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.

Low-density koala (Phascolarctos cinereus) populations in the mulgalands of south-west Queensland. I. Faecal pellet sampling protocol

Koala (Phascolarctos cinereus) populations in eastern Australia are threatened by land clearing for agricultural and urban development. At the same time, conservation efforts are hindered by a dearth of information about inland populations. Faecal deposits offer a source of information that is readily available and easily collected non-invasively. We detail a faecal pellet sampling protocol that was developed for use in a large rangeland biogeographic region. The method samples trees in belt transects, uses a thorough search at the tree base to quickly identify trees with koala pellets under them, then estimates the abundance of faecal pellets under those trees using 1-m(2) quadrats. There was a strong linear relationship between these estimates and a complete enumeration of pellet abundance under the same trees. We evaluated the accuracy of our method in detecting trees where pellets were present by means of a misclassification index that was weighed more heavily for missed trees that had high numbers of pellets under them. This showed acceptable accuracy in all landforms except riverine, where some trees with large numbers of pellets were missed. Here, accuracy in detecting pellet presence was improved by sampling with quadrats, rather than basal searches. Finally, we developed a method to reliably age pellets and demonstrate how this protocol could be used with the faecal-standing-crop method to derive a regional estimate of absolute koala abundance.

Transformation processes, pathways, and possible sources of distinctive polychlorinated dibenzo-p-dioxin signatures in sink environments

In recent years, studies on environmental samples with unusual dibenzo-p-dioxin (PCDD) congener profiles were reported from a range of countries. These profiles, characterized by a dominance of octachlorinated dibenzodioxin (OCDD) and relatively low in dibenzofuran (PCDF) concentrations, could not be attributed to known sources or formation processes. In the present study, the processes that result in these unusual profiles were assessed using the concentrations and isomer signatures of PCDDs from dated estuarine sediment cores in Queensland, Australia. Increases in relative concentrations of lower chlorinated PODS and a relative decrease of OCDD were correlated with time of sediment deposition. Preferred lateral, anaerobic dechlorination of OCDD represents a likely pathway for these changes. In Queensland sediments, these transformations result in a distinct dominance of isomers fully chlorinated in the 1,4,6,9-positions (1,4-patterns), and similar 1,4-patterns were observed in sediments from elsewhere. Consequently, these environmental samples may not reflect the signatures of the original source, and a reevaluation of source inputs was undertaken. Natural formation of PCDDs, which has previously been suggested, is discussed; however, based on the present results and literature comparisons, we propose an alternative scenario. This scenario hypothesizes that an anthropogenic PCDD precursor input (e.g. pentachlorophenol) results in the contamination. These results and hypothesis imply further investigations are warrented into possible anthropogenic sources in areas where natural PCDD formation has been suggested.

Genetic algorithm based distance spectrum technique for performance union bound of space-time trellis coded OFDM

This paper derives the performance union bound of space-time trellis codes in orthogonal frequency division multiplexing system (STTC-OFDM) over quasi-static frequency selective fading channels based on the distance spectrum technique. The distance spectrum is the enumeration of the codeword difference measures and their multiplicities by exhausted searching through all the possible error event paths. Exhaustive search approach can be used for low memory order STTC with small frame size. However with moderate memory order STTC and moderate frame size the computational cost of exhaustive search increases exponentially, and may become impractical for high memory order STTCs. This requires advanced computational techniques such as Genetic Algorithms (GAS). In this paper, a GA with sharing function method is used to locate the multiple solutions of the distance spectrum for high memory order STTCs. Simulation evaluates the performance union bound and the complexity comparison of non-GA aided and GA aided distance spectrum techniques. It shows that the union bound give a close performance measure at high signal-to-noise ratio (SNR). It also shows that GA sharing function method based distance spectrum technique requires much less computational time as compared with exhaustive search approach but with satisfactory accuracy.

Structure determination of the three disulfide bond isomers of alpha-conotoxin GI: A model for the role of disulfide bonds in structural stability

The three possible disulfide bonded isomers of alpha-conotoxin GI have been selectively synthesised and their structures determined by H-1 NMR spectroscopy. alpha-Conotoxin GI derives from the venom of Conus geographus and is a useful neuropharmacological tool as it selectively binds to the nicotinic acetylcholine receptor (nAChR), a ligand-gated ion channel involved in nerve signal transmission. The peptide has the sequence ECCNPACGRHYSC-NH2, and the three disulfide bonded isomers are referred to as GI(2-7;3-13), GI(2-13;3-7) and GI(2-3;7-13). The NMR structure for the native isomer GI(2-7;3-13) is of excellent quality, with a backbone pairwise RMSD of 0.16 Angstrom for a family of 35 structures, and comprises primarily a distorted 3(10),, helix between residues 5 to 11. The two non-native isomers exhibit multiple conformers in solution, with the major populated forms being different in structure both from each other and from the native form. Structure-activity relationships for the native GI(2-7;3-13) as well as the role of the disulfide bonds on folding and stability of the three isomers are examined. It is concluded that the disulfide bonds in alpha-conotoxin GI play a crucial part in determining both the structure and stability of the peptide. A trend for increased conformational heterogeneity was observed in the order of GI(2-7;3-13) < GI(2-13;3-7) < GI(2-3;7-13). It was found that the peptide bond joining Cys2 to Cys3 in GI(2-3;7-13) is predominantly trans, rather than cis as theoretically predicted. These structural data are used to interpret the varying nAChR binding of the non-native forms. A model for the binding of native GI(2-7;3-13) to the mammalian nAChR is proposed, with an alpha-subunit binding face made up of Cys2, Asn4, Pro5, Ala6 and Cys7 and a selectivity face, comprised of Arg9 and His10. These two faces orient the molecule between the alpha and delta subunits of the receptor. The structure of the CCNPAC sequence of the native GI(2-7;3-13) is compared to the structure of the identical sequence from the toxic domain of heat-stable enterotoxins, which forms part of the receptor binding region of the enterotoxins, but which has a different disulfide connectivity. (C) 1998 Academic Press Limited.

