Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Structure of TcpG, the DsbA protein folding catalyst from Vibrio cholerae

The efficient and correct folding of bacterial disulfide bonded proteins in vivo is dependent upon a class of periplasmic oxidoreductase proteins called DsbA, after the Escherichia coli enzyme. In the pathogenic bacterium Vibrio cholerae, the DsbA homolog (TcpG) is responsible for the folding, maturation and secretion of virulence factors. Mutants in which the tcpg gene has been inactivated are avirulent; they no longer produce functional colonisation pill and they no longer secrete cholera toxin. TcpG is thus a suitable target for inhibitors that could counteract the virulence of this organism, thereby preventing the symptoms of cholera. The crystal structure of oxidized TcpG (refined at a resolution of 2.1 Angstrom) serves as a starting point for the rational design of such inhibitors. As expected, TcpG has the same fold as E. coli DsbA, with which it shares similar to 40% sequence identity. Ln addition, the characteristic surface features of DsbA are present in TcpG, supporting the notion that these features play a functional role. While the overall architecture of TcpG and DsbA is similar and the surface features are retained in TcpG, there are significant differences. For example, the kinked active site helix results from a three-residue loop in DsbA, but is caused by a proline in TcpG (making TcpG more similar to thioredoxin in this respect). Furthermore, the proposed peptide binding groove of TcpG is substantially shortened compared with that of DsbA due to a six-residue deletion. Also, the hydrophobic pocket of TcpG is more shallow and the acidic patch is much less extensive than that of E. coli DsbA. The identification of the structural and surface features that are retained or are divergent in TcpG provides a useful assessment of their functional importance in these protein folding catalysts and is an important prerequisite for the design of TcpG inhibitors. (C) 1997 Academic Press Limited.

Genetic population structure of the catadromous perciform: Macquaria novemaculeata (Percichthyidae)

Genetic population structure in the catadromous Australian bass Macquaria novemaculeata was investigated using samples from four locations spanning 600 km along the eastern Australian coastline. Both allozymes and mtDNA control region sequences were examined. Population subdivision estimates based on allozymes revealed low levels of population structuring (G(st)=0.043, P<0.05). However, mtDNA indicated moderate levels of geographic population structure (G(st)=0.146, P<0.01). Phylogenetic analysis of mtDNA control region sequences (mean sequence divergence 1.9%) indicated little phylogeographic structuring. Results suggested that genotypic variation within each river population, while bring affected primarily by genetic drift, was also prevented from more significant divergence by homogenizing levels of gene flow-synonymous with a one-dimensional stepping-stone model of population structure. The catadromous life history of Macquaria novemaculeata was considered to br influential on the pattern of population structure displayed. Results were compared to the few population genetic studies involving catadromous fishes, indicating that catadromy alone is unlikely to be a good predictor of population structure. A more comprehensive suite of biological characteristics than simple life-history traits must be considered fully to allow reliable predictive models of population structure to be formulated. (C) 1997 The Fisheries Society of the British Isles.

Solution structure of the sodium channel antagonist conotoxin GS: A new molecular caliper for probing sodium channel geometry

Background: The venoms of Conus snails contain small, disulfide-rich inhibitors of voltage-dependent sodium channels. Conotoxin GS is a 34-residue polypeptide isolated from Conus geographus that interacts with the extracellular entrance of skeletal muscle sodium channels to prevent sodium ion conduction. Although conotoxin GS binds competitively with mu conotoxin GIIIA to the sodium channel surface, the two toxin types have little sequence identity with one another, and conotoxin GS has a four-loop structural framework rather than the characteristic three-loop mu-conotoxin framework. The structural study of conotoxin GS will form the basis for establishing a structure-activity relationship and understanding its interaction with the pore region of sodium channels. Results: The three-dimensional structure of conotoxin GS was determined using two-dimensional NMR spectroscopy. The protein exhibits a compact fold incorporating a beta hairpin and several turns. An unusual feature of conotoxin GS is the exceptionally high proportion (100%) of cis-imide bond geometry for the three proline or hydroxyproline residues. The structure of conotoxin GS bears little resemblance to the three-loop mu conotoxins, consistent with the low sequence identity between the two toxin types and their different structural framework. However, the tertiary structure and cystine-knot motif formed by the three disulfide bonds is similar to that present in several other polypeptide ion channel inhibitors. Conclusions: This is the first three-dimensional structure of a 'four-loop' sodium channel inhibitor, and it represents a valuable new structural probe for the pore region of voltage-dependent sodium channels. The distribution of amino acid sidechains in the structure creates several polar and charged patches, and comparison with the mu conotoxins provides a basis for determining the binding surface of the conotoxin GS polypeptide.

