X-ray structural analysis and antitumor activity of new salicylic acid derivatives

Tetrakis-, tris-, bis-, and mono salicylic acid derivatives 1–4 were synthesized by reaction of methyl 2-hydroxy benzoate (methyl salicylate) with 2,2-bis (hydroxymethyl) propane-1,3-diol (pentaerythritol) in the presence of sodium. Yields of different salicyloyloxy derivatives were changed by varying the molar ratios of reactants. For compounds 2 and 3, X-ray structure analysis was performed, as well as molecular energy minimization, to define their conformation in terms of their energy minima. Comparison of crystal and energy minimized structures for these two compounds (2 and 3) revealed that the intramolecular hydrogen bonds play an important role, stabilizing conformation of the most part of the molecule. The antioxidant activity and cytotoxicity of the synthesized derivatives were evaluated in a series of in vitro tests, as well as 17β-hydroxysteroid dehydrogenase type 2 inhibition potency. Tetrakis salicyloyloxy derivative 1 expressed the highest antioxidant potency, tris salicyloyloxy derivative 2 was the best inhibitor of 17βHSD2 enzyme, while bis salicyloyloxy derivative 3 showed strong cytotoxicity against prostate and breast cancer cells with no cytotoxicity against healthy cells.     

Topological structure preserving numerical simulations of dynamical models

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined application.     

Parametric Interval Linear Solver

IntervalComputations‘LinearSystems’ is a Mathematica package supporting tools for solving parametric and nonparametric linear systems involving uncertainties. It includes a variety of functions, implementing different interval techniques, that help in producing sharp and rigorous results in validated interval arithmetic. The package is designed to be easy to use, versatile, to provide a necessary background for further exploration, comparisons and prototyping, and to provide some indispensable tools for solving parametric interval linear systems. This paper presents the functionality, provided by the current version of the package, and briefly discusses the underlying methodology. A new hybrid approach for sharp parametric enclosures, that combines parametric residual iteration, exact bounds, based on monotonicity properties, and refinement by interval subdivision, is outlined.     

X-ray structural analysis, antioxidant and cytotoxic activity of newly synthesized salicylic acid derivatives

New salicylic (2-hydroxybenzoic) acid derivatives 1–6 were prepared by conventional heating or microwave irradiation of a mixture consisting of methyl salicylate and the corresponding amino alcohol (2,2′-dihydroxydiethylamine, 2,2′,2″-trihydroxytriethylamine or N-phenyl-2,2′-dihydroxydiethylamine) and metallic sodium as catalyst. For compounds 1, 3, and 5 X-ray structure analysis was performed, as well as molecular mechanics calculations (MMC), to define their conformation in terms of their energy minima. Comparison of crystal and MMC structures for these three compounds (1, 3, and 5) revealed that the intramolecular hydrogen bonds play an important role, stabilizing conformation of the most part of the molecule. The antioxidant activity and cytotoxicity of the synthesized derivatives were evaluated in a series of in vitro tests. The newly synthesized compounds exhibited strong activity against hydroxyl radical, as well as promising lipid peroxidation inhibition. The study showed that the electronic effects of the groups at the N atom are responsible for neutralization of the OH radical, i.e., antioxidant activity. Compounds 1–3 exhibited sub-micromolar cytotoxicity against HeLa S3, whereas compounds 1, 3 and 5 efficiently inhibited the growth of PC3 cells.     

17β‐Ethoxy‐3‐methoxy‐8‐isoestra‐1,3,5(10)‐triene

The conformation of the crystal of 17β‐ethoxy‐3‐methoxy‐8‐iso­estra‐1,3,5(10)‐triene, C₂₁H₃₀O₂, (I), has been established and compared with the molecular structure of a typical steroid estrogen 8‐iso‐analogue, (II). Calculations of distances separating some of the H‐atom pairs in (I) and (II) by molecular‐mechanical and semi‐empirical methods revealed the similarity of the values to the H⃛H distances obtained from X‐ray analysis.     

A novel fragmentation-cyclization reaction of steroidal α-hydroxy oximes

By a novel “one pot” fragmentation-cyclization reaction 17β-hydroxy-17α-substituted-16-oximino derivatives in the androstane and estrane series were converted to a new type of D-homo derivative.     

Inner and outer bounds for the solution set of parametric linear systems

Consider linear systems involving affine-linear dependencies on interval parameters. Presented is a free C-XSC software implementing a generalized parametric fixed-point iteration method for verified enclosure of the parametric solution set. Some specific features of the corresponding algorithm concerning sharp enclosure of the contracting matrix and inner approximation of the solution enclosure are discussed.     

Proving endpoint dependence in solving interval parametric linear systems

Numerical Algorithms - Linear algebraic systems involving linear dependencies between interval valued parameters and the so-called united parametric solution set of such systems are considered. The...