Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

New calibration technique for multiple-component stress wave force balances

Force measurement in hypervelocity expansion tubes is not possible using conventional techniques. The stress wave force balance technique can be applied in expansion tubes to measure forces despite the short test times involved. This paper presents a new calibration technique for multiple-component stress wave force balances where an impulse response created using a load distribution is required and no orthogonal surfaces on the model exist.. This new technique relies on the tensorial superposition of single-component impulse responses analogous to the vectorial superposition of the calibration loads. The example presented here is that of a scale model of the Mars Pathfinder, but the technique is applicable to any geometry and may be useful for cases where orthogonal loads cannot be applied.

Solution structure of methionine-oxidized amyloid beta-peptide (1-40). Does oxidation affect conformational switching?

The solution structure of A beta(1-40)Met(O), the methionine-oxidized form of amyloid beta-peptide A beta(1-40), has been investigated by CD and NMR spectroscopy. Oxidation of Met35 may have implications in the aetiology of Alzheimer's disease. Circular dichroism experiments showed that whereas A beta(1-40) and A beta(1-40)Met(O) both adopt essentially random coil structures in water (pH 4) at micromolar concentrations, the former aggregates within several days while the latter is stable for at least 7 days under these conditions. This remarkable difference led us to determine the solution structure of A beta(1-40)Met(O) using H-1 NMR spectroscopy. In a water-SDS micelle medium needed to solubilize both peptides at the millimolar concentrations required to measure NMR spectra, chemical shift and NOE data for A beta(1-40)Met(O) strongly suggest the presence of a helical region between residues 16 and 24. This is supported by slow H-D exchange of amide protons in this region and by structure calculations using simulated annealing with the program XPLOR. The remainder of the structure is relatively disordered. Our previously reported NMR data for A beta(1-40) in the same solvent shows that helices are present over residues 15-24 (helix 1) and 28-36 (helix 2), Oxidation of Met35 thus causes a local and selective disruption of helix 2. In addition to this helix-coil rearrangement in aqueous micelles, the CD data show that oxidation inhibits a coil-to-beta-sheet transition in water. These significant structural rearrangements in the C-terminal region of A beta may be important clues to the chemistry and biology of A beta(1-40) and A beta(1-42).

Epidermal iontophoresis: I. Development of the ionic mobility-pore model

Purpose, An integrated ionic mobility-pore model for epidermal iontophoresis is developed from theoretical considerations using both the free volume and pore restriction forms of the model for a range of solute radii (r(j)) approaching the pore radii (r(p)) as well as approximation of the pore restriction form for r(j)/r(p) < 0.4. In this model, we defined the determinants for iontophoresis as solute size (defined by MV, MW or radius), solute mobility, solute shape, solute charge, the Debye layer thickness, total current applied, solute concentration, fraction ionized, presence of extraneous ions (defined by solvent conductivity), epidermal permselectivity, partitioning rates to account for interaction of unionized and ionized lipophilic solutes with the wall of the pore and electroosmosis. Methods, The ionic mobility-pore model was developed from theoretical considerations to include each of the determinants of iontophoretic transport. The model was then used to reexamine iontophoretic flux conductivity and iontophoretic flux-fraction ionized literature data on the determinants of iontophoretic flux. Results. The ionic mobility-pore model was found to be consistent with existing experimental data and determinants defining iontophoretic transport. However, the predicted effects of solute size on iontophoresis are more consistent with the pore-restriction than free volume form of the model. A reanalysis of iontophoretic flux-conductivity data confirmed the model's prediction that, in the absence of significant electroosmosis, the reciprocal of flux is linearly related to either donor or receptor solution conductivity. Significant interaction with the pore walls, as described by the model, accounted for the reported pH dependence of the iontophoretic transport for a range of ionizable solutes. Conclusions. The ionic mobility-pore iontophoretic model developed enables a range of determinants of iontophoresis to be described in a single unifying equation which recognises a range of determinants of iontophoretic flux.

Three-dimensional solution structure of alpha-conotoxin MII by NMR spectroscopy: Effects of solution environment on helicity

alpha-Conotoxin MII, a 16-residue polypeptide from the venom of the piscivorous cone snail Conus magus, is a potent and highly specific blocker of mammalian neuronal nicotinic acetylcholine receptors composed of alpha 3 beta 2 subunits. The role of this receptor type in the modulation of neurotransmitter release and its relevance to the problems of addiction and psychosis emphasize the importance of a structural understanding of the mode of interaction of MII with the alpha 3 beta 2 interface. Here we describe the three-dimensional solution structure of MIT determined using 2D H-1 NMR spectroscopy. Structural restraints consisting of 376 interproton distances inferred from NOEs and 12 dihedral restraints derived from spin-spin coupling constants were used as input for simulated annealing calculations and energy minimization in the program X-PLOR. The final set of 20 structures is exceptionally well-defined with mean pairwise rms differences over the whole molecule of 0.07 Angstrom for the backbone atoms and 0.34 Angstrom for all heavy atoms. MII adopts a compact structure incorporating a central segment of alpha-helix and beta-turns at the N- and C-termini. The molecule is stabilized by two disulfide bonds, which provide cross-links between the N-terminus and both the middle and C-terminus of the structure. The susceptibility of the structure to conformational change was examined using several different solvent conditions. While the global fold of MII remains the same, the structure is stabilized in a more hydrophobic environment provided by the addition of acetonitrile or trifluoroethanol to the aqueous solution. The distribution of amino acid side chains in MII creates distinct hydrophobic and polar patches on its surface that may be important for the specific interaction with the alpha 3 beta 2 neuronal nAChR. A comparison of the structure of MII with other neuronal-specific alpha-conotoxins provides insights into their mode of interaction with these receptors.

