An Estimate for Ideals in H ∞(D)

In light of Treil’s negative solution to an ideal problem of T. Wolff, we improve on a theorem of Cegrell concerning membership in certain ideals in H^∞(D).     

Structure-activity relationship studies on CXCR4 antagonists having cyclic pentapeptide scaffolds

Structure-activity relationship studies on CXCR4 antagonists, which were previously found by using cyclic pentapeptide libraries, were performed to optimize side-chain functional groups, involving conformationally constrained analogues. In addition, a new lead of cyclic pentapeptides with the introduction of a novel pharmacophore was developed.     

Magnetically ordered (Tc= 200 K) bis(tetracyanopyrazine)vanadium, V[TCNP]2.yCH2Cl2

A new organic-based magnet, V[TCNP]2.yCH2Cl2 (TCNP = tetracyanopyrazine), has been synthesized, and its magnetic properties have been examined. The amorphous nature of V[TCNP]2.yCH2Cl2 makes it difficult to determine the structure of the material; however, ac and dc magnetic measurements indicate that it is a ferrimagnet below 200 K with a small coercive field of 8 Oe at 5 K.     

Enhancement of the T140-based pharmacophores leads to the development of more potent and bio-stable CXCR4 antagonists

A CXCR4 antagonistic peptide, T140, and its bio-stable analogs, such as Ac-TE14011, were previously developed. These peptides inhibit the entry of T cell line-tropic strains of HIV-1 (X4-HIV-1) into T cells. Herein, a series of TE14011 analogs having modifications in the N-terminal region were synthesized to develop effective compounds with increased biostability. Among these analogs, 4F-benzoyl-TE14011 (TF14013) showed the strongest anti-HIV activity derived from CXCR4-antagonism, suggesting that a 4-fluorobenzoyl moiety at the N-terminus of T140 analogs constitutes a novel T140-based pharmacophore for CXCR4 antagonists. Structure-activity relationship (SAR) studies on TE14011 analogs with N(alpha)-acylation by several benzoic acid derivatives have disclosed a significant relationship between the anti-HIV activity and the Hammett constant (sigma) of substituted benzoic acids. TF14013 was found to be stable in mouse serum, but not completely stable in rat liver homogenate due to deletion of the C-terminal Arg14-NH2 from the parent peptide. This biodegradation was completely suppressed by N-alkyl-amidation at the C-terminus. Taken together, the enhancement of the T140-based pharmacophores led to development of a novel CXCR4 antagonist, 4F-benzoyl-TE14011-Me (TF14013-Me), which has very high anti-HIV activity and increased biostability.     

1,4,5,8,9,12-Hexamethyltriphenylene. A molecule with a flipping twist

The synthesis and characterization of 1,4,5,8,9,12-hexamethyltriphenylene (5) is described. In the solid state, X-ray crystallographic studies reveal that compound 5 presents a highly distorted C2 geometry with a 53 degrees end-to-end twist. In solution, variable-temperature 1H NMR studies and molecular modeling present a story of rapid dynamic conformational interconversions between two C2 enantiomers (with a low activation barrier) and a slower C2-D3 interconversion (with a relatively high barrier)--the first time clear evidence of conformational interchange for these hindered triphenylenes has been provided. Further studies have established that 5 is a fluorescent stable blue emitter, and that the compound undergoes an irreversible one-electron electrochemical oxidation. Calculations have predicted this to be a radical cation of C2 geometry with 60 degrees end-to-end twist.     

Solid‐state NMR Study of the YadA Membrane‐Anchor Domain in the Bacterial Outer Membrane

MAS‐NMR was used to study the structure and dynamics at ambient temperatures of the membrane‐anchor domain of YadA (YadA‐M) in a pellet of the outer membrane of E. coli in which it was expressed. YadA is an adhesin from the pathogen Yersinia enterocolitica that is involved in interactions with the host cell, and it is a model protein for studying the autotransport process. Existing assignments were sucessfully transferred to a large part of the YadA‐M protein in the E. coli lipid environment by using ¹³C‐¹³C DARR and PDSD spectra at different mixing times. The chemical shifts in most regions of YadA‐M are unchanged relative to those in microcrystalline YadA‐M preparations from which a structure has previously been solved, including the ASSA region that is proposed to be involved in transition‐state hairpin formation for transport of the soluble domain. Comparisons of the dynamics between the microcrystalline and membrane‐embedded samples indicate greater flexibility of the ASSA region in the outer‐membrane preparation at physiological temperatures. This study will pave the way towards MAS‐NMR structure determination of membrane proteins, and a better understanding of functionally important dynamic residues in native membrane environments.     

A Constructive Proof of the Leech Theorem for Rational Matrix Functions

We give a constructive proof of Leech’s theorem for rational matrix functions. This enables us to provide an algorithm for solving rational matrix corona problems.