Equilibrating isomers: Bromoindoles and a seco-xanthine encountered during a study of nematocides from the southern Australian marine sponge Hymeniacidon sp.

Bioassay-directed fractionation of a Hymeniacidon sp. yielded as nematocidal agents the equilibrating E/Z bromoindole ethyl esters 1 and 2 and corresponding methyl esters 3 and 4. Also isolated for the first time as a natural product was an equilibrating mixture of seco-xanthine formamides, attributed the trivial name hymeniacidin (5). The structure for 5 was assigned on the basis of detailed spectroscopic analysis and total synthesis.

Disposition of naproxen, naproxen acyl glucuronide and its rearrangement isomers in the isolated perfused rat liver

1. An isolated perfused rat liver (IPRL) preparation was used to investigate separately the disposition of the non-steroidal anti-inflammatory drug (NSAID) naproxen (NAP), its reactive acyl glucuronide metabolite (NAG) and a mixture of NAG rearrangement isomers (isoNAG), each at 30 mug NAP equivalents ml(-1) perfusate (n = 4 each group). 2. Following administration to the IPRL, NAP was eliminated slowly in a log-linear manner with an apparent elimination half-life (t(1/2)) of 13.4 +/-4.4 h. No metabolites were detected in perfusate, while NAG was the only metabolite present in bile in measurable amounts (3.9 +/-0.8%, of the dose). Following their administration to the IPRL, both NAG and isoNAG were rapidly hydrolysed (t(1/2) in perfusate=57 +/-3 and 75 +/- 14min respectively). NAG also rearranged to isoNAG in the perfusate. Both NAG and isoNAG were excreted intact in bile (24.6 and 14.8% of the NAG and isoNAG doses, respectively). 3. Covalent NAP-protein adducts in the liver increased as the dose changed from NAP to NAG to isoNAG (0.20 to 0.34 to 0.48% of the doses, respectively). Similarly, formation of covalent NAP-protein adducts in perfusate were greater in isoNAG-dosed perfusions. The comparative results Suggest that isoNAG is a better substrate for adduct formation with liver proteins than NAG.

Rearrangement of diflunisal acyl glucuronide into its beta-glucuronidase-resistant isomers facilitates transport through the small intestine to the colon of the rat

Many non-steroidal anti-inflammatory drugs (NSAIDs) which form acyl glucuronide conjugates as major metabolites have shown an antiproliferative effect on colorectal tumors. This study assesses the extent to which rearrangement of an acyl glucuronide metabolite of a model NSAID into beta -glucuronidase-resistant isomers facilitates its passage through the small intestine to reach the colon. Rats were dosed orally with diflunisal (DF), its acyl glucuronide (DAG) and a mixture of rearrangement isomers (iso-DAG) at 10 mg DF equivalents/kg. The parent drug DF appeared in plasma after all doses, with maximum concentrations of 20.5 +/- 2.5, 28.8 +/- 8.3 and 11.0 +/- 1.6 mug DF/ml respectively, obtained at 3.8 +/- 0.3, 3.6 +/- 1.8 and 7.5 +/- 0.9 hr after the DF, DAG and iso-DAG doses respectively. At 48 hr, 16.2 +/- 3.3, 19.8 +/- 0.8 and 42.9 +/- 10.1% of the doses respectively were recovered in feces, with less than or equal to 1% remaining in the intestine. About half of each dose was recovered as DF and metabolites in 48 hr urine: for DF and DAG doses, the majority was in the first 24 hr urine. whereas for iso-DAG doses, recoveries in the first and second 24 hr periods were similar. The results show that hydrolysis of both DAG and iso-DAG, and absorption of liberated DF, occur during passage through the gut, but that these processes occur more slowly and to a lesser degree for iso-DAG. The intrinsic hydrolytic capacities of various intestinal segments (including contents) towards DAG and iso-DAG were obtained by incubating homogenates under saturating concentrations of DAG/iso-DAG at 37 degreesC. Upper small intestine, lower small intestine, caecum and colon released 2400, 3200, 9200 and 22800 mug DF/hr/g tissue plus contents respectively from DAG substrate, and 18, 10, 140 and 120 mug DF/hr/g tissue plus contents respectively from iso-DAG substrate. The much greater resistance of iso-DAG to hydrolysis appears attributable to its resistance to beta -glucuronidases. The data suggest that in rats dosed with DF, DAG excreted in bile would be substantially hydrolysed in the small intestine and liberated DF reabsorbed, but that portion which rearranges to iso-DAG would likely reach the colon. (C) 2001 Elsevier Science Inc. All rights reserved.

