The Prenucleation Equilibrium of the Parathyroid Hormone Determines the Critical Aggregation Concentration and Amyloid Fibril Nucleation

Nucleation and growth of amyloid fibrils were found to only occur in supersaturated solutions above a critical concentration (c_crit). The biophysical meaning of c_crit remained mostly obscure, since typical low values of c_crit in the sub-μM range hamper investigations of potential oligomeric states and their structure. Here, we investigate the parathyroid hormone PTH₈₄ as an example of a functional amyloid fibril forming peptide with a comparably high c_crit of 67±21 μM. We describe a complex concentration dependent prenucleation ensemble of oligomers of different sizes and secondary structure compositions and highlight the occurrence of a trimer and tetramer at c_crit as possible precursors for primary fibril nucleation. Furthermore, the soluble state found in equilibrium with fibrils adopts to the prenucleation state present at c_crit. Our study sheds light onto early events of amyloid formation directly related to the critical concentration and underlines oligomer formation as a key feature of fibril nucleation. Our results contribute to a deeper understanding of the determinants of supersaturated peptide solutions. In the current study we present a biophysical approach to investigate c_crit of amyloid fibril formation of PTH₈₄ in terms of secondary structure, cluster size and residue resolved intermolecular interactions during oligomer formation. Throughout the investigated range of concentrations (1 μM to 500 μM) we found different states of oligomerization with varying ability to contribute to primary fibril nucleation and with a concentration dependent equilibrium. In this context, we identified the previously described c_crit of PTH₈₄ to mark a minimum concentration for the formation of homo-trimers/tetramers. These investigations allowed us to characterize molecular interactions of various oligomeric states that are further converted into elongation competent fibril nuclei during the lag phase of a functional amyloid forming peptide.     

Angular distributions of light projectile fragments in deep inelastic Pb + Em interactions at 160 A GeV

The nuclear emulsion was exposed at CERN by the lead projectile at 160 A GeV. The angles between any pair of fragments with Z = 2-4 have been measured in the emulsion plane for the events which did not contain heavy fragments. The constant characterizing the normal angle (J) distribution of the fragment momentum projection onto the emulsion plane with respect to initial projectile momentum p₀ is found to be C_J = (0.37 - 0.02) mrad. Corresponding value C₀ = (121 - 6) MeV/c of nucleon momentum distribution in the lead nucleus coincides with that expected from Fermi momentum distribution for this nucleus. The peak in the pair-angle distribution of double-charged fragments, ⁸Be M 2!, is presented for the region of small angles (<0.1 mrad). The fraction of !-particles coming from the decay of the ground state ⁸Be is found to be (13 - 2)% of their whole number.     

Effects of structural properties of silicon carbide-derived carbons on their electrochemical double-layer capacitance in aqueous and organic electrolytes

High surface area silicon carbide-derived carbons (Si-CDCs) synthesized by chlorination of beta silicon carbide (βSiC) with two different particle sizes (6 μm and 50 nm) show different porosities with graphitic structure. Transmission electron microscopy, Raman spectroscopy and argon (Ar) and carbon dioxide (CO₂) sorption analyses are used to examine the textural properties of the Si-CDCs. The results show that the particle size of the precursor affects the surface area and porosity of carbons. Furthermore, an additional heat treatment of the Si-CDC with 50-nm particle size for 24 h at 1,000 °C results in a collapse of the pore structure and reduces the surface area. The capacitive behaviours are investigated in H₂SO₄ and in tetraethyl ammonium tetrafluoroborate (TEABF₄)/acetonitrile (AN). The electrochemical performance of the Si-CDCs is influenced by the particle size, surface area, pore volume and pore size distribution. The Si-CDCs exhibit capacitances in 1 M H₂SO₄ of up to 179 F g^?1 and very stable charge–discharge performance over 5,000 cycles. This study shows the crucial importance of ultramicropores less than 1 nm combined with nanosized particles for achieving high capacitance in aqueous electrolyte. Moreover, the graphitic degree at the surface of the Si-CDCs enhances considerably the rate capability and stability in both electrolytes.     

