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.     

Comparative evaluation of methods for assessing peak homogeneity in liquid isocratic reversed-phase chromatography

A significant problem in the development of an automated system for the interpretation of chromatographic profiles is the detection of cases of co-elution without the use of a considerable amount of computer time or intervention by a human operator. A partial solution to this problem is offered by a range of tests which can be implemented on a suitable microcomputer to provide an estimate of peak homogeneity. Several such tests are described and their application to the three-dimensional data sets produced by a photodiode-array detector is illustrated. The sensitivity of each of the different tests to the presence of a second component varies according to the relative amplitude, separation and spectral similarity of the two components. The extent of this variation is assessed for each of the tests and an indication is given of the reliability of each method under typical chromatographic conditions.     

A fluorescence study of DNS-labelled chymotrypsin and related enzymes

Various dansyl (DNS)-conjugates of chymotrypsin, chymotrypsinogen and elastase have been prepared. Excitation and emission spectra, and fluorescence depolarization measurements have been obtained in a spectrophotofluorometer, and relevant fluorescent lifetimes have been derived from fluorescence decay measurements.Free DNS-OH gave a lifetime of 13 nsec in fair agreement with other estimates, but combined DNS gave significantly lower values. In particular, ?-DNS lysine in water gave a value of 4 nsec, with higher values (up to 10 nsec) at increasing glycerol concentration. Of the various protein conjugates, specifically labelled chymotrypsin gave the lowest lifetime (6 nsec); for the others, higher values were observed, the values increasing with pH of labelling. Of the protein conjugates, only in the case of specifically labelled elastase, did 'glycerol concentration cause an increase in the measured τ value from 8 to 12 nsec.Active-site labelled chymotrypsin was unusual in that its fluorescent spectrum was dependent upon excitation wavelength and its excitation spectrum upon the selected emission wavelength. The addition of further non-specifically attached DNS-groups caused a shift towards the spectra of such DNS-groups, and saturation with indole gave spectra of such a type as well as erasing wavelength dependence. It seemed that specifically attached DNS groups were probably within the “tosyl hole” but could be dislodged by indole, a competitive inhibitor.Depolarization properties were in all cases markedly dependent upon excitation wavelength. Experiments performed with varying temperature gave relaxation times which were smaller than expected for a rigid molecule with the molecular weight of chymotrypsin but, also, considerable increases were observed with increasing excitation wavelength. It seemed that the susceptibility to temperature-activated rotation of the DNS group increased with the energy of the incident radiation. At constant temperature, apart from specifically-labelled chymotrypsin, spuriously high relaxation times were observed, for which an explanation is required. Until this is provided, depolarization measurements cannot be regarded as providing a sound method of measuring relaxation times of protein molecules in solution.     

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.     

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.     

Vibration characteristics of a bi-density drumhead

The dayan tabla is a percussion instrument used as an accompaniment to classical Indian singing or music. In this work, a mathematical model was developed to describe the response of this instrument and to analytically determine the areal density distribution required to obtain overtones that were rational multiples of each other. The model was verified by comparing the exact Bessel function solution of the constant density drum with the results obtained using the approximate method outlined in this paper. The maximum error obtained for the first 10 natural frequencies was less than 1% while the associated mode shapes differed by less than 5%. The bi-density model of the tabla, with a mass ratio of 4.1 and a radius ratio of 0.49, predicted natural frequency ratios of approximately 1.1:2:3 (twice):4 (twice) for the fundamental and the first few overtones. This compares well with previously reported experimental data.