Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Design and self-assembly of ditopic and tetratopic cavitand complexes

The self-assembly of open ditopic and tetratopic cavitand complexes has been investigated by using monofunctionalized cavitand ligands and suitable metal precursors. In the case of ditopic complexes, self-assembly protocols, leading exclusively to the formation of both thermodynamically stable cis-Pt square-planar complexes 8 and 9 and the kinetically inert fac-Re octahedral complex 14, have been elaborated. The use of cis-[Pt(CH3)CN)2Cl2] as metal precursor led to the formation of monotopic trans-10 and ditopic trans-11 cavitand complexes, while cis-[Pt(dmso)2Cl2] afforded both cis-13 and trans-11 isomers. The self-assembly of tetratopic cavitand complexes has been achieved by using mononuclear [Pd(CH3CN)4(BF4)2] and dinuclear [M2(tppb)(OTf)4] (19: M = Pt; 20: M = Pd) metal precursors. Only the tetratopic dinuclear complexes 21 and 22 were stable. The ligand configuration with two phosphorus and two cavitand ligands at the metal centers is the most appropriate to build tetratopic cavitand complexes with sufficient kinetic stability.     

Reaction of dichloroketene and sulfene with N,N-disubstituted α-aminomethyleneketones. Synthesis of pyrano[2,3-e]indazole and 1,2-oxathiino[6,5-e]indazole derivatives

The polar 1,4-cycloaddition of dichloroketene to N,N-disubstituted (E)-5-aminomethylene-1,5,6,7-tetrahydro-(1-methyl)(1-phenyl)-4H-indazol-4-ones V, prepared from 1,5,6,7-tetrahydro-(1-methyl)(1-phenyl)-4H-indazol-4-ones via the 5-hydroxymethylene derivatives, gave in good yield N,N-disubstituted 4-amino-3,3-dichloro-4,5,6,7-tetrahydro-(7-methyl)(7-phenyl)pyrano[2,3-e]indazol-(3H)ones VI, which are derivatives of the new heterocyclic system pyrano[2,3-e]indazole. Dehydrochlorination of VI with DBN afforded N,N-disubstituted 4-amino-3-chloro-6,7-dihydro(7-methyl)(7-phenyl)pyrano[2,3-e]indazol-2(5H]-ones VII generally in satisfactory yield. Full aromatization with DDQ of VII was tried only in the case of dimethylamino derivatives, giving a moderate yield of 3-chloro-4-dimethylamino(7-methyl)(7-phenyl)pyrano[2,3-e]indazol-2(7H)-ones. Cycloaddition of sulfene to V occurred only in the case of aliphatic N-substitution to give in moderate yield 4-dialkylamino-4,5,6,7-tetrahydro-(7-methyl)(7-phenyl)-3H-1,2-oxathiino[6,5-e]indazole 2,2-dioxides, which are derivatives of the new heterocyclic system 1,2-oxathiino[6,5-e]indazole.     

A Bis-Chelating / Ligand for the Synthesis of Heterobimetallic Platinum(II)/Rhenium(I) Complexes: Tools for the Optimization of a New Class of Platinum(II) Anticancer Agents

The two independent and coordination sites of a newly synthesized bis[2-(hydroxyphenyl)-1,2,4-triazole] platform have been exploited to prepare four monometallic neutral ()Pt^II complexes carrying DMSO, pyridine, triphenylphosphine, or N-heterocyclic carbene as the fourth ligand. Then, the second coordination site was used to introduce an IR-active rhenium tricarbonyl entity, affording the four corresponding heterobimetallic neutral Pt^II/Re^I complexes, as well as a cationic Pt^II/Re^I derivative. X-ray crystallographic studies showed that distortion of the organic platform occurred to accommodate the coordination geometry of both metal centers. No ligand exchange or transchelation occurred upon incubation of the Pt^II complexes in aqueous environment or in the presence of Fe^III, respectively. The antiproliferative activity of the ligand and complexes was first screened on the triple-negative breast cancer cell line MDA-MB-231. Then, the IC₅₀ values of the most active candidates were determined on a wider panel of human cancer cells (MDA-MB-231, MCF-7, and A2780), as well as on a nontumorigenic cell line (MCF-10A). Low micromolar activities were reached for the complexes carrying a DMSO ligand, making them the first examples of highly active, but hydrolytically stable, Pt^II complexes. Finally, the characteristic mid-IR signature of the {Re(CO)₃} fragment in the Pt/Re heterobimetallic complexes was used to quantify their uptake in breast cancer cells.     

