Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Resolving the energy paradox of chaperone/usher-mediated fibre assembly

Periplasmic chaperone/usher machineries are used for assembly of filamentous adhesion organelles of Gram-negative pathogens in a process that has been suggested to be driven by folding energy. Structures of mutant chaperone-subunit complexes revealed a final folding transition (condensation of the subunit hydrophobic core) on the release of organelle subunit from the chaperone-subunit pre-assembly complex and incorporation into the final fibre structure. However, in view of the large interface between chaperone and subunit in the pre-assembly complex and the reported stability of this complex, it is difficult to understand how final folding could release sufficient energy to drive assembly. In the present paper, we show the X-ray structure for a native chaperone-fibre complex that, together with thermodynamic data, shows that the final folding step is indeed an essential component of the assembly process. We show that completion of the hydrophobic core and incorporation into the fibre results in an exceptionally stable module, whereas the chaperone-subunit preassembly complex is greatly destabilized by the high-energy conformation of the bound subunit. This difference in stabilities creates a free energy potential that drives fibre formation.

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character. (c) 2006 American Institute of Physics.

Suttonella ornithocola sp nov., from birds of the tit families, and emended description of the genus Suttonella

Phenotypic and phylogenetic studies were performed on three strains of Gram-negative, rod-shaped organisms recovered from dead birds of the tit families (blue tit, coal tit and long-tailed tit). Morphological, cultural and biochemical studies indicated that the organisms were related to the family Cardiobacteriaceae in the gamma-subclass of the Proteobacteria. Comparative 16S rRNA gene sequencing studies confirmed these findings and demonstrated that the bacterium represents a hitherto unknown subline within this family. The closest phylogenetic relative of the strains isolated from the birds was found to be Suttonella indologenes, although a sequence divergence of approximately 5 % demonstrated that the unknown bacterium represented a novel species. On the basis of the results of the phylogenetic analysis and phenotypic criteria, it is proposed that the bacteria recovered from the diseased birds represent a novel species, Suttonella ornithocola sp. nov., with strain B6/99/2(T) (=CCUG 49457(T)=NCTC 13337(T)) as the type strain.

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

Simplified parameter adaptive control

A simple parameter adaptive controller design methodology is introduced in which steady-state servo tracking properties provide the major control objective. This is achieved without cancellation of process zeros and hence the underlying design can be applied to non-minimum phase systems. As with other self-tuning algorithms, the design (user specified) polynomials of the proposed algorithm define the performance capabilities of the resulting controller. However, with the appropriate definition of these polynomials, the synthesis technique can be shown to admit different adaptive control strategies, e.g. self-tuning PID and self-tuning pole-placement controllers. The algorithm can therefore be thought of as an embodiment of other self-tuning design techniques. The performances of some of the resulting controllers are illustrated using simulation examples and the on-line application to an experimental apparatus.

Preparation of (–)-epigallocatechin gallate from commercial green tea by caffeine precipitation and solvent partition

A method has been developed which enables the easy and inexpensive preparation of gram quantities of (–)-epigallocatechin gallate from green tea (Camellia sinensis). A decaffeinated aqueous brew of commercial green tea is treated with caffeine (30 m ). The precipitate is redissolved after decaffeination with chloroform and further purified by solvent partition with ethyl hexanoate and propyl acetate. Commercial leaf (25 g) yields 400 mg (–)-epigallocatechin gallate at better than 80% purity, as judged by reversed phase HPLC.

