Characterising the background errors for the boundary-layer capping inversion

The one-dimensional variational assimilation of vertical temperature information in the presence of a boundary-layer capping inversion is studied. For an optimal analysis of the vertical temperature profile, an accurate representation of the background error covariances is essential. The background error covariances are highly flow-dependent due to the variability in the presence, structure and height of the boundary-layer capping inversion. Flow-dependent estimates of the background error covariances are shown by studying the spread in an ensemble of forecasts. A forecast of the temperature profile (used as a background state) may have a significant error in the position of the capping inversion with respect to observations. It is shown that the assimilation of observations may weaken the inversion structure in the analysis if only magnitude errors are accounted for as is the case for traditional data assimilation methods used for operational weather prediction. The positional error is treated explicitly here in a new data assimilation scheme to reduce positional error, in addition to the traditional framework to reduce magnitude error. The distribution of the positional error of the background inversion is estimated for use with the new scheme.

Orography in a contour dynamics model of large-scale atmospheric flow

The influence of orography on the structure of stationary planetary Rossby waves is studied in the context of a contour dynamics model of the large-scale atmospheric flow. Orography of infinitesimal and finite amplitude is studied using analytical and numerical techniques. Three different types of orography are considered: idealized orography in the form of a global wave, idealized orography in the form of a local table mountain, and the earth's orography. The study confirms the importance of resonances, both in the infinitesimal orography and in the finite orography cases. With finite orography the stationary waves organize themselves into a one-dimensional set of solutions, which due to the resonances, is piecewise connected. It is pointed out that these stationary waves could be relevant for atmospheric regimes.

Microbial relatives of the seed storage proteins of higher plants: conservation of structure and diversification of function during evolution of the cupin superfamily.

This review summarizes the recent discovery of the cupin superfamily (from the Latin term "cupa," a small barrel) of functionally diverse proteins that initially were limited to several higher plant proteins such as seed storage proteins, germin (an oxalate oxidase), germin-like proteins, and auxin-binding protein. Knowledge of the three-dimensional structure of two vicilins, seed proteins with a characteristic beta-barrel core, led to the identification of a small number of conserved residues and thence to the discovery of several microbial proteins which share these key amino acids. In particular, there is a highly conserved pattern of two histidine-containing motifs with a varied intermotif spacing. This cupin signature is found as a central component of many microbial proteins including certain types of phosphomannose isomerase, polyketide synthase, epimerase, and dioxygenase. In addition, the signature has been identified within the N-terminal effector domain in a subgroup of bacterial AraC transcription factors. As well as these single-domain cupins, this survey has identified other classes of two-domain bicupins including bacterial gentisate 1, 2-dioxygenases and 1-hydroxy-2-naphthoate dioxygenases, fungal oxalate decarboxylases, and legume sucrose-binding proteins. Cupin evolution is discussed from the perspective of the structure-function relationships, using data from the genomes of several prokaryotes, especially Bacillus subtilis. Many of these functions involve aspects of sugar metabolism and cell wall synthesis and are concerned with responses to abiotic stress such as heat, desiccation, or starvation. Particular emphasis is also given to the oxalate-degrading enzymes from microbes, their biological significance, and their value in a range of medical and other applications.

Nuclear magnetic resonance structure shows that the severe acute respiratory syndrome coronavirus-unique domain contains a macrodomain fold

The nuclear magnetic resonance (NMR) structure of a central segment of the previously annotated severe acute respiratory syndrome (SARS)-unique domain (SUD-M, for "middle of the SARS-unique domain") in SARS coronavirus (SARS-CoV) nonstructural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3 residues 528 to 648, and there is a flexibly extended N-terminal tail with the residues 513 to 527 and a C-terminal flexible tail of residues 649 to 651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527 to 651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly(A) and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In a further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1 ''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows three-dimensional structure homology with several helicases and nucleoside triphosphate-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.

From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

NMR structure shows that the SARS-unique domain contains a macrodomain fold

The NMR structure of a central segment of the previously annotated "SARS-unique domain" (SUD-M; "middle of the SARS-unique domain") in the SARS coronavirus (SARS-CoV) non-structural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3-residues 528-648, and there is a flexibly extended N-terminal tail with the residues 513-527 and a C-terminal flexible tail of residues 649-651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527-651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly-A and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows 3D structure homology with several helicases and NTP-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.

