Density of solutions to quadratic congruences

A classical result in number theory is Dirichlet’s theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k > 1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree n ≤ x with k prime factors such that a fixed quadratic equation has exactly 2 ^k solutions modulo n.     

Molecular dynamics simulations of CXCL-8 and its interactions with a receptor peptide, heparin fragments, and sulfated linked cyclitols

CXCL-8 (Interleukin 8) is a CXC chemokine with a central role in the human immune response. We have undertaken extensive in silico analyses to elucidate the interactions of CXCL-8 with its various binding partners, which are crucial for its biological function. Sequence and structure analyses showed that residues in the thirdq β-sheet and basic residues in the heparin binding site are highly variable, while residues in the second β-sheet are highly conserved. Molecular dynamics simulations in aqueous solution of dimeric CXCL-8 have been performed with starting geometries from both X-ray and NMR structures showed shearing movements between the two antiparallel C-terminal helices. Dynamic conservation analyses of these simulations agreed with experimental data indicating that structural differences between the two structures at quaternary level arise from changes in the secondary structure of the N-terminal loop, the 3(10)-helix, the 30s, 40s, and 50s loops and the third β-sheet, resulting in a different interhelical separation. Nevertheless, the observation of these different states indicates that CXCL-8 has the potential to undergo conformational changes, and it seems likely that this feature is relevant to the mode of binding of glycosaminoglycan (GAG) mimetics such as cyclitols. Simulations of the receptor peptide fragment-CXCL-8 complex identified several specific interactions of the receptor peptide with CXCL-8 that could be exploited in the structure-based design of competitive peptides and nonpeptidic molecules targeting CXCL-8 for combating inflammatory diseases. Simulations of the CXCL-8 dimer complexed with a 24-mer heparin fragment and of the CXCL-8-receptor peptide complex revealed that Arg60, Lys64, and Arg68 in the dimer bind to cyclitols in a horseshoe pattern, defining a region which is spatially distinct from the receptor binding site. There appears to be an optimum number of sulfates and an optimum length of alkyl spacers required for the interaction of cyclitol inhibitors with the dimeric form of CXCL-8. Calculation of the binding affinities of cyclitol inhibitors reflected satisfactorily the ranking of experimentally determined inhibitory potencies. The findings of these molecular modeling studies will help in the search for inhibitors which can modulate various CXCL-8 biological activities and serve as an excellent model system to study CXC-inhibitor interactions.     

Production of lantipeptides in Escherichia coli

Lantipeptides are ribosomally synthesized and posttranslationally modified peptides containing thioether cross-links. We describe the preparation of seven different lantipeptides in Escherichia coli and demonstrate that this methodology can be used to incorporate nonproteinogenic amino acids.     

Examining the mechanism of action of a kinesin inhibitor using stable isotope labeled inhibitors for cross-linking (SILIC)

It is difficult to determine a chemical inhibitor's binding site in multiprotein mixtures, particularly when high-resolution structural studies are not straightforward. Building upon previous research involving photo-cross-linking and the use of mixtures of stable isotopes, we report a method, Stable Isotope Labeled Inhibitors for Cross-linking (SILIC), for mapping a small molecule inhibitor's binding site in its target protein. In SILIC, structure-activity relationship data is used to design inhibitor analogues that incorporate a photo-cross-linking group along with either natural or 'heavy' stable isotopes. An equimolar mixture of these inhibitor analogues is cross-linked to the target protein to yield a robust signature for identifying inhibitor-modified peptide fragments in complex mass spectrometry data. As a proof of concept, we applied this approach to an ATP-competitive inhibitor of kinesin-5, a widely conserved motor protein required for cell division and an anticancer drug target. This analysis, along with mutagenesis studies, suggests that the inhibitor binds at an allosteric site in the motor protein.     

Polarographic behaviour of zinc in acetate buffer

Summary Zinc may be determined polarographically in acetate buffered solutions of P_H 4 to 5.6.

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Zusammenfassung Die polarographische Bestimmung von Zink ist möglich in mit Acetat gepufferten Lösungen vom P_H 4 bis 5,6.

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Résumé On peut doser le zinc par polarographie dans des solutions de p_H 4 à 5,6 tamponnées à l'acétate.

