Capillary electrophoresis of proteins 2003-2005

This review article with 304 references describes recent developments in CE of proteins, and covers the two years since the previous review (Hutterer, K., Dolník, V., Electrophoresis 2003, 24, 3998-4012) through Spring 2005. It covers topics related to CE of proteins, including modeling of the electrophoretic migration of proteins, sample pretreatment, wall coatings, improving separation, various forms of detection, special electrophoretic techniques such as affinity CE, CIEF, and applications of CE to the analysis of proteins in real-world samples including human body fluids, food and agricultural samples, protein pharmaceuticals, and recombinant protein preparations.     

Effect of photonic crystal structure on the nonlinear optical anisotropy of birefringent porous silicon

Anisotropic photonic crystal structures consisting of birefringent porous silicon layers with alternating porosity were fabricated. The in-plane birefringence formed as a result of anisotropic etching in Si(110) results in unique multilayered structures with two distinct photonic bandgaps for orthogonal light polarizations. Nonlinear optical studies based on the third-harmonic generation from these structures demonstrate variation in the symmetry of the nonlinear optical response.     

Modification of Arabinogalactan Isolated from Larix sibirica Ledeb. into Sulfated Derivatives with the Controlled Molecular Weights

The process of sulfation of arabinogalactan—a natural polysaccharide from Larix sibirica Ledeb.—with sulfamic acid in 1,4-dioxane using different activators has been studied for the first time. The dynamics of the molecular weight of sulfated arabinogalactan upon variation in the temperature and time of sulfation of arabinogalactan with sulfamic acid in 1,4-dioxane has been investigated. It has been found that, as the sulfation time increases from 10 to 90 min, the molecular weights of the reaction products grow due to the introduction of sulfate groups without significant destruction of the initial polymer and sulfation products. Sulfation at 95 °C for 20 min yields the products with a higher molecular weight than in the case of sulfation at 85 °C, which is related to an increase in the sulfation rate; however, during the further process occurring under these conditions, sulfation is accompanied by the destruction and the molecular weight of the sulfated polymer decreases. The numerical optimization of arabinogalactan sulfation process has been performed. It has been shown that the optimal parameters for obtaining a product with a high sulfur content are a sulfamic acid amount of 20 mmol per 1 g of arabinogalactan, a process temperature of 85 °C, and a process time of 2.5 h.     

A Very Smooth Ride in a Rough Sea

It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time Serfati (C. R. Acad. Sci. Paris Série I 320:175–180, 1995), Shnirelman (Glob. Stoch. Anal., http://arxiv.org/abs/1205.5837v1, 2012). Here an elementary derivation is given, based on Cauchy’s form of the Euler equations in Lagrangian coordinates. This form implies simple recurrence relations among the time-Taylor coefficients of the Lagrangian map, used here to derive bounds for the C ^1,γ Hölder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C ^1,γ.     

Desmotropy, polymorphism, and solid-state proton transfer: four solid forms of an aromatic o-hydroxy Schiff base

The Schiff base derived from salicylaldehyde and 2-amino-3-hydroxypyridine affords a diversity of solid forms, two polymorphic pairs of the enol-imino (D1?a and D1?b) and keto-amino (D2?a and D2?b) desmotropes. The isolated phases, identified by IR spectroscopy, X-ray crystallography, and (13)C cross-polarization/magnetic angle spinning (CP/MAS) NMR spectroscopy, display essentially planar molecular conformations characterized by strong intramolecular hydrogen bonds of the O-H???N (D1) or N-H???O (D2) type. A change in the position of the proton within this O???H???N system is accompanied by substantially different molecular conformations and, subsequently, by divergent supramolecular architectures. The appearance and interconversion conditions for each of the four phases have been established on the basis of a number of solution and solvent-free experiments, and evaluated against the results of computational studies. Solid phases readily convert into the most stable form (D1?a) upon exposure to methanol vapor, heating, or by mechanical treatment, and these transformations are accompanied by a change in the color of the sample. The course of thermally induced transformations has been monitored in detail by means of temperature-resolved powder X-ray diffraction and infrared spectroscopy. Upon dissolution, all forms equilibrate immediately, as confirmed by NMR and UV/Vis spectroscopy in several solvents, with the equilibrium shifted far towards the enol tautomer. This study reveals the significance of peripheral groups in the stabilization of metastable tautomers in the solid state.     

Desmotropy,Polymorphism, and Solid‐State Proton Transfer: Four Solid Forms of an Aromatic o‐Hydroxy Schiff Base

The Schiff base derived from salicylaldehyde and 2‐amino‐3‐hydroxypyridine affords a diversity of solid forms, two polymorphic pairs of the enol‐imino ( D1 a and D1 b ) and keto‐amino ( D2 a and D2 b ) desmotropes. The isolated phases, identified by IR spectroscopy, X‐ray crystallography, and ¹³C cross‐polarization/magnetic angle spinning (CP/MAS) NMR spectroscopy, display essentially planar molecular conformations characterized by strong intramolecular hydrogen bonds of the O? H???N ( D1 ) or N? H???O ( D2 ) type. A change in the position of the proton within this O???H???N system is accompanied by substantially different molecular conformations and, subsequently, by divergent supramolecular architectures. The appearance and interconversion conditions for each of the four phases have been established on the basis of a number of solution and solvent‐free experiments, and evaluated against the results of computational studies. Solid phases readily convert into the most stable form ( D1 a ) upon exposure to methanol vapor, heating, or by mechanical treatment, and these transformations are accompanied by a change in the color of the sample. The course of thermally induced transformations has been monitored in detail by means of temperature‐resolved powder X‐ray diffraction and infrared spectroscopy. Upon dissolution, all forms equilibrate immediately, as confirmed by NMR and UV/Vis spectroscopy in several solvents, with the equilibrium shifted far towards the enol tautomer. This study reveals the significance of peripheral groups in the stabilization of metastable tautomers in the solid state.     

Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications

We obtained new exact inequalities that estimate the L _?? -norm of the Riesz derivative D ^?? f of a function f defined on $ {\mathbb{R}^m} $ in terms of the uniform norm of the function itself and the L _s -norm of the function acted by the Laplace operator. On a class of functions f such that ||??f||s ?? 1, we solved the problem of approximation of an unbounded operator D ^?? by bounded ones and the problem of optimal recovery of the operator D ^?? on elements of this class given with known error.