Zinc(II) mediated synthesis of an N-substituted 2-(2-pyridyl)imidazole from a 1,2-diketone and 2-(aminomethyl)pyridine and its ligational behaviour

Reaction of anhydrous ZnCl2 with the 1:2 condensate (L) of benzil and 2-(aminomethyl)pyridine in methanol gives monomeric ZnL'Cl-2 (1) where L' is 2-[(4,5-diphenyl-2-pyridin-2-yl-1H-imidazol-1-yl)-methyl]pyridine. In the X-ray crystal structure, 1 is found to contain tetrahedral zinc with an N2Cl2 coordination sphere and the N-substituent methylpyridine fragment hanging as a free arm. A tentative mechanism is proposed for the zinc mediated conversion of L-->L'. Demetallation of 1 by the action of aqueous NaOH yields L' in the free state. When L' is reacted with Zn(ClO4)(2).6H(2)O in a 1:2 molar proportion, [Zn(L')(2)](n)(ClO4)(2n).(H2O)(n/2).(CH2Cl2)(n/2) (2) is obtained. The zinc atom in 2, as revealed by X-ray crystallography, has a trigonal bipyramidal N-5 coordination sphere. There are two independent ligands in the asymmetric unit of 2. One of them bonds only to one zinc atom in a bidentate mode with the N-substituent methylpyridine hanging free while the other ligand binds to two different zinc atoms in a tridentate fashion, employing the N-substituent methylpyridine nitrogen atom to form the polymeric one-dimensional chain cation.

Novel charge transfer supramolecular assemblies with Keggin anions and 2-amino-5-nitropyridine

Several novel compounds with the non-linear optical chromophore 2-amino-5-nitropyridine (2A5NP) and Keggin polyoxoanions (alpha-isomers), having the general formula (2A5NP)(m)H-n[XM12O40]center dot xH(2)O, M = Mo, W, were synthesised. Compounds were obtained with X = P, n = 3, m = 3 and 4 and X = Si, n = m = 4 ( x = 2 - 6). Thus, for each of the anions [PMo12O40](3-) and [PW12O40](3-) two different compounds were obtained, with the same anion and organic counterpart but with a different stoichiometric ratio. These presented different charge transfer properties and thermal stability. All compounds were characterised by spectroscopic and analytical techniques. The single crystal X-ray diffraction structure of (2A5NP)(4)H-3[PMo12O40]center dot 2.5H(2)O center dot 0.5C(2)H(5)OH showed that the water solvent molecules and the organic chromophores are assembled via infinite one-dimensional chains of hydrogen bonds with formation of open channels, which accommodate [ PMo12O40] 3- and ethanol solvent molecules.

Syntheses, structural analyses, and magneto-structural correlations of three polymeric Fe(II) complexes with azide ligand

