Metabolites of bird's nest fungi-19 : New triterpenoid carboxylic acids from cyathus striatus and cyathus pygmaeus

The bird's nest fungus Cyathus striatus Willd. ex, Pers. yielded the known triterpenes glochidone (1), glochidonol (2), glochidiol (3) and glochidiol diacetate (4) as well as four new triterpenoic acids, cyathic acid (5), striatic acid (6), cyathadonic acid (7) and epistriatic acid (8). Another species, Cyathus pygmaeus Lloyd, contained cyathic acid (5) and an additional new compound, pygmaeic acid (9). The structural assignments are based on spectroscopic data and chemical correlations.     

alpha-L-ribo-configured locked nucleic acid (alpha-L-LNA): synthesis and properties

The syntheses of monomeric nucleosides and 3'-O-phosphoramidite building blocks en route to alpha-L-ribo-configured locked nucleic acids (alpha-L-LNA), composed entirely of alpha-L-LNA monomers (alpha-L-ribo configuration) or of a mixture of alpha-L-LNA and DNA monomers (beta-D-ribo configuration), are described and the alpha-L-LNA oligomers are studied. Bicyclic 5-methylcytosin-1-yl and adenine-9-yl nucleoside derivatives have been prepared and the phosphoramidite approach has been used for the automated oligomerization leading to alpha-L-LNA oligomers. Binding studies revealed very efficient recognition of single-stranded DNA and RNA target oligonucleotide strands. Thus, stereoirregular alpha-L-LNA 11-mers containing a mixture of alpha-L-LNA monomers and DNA monomers ("mix-mer alpha-L-LNA") were shown to display DeltaT(m) values of +1 to +3 degrees C per modification toward DNA and +4 to +5 degrees C toward RNA when compared with the corresponding unmodified DNA x DNA and DNA x RNA reference duplexes. The corresponding DeltaT(m) values per modification for the stereoregular fully modified alpha-L-LNA were determined to be +4 degrees C (against DNA) and +5 degrees C (against RNA). 11-Mer alpha-L-LNAs (mix-mer alpha- L-LNA or fully modified alpha- L-LNA) were shown in vitro to be significantly stabilized toward 3'-exonucleolytic degradation. A duplex formed between RNA and either mix-mer alpha-L-LNA or fully modified alpha-L-LNA induced in vitro Escherichia coli RNase H-mediated cleavage, albeit very slow, of the RNA targets at high enzyme concentrations.     

Reactivities of methylenetriangulanes and spirocyclopropanated bicyclopropylidenes toward bromine. Relative stabilities of spirocyclopropanated versus methyl-substituted bromonium ions

The bromine additions to methylenecyclopropane (1), bicyclopropylidene (2), and spirocyclopropanated methylenecyclopropanes and bicyclopropylidenes 3-6 in methanol at 25 degrees C proceed essentially with the same rate as those to the corresponding oligomethyl-substituted ethylenes. An increasing number of spiroannelated three-membered rings enhances the rate of bromination and stabilizes the intermediate cyclopropyl bromonium cations against ring opening in the course of bromine addition. Calculations at the B3LYP/6-311G(d,p) level show that unsymmetrical bromonium ions are the intermediates, and that they are stabilized by the spiroannelation with cyclopropane rings. The bromonium ion derived from 1 is less stable by 6.3 kcal mol-1 than that from isobutene. One or two spirocyclopropane rings as in 3 and 4 stabilize the corresponding bromonium ion by 9.6 and 16.4 kcal mol-1, respectively, while one or two alpha-cyclopropyl substituents as in ethenylcyclopropane (7) and 1,1-dicyclopropylethene (8) stabilize the corresponding bromonium ions by 13 and 29 kcal mol-1, respectively. The experimental bromination rates of all the studied alkenes correlate reasonably well (r2 = 0.93) with calculated relative energies of the corresponding bromonium ions. The correlation is even better within the series of methylenecyclopropanes 1, 3, and 4 (r2 = 0.974) and bicyclopropylidenes 2, 5, and 6 (r2 = 0.999). The experimental bromination rates also correlate fairly well with the first ionization energies of the corresponding alkenes 1-12 (with r2 = 0.963) and 13-19 (with r2 = 0.991). The calculated preferred nucleophilic attack of a water molecule at both the C1' and C1 atoms of representative bromonium ions conforms well to the experimentally observed product distribution.     

