A short proof for a generalization of Vizing's theorem

For a simple graph of maximum degree Δ, it is always possible to color the edges with Δ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Δ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these results to multigraphs. Instead of considering several color interchanges along alternating chains (Vizing, Gupta), using counting arguments (Ehrenfeucht, Faber, Kierstead), or improving nonvalid colorings with Fournier's Lemma, the method of proof consists of using one single easy transformation, called “sequential recoloring”, to augment a partial k-coloring of the edges.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (n - 1) II

We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (n - 1). This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2-, 3- and 4-hypomorphic. As a corollary we obtain that any binary relation is (n - 4)-reconstructible (when n > 9).     

Möbius aromaticity in [12]annulene: cis-trans isomerization via twist-coupled bond shifting

Density functional and coupled cluster calculations show that facile thermal configuration change in [12]annulene occurs via a twist-coupled bond-shifting mechanism. The transition state for this process is highly aromatic with M?bius topology. At the CCSD(T)/cc-pVDZ//BH&HLYP/6-311+G** level, the isomerization of tri-trans-[12]annulene 1a (CTCTCT) to its di-trans isomer 2 (CCCTCT) via such a mechanism has a barrier of 18.0 kcal/mol, in good agreement with earlier experiments. Two other aromatic M?bius bond-shifting transition states were located that result in configuration change for other [12]annulene conformers. This mechanism contrasts sharply with diradical configuration change for acyclic polyenes and with planar bond-shifting mechanisms generally assumed for annulenes. This constitutes evidence that neutral M?bius aromatic annulenes play a role in the dynamic processes of neutral [4n]annulenes.     

Bonding of acetylene to copper atom,dimer, and trimer

The bonding of acetylene to copper atom, dimer, and trimer was investigated with a Kohn–Sham density functional approach. Full geometry optimization yielded the equilibrium structures of various Cu_nC₂H₂ species. Gradient corrections were included in the calculation of binding energies (BE ). The Cu—C₂H₂ complex was found to have a C_s structure and a BE of 10 kcal/mol. Three isomers of Cu₂C₂H₂ have similar total energies: a C_2v end-bonded structure with a BE of 18 kcal/mol, and two 1,2-dicupro ethylene isomers—a cis form with a BE of 12 kcal/mol and a trans form with a BE of 15 kcal/mol. Two stable C_2v isomers of Cu₃C₂H₂ were found. In both isomers, the Cu₃ ring relaxes from its isosceles structure, with two short bonds (2.247 Å) and one long bond (2.478 Å), and adopts a nearly equilateral geometry. In one isomer of Cu₃C₂H₂, the acetylene is bonded to one apex of the Cu₃ ring with a BE of 29 kcal/mol. In the other, it is bonded to two copper atoms of one side of the Cu₃ ring with a BE of 33 kcal/mol. © 1994 John Wiley & Sons, Inc.     

Screening an In-House Isoquinoline Alkaloids Library for New Blockers of Voltage-Gated Na+ Channels Using Voltage Sensor Fluorescent Probes: Hits and Biases

Voltage-gated Na⁺ (Na_V) channels are significant therapeutic targets for the treatment of cardiac and neurological disorders, thus promoting the search for novel Na_V channel ligands. With the objective of discovering new blockers of Na_V channel ligands, we screened an In-House vegetal alkaloid library using fluorescence cell-based assays. We screened 62 isoquinoline alkaloids (IA) for their ability to decrease the FRET signal of voltage sensor probes (VSP), which were induced by the activation of Na_V channels with batrachotoxin (BTX) in GH3b6 cells. This led to the selection of five IA: liriodenine, oxostephanine, thalmiculine, protopine, and bebeerine, inhibiting the BTX-induced VSP signal with micromolar IC₅₀. These five alkaloids were then assayed using the Na⁺ fluorescent probe ANG-2 and the patch-clamp technique. Only oxostephanine and liriodenine were able to inhibit the BTX-induced ANG-2 signal in HEK293-hNa_V1.3 cells. Indeed, liriodenine and oxostephanine decreased the effects of BTX on Na⁺ currents elicited by the hNa_V1.3 channel, suggesting that conformation change induced by BTX binding could induce a bias in fluorescent assays. However, among the five IA selected in the VSP assay, only bebeerine exhibited strong inhibitory effects against Na⁺ currents elicited by the hNav1.2 and hNav1.6 channels, with IC₅₀ values below 10 µM. So far, bebeerine is the first BBIQ to have been reported to block Na_V channels, with promising therapeutical applications.     

Development of a practical solid-phase synthesis approach to 1,3,5-triazepan-2,6-diones

1,3,5-Triazepan-2,6-diones are a class of conformationally restricted heterocycles derived from dipeptides. With the aim to develop a general and practical method useful for library production, three polymer-assisted syntheses, all based on a catch and release approach, have been evaluated and compared. The method involving a Hofmann rearrangement of N-Boc dipeptide carboxamides and subsequent trapping of the isocyanate on polymer-supported N-hydroxysuccinimide (PS-HOSu) was found to be the most reliable and versatile, allowing rapid access to the 1,3,5-triazepan-2,6-dione skeleton.