     

Improved Mucoadhesion,Permeation and In Vitro Anticancer Potential of Synthesized Thiolated Acacia and Karaya Gum Combination: A Systematic Study

Thiolation of polymers is one of the most appropriate approaches to impart higher mechanical strength and mucoadhesion. Thiol modification of gum karaya and gum acacia was carried out by esterification with 80% thioglycolic acid. FTIR, DSC and XRD confirmed the completion of thiolation reaction. Anticancer potential of developed thiomer was studied on cervical cancer cell lines (HeLa) and more than 60% of human cervical cell lines (HeLa) were inhibited at concentration of 5 µg/100 µL. Immobilized thiol groups were found to be 0.8511 mmol/g as determined by Ellman’s method. Cytotoxicity studies on L929 fibroblast cell lines indicated thiomers were biocompatible. Bilayered tablets were prepared using Ivabradine hydrochloride as the model drug and synthesized thiolated gums as mucoadhesive polymer. Tablets prepared using thiolated polymers in combination showed more swelling, mucoadhesion and residence time as compared to unmodified gums. Thiol modification controlled the release of the drug for 24 h and enhanced permeation of the drug up to 3 fold through porcine buccal mucosa as compared to tablets with unmodified gums. Thiolated polymer showed increased mucoadhesion and permeation, anticancer potential, controlled release and thus can be utilized as a novel excipient in formulation development.     

Virtual Screening of Alkaloid and Terpenoid Inhibitors of SMT Expressed in Naegleria sp.

The pathogenic form of thermophilic Naegleria sp. i.e., Naegleria fowleri, also known as brain eating amoeba, causes primary amoebic encephalitis (PAM) with a >97% fatality rate. To date, there are no specific drugs identified to treat this disease specifically. The present antimicrobial combinatorial chemotherapy is hard on many patients, especially children. Interestingly, Naegleria fowleri has complex lipid biosynthesis pathways like other protists and also has a strong preference to utilize absorbed host lipids for generating energy. The ergosterol biosynthesis pathway provides a unique drug target opportunity, as some of the key enzymes involved in this pathway are absent in humans. Sterol 24-C Methyltransferase (SMT) is one such enzyme that is not found in humans. To select novel inhibitors for this enzyme, alkaloids and terpenoids inhibitors were screened and tested against two isozymes of SMT identified in N. gruberi (non-pathogenic) as well as its homolog found in yeast, i.e., ERG6. Five natural product derived inhibitors i.e., Cyclopamine, Chelerythrine, Berberine, Tanshinone 2A, and Catharanthine have been identified as potential drug candidates based on multiple criteria including binding affinity, ADME scores, absorption, and, most importantly, its ability to cross the blood brain barrier. This study provides multiple leads for future drug exploration against Naegleria fowleri.     

Effect of heat and time-period on the growth of ZnO nanorods by sol–gel technique

Sol–gel routes to metal oxide nanoparticles in organic solvents under exclusion of water have become a versatile alternative to aqueous methods. We focus on the preparation of well-aligned ZnO nanorod arrays using non-aqueous sol–gel synthesis route, where ZnO nanorods arrays have been grown on glass substrates. This work provides a systematic study of controlled morphology and crystallinity of ZnO nanorod arrays. The investigation demonstrates that the synthesis process conditions of ZnO thin film have strong influences on the morphology and crystallinity of the ZnO nanorod arrays grown thereon, where non-aqueous process offers the possibility of better understanding and controlling the reaction pathways on the molecular level, enabling the synthesis of nanomaterials with high crystallinity and well-defined, uniform particle morphologies. Here the annealing temperature plays an important role on the growth of nanostructures of the ZnO grains and nanorod arrays. The scanning electron microscopy (SEM) image shows that the growth of ZnO nanorod arrays are high-quality single crystals growing along the c-axis perpendicular to the substrates. A detailed analysis of the growth characteristics of ZnO nanostructures as functions of growth time is also reported.     

Effect of mixed glass formers on the crystallization kinetics in AgI–Ag<Subscript>2</Subscript>O–V<Subscript>2</Subscript>O<Subscript>5</Subscript>–MoO<Subscript>3</Subscript> glassy superionic system

The crystallization and glass transition kinetics using differential scanning calorimetry (DSC) in 50AgI–33.33Ag₂O–16.67[(V₂O₅)_1−x –(MoO₃) _x ] superionic glassy system is discussed. Thermal stability of glass, studied using various criteria, does not vary significantly with glass former variation. However, the activation energies for structural relaxation (E _s) at glass transition temperature and crystallization (E _c) obtained using Moynihan and Kissinger, Matusita-Sakka formulations found to exhibit interesting trends with MoO₃ substitution in the glass matrix. It is noticed that the electrical conductivity (σ)–temperature (T) cycles obtained at a typical heating rate of 1 °C/min do exhibit significant thermal events. The conductivity after first heating cycle at room temperature is found to be increasing with MoO₃ content and maximum for x = 0.3 (~10⁻³ Ω⁻¹ cm⁻¹ at 30 °C) which is comparable to that of the host 50AgI–33.33Ag₂O–16.67V₂O₅ glassy system. The parameters obtained from σ–T plots and DSC scans do complement each other in a particular range of composition.