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

In vitro human epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 from a range of solvents

Purpose. To study epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 (BP) from a range of single solvent vehicles and evaluate solvent effects on permeability parameters. Methods. The solubility of BP was measured in a number of solvents. Penetration of BP across human epidermis and high density polyethylene (HDPE) membranes was studied from 50% saturated solutions in each solvent. Results. Maximal BP fluxes from the solvents across the two membranes varied widely. Highest fluxes were observed from 90% ethanol (EtOH) for epidermis and from isopropyl myristate (IPM) and C12-15 benzoate alcohols (C12-15 BA) for HDPE membrane. Both the flux and estimated permeability coefficient and skin-vehicle partitioning of BP appeared to be related to the vehicle solubility parameter (delta(v)). The major effects of solvents on BP flux appear to be via changes in BP diffusivity through the membranes. Conclusions. Minimal penetration of sunscreens such as BP is best achieved by choosing vehicles with a delta(v) substantially different to the solubility parameter of the membrane.

Solution structure of alpha-conotoxin ImI by H-1 nuclear magnetic resonance

alpha-Conotoxin ImI derives from the venom of Conus imperialis and is the first and only small-peptide ligand that selectively binds to the neuronal alpha(7) homopentameric subtype of the nicotinic acetylcholine receptor (nAChR). This receptor subtype is a possible drug target for several neurological disorders. The cysteines are connected in the pairs Cys2-Cys8 and Cys3-Cys12, To date it is the only alpha-conotoxin with a 4/3 residue spacing between the cysteines, The structure of ImI has been determined by H-1 NMR spectroscopy in aqueous solution, The NMR structure is of high quality, with a backbone pairwise rmsd of 0.34 Angstrom for a family of 19 structures, and comprises primarily a series of nested beta turns. Addition of organic solvent does not perturb the solution structure. The first eight residues of ImI are identical to the larger, but related, conotoxin EpI and adopt a similar structure, despite a truncated second loop. Residues important for binding of ImI to the alpha 7 nAChR are all clustered on one face of the molecule. Once further binding data for EPI and ImI are available, the ImI structure will allow for design of novel alpha(7) nAChR-specific agonists and antagonists with a wide range of potential pharmaceutical applications.

Chemical synthesis and folding pathways of large cyclic polypeptide: Studies of the cystine knot polypeptide kalata B1

Kalata B1 is a member of a new family of polypeptides, isolated from. plants, which have a cystine knot structure embedded within an amide-cyclized backbone. This family of molecules are the largest known cyclic peptides, and thus, the mechanism of synthesis and folding is of great interest. To provide information about both these phenomena, we have synthesized kalata B1 using two distinct strategies. In the first, oxidation of the cysteine residues of a linear precursor peptide to form the correct disulfide bonds results in folding of the three-dimensional structure and preorganization of the termini in close proximity for subsequent cyclization. The second approach involved cyclization prior to oxidation. In the first method, the correctly folded peptide was produced only in the presence of partially hydrophobic solvent conditions. These conditions are presumably required to stabilize the surface-exposed hydrophobic residues. However,; in the synthesis,involving cyclization prior to oxidation, the cyclic reduced peptide folded to a significant degree in the absence of hydrophobic solvents and even more efficiently in the presence of hydrophobic solvents. Cyclization clearly has a major effect on the folding pathway and facilitates formation of the correctly disulfide-bonded form in aqueous solution; In addition to facilitating folding to a compact stable structure cyclization has an important effect on biological activity as assessed by hemolytic activity.

NMR studies of the low-density lipoprotein receptor-binding peptide of apolipoprotein E bound to dodecylphosphocholine micelles

Circular dichroism and NMR spectroscopy have been used to determine the structure of the low-density lipoprotein (LDL) receptor-binding peptide, comprising residues 130-152, of the human apolipoprotein E. This peptide has little persistent three-dimensional structure in solution, but when bound to micelles of dodecylphosphocholine (DPC) it adopts a predominantly alpha-helical structure. The three-dimensional structure of the DPC-bound peptide has been determined by using H-1-NMR spectroscopy: the structure derived from NOE-based distance constraints and restrained molecular dynamics is largely helical. The derived phi and psi angle order parameters show that the helical structure is well defined but with some flexibility that causes the structures not to be superimposable over the full peptide length. Deuterium exchange experiments suggest that many peptide amide groups are readily accessible to the solvent, but those associated with hydrophobic residues exchange more slowly, and this helix is thus likely to be positioned on the surface of the DPC micelles. In this conformation the peptide has one hydrophobic face and two that are rich in basic amino acid side chains. The solvent-exposed face of the peptide contains residues previously shown to be involved in binding to the LDL receptor.

