On Local LYM Identities

The LYMinequality (Lubell, Yamamoto, Meshalkin) is a generalization of Sperner’s theorem for antichains. Kleitman and Harper independently proved that the LYM inequality and the normalized matching property (or local LYM inequality) are equivalent. Many contributions have been proposed to sharpen the LYM inequality. Noticeably, Ahlswede and Zhang lifted the LYM inequality to an identity, called the AZ identity. Thus, one expects that the same sharpening of the local LYM inequality is equivalent to the AZ identity. In this paper, we introduce a local LYM identity which sharpens the local LYM inequality and prove that it is equivalent to the AZ identity. The local LYM identity shows local relationships between components in the AZ identity.     

Synthesis,Complexes and Metal Extraction Ability of R1R2NC(X)NHP(Y)(0Ph)2

Abstract

The new 1,1-disubstituted 3-diphenoxy(thio)phosphoryl-(thio)ureas, R¹R²NC(X)NHP(0Ph)₂, HA, with X,Y = O,S, were synthesized by addition of secondary mines to the corresponding P-iso(thio)cyanates. This reaction is reversible if X,Y = S. (PhO)₂P(Y)Cl reacts with H₂NC(X)NR₂ in the presence of an HCl acceptor only if X,Y a 0. Side reactions are observed. Phosphorylated derivatives of biuret were isolated from such a reaction mixture.     

A Complex between C-Methylcalix[4]resorcinarene and Triethylammonium Nitrate

Abstract

The synthesis and crystal structure of the complex formed by the all-cis epimer of C-methylcalix[4]resorcinarene (1) and triethylammonium nitrate are reported. “1.(HNEt⁺ ₃)₄. (NO^? ₃)₄(2)”, crystallizes in the monoclinic space group P2₁/n, a=25.796(2), b=16.6048(11), c=29.5659(10) Å, β=94.636(4)°, V=12623(2) ų, Z=8. Refinement led to a final conventional R₁ value of 0.128 for 12428 reflections and 1473 parameters. The resorcinarene displays the usual bowl-type shape, with four hydroxyl protons involved in intramolecular hydrogen bonds, whereas the remaining four make hydrogen bonds with four bridging nitrate ions, which results in the formation of infinite chains. Those chains are arranged so as to form layers, between which the triethylammonium ions and the remaining nitrate ions are hydrogen-bonded one to another.     

Calixarenes as Polyhapto-aromatic Ligands: Alkali Metal Ions and Sulfonated Calixarenes

Crystal structure determinations for the hexarubidium and octacesium derivatives of calix[6]arene hexasulfonic acid, as well as of a new solvate of the pentasodium derivative of calix[4]arene tetrasulfonic acid, and comparison with structural data from the literature for alkali metal complexes of sulfonated calixarenes, have provided further evidence for the importance of interactions with aromatic ~ -electrons for the heavier alkali metal cations. There is evidence as well that this interaction can be enhanced by extended ionization of the sulfonated calixarene.     

A Bis(p-tert-butyloctahomotetraoxacalix[8]arene) Capsule with [(UO2)2(OH)2] Links and a Disordered [Rb4(H2O)4] Inner Core

p-tert-Butyloctahomotetraoxacalix[8]arene (LH⁸) reacts with uranyl nitrate hexahydrate in the presence of rubidium hydroxide to give a mixed complex that can be viewed as a tetrauranate dimer [(UO²)⁴(LH⁴)²(OH)⁴] containing four disordered rubidium ions and water molecules. Two uranyl ions are complexed in an “external” fashion by each macrocycle, each of them bound to two phenoxide groups and one ether group, as well as to two bridging hydroxide ions. The latter ensure the formation of a dimeric capsule that contains the disordered set of alkali metal ions. Apart from water molecules, the Rb⁺ ions are bound to the uranyl oxo groups directed towards the inner cavity, and to phenol and ether oxygen atoms from the macrocycle. The resulting octanuclear complex presents an unprecedented geometry evidencing the assembling potential of uranyl ions.

p-tert-Butyloctahomotetraoxacalix[8]arene (LH₈) reacts with uranyl nitrate hexahydrate in the presence of rubidium hydroxide to give a mixed complex that can be viewed as a tetrauranate dimer [(UO₂)₄(LH₄)₂(OH)₄] containing four disordered rubidium ions and water molecules. Two uranyl ions are complexed in an “external” fashion by each macrocycle, each of them bound to two phenoxide groups and one ether group, as well as to two bridging hydroxide ions. The latter ensure the formation of a dimeric capsule that contains the disordered set of alkali metal ions. Apart from water molecules, the Rb^+| ions are bound to the uranyl oxo groups directed towards the inner cavity, and to phenol and ether oxygen atoms from the macrocycle. The resulting octanuclear complex presents an unprecedented geometry evidencing the assembling potential of uranyl ions.     

Improvement of Regio-Specific Production of Myricetin-3-O-α-l-Rhamnoside in Engineered Escherichia coli

Myricetin is an important flavonol whose medically important properties include activities as an antioxidant, anticarcinogen, and antimutagen. The solubility, stability, and other biological properties of the compounds can be enhanced by conjugating aglycon with sugar moieties. The type of sugar moiety also plays a significant role in the biological and physical properties of the natural product glycosides. Reconstructed Escherichia coli containing thymidine diphosphate-α-l-rhamnose sugar gene cassette and Arabidopsis-derived glycosyltransferase were used for rhamnosylation of myricetin. Myricetin (100 μM) was exogenously supplemented to induced cultures of engineered E. coli. The formation of target product—myricetin-3-O-α-l-rhamnoside—was confirmed by chromatographic and NMR analyses. The yield of product was improved by using various mutants and methylated cyclodextrin as a molecular carrier for myricetin in combination with E. coli M3G3. The maximal yield of product is 55.6 μM (3.31-fold higher than the control E. coli MG3) and shows 55.6 % bioconversion of substrate under optimized conditions.     

Linear and Cyclic Hybrids of Alternating Thiophene–Amino Acid Units: Synthesis and Effects of Chirality on Conformation and Molecular Packing

The dipeptide isostere 5‐aminothiophene carboxylic acid has been combined with L ‐phenylalanine moieties to provide linear and cyclic hybrid oligopeptides. A suitable protecting group strategy and appropriate coupling methods have been developed to guarantee a high degree of enantiopurity of the resulting amides. Cyclic tetraamides have been efficiently obtained by macrocyclization of the linear derivatives. In the case of racemized cyclization precursors, two diastereomeric macrocycles (S,S/R,R and meso) have been isolated. Their crystal structures show clear effects of the stereogenic centers on the ring conformations and molecular packing.