Dynamic and redundant regulation of LRRK2 and LRRK1 expression

Background  

Mutations within the leucine-rich repeat kinase 2 (LRRK2) gene account for a significant proportion of autosomal-dominant and some late-onset sporadic Parkinson's disease. Elucidation of LRRK2 protein function in health and disease provides an opportunity for deciphering molecular pathways important in neurodegeneration. In mammals, LRRK1 and LRRK2 protein comprise a unique family encoding a GTPase domain that controls intrinsic kinase activity. The expression profiles of the murine LRRK proteins have not been fully described and insufficiently characterized antibodies have produced conflicting results in the literature.     

Selection of suitable operating conditions to minimize the gradient equilibration time in the separation of drugs by Ultra-High-Pressure Liquid Chromatography with volatile (mass spectrometry-compatible) buffers

Reversed phase gradient elution is the method of choice for pharmaceuticals analysis since it allows reducing the analysis time while improving both the quality of the separation and the detection limits. The current trends are towards faster separations which can be achieved thanks to equipments withstanding ultra-high pressures and/or high temperatures. Under such conditions, gradient separations can be carried out within a few minutes or even a few tens of seconds. A long equilibration time in addition to the gradient time can be therefore very detrimental. In this work, we investigated the extent to which the gradient equilibration time can be reduced and which parameters mainly affect the retention variability of ionizable compounds when using volatile buffers. We first found out an excellent repeatability between run-to-run experiments whatever the equilibration time and the operating conditions. We then pointed out the key operating parameters which allow achieving reproducible runs when varying the equilibration time between runs. With a view of reducing the equilibration time, the effects of various conditions were examined. The latter include the type of additive for mobile phase pH adjustment, the initial eluent composition, the type of stationary phase, the temperature and the flow-rate. Although much remains to be understood about the equilibration process, our study allows making progress in the knowledge of this phenomenon. Based on the present results, a beneficial effect of both temperature and flow-rate was highlighted and operating conditions leading to faster column equilibration are suggested.     

Density estimates for a random noise propagating through a chain of differential equations

We here provide two sided bounds for the density of the solution of a system of n differential equations of dimension d, the first one being forced by a non-degenerate random noise and the n−1 other ones being degenerate. The system formed by the n equations satisfies a suitable Hörmander condition: the second equation feels the noise plugged into the first equation, the third equation feels the noise transmitted from the first to the second equation and so on … , so that the noise propagates one way through the system. When the coefficients of the system are Lipschitz continuous, we show that the density of the solution satisfies Gaussian bounds with non-diffusive time scales. The proof relies on the interpretation of the density of the solution as the value function of some optimal stochastic control problem.     

Allenylzincs and tert-butylsulfinylimines: a fruitful marriage for synthesis

The stereoselective synthesis of alkynyl 1,2-amino alcohols by the addition of 3-chloro- and 3-methoxymethoxy- allenylzincs to chiral tert-butylsulfinylimines is described. The methodology is applicable to the preparation of alkynyl 2-amino-1,3-diols (O,N,O stereotriads) using α-alkoxy tert-butylsulfinylimines as chiral starting materials. The scope and limitations of the methodology along with recent applications to the efficient asymmetric syntheses of natural and/or bioactive alkaloids and polyhydroxylated alkaloids are presented.