Role of chemical cues from cotton in mediating host selection and oviposition behaviour in Helicoverpa armigera (Hubner) (Lepidoptera : Noctuidae)

We investigated the role of chemoreception in the host selection and oviposition behaviour of Helicoverpa armigera in the laboratory using five cotton genotypes and synthetic volatile terpenes. Female moths oviposited on substrates treated with methanol, ethanol, acetone and pentane extracts of leaves, squares and flowers of the cotton genotypes. Phytochemicals soluble in pentane were the most efficient in eliciting oviposition behaviour. In a two-way bioassay, pentane extracts of leaves or squares of a Multiple Host-plant Resistance genotype (MHR11), Deltapine commercial (DP90), and Smith Red Leaf (SRL) received significantly more eggs than solvent-treated controls. Extracts of squares of the native genotype Gossypium nelsonii did not receive more eggs. Females preferred DP90 and MHR11 to SRL and G. nelsonii. Female moths also laid more eggs on pentane extracts of MHR11 flowers than MHR11 leaves from preflowering, early flowering and peak-flowering plants. In a flight chamber, female moths used olfactory cues at short range to mediate oviposition and discrimination between host plants. Egg-laying, mated females were attracted at a distance (1.5 m) to volatile compounds released by whole plants and odours emanating from filter papers treated with synthetic volatile terpenes. Individually, the terpenes did not stimulate any significant oviposition response. However, there was a significant oviposition response to a mixture of equal volumes of the terpenes (trans-beta-caryophyllene, alpha-pinene, beta-pinene, myrcene, beta-bisabolol, and alpha-humulene). Conversely, antennectomised (moths with transected antennae), egg-laying, mated females did not stimulate any significant oviposition response. The significance of these findings in relation to H. armigera hostplant selection are discussed.

Role of phosphorylation in the conformation of tau peptides implicated in Alzheimer's disease

A series of peptides corresponding to isolated regions of Tau (tau) protein have been synthesized and their conformations determined by H-1 NMR spectroscopy. Immunodominant peptides corresponding to tau(224-240) and a bisphosphorylated derivative in which a single Thr and a single Ser are phosphorylated at positions 231 and 235 respectively, and which are recognized by an Alzheimer's disease-specific monoclonal antibody, were the main focus of the study. The nonphosphorylated peptide adopts essentially a random coil conformation in aqueous solution, but becomes slightly more ordered into P-type structure as the hydrophobicity of the solvent is increased by adding up to 50% trifluoroethanol (TFE). Similar trends are observed for the bisphosphorylated peptide, with a somewhat stronger tendency to form an extended structure, There is tentative NMR evidence for a small population of species containing a turn at residues 229-231 in the phosphorylated peptide, and this is strongly supported by CD spectroscopy. A proposal that the selection of a bioactive conformation from a disordered solution ensemble may be an important step (in either tubulin binding or in the formation of PHF) is supported by kinetic data on Pro isomerization. A recent study showed that Thr231 phosphorylation affected the rate of prolyl isomerization and abolished tubulin binding. This binding was restored by the action of the prolyl isomerase Pin1. In the current study, we find evidence for the existence of both trans and cis forms of tau peptides in solution but no difference in the equilibrium distribution of cis-trans isomers upon phosphorylation. Increasing hydrophobicity decreases the prevalence of cis forms and increases the major trans conformation of each of the prolines present in these molecules. We also synthesized mutant peptides containing Tyr substitutions preceding the Pro residues and found that phosphorylation of Tyr appears to have an effect on the equilibrium ratio of cis-trans isomerization and decreases the cis content.

Solution structures in aqueous SDS micelles of two amyloid beta peptides of A beta(1-28) mutated at the alpha-secretase cleavage site (K16E, K16F)

NMR solution structures are reported for two mutants (K16E, K16F) of the soluble amyloid beta peptide A beta(1-28). The structural effects of these mutations of a positively charged residue to anionic and hydrophobic residues at the alpha-secretase cleavage site (Lys16-Leu17) were examined in the membrane-simulating solvent aqueous SDS micelles. Overall the three-dimensional structures were similar to that for the native A beta(1-28) sequence in that they contained an unstructured N-terminus and a helical C-terminus. These structural elements are similar to those seen in the corresponding regions of full-length A beta peptides A beta(1-40) and A beta(1-42), showing that the shorter peptides are valid model systems. The K16E mutation, which might be expected to stabilize the macrodipole of the helix, slightly increased the helix length (residues 13-24) relative to the K16F mutation, which shortened the helix to between residues 16 and 24. The observed sequence-dependent control over conformation in this region provides an insight into possible conformational switching roles of mutations in the amyloid precursor protein from which A beta peptides are derived. In addition, if conformational transitions from helix to random coil to sheet precede aggregation of A beta peptides in vivo, as they do in vitro, the conformation-inducing effects of mutations at Lys16 may also influence aggregation and fibril formation. (C) 2000 Academic Press.