Chemistry of Succinylsuccinic Acid Derivatives. Part II. The crystal and molecular structure of diethyl succinylsuccinate

X-ray structure analysis of the title compound (I) is reported. The results are interpreted to predict formation of anti-tricyclo[4.4.0^1,6.0^7,12]-1,4,7,10-tetraethoxycarbonyl-3,6,9,12-tetrahydroxy-dodeca-3,9-diene on UV.-irradiation of solid (I).     

Conformations of the ten-membered ring in 5,10-secosteroids I. X-ray and NMR. Analysis of (E)-3 β-hydroxy-5,10-seco-1(10)-cholesten-5-one esters

X-ray structure determination of the p-bromobenzoate 2b of one of the (E/Z)-isomeric 3β-hydroxy-5,10-seco-1(10)-cholesten-5-ones confirmed the (E)-configuration proposed previously and showed the cyclodecenone ring to adopt an extended crown conformation of type A ₁ (Fig. 9). Analysis of the ¹H- and ¹³C-NMR. spectra of acetate 2a revealed that in solution the ten-membered ring of this steroid exists in at least two distinct forms, the predominant (about 85%) corresponding to the solid-state conformation of 2b (= A ₁), and the minor most likely to B ₂ (Fig. 9). From NMR. data the energy difference between the two species and the relevant activation energy were estimated. A number of conformational force field calculations using a simplified partial structural model was performed; but the computed energy differences between the various possible conformations do not reproduce the effective situation, neither in solution nor in the crystal lattice, indicating that additional effects such as the transannular interaction of the double bond with the carbonyl group may strongly influence the thermodynamic stability of the system. The conformations deduced were used to rationalize the stereochemical course of different chemical reactions of 2a .     

Monitoring folding transitions of synthetic,branched-chain polypeptides by capillary zone electrophoresis

The coil/helix transition of a synthetic, branched-chain polymeric polypeptide (poly (Lys(Glu(1)-DL-Ala(3))EAK), 50-Lys residues long in the backbone, as a function of increasing molarities of methanol in solution, is here studied by both, circular dichroism (CD) and capillary zone electrophoresis. CD spectra showed that, at 75% v/v methanol, the transition from random coil to fully helical structure was obtained, in a pH 1.1 HCI solution in the presence of 20 mM NaCI. CZE studies, run in parallel, exhibited the classical unfolding to folding sigmoidal transition, with mid-point at 60% v/v methanol concentration, plateauing at ca. 80% v/v organic solvent. Surprisingly, though, such unfolding to folding transition was accompanied by an expansion, rather than a contraction, of the resulting ordered polypeptide. As the charge of the polypeptide (a pure polycation at a pH of 2.1 in CZE) was kept rigorously constant, a plot of the radius of the polymer along the sigmoidal transition clearly showed that the radius of gyration of the helical, structured polypeptide was in fact larger than that of the random coil. Such results were confirmed by molecular dynamics simulations, which indicated that the dimensions of such polypeptide, in alpha-helix configuration, were 8.5 nm (in length) and 3.2 nm (in diameter), whereas those of the corresponding random coil were 7.2 nm (in length) and 5.1 nm (length of shorter axis). It would thus appear that the randomized structure assumes the shape of a more compact object, roughly resembling a "rugby ball".     

Capillary zone electrophoresis of proteins applying ionic liquids for dynamic coating and as background electrolyte component

The use of ionic liquids in capillary electrophoresis, either as coating material or as components of the background electrolyte needs systematic standardization to set up optimal conditions. Excellent separation of the proteins was achieved using 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF₄]) or 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF₄]) ionic liquids using the properly made ionic-liquid–water binary mixtures for the experiments. The binary mixture has a distinctly stable and well perceptible low pH, which depends on the concentration of the ionic liquid, and on the preparation time of the mixture. Optimal conditions for the electrophoretic separation were obtained upon a multivariate analysis of the experimental parameters (applied voltage, migration time, concentration, and type of the ionic liquid). The standardized condition provides a low electroendosmotic flow toward the anode, which, however, did not hinder the proteins to migrate toward the cathode. The migration of cytochrome c, lysozyme, myoglobin, trypsin, and apo-transferrin at a pH around 2, far below the isoelectric points of the proteins, showed RSD values of the migration times less than 7.5% and less than 6.5% when using [emim][BF₄] or [bmim][BF₄], respectively, either in run-to-run or day-to-day experiments. The determination of the extent of the EOF is not possible with the commonly used EOF markers, due to interaction with the ionic-liquid constituents. The interaction of the ionic liquids with the proteins influences the migration order in zone electrophoresis. This method has been applied successfully for the analyses of real biological samples such as proteins from egg whites and human tears.     

Synthesis of the non-reducing end trisaccharide of the antithrombin-binding domain of heparin and its bioisosteric sulfonic acid analogues

A glucoronic acid-containing trisaccharide related to the antithrombin-binding DEFGH domain of heparin and its methanesulfonic acid analogues were synthesized. Trisaccharides without sulfonic acid content or possessing a sulfonatomethyl moiety at position 2 or 6 of unit F were prepared in high yields by [DE+F] couplings using the same disaccharide uronate donor, respectively. Synthesis of the trisaccharide with a 3-deoxy-3-sulfonatomethyl function was accomplished in three different pathways, from which a [D+EF] coupling and applying a non-oxidized precursor of the glucuronic acid afforded the trisaccharide in the highest yield.     

Some polynomials associated with the $${\vavec{}}$$-Whitney numbes

In the present article, we study three families of polynomials associated with the r-Whitney numbers of the second kind. They are the r-Dowling polynomials, r-Whitney–Fubini polynomials and the r-Eulerian–Fubini polynomials. Then we derive several combinatorial results by using algebraic arguments (Rota’s method), combinatorial arguments (set partitions) and asymptotic methods.     

A family of polylog-trigonometric integrals

In this paper, we study the sequences

$$\begin{aligned} I_n=\int _0^1\mathrm {Li}_n(\sin \pi x)\mathrm {d}x\quad \text{ and }\quad J_n=\int _0^1\mathrm {Li}_n(\cos \pi x)\mathrm {d}x, \end{aligned}$$

where \(\mathrm {Li}_n\) is the nth polylogarithm function. Among others, we determine their generating functions, asymptotic behaviour and their connection to the well-known log-sine integrals

$$\begin{aligned} S_n=(-1)^n\int _0^1\log ^n(\sin \pi x)\mathrm {d}x. \end{aligned}$$

With the help of the explicit forms of \(I_n\) and \(J_n\), we deduce closed-form evaluations for a number of polylog-trigonometric definite integrals.

     

New properties of r-Stirling series

The summation of some series involving the Stirling numbers of the first kind can be found in several works but there is no such a computation for Stirling numbers of the second kind let alone the r-Stirlings. We offer a comprehensive survey and prove new results.      

Several explicit formulae of Cauchy polynomials in terms of {r}-Stirling numbers

The integer values of Cauchy polynomials are expressed in terms of \({r}\)-Stirling numbers of the first kind. Several relations between the integral values of Bernoulli polynomials and those of Cauchy polynomials are obtained in terms of \({r}\)-Stirling numbers of both kinds. Also, we find a relation between the Cauchy polynomials and hyperharmonic numbers.