The inhibitory effect of natural microflora of food on growth of Listeria monocytogenes in enrichment broths

The aims of this study were to (i) compare the inhibitory effects of the natural microflora of different foods on the growth of Listeria monocytogenes during enrichment in selective and non-selective broths; (ii) to isolate and identify components of the microflora of the most inhibitory food; and (iii) to determine which of these components was most inhibitory to growth of L. monocytogenes in co-culture studies. Growth of an antibioticresistant marker strain of L. monocytogenes was examined during enrichment of a range of different foods in Tryptone Soya Broth (TSB), Half Fraser Broth (HFB) and Oxoid Novel Enrichment (ONE) Broth. Inhibition of L. monocytogenes was greatest in the presence of minced beef, salami and soft cheese and least with prepared fresh salad and chicken pâté. For any particular food the numbers of L. monocytogenes present after 24 h enrichment in different broths increased in the order: TSB, HFB and ONE Broth. Numbers of L. monocytogenes recovered after enrichment in TSB were inversely related to the initial aerobic plate count (APC) in the food but with only a moderate coefficient of determination (R2) of 0.51 implying that microbial numbers and the composition of the microflora both influenced the degree of inhibition of L. monocytogenes. In HFB and ONE Broth the relationship between APC and final L. monocytogenes counts was weaker. The microflora of TSB after 24 h enrichment of minced beef consisted of lactic acid bacteria, Brochothrix thermosphacta, Pseudomonas spp., Enterobacteriaceae, and enterococci. In co-culture studies of L. monocytogenes with different components of the microflora in TSB, the lactic acid bacteria were the most inhibitory followed by the Enterobacteriaceae. The least inhibitory organisms were Pseudomonas sp., enterococci and B. thermosphacta. In HFB and ONE Broth the growth of Gram-negative organisms was inhibited but lactic acid bacteria still reached high numbers after 24 h. A more detailed study of the growth of low numbers of L. monocytogenes during enrichment of minced beef in TSB revealed that growth of L. monocytogenes ceased at a cell concentration of about 102 cfu/ml when lactic acid bacteria entered stationary phase. However in ONE Broth growth of lactic acid bacteria was slower than in TSB with a longer lag time allowing L. monocytogenes to achieve much higher numbers before lactic acid bacteria reached stationary phase. This work has identified the relative inhibitory effects of different components of a natural food microflora and shown that the ability of low numbers of L. monocytogenes to achieve high cell concentrations is highly dependent on the extent to which enrichment media are able to inhibit or delay growth of the more effective competitors.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Large is fast, small is tight: determinants of speed and affinity in subunit capture by a periplasmic chaperone

The chaperone/usher pathway assembles surface virulence organelles of Gram-negative bacteria, consisting of fibers of linearly polymerized protein subunits. Fiber subunits are connected through 'donor strand complementation': each subunit completes the immunoglobulin (Ig)-like fold of the neighboring subunit by donating the seventh β-strand in trans. Whereas the folding of Ig domains is a fast first-order process, folding of Ig modules into the fiber conformation is a slow second-order process. Periplasmic chaperones separate this process in two parts by forming transient complexes with subunits. Interactions between chaperones and subunits are also based on the principle of donor strand complementation. In this study, we have performed mutagenesis of the binding motifs of the Caf1M chaperone and Caf1 capsular subunit from Yersinia pestis and analyzed the effect of the mutations on the structure, stability, and kinetics of Caf1M-Caf1 and Caf1-Caf1 interactions. The results suggest that a large hydrophobic effect combined with extensive main-chain hydrogen bonding enables Caf1M to rapidly bind an early folding intermediate of Caf1 and direct its partial folding. The switch from the Caf1M-Caf1 contact to the less hydrophobic, but considerably tighter and less dynamic Caf1-Caf1 contact occurs via the zip-out-zip-in donor strand exchange pathway with pocket 5 acting as the initiation site. Based on these findings, Caf1M was engineered to bind Caf1 faster, tighter, or both faster and tighter. To our knowledge, this is the first successful attempt to rationally design an assembly chaperone with improved chaperone function.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Synthesis and biological analysis of novel glycoside derivatives of L-AEP, as targeted antibacterial agents