Three new metal-organic polymeric complexes, [Fe(N-3)(2)(bPP)(2)] (1), [Fe(N-3)(2)(bpe)] (2), and [Fe(N-3)(2)(phen)] (3) [bpp = (1,3-bis(4-pyridyl)-propane), bpe = (1,2-bis(4-pyridyl)-ethane), phen = 1,10-phenanthroline], have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature magnetic measurements in the range 300-2 K. Complexes 1 and 2 crystallize in the monoclinic system, space group C2/c, with the following cell parameters: a = 19.355(4) Angstrom, b = 7.076(2) Angstrom, c = 22.549(4) Angstrom, beta = 119.50(3)degrees, Z = 4, and a = 10.007(14) Angstrom, b = 13.789(18) Angstrom, c = 10.377(14) Angstrom, beta = 103.50(1)degrees, Z = 4, respectively. Complex 3 crystallizes in the triclinic system, space group P (1) over bar, with a = 7.155(12) Angstrom, b = 10.066(14) Angstrom, c = 10.508(14) Angstrom, alpha = 109.57(1)degrees, beta = 104.57(1)degrees, gamma = 105.10(1)degrees, and Z = 2. All coordination polymers exhibit octahedral Fe(II) nodes. The structural determination of 1 reveals a parallel interpenetrated structure of 2D layers of (4,4) topology, formed by Fe(II) nodes linked through bpp ligands, while mono-coordinated azide anions are pendant from the corrugated sheet. Complex 2 has a 2D arrangement constructed through 1D double end-to-end azide bridged iron(11) chains interconnected through bpe ligands. Complex 3 shows a polymeric arrangement where the metal ions are interlinked through pairs of end-on and end-to-end azide ligands exhibiting a zigzag arrangement of metals (Fe-Fe-Fe angle of 111.18degrees) and an intermetallic separation of 3.347 Angstrom (through the EO azide) and of 5.229 Angstrom (EE azide). Variable-temperature magnetic susceptibility data suggest that there is no magnetic interaction between the metal centers in 1, whereas in 2 there is an antiferromagnetic interaction through the end-to-end azide bridge. Complex 3 shows ferro- as well as anti-ferromagnetic interactions between the metal centers generated through the alternating end-on and end-to-end azide bridges. Complex I has been modeled using the D parameter (considering distorted octahedral Fe(II) geometry and with any possible J value equal to zero) and complex 2 has been modeled as a one-dimensional system with classical and/or quantum spin where we have used two possible full diagonalization processes: without and with the D parameter, considering the important distortions of the Fe(II) ions. For complex 3, the alternating coupling model impedes a mathematical solution for the modeling as classical spins. With quantum spin, the modeling has been made as in 2.

Two new mu-(1,3-azido)-bridged polymers: alternating single and double bridges in a 1D nickel(II) complex and uniform bridge in a 2D copper(II) complex: Syntheses, single-crystal structures and magnetic studies

Two polymeric azido bridged complexes [Ni2L2(N-3)(3)](n)(ClO4). (1) and [Cu(bpdS)(2)(N-3)],(ClO4),(H2O)(2.5n) (2) [L = Schiff base, obtained from the condensation of pyridine-2-aldehyde with N,N,2,2-tetramethyl-1,3-propanediamine; bpds = 4,4'-bipyridyl disulfide] have been synthesized and their crystal structures have been determined. Complex 1, C26H42ClN15Ni2O4, crystallizes in a triclinic system, space group P1 with a 8.089(13), b = 9.392(14), c = 12.267(18) angstrom, a = 107.28(l), b 95.95(1), gamma = 96.92(1)degrees and Z = 2; complex 2, C20H21ClCuN7O6.5S4, crystallizes in an orthorhombic system, space group Pnna with a = 10.839(14), b = 13.208(17), c = 19.75(2) angstrom and Z = 4. The crystal structure of I consists of 1D polymers of nickel(L) units, alternatively connected by single and double bridging mu-(1,3-N-3) ligand with isolated perchlorate anions. Variable temperature magnetic susceptibility data of the complex have been measured and the fitting,of magnetic data was carried out applying the Borris-Almenar formula for such types of alternating one-dimensional S = 1 systems, based on the Hamiltonian H = -J Sigma(S2iS2i-1 + aS(2i)S(2i+1)). The best-fit parameters obtained are J = -106.7 +/- 2 cm(-1); a = 0.82 +/- 0.02; g = 2.21 +/- 0.02. Complex 2 is a 2D network of 4,4 topology with the nodes occupied by the Cu-II ions, and the edges formed by single azide and double bpds connectors. The perchlorate anions are located between pairs of bpds. The magnetic data have been fitted considering the complex as a pseudo-one-dimensional system, with all copper((II)) atoms linked by [mu(1,3-azido) bridging ligands at axial positions (long Cu...N-3 distances) since the coupling through long bpds is almost nil. The best-fit parameters obtained with this model are J = -1.21 +/- 0.2 cm(-1), g 2.14 +/- 0.02. (c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005).