Use of zirconium(IV) and antimony(III) for structural investigation of flavonoids

Summary The absorption spectra (in the visible and ultraviolet) of the complexes formed in absolute methanol between Zr⁴⁺, V⁴⁺, Y³⁺ and Sb³⁺ with 3-hydroxyflavone, apigenin, hesperidin, naringenin, morin, kaempferol, quercetin, rutin and myricetin have been studied. Zr⁴⁺ and Sb³⁺ form complexes that are stable in acid medium. The stoichiometry of the vairous Zr⁴⁺-flavonoid complexes formed in methanol and methanol/HClO₄ media has been determined by the molar ratio method. The preferred sites for complex formation of flavonoids with Zr⁴⁺ are postulated. Zr⁴⁺ forms chelates with the 3-hydroxy-4-keto and 5-hydroxy-4-keto systems simultaneously. Sb³⁺ forms complexes only with the 3,5-dihydroxy system in flavonoids. The results permit estimation of the relative order of chelating power of each type of binding site and are useful in elucidation of the structure of the flavonoids.

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Verwendung von Zirkonium(III) und Antimon(III) für die Erforschung der Flavonoide

Zusammenfassung Die Absorptions-Spektren (im sichtbaren und UV-Bereich) der in absolutem Methanol hergestellten Komplexe von Zr⁴⁺, V⁴⁺, Y³⁺ und Sb³⁺ mit 3-Hydroxyflavon, Apigenin, Hesperidin, Naringenin, Morin, Kaempferol, Quercetin, Rutin und Myricetin wurden untersucht. Zr⁴⁺ und Sb³⁺ bilden in saurem Milieu beständige Komplexe. Die Stöchiometrie der verschiedenen Zr⁴⁺-Flavonoid-Komplexe, die in Methanol bzw. Methanol/ HClO₄ hergestellt wurden, wurde durch Bestimmung der Molarverhältnisse ermittelt. Die für die Komplexbildung bevorzugten Stellen (im Molekül) wurden angegeben. Zr⁴⁺ bildet Chelate mit der 3-Hydroxy-4-keto- und mit der 5-Hydroxy~4-ketogruppe. Sb³⁺ bildet solche Komplexe nur mit der 3,5-Dihydroxy-4-keto-Gruppe in Flavonoiden. Die Untersuchungsergebnisse ermöglichen die Abschätzung der Komplexbildungsfähigkeit der verschiedenen Gruppierungen und sind für die Strukturaufklärung von Nutzen.

     

More Operator Versions of the Schwarz Inequality

Some new operator versions of the Schwarz inequality are obtained. One of them is a counterpart of the variance-covariance inequality in the context of noncommutative probability. Received: 14 April 2000 / Accepted: 10 May 2000     

Cobalt(II) Complex Catalysed Epoxidation with Molecular Oxygen

Cobalt(II) complexes 1 or 2, catalyses the epoxidation of alkenes in the presence of molecular oxygen and 2-methylpropanal in high yields.     

Efficient derivative-free variants of Hansen-Patrick’s family with memory for solving nonlinear equations

In this paper, we present a new tri-parametric derivative-free family of Hansen-Patrick type methods for solving nonlinear equations numerically. The proposed family requires only three functional evaluations to achieve optimal fourth order of convergence. In addition, acceleration of convergence speed is attained by suitable variation of free parameters in each iterative step. The self-accelerating parameters are estimated from the current and previous iteration. These self-accelerating parameters are calculated using Newton’s interpolation polynomials of third and fourth degrees. Consequently, the R-order of convergence is increased from 4 to 7, without any additional functional evaluation. Furthermore, the most striking feature of this contribution is that the proposed schemes can also determine the complex zeros without having to start from a complex initial guess as would be necessary with other methods. Numerical experiments and the comparison of the existing robust methods are included to confirm the theoretical results and high computational efficiency.     

Stability of Parametric Quasivariational Inequality of the Minty Type

In this paper, stability of a parametric quasivariational inequality of the Minty type is studied via various sufficient conditions characterizing upper and lower semicontinuity of the solution sets as well as the approximate solution sets. Sufficient conditions ensuring upper semicontinuity of the approximate solution sets of an optimization problem with quasivariational inequality constraints are also presented.     

Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.