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.     

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.     

Reliability of Speaking and Maximum Voice Range Measures in Screening for Dysphonia

Speech range profile (SRP) is a graphical display of frequency-intensity occurring interactions during functional speech activity. Few studies have suggested the potential clinical applications of SRP. However, these studies are limited to qualitative case comparisons and vocally healthy participants. The present study aimed to examine the effects of voice disorders on speaking and maximum voice ranges in a group of vocally untrained women. It also aimed to examine whether voice limit measures derived from SRP were as sensitive as those derived from voice range profile (VRP) in distinguishing dysphonic from healthy voices. Ninety dysphonic women with laryngeal pathologies and 35 women with normal voices, who served as controls, participated in this study. Each subject recorded a VRP for her physiological vocal limits. In addition, each subject read aloud the "North Wind and the Sun" passage to record SRP. All the recordings were captured and analyzed by Soundswell's computerized real-time phonetogram Phog 1.0 (Hitech Development AB, T?by, Sweden). The SRPs and the VRPs were compared between the two groups of subjects. Univariate analysis results demonstrated that individual SRP measures were less sensitive than the corresponding VRP measures in discriminating dysphonic from normal voices. However, stepwise logistic regression analyses revealed that the combination of only two SRP measures was almost as effective as a combination of three VRP measures in predicting the presence of dysphonia (overall prediction accuracy: 93.6% for SRP vs 96.0% for VRP). These results suggest that in a busy clinic where quick voice screening results are desirable, SRP can be an acceptable alternate procedure to VRP.     

Carbon–chalcogen bond formation initiated by [Al(NONDipp)(E)]− anions containing Al–E{16} (E{16} = S,Se) multiple bonds

Multiply-bonded main group metal compounds are of interest as a new class of reactive species able to activate and functionalize a wide range of substrates. The aluminium sulfido compound K[Al(NON^Dipp)(S)] (NON^Dipp = [O(SiMe₂NDipp)₂]²⁻, Dipp = 2,6-ⁱPr₂C₆H₃), completing the series of [Al(NON^Dipp)(E)]⁻ anions containing Al–E{16} multiple bonds (E{16} = O, S, Se, Te), was accessed via desulfurisation of K[Al(NON^Dipp)(S₄)] using triphenylphosphane. The crystal structure showed a tetrameric aggregate joined by multiple K⋯S and K⋯π(arene) interactions that were disrupted by the addition of 2.2.2-cryptand to form the separated ion pair, [K(2.2.2-crypt)][Al(NON^Dipp)(S)]. Analysis of the anion using density functional theory (DFT) confirmed multiple-bond character in the Al–S group. The reaction of the sulfido and selenido anions K[Al(NON^Dipp)(E)] (E = S, Se) with CO₂ afforded K[Al(NON^Dipp)(κ²E,O-EC{O}O)] containing the thio- and seleno-carbonate groups respectively, consistent with a [2 + 2]-cycloaddition reaction and C–E bond formation. An analogous cycloaddition reaction took place with benzophenone affording compounds containing the diphenylsulfido- and diphenylselenido-methanolate ligands, [κ²E,O-EC{O}Ph₂]²⁻. In contrast, when K[Al(NON^Dipp)(E)] (E = S, Se) was reacted with benzaldehyde, two equivalents of substrate were incorporated into the product accompanied by formation of a second C–E bond and complete cleavage of the Al–E{16} bonds. The products contained the hitherto unknown κ²O,O-thio- and κ²O,O-seleno-bis(phenylmethanolate) ligands, which were exclusively isolated as the cis-stereoisomers. The mechanisms of these cycloaddition reactions were investigated using DFT methods.

Reaction of Al–E (E = S, Se) multiple bonds with C O functionalities generates new C–E bonds.     

Design of Oligourea-Based Foldamers with Antibacterial and Antifungal Activities

There is an urgent need to develop new therapeutic strategies to fight the emergence of multidrug resistant bacteria. Many antimicrobial peptides (AMPs) have been identified and characterized, but clinical translation has been limited partly due to their structural instability and degradability in physiological environments. The use of unnatural backbones leading to foldamers can generate peptidomimetics with improved properties and conformational stability. We recently reported the successful design of urea-based eukaryotic cell-penetrating foldamers (CPFs). Since cell-penetrating peptides and AMPs generally share many common features, we prepared new sequences derived from CPFs by varying the distribution of histidine- and arginine-type residues at the surface of the oligourea helix, and evaluated their activity on both Gram-positive and Gram-negative bacteria as well as on fungi. In addition, we prepared and tested new amphiphilic block cofoldamers consisting of an oligourea and a peptide segment whereby polar and charged residues are located in the peptide segment and more hydrophobic residues in the oligourea segment. Several foldamer sequences were found to display potent antibacterial activities even in the presence of 50% serum. Importantly, we show that these urea-based foldamers also possess promising antifungal properties.