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.     

Superparamagnetic iron oxide particles and positive enhancement for myocardial perfusion studies assessed by subsecond T1-weighted MRI

Superparamagnetic iron oxide particles (SPIOs) are usually referred to as T₂ MR contrast agents, reducing signal intensity (SI) on T₂-weighted MR images (negative enhancement). This study reports the original use of SPIOs as T₁-enhancing contrast agents, primarily assessed in vitro, and then applied to an in vivo investigation of a myocardial perfusion defect. Using a strongly T₁-weighted subsecond MR sequence with SPIOs intravenous (IV) bolus injection, MR imaging of myocardial vascularization after reperfusion was performed, on a dog model of coronary occlusion followed by reperfusion. Immediately after the intravenous bolus injection of 20 μmol/kg of SPIOs, a positive signal intensity enhancement was observed respectively, in the right and left ventricular cavity and in the nonischemic left myocardium. Moreover, compared to normal myocardium, the remaining ischemic myocardial region (anterior wall of the left ventricle) appeared as a lower and delayed SI enhancing area (cold spot). Mean peak SIE in the nonischemic myocardium (posterior wall) was significantly higher than in the ischemic myocardium (anterior wall) (110 ± 23% vs. 74 ± 22%, Mann-Whitney test < 1%, n₁ = 6, n₂ − n₁ = 0, U > 2). In conclusion, the T₁ effect of SPIOs at low dose, during their first intravascular distribution, suggests their potential use as positive markers to investigate the regional myocardial blood flow and some perfusion defects such as the “no-reflow phenomenon”.     

SR XRF and micro-PIXE studies on ancient metallurgy of thirteen Dacian gold bracelets

A thorough microscopic investigation by SR XRF and micro-PIXE brings insight into the probable techniques used in the manufacture of thirteen Dacian gold bracelets, one of the most spectacular archaeological finds ever on the territory of Romania.     

Exploring the origins of the power-law properties of energy landscapes: An egg-box model

Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously be true, we introduce an “egg-box” model. In these model landscapes, the Gaussian energy distribution is used as a starting point and we examine whether a power-law basin area distribution can arise as a natural consequence through the swallowing up of higher-energy minima by larger low-energy basins when the variance of this Gaussian is increased sufficiently. Although the basin area distribution is substantially broadened by this process, it is insufficient to generate power-laws, highlighting the role played by the inhomogeneous distribution of basins in configuration space for actual PELs.