To develop targeted methods for treating bacterial infections, the feasibility of using glycoside derivatives of the antibacterial compound L-R-aminoethylphosphonic acid (L-AEP) has been investigated. These derivatives are hypothesized to be taken up by bacterial cells via carbohydrate uptake mechanisms, and then hydrolysed in situ by bacterial borne glycosidase enzymes, to selectively afford L-AEP. Therefore the synthesis and analysis of ten glycoside derivatives of L-AEP, for selective targeting of specific bacteria, is reported. The ability of these derivatives to inhibit the growth of a panel of Gram-negative bacteria in two different media is discussed. β-Glycosides (12a) and (12b) that contained L-AEP linked to glucose or galactose via a carbamate linkage inhibited growth of a range of organisms with the best MICs being <0.75 mg/ml; for most species the inhibition was closely related to the hydrolysis of the equivalent chromogenic glycosides. This suggests that for (12a) and (12b), release of L-AEP was indeed dependent upon the presence of the respective glycosidase enzyme.

Caf1A usher possesses a Caf1 subunit-like domain that is crucial for Caf1 fibre secretion

The chaperone/usher pathway controls assembly of fibres of adhesive organelles of Gram-negative bacteria. The final steps of fibre assembly and fibre translocation to the cell surface are co-ordinated by the outer membrane proteins, ushers. Ushers consist of several soluble periplasmic domains and a single transmembrane beta-barrel. Here we report isolation and structural/functional characterization of a novel middle domain of the Caf1A usher from Yersinia pestis. The isolated UMD (usher middle domain) is a highly soluble monomeric protein capable of autonomous folding. A 2.8 angstrom (1 angstrom = 0.1 nm) resolution crystal structure of UMD revealed that this domain has an immunoglobulin-like fold similar to that of donor-strand-complemented Caf1 fibre subunit. Moreover, these proteins displayed significant structural similarity. Although UMD is in the middle of the predicted amphipathic beta-barrel of Caf1A, the usher still assembled in the membrane in the absence of this domain. UMD did not bind Caf1M-Caf1 complexes, but its presence was shown to be essential for Caf1 fibre secretion. The study suggests that UMD may play the role of a subunit-substituting protein (dummy subunit), plugging or priming secretion through the channel in the Caf1A usher. Comparison of isolated UMD with the recent strcture of the corresponding domain of PapC usher revealed high similarity of the core structures, suggesting a universal structural adaptation of FGL (F(1)G(1) long) and FGS (F(1)G(1) short) chaperone/usher pathways for the secretion of different types of fibres. The functional role of two topologically different states of this plug domain suggested by structural and biochemical results is discussed.

Corynebacterium suicordis sp. nov., from pigs

Nineteen strains of Gram-positive, non-motile, non-spore-forming, catalase-positive, rod-shaped bacteria isolated from pigs were characterized by using biochemical, molecular chemical and molecular genetic methods. Two distinct groups of organisms were discerned, based on their colonial morphology, CAMP (Christie-Atkins-Munch-Petersen) reaction and numerical profile by using the API Coryne system. The first group (113 strains) gave a doubtful discrimination between Corynebacterium striatum and Corynebacterium amycolatum, whilst the second group (six strains) were identified tentatively as Corynebacterium urealyticum. Comparative 16S rRNA gene sequencing studies demonstrated that all of the isolates belonged phylogenetically to the genus Corynebacterium. The first group of organisms was highly similar to Corynebacterium testudinoris with respect to 16S rRNA gene sequences and physiological characteristics, whereas the remaining six isolates formed a hitherto unknown subline within the genus, associated with a small subcluster of species that included Corynebacterium auriscanis and its close relatives. The unknown Corynebacterium sp. was distinguished readily from these and other species of the genus by biochemical tests. Based on both phenotypic and phylogenetic evidence, it is proposed that the new isolates from pigs should be classified as a novel species, Corynebacterium suicordis sp. nov. The type strain is P81/02(T) (=CECT 5724(T) =CCUG 46963(T)).