Organic syntheses based on 2-oxoglutaric acid. V. Syntheses of novel 2H-1,4-benzothiazines and a 2,5-dihydro-1,5-benzothiazepine

Syntheses aimed on the incorporation in heterocycles of segments originating in the precursor 2-oxoglutaric acid are described. Cylocondensation of dimethyl 2-oxoglutarate 1 , dimethyl 3-bromo-2-oxoglutarate 2 , and dimethyl (E)-2-oxoglutaconate 3 with 2-aminobenzenethiol gave rise to the novel 2H-1,4-benzothiazines 4 and 5 , and the 2,5-dihydro-1,5-benzothiazepine 6 , respectively, by incorporation of either the segments C-1/C-2 or C-2/C-3 or C-3/C-4/C-5 of the precursor.     

Computing Cartograms with Optimal Complexity

In a rectilinear dual of a planar graph vertices are represented by simple rectilinear polygons, while edges are represented by side-contact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each region is equal to a pre-specified weight. The complexity of a cartogram is determined by the maximum number of corners (or sides) required for any polygon. In a series of papers the polygonal complexity of such representations for maximal planar graphs has been reduced from the initial 40 to 34, then to 12 and very recently to the currently best known 10. Here we describe a construction with 8-sided polygons, which is optimal in terms of polygonal complexity as 8-sided polygons are sometimes necessary. Specifically, we show how to compute the combinatorial structure and how to refine it into an area-universal rectangular layout in linear time. The exact cartogram can be computed from the area-universal layout with numerical iteration, or can be approximated with a hill-climbing heuristic. We also describe an alternative construction of cartograms for Hamiltonian maximal planar graphs, which allows us to directly compute the cartograms in linear time. Moreover, we prove that even for Hamiltonian graphs 8-sided rectilinear polygons are necessary, by constructing a non-trivial lower bound example. The complexity of the cartograms can be reduced to 6 if the Hamiltonian path has the extra property that it is one-legged, as in outer-planar graphs. Thus, we have optimal representations (in terms of both polygonal complexity and running time) for Hamiltonian maximal planar and maximal outer-planar graphs. Finally we address the problem of constructing small-complexity cartograms for 4-connected graphs (which are Hamiltonian). We first disprove a conjecture, posed by two set of authors, that any 4-connected maximal planar graph has a one-legged Hamiltonian cycle, thereby invalidating an attempt to achieve a polygonal complexity 6 in cartograms for this graph class. We also prove that it is NP-hard to decide whether a given 4-connected plane graph admits a cartogram with respect to a given weight function.     

Conditions on Ramsey Nonequivalence

Given a graph H , a graph G is called a Ramsey graph of H if there is a monochromatic copy of H in every coloring of the edges of G with two colors. Two graphs G , H are called Ramsey equivalent if they have the same set of Ramsey graphs. Fox et al. (J Combin Theory Ser B 109 (2014), 120–133) asked whether there are two nonisomorphic connected graphs that are Ramsey equivalent. They proved that a clique is not Ramsey equivalent to any other connected graph. Results of Ne?et?il et al. showed that any two graphs with different clique number (Combinatorica 1(2) (1981), 199–202) or different odd girth (Comment Math Univ Carolin 20(3) (1979), 565–582) are not Ramsey equivalent. These are the only structural graph parameters we know that “distinguish” two graphs in the above sense. This article provides further supportive evidence for a negative answer to the question of Fox et al. by claiming that for wide classes of graphs, the chromatic number is a distinguishing parameter. In addition, it is shown here that all stars and paths and all connected graphs on at most five vertices are not Ramsey equivalent to any other connected graph. Moreover, two connected graphs are not Ramsey equivalent if they belong to a special class of trees or to classes of graphs with clique‐reduction properties.