Solution Structures of the cis- and trans-Pro30 Isomers of a Novel 38-Residue Toxin from the Venom of Hadronyche Infensa sp. that Contains a Cystine-Knot Motif within Its Four Disulfide Bonds

The primary sequence and three-dimensional structure of a novel peptide toxin isolated from the Australian funnel-web spider Hadronyche infensa sp. is reported. ACTX-HI:OB4219 contains 38 amino acids, including eight-cysteine residues that form four disulfide bonds. The connectivities of these disulfide bonds were previously unknown but have been unambiguously determined in this study. Three of these disulfide bonds are arranged in an inhibitor cystine-knot (ICK) motif, which is observed in a range of other disulfide-rich peptide toxins. The motif incorporates an embedded ring in the structure formed by two of the disulfides and their connecting backbone segments penetrated by a third disulfide bond. Using NMR spectroscopy, we determined that despite the isolation of a single native homologous product by RP-HPLC, ACTX-HI:OB4219 possesses two equally populated conformers in solution. These two conformers were determined to arise from cis/trans isomerization of the bond preceding Pro30. Full assignment of the NMR spectra for both conformers allowed for the calculation of their structures, revealing, the presence of a triple-stranded antiparallel sheet consistent with the inhibitor cystine-knot (ICK) motif.

Geometric isomers of chloro(6-methyl-1,4,8,11-tetraazacyclotetradecane-6-amine)cobalt(III) tetrachlorozincate(II)

The crystal structures of a pair of cis and trans isomers of the macrocyclic chloropentaamine title complex, as their tetrachlorozincate(II) salts, [CoCl(C11H27N5)][ZnCl4], are reported. The two distinct isomeric forms lead to significant variations in the Co-N bond lengths and, furthermore, hydrogen bonding between the complex ions is influenced by the folded (cis) or planar (trans) conformations of the coordinated ligand.

Isomers of 1,4,8,11-tetraazacyclotetradecane-6,13-dicarboxylate characterized as cobalt(III) complexes

The major trans (1) and minor cis (2) isomers of 1,4,8,11-tetraazacyclotetradecane-6,13-dicarboxylate have been characterized as the complexes [Co(1)](ClO4) and [Co(H-2)(OH2)]Cl(ClO4).H2O. The former crystallized in the C-2/c space group and the latter in the P2(1)/c space group, with cell parameters a 16.258(7), b 9.050(3), c 15.413(6) Angstrom, beta133.29(3)degrees, and a 9.694(4), b 16.135(1), c 12.973(5) Angstrom, beta 93.00(2)degrees, respectively. Their characterization completes identification of the respective trans and cis isomers for the series of C-pendant macrocycles also including 1,4,8,11-tetraazacyclotetradecane-6-amine-13-carboxylate ((3), (4)) and 1,4,8,11-tetraazacyclotetradecane-6,13-diamine ((5), (6)). The complexes show limited distortion from octahedral geometry with the strain in the presence of the coordinated C-pendant carboxylate significantly reduced compared with that for the C-pendant amine in analogues, a consequence mainly of six-membered as opposed to five-membered chelate rings involving the pendant donor. A comparison of the physical properties for the trans isomers of the octahedral complexes of (1), (3), and (5), which reflect progressively increasing strain, is presented.

Disposition kinetics of propranolol isomers in the perfused rat liver

The aim of this study was to define the determinants of the linear hepatic disposition kinetics of propranolol optical isomers using a perfused rat liver. Monensin was used to abolish the lysosomal proton gradient to allow an estimation of propranolol ion trapping by hepatic acidic vesicles. In vitro studies were used for independent estimates of microsomal binding and intrinsic clearance. Hepatic extraction and mean transit time were determined from outflow-concentration profiles using a nonparametric method. Kinetic parameters were derived from a physiologically based pharmacokinetic model. Modeling showed an approximate 34-fold decrease in ion trapping following monensin treatment. The observed model-derived ion trapping was similar to estimated theoretical values. No differences in ion-trapping values was found between R(+)- and S(-)- propranolol. Hepatic propranolol extraction was sensitive to changes in liver perfusate flow, permeability-surface area product, and intrinsic clearance. Ion trapping, microsomal and nonspecific binding, and distribution of unbound propranolol accounted for 47.4, 47.1, and 5.5% of the sequestration of propranolol in the liver, respectively. It is concluded that the physiologically more active S(-)- propranolol differs from the R(+)- isomer in higher permeability-surface area product, intrinsic clearance, and intracellular binding site values.