Cell-wall polysaccharides from Australian red algae of the family Solieriaceae (Gigartinales, Rhodophyta): Novel, highly pyruvated carrageenans from the genus Callophycus

Cell-wall polysaccharides from six species of red algae of the genus Callophycus were mainly galactans comprised predominantly of galactose (Gal) and 3,6-anhydrogalactose (AnGal), and were rich in pyruvate and sulfate. The Fourier Transform Infrared (FTIR) spectra of the polysaccharides superficially resembled that of alpha-carrageenan (composed of the repeating disaccharide carrabiose 2-sulfate), with major bands of absorption indicative of if-linked AnGal, axial 2-sulfate on 4-linked AnGal, and unsulfated, 3-linked Gal. The FTIR spectra of solutions of Callophycus polysaccharides in D2O-phosphate buffer displayed absorption, corresponding to the carboxylate anion of the pyruvate acetal substituent. Methylation analysis showed that 3,4,6-linked Galp (interpreted as 4,6-pyruvated, 3-linked Galp) and 2,4-linked AnGalp (interpreted as 4-linked AnGalp 2-sulfate) were the dominant links, together with significant quantities of 3-linked Galp. Proton-decoupled C-13 nuclear magnetic resonance (NMR) spectroscopy showed the polysaccharides to be composed predominantly of pyruvated carrageenans. The C-13 NMR spectra were completely assigned by a J-modulated spin-echo pulse sequence and 2D experiments employing gradient Heteronuclear Multiple Bond Correlation (HMBC), C-13/H-1 Heteronuclear Multiple Quantum Coherence (HMQC), and HMQC Total Correlation Spectroscopy (HMQC-TOCSY). The Callophycus galactans thus consist predominantly of the novel repeating disaccharide 4',6'-O-(1-carboxyethylidene)carrabiose 2-sulfate and minor amounts of the alpha-carrageenan repeating unit (carrabiose 2-sulfate), and other structural variations. (C) 1997 Elsevier Science Ltd.

Ideal soliton environment using parametric band gaps

Simultaneous solitary wave solutions for laser propagation in nonlinear parametric media with up to (3 + 1) dimensions are proved to exist. The combination of the large dispersion of a Bragg grating and the strong nonlinearity of chi((2)) optical material results in stable behavior with short interaction distances and low power requirements. The solutions are obtained by using the effective mass approximation to reduce the coupled propagation equations to those describing a dispersive parametric nonlinear waveguide, and are verified by solving the complete set of coupled band-gap equations numerically.

Molecular motion in miscible polymer blends .1. Motion in blends of PEO and PVPh studied by solid-state C-13 T-1 rho measurements

Changes in molecular motion in blends of PEO-PVPh have been studied using measurements of C-13 T-1 rho relaxation times. C-13 T-1 rho relaxation has been confirmed as arising from spin-lattice interactions by observation of the variation in T-1 rho with rf field strength and temperature. In the pure homopolymers a minimum in T-1 rho is observed at ca. 50 K above the glass transition temperatures detected by DSC. After blending, the temperature of the minimum in T-1 rho for PEO increased, while that for PVPh decreased, however, the minima, which correspond to the temperatures where the average correlation times for reorientation are close to 3.1 mu s, are separated by 45 K (in a 45% PEO-PVPh blend). These phenomena are explained in terms of the local nature of T-1 rho measurements. The motions of the individual homopolymer chains are only partially coupled in the blend. A short T-1 rho has been observed for protonated aromatic carbons, and assigned to phenyl rings undergoing large-angle oscillatory motion, The effects of blending, and temperature, on the proportion of rings undergoing oscillatory motion are analyzed.

The structure of a novel insecticidal neurotoxin, omega-atracotoxin-HV1, from the venom of an Australian funnel web spider

A family of potent insecticidal toxins has recently been isolated from the venom of Australian funnel web spiders. Among these is the 37-residue peptide omega-atracotoxin-HV1 (omega-ACTX-HV1) from Hadronyche versuta. We have chemically synthesized and folded omega-ACTX-HV1, shown that it is neurotoxic, ascertained its disulphide bonding pattern, and determined its three-dimensional solution structure using NMR spectroscopy. The structure consists of a solvent-accessible beta-hairpin protruding from a disulphide-bonded globular core comprising four beta-turns. The three intramolecular disulphide bonds form a cystine knot motif similar to that seen in several other neurotoxic peptides. Despite limited sequence identity, omega-ACTX-HV1 displays significant structural homology with the omega-agatoxins and omega-conotoxins, both of which are vertebrate calcium channel antagonists; however, in contrast with these toxins, we show that omega-ACTX-HV1 inhibits insect, but not mammalian, voltage-gated calcium channel currents.