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcal/mol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively. (C) 2008 American Institute of Physics.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

The power of NMR.: in two and three dimensions

Soon after its discovery in the 1950s, NMR had become an indispensable tool fr chemists. In the 1970s and 1980s, the power of the technique was extended from one dimension to two and even three dimensions, opening up exciting applkications in both chemistry and biochemistry. the success of one dimensional. high-resolution NMR stems from the unique insights that it can provide about molecular structure. The chemical shift of a nucleus gives invaluable information abut the chemical environment in which that nucleus is located, Coupling interactions between hydorgen nuclei, as revealed by characteristic splitting patterns inthe 1H-NMR spectrum, provide informaton about the loaction of one group of hydorgen atoms relative to others inthe molecule. And the nuclearf Overhauser effect (nOe) can shed light on molecular stereochemistry.

Use of a reduced Schiff-Base ligand to prepare novel chloro-bridged chains of rare Cu(II) trinuclear complexes with mixed azido/oxo and chloro/oxo bridges

Two mixed bridged one-dimensional (1D) polynuclear complexes, [Cu3L2(mu(1,1)-N-3)(2)(mu-Cl)Cl](n) (1) and {[Cu3L2(mu-Cl)(3)Cl]center dot 0.46CH(3)OH}(n), (2), have been synthesized using the tridentate reduced Schiff-base ligand HL (2-[(2-dimethylamino-ethylamino)-methyl]-phenol). The complexes have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. In both complexes the basic trinuclear angular units are joined together by weak chloro bridges to form a 1D chain. The trinuclear structure of 1 is composed of two terminal square planar [Cu(L)(mu(1,1)-N-3)] units connected by a central Cu(II) atom through bridging nitrogen atoms of end-on azido ligands and the phenoxo oxygen atom of the tridentate ligand. These four coordinating atoms along with a chloride ion form a distorted trigonal bipyramidal geometry around the central Cu(II). The structure of 2 is similar; the only difference being a Cl bridge replacing the mu(1,1)-N-3 bridge in the trinuclear unit. The magnetic properties of both trinuclear complexes can be very well reproduced with a simple linear symmetrical trimer model (H = JS(i)S(i+1)) with only one intracluster exchange coupling (J) including a weak intertrimer interaction (.j) reproduced with the molecular field approximation. This model provides very satisfactory fits for both complexes in the whole temperature range with the following parameters: g = 2.136(3), J = 93.9(3) cm(-1) and zj= -0.90(3) cm(-1) (z = 2) for 1 and g = 2.073(7), J = -44.9(4) cm(-1) and zJ = -1.26(6) cm(-1) (z = 2) for 2.

A unique example of structural and magnetic diversity in four interconvertible copper(II)−azide complexes with the same Schiff base ligand: a monomer, a dimer, a chain, and a layer

Four new Cu(II)-azido complexes of formula [CuL(N-3)] (1), [CuL(N-3)](2) (2), [Cu7L2(N-3)(12)](n) (3), and [Cu2L(dmen)-(N-3)(3)](n) (4) (dmen = N,N-dimethylethylenediamine) have been synthesized using the same tridentate Schiff base ligand HL (2-[1-(2-dimethylaminoethylimino)ethyl]phenol, the condensation product of dmen and 2-hydroxyacetophenone). The four compounds have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. Complex 1 is mononuclear, whereas 2 is a single mu-1,1 azido-bridged dinuclear compound. The polymeric compound 3 possesses a 2D structure in which the Cu(II) ions are linked by phenoxo oxygen atoms and two different azide bridges (mu-1,1 and mu-1,1,3). The structure of complex 4 is a double helix in which two mu-1,3-azido-bridged alternating one-dimensional helical chains of CuL(N-3) and Cu(dmen)(N-3)(2) are joined together by weak mu-1,1 azido bridges and H-bonds. The complexes interconvert in solution and can be obtained in pure form by carefully controlling the conditions. The magnetic properties of compounds 1 and 2 show the presence of very weak antiferromagnetic exchange interactions mediated by a ligand pi overlap (J = -1.77) and by an asymmetric 1,1-N-3 bridge (J = -1.97 cm(-1)), respectively. Compound 3 presents, from the magnetic point of view, a decorated chain structure with both ferro- and antiferromagnetic interactions. Compound 4 is an alternating helicoidal chain with two weak antiferromagnetic exchange interactions (J -1.35 and -2.64 cm(-1)).