the surface diffusivity of these strongly adsorbing vapours increases rapidly with loading, and the surface diffusion flux contributes significantly to the total flux and cannot be ignored. The surface diffusivity increases with temperature according to the Arrhenius law, and for the paraffins tested it decreases with the molecular weight of the adsorbate. (C) 2002 Elsevier Science Ltd. All rights reserved.

Ion transport induced by proteinase-activated receptors (PAR2) in colon and airways

Protease-activated receptors type 2 (PAR2) are activated by serine proteases like trypsin and mast cell tryptase. The function and physiological significance of PAR2 receptors is poorly understood, but recent studies suggest a role during inflammatory processes in both airways and intestine. PAR2 receptors are also likely to participate in the control of ion transport in these tissues. We demonstrate that stimulation of PAR2 in airways and intestine significantly enhanced ion transport. Trypsin induced CI- secretion in both airways and intestine when added to the basolateral but not to the luminal side of these tissues. In both airways and intestine, stimulation of ion transport was largely dependent on the increase in intracellular Ca2+. Effects of trypsin were largely reduced by basolateral bumetanide and barium and by trypsin inhibitor. Thrombin, an activator of proteinase-activated receptors types 1, 3, and 4 had no effects on equivalent short-circuit current in either airways or intestine. Expression of PAR2 in colon and airways was further confirmed by reverse transcription-polymerase chain reaction. We postulate that these receptors play a significant role in the regulation of electrolyte transport, which might be important during inflammatory diseases of airways and intestine.

Activation of ion secretion via proteinase-activated receptor-2 in human colon

Proteinase-activated receptor (PAR) type 2 (PAR-2) has been shown to mediate ion secretion in cultured epithelial cells and rat jejunum. With the use of a microUssing chamber, we demonstrate the role of PAR-2 for ion transport in native human colonic mucosa obtained from 30 normal individuals and 11 cystic fibrosis (CF) patients. Trypsin induced Cl- secretion when added to the basolateral but not luminal side of normal epithelia. Activation of Cl- secretion by trypsin was inhibited by indomethacin and was further increased by cAMP in normal tissues but was not present in CF colon, indicating the requirement of luminal CF transmembrane conductance regulator. Effects of trypsin were largely reduced by low Cl-,by basolateral bumetanide, and in the presence of barium or clotrimazole, but not by tetrodotoxin. Furthermore, trypsin-induced secretion was inhibited by the Ca2+-ATPase inhibitor cyclopiazonic acid and in low-Ca2+ buffer. The effects of trypsin were almost abolished by trypsin inhibitor. Thrombin, an activator of PAR types 1, 3, and 4, had no effects on equivalent short-circuit currents. The presence of PAR-2 in human colon epithelium was confirmed by RT-PCR and additional experiments with PAR-2-activating peptide. PAR-2-mediated intestinal electrolyte secretion by release of mast cell tryptase and potentiation of PAR-2 expression by tumor necrosis factor-alpha may contribute to the hypersecretion observed in inflammatory processes such as chronic inflammatory bowel disease.

Effects of polyunsaturated fatty acids on voltage-gated K+ and Na+ channels in rat olfactory receptor neurons

Although the polyunsaturated fatty acids arachidonic acid (AA) and docosahexaenoic acid (DHA) are enriched in the olfactory mucosa, their possible contribution to olfactory transduction has not been investigated. This study characterized their effects on voltage-gated K+ and Na+ channels of rat olfactory receptor neurons. Physiological (3-10 mum) concentrations of AA and DHA potently and irreversibly inhibited the voltage-gated K+ current in a voltage-independent manner. In addition, both compounds significantly reduced the inhibitory potency of the odorants acetophenone and amyl acetate at these channels. By comparison, the steady-state effects of both AA and DHA on the voltage-gated Na+ channel were relatively weak, with half-maximal inhibition requiring approximate to 35 mum of either compound. However, a surprising finding was that the initial application of 3 mum AA to a naive neuron caused a strong but transient inhibition of the Na+ current. The channels became almost completely resistant to this inhibition within 1 min, and a 2-min wash in control solution was insufficient to restore the strong inhibitory effect. These observations suggest that polyunsaturated fatty acids have the potential to strongly influence the coding of odorant information by olfactory receptor neurons.