Population structure of Phytophthora cinnamomi in South Africa

Phytophthora cinnamomi isolates collected from 1977 to 1986 and 1991 to 1993 in two regions in South Africa were analyzed using isozymes. A total of 135 isolates was analyzed for 14 enzymes representing 20 putative loci, of which four were polymorphic. This led to the identification of nine different multilocus isozyme genotypes. Both mating types of P. cinnamomi occurred commonly in the Cape region, whereas, predominantly, the A2 mating type occurred in the Mpumalanga region of South Africa. A2 mating type isolates could be resolved into seven multilocus isozyme genotypes, compared with only two multilocus isozyme genotypes for the A1 mating type isolates. Low levels of gene (0.115) and genotypic (2.4%) diversity and a low number of alleles per locus (1.43) were observed for the South African P. cinnamomi population. The genetic distance between the Cape and Mpumalanga P. cinnamomi populations was relatively low (D-m = 0.165), and no specific pattern in regional distribution of multilocus isozyme genotypes could be observed. The genetic distance between the ''old'' (isolated between 1977 and 1986) and ''new'' (isolated between 1991 and 1993) P. cinnamomi populations from the Cape was low (D-m = 0.164), indicating a stable population over time. Three of the nine multilocus isozyme genotypes were specific to the ''old'' population, and only one multilocus isozyme genotype was specific to the ''new'' population. Significant differences in allele frequencies, a high genetic distance (D-m = 0.581) between the Cape A1 and A2 mating type isolates, significant deviations from Hardy-Weinberg equilibrium, a low overall level of heterozygosity, and a high fixation index (0.71) all indicate that sexual reproduction occurs rarely, if at all, in the South African P. cinnamomi population.

Pulsed quadrature-phase squeezing of solitary waves in chi((2)) parametric waveguides

It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive chi((2)) waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched chi((2)) waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Structure of galactosylononitol

A cyclitol galactoside was isolated from the seeds of Vigna angularis and shown to be identical with galactosylononitol. However, detailed 2D NMR data and methylation analysis resulted in the revision of the structure of galactosylononitol to O-alpha-D-galactopyranosyl-(1-->3)-4-O-methyl-D-myo-inositol (1). Thus, compound 1 represents the only naturally occuring methylated derivative of galactinol.

A two-dimensional fuzzy random model of soil pore structure

A new conceptual model for soil pore-solid structure is formalized. Soil pore-solid structure is proposed to comprise spatially abutting elements each with a value which is its membership to the fuzzy set ''pore,'' termed porosity. These values have a range between zero (all solid) and unity (all pore). Images are used to represent structures in which the elements are pixels and the value of each is a porosity. Two-dimensional random fields are generated by allocating each pixel a porosity by independently sampling a statistical distribution. These random fields are reorganized into other pore-solid structural types by selecting parent points which have a specified local region of influence. Pixels of larger or smaller porosity are aggregated about the parent points and within the region of interest by controlled swapping of pixels in the image. This creates local regions of homogeneity within the random field. This is similar to the process known as simulated annealing. The resulting structures are characterized using one-and two-dimensional variograms and functions describing their connectivity. A variety of examples of structures created by the model is presented and compared. Extension to three dimensions presents no theoretical difficulties and is currently under development.

Infrared seeded parametric four-wave mixing for sensitive detection of molecules

We have developed a sensitive resonant four-wave mixing technique based on two-photon parametric four-wave mixing with the addition of a phase matched ''seeder'' field. Generation of the seeder field via the same four-wave mixing process in a high pressure cell enables automatic phase matching to be achieved in a low pressure sample cell. This arrangement facilitates sensitive detection of complex molecular spectra by simply tuning the pump laser. We demonstrate the technique with the detection of nitric oxide down to concentrations more than 4 orders of magnitude below the capability of parametric four-wave mixing alone, with an estimated detection threshold of 10(12) molecules/cm(3).

Crystal structure at 1.1 angstrom resolution of alpha-conotoxin PnIB: Comparison with alpha-conotoxins PnIA and GI

Conotoxins are small, cysteine-rich peptides isolated from the venom of Conus spp. of predatory marine snails, which selectively target specific receptors and ion channels critical to the functioning of the neuromuscular system. alpha-Conotoxins PnIA and PnIB are both 16-residue peptides (differing in sequence at only two positions) isolated from the molluscivorous snail Conus pennaceus. In contrast to the muscle-selective alpha-conotoxin GI from Conus geographus, PnIA and PnIB block the neuronal nicotinic acetylcholine receptor (nAChR). Here, we describe the crystal structure of PnIB, solved at a resolution of 1.1 Angstrom and phased using the Shake-and-Bake direct methods program. PnIB crystals are orthorhombic and belong to the space group P2(1)2(1)2(1) with the following unit cell dimensions: a = 14.6 Angstrom, b = 26.1 Angstrom, and c = 29.2 Angstrom. The final refined structure of alpha-conotoxin PnIB includes all 16 residues plus 23 solvent molecules and has an overall R-factor of 14.7% (R-free of 15.9%). The crystal structures of the alpha-conotoxins PnIB and PnIA are solved from different crystal forms, with different solvent contents. Comparison of the structures reveals them to be very similar, showing that the unique backbone and disulfide architecture is not strongly influenced by crystal lattice constraints or solvent interactions. This finding supports the notion that this structural scaffold is a rigid support for the presentation of important functional groups. The structures of PnIB and PnIA differ in their shape and surface charge distribution from that of GI.