Recent advances in the analysis of steroid hormones and related drugs.

The development during the last 15 years and the state-of-the-art in the analysis of bulk steroid hormone drugs and hormone-like structures and pharmaceutical formulations made thereof are summarized. Other steroids (sterols, bile acids, cardiac glycosides, vitamins D) as well as biological-clinical aspects and pharmacokinetic and metabolic studies are excluded from this review. The state-of-the-art is summarized based on comparisons of monographs in the latest editions of the European Pharmacopoeia, United States Pharmacopoeia and the Japanese Pharmacopoeia. This is followed by sections dealing with new developments in the methodology for the fields of spectroscopic and spectrophotometric, chromatographic, electrophoretic and hyphenated techniques as well electroanalytical methods. The review is terminated by two problem-oriented sections: examples on impurity and degradation profiling as well as enantiomeric analysis.     

Influence of surfactant and lipid chain length on the solubilisation of phosphatidylcholine vesicles by micelles comprised of polyoxyethylene sorbitan monoesters

Photon correlation spectroscopy and freeze-fracture electron microscopy have been used to determine the ability of a range of micelle-forming, polyoxyethylene (20) sorbitan monoesters (Tweens) to solubilise vesicles prepared from phosphatidylcholines of different acyl chain lengths and degrees of saturation with a view to rationalising (in terms of their membrane toxicity) which of the micelle-forming surfactants to use as drug delivery vehicles. The phosphatidylcholines used were dimyristoyl-, dipalmitoyl-, distearoyl- and dioleoylphosphatidylcholine (DMPC, DPPC, DSPC and DOPC, respectively) while the nonionic polyoxyethylene sorbitan monoesters studied were polyoxyethylene (20) sorbitan monolaurate (Tween 20), a 9:1 weight ratio mixture of polyoxyethylene (20) sorbitan monopalmitate and monostearate (Tween 40), a 1:1 weight ratio mixture of polyoxyethylene (20) sorbitan monopalmitate and monostearate (Tween 60), and polyoxyethylene (20) sorbitan monooleate (Tween 80). The ability of the Tween micelles to solubilise phospholipid vesicles was found to depend both upon the length of the surfactant acyl chain and the length of the acyl chains of the phospholipid comprising the vesicle. Vesicles composed of long saturated diacyl chain phospholipids, namely DSPC and DPPC, were the most resistant to solubilisation, while those prepared from the shorter acyl chained DMPC were more readily solubilised. In terms of their solubilisation behaviour, vesicles made from phospholipids containing long, unsaturated acyl chains, namely DOPC behaved more akin to those vesicles prepared from DMPC. None of the Tween surfactants were effective at solubilising vesicles prepared from DPPC or DSPC. In contrast, there were clear differences in the ability of the various surfactants to solubilise vesicles prepared from DMPC and DOPC, in that micelles formed from Tween 20 were the most effective solubilising agent while those formed by Tween 60 were the least effective. As a consequence of these observations it was considered that Tween 60 was the surfactant least likely to cause membrane damage in vivo and, therefore, is the most suitable surfactant for use as a micellar drug delivery vehicle.     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

New Classes of Toda Soliton Solutions

We provide a detailed investigation of limits of N–soliton solutions of the Toda lattice as N tends to infinity. Our principal results yield new classes of Toda solutions including, in particular, new kinds of soliton–like (i.e., reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one–dimensional Jacobi operators and explicitly construct tri–diagonal matrices that yield a purely absolutely continuous spectrum in (-1,1) and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of . Received: 16 October 1995/Accepted: 23 July 1996     

Chemical composition and reaction analysis of single aerosol particles

In situ measurements of gas-liquid surface reactions of single aerosol microdroplets are presented. By means of optical levitation in combination with elastic (Mie) and inelastic (Raman) light scattering it is possible to get information on the chemistry of e.g. acid/base reactions as well as the physical behavior of single microparticles.     

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

A Primitive Non-symmetric 3-Class Association Scheme on 36 Elements with p11 = 0 Exists and is Unique

In this paper we construct a primitive, non-symmetric 3-class association scheme with parameters v = 36, v₁ = 7, p¹₁₁ = 0 and p²₁₁ = 4 and show that such a scheme is determined by its parameters.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.