The Spectrum and Convergence Rates of Exclusion and Interchange Processes on the Complete Graph

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a. random transpositions) on the complete graph. In the case of the exclusion process, this gives a simple closed-form expression for all the eigenvalues and their multiplicities. This result is then used to give an exact expression for the distance in \( L^2 \) from stationarity at any time and upper and lower bounds on the convergence rate for the exclusion process. In the case of the interchange process, upper and lower bounds are similarly found. Our results strengthen or reprove many known results about the mixing time for the two processes in a very simple way.     

Nonlinear estimates for hypersurfaces in terms of their fundamental forms

A sufficiently regular hypersurface immersed in the $(n+1)$-dimensional Euclidean space is determined up to a proper isometry of ${\mathbb{R}}^{n+1}$ by its first and second fundamental forms. As a consequence, a sufficiently regular hypersurface with boundary, whose position and positively-oriented unit normal vectors are given on a non-empty portion of its boundary, is uniquely determined by its first and second fundamental forms. We establish here stronger versions of these uniqueness results by means of inequalities showing that an appropriate distance between two immersions from a domain ω of ${\mathbb{R}}^n$ into ${\mathbb{R}}^{n+1}$ is bounded by the $L^p$-norm of the difference between matrix fields defined in terms of the first and second fundamental forms associated with each immersion.     

Phenolic Profile,Antioxidant Capacity and Antimicrobial Activity of Nettle Leaves Extracts Obtained by Advanced Extraction Techniques

Nettle is a widely known plant whose high biological activity and beneficial medicinal effects are attributed to various bioactive compounds, among which polyphenols play an important role. In order to isolate polyphenols and preserve their properties, advanced extraction techniques have been applied to overcome the drawbacks of conventional ones. Therefore, microwave-assisted extraction (MAE) has been optimized for the isolation of nettle leaves polyphenols and it was compared to pressurized liquid extraction (PLE) and conventional heat-reflux extraction (CE). The obtained extracts were analyzed for their individual phenolic profile by UPLC MS² and for their antioxidant capacity by ORAC assay. MAE proved to be the more specific technique for the isolation of individual phenolic compounds, while PLE produced extracts with higher amount of total phenols and higher antioxidant capacity. Both techniques were more effective compared to CE. PLE nettle extract showed antimicrobial activity against bacteria, especially against Gram-negative Pseudomonas fragi ATCC 4973 and Campylobacter jejuni NCTC 11168 strains. This suggests that PLE is suitable for obtaining a nettle extract with antioxidant and antimicrobial potential, which as such has great potential for use as a value-added ingredient in the food and pharmaceutical industry.     

Synthesis of Thymidine Derivatives as Potential Pharmaceuticals against HIV/AIDS Infection

Data on preparation methods for 3'-modified oxythymidines are summarized and systematized. A synthesis tree is presented permitting a selection of rational schemes for thymidine derivatives preparation, in particular those that can be potential anti-HIV/AIDS drugs.     

Electrodynamics in terms of functions over the groupSU(2): II. Quantization

In a previous article by two of the present authors Carmeli's group-theoretic method for the formulation of wave equations was applied to the case of the electromagnetic field, and the equations for the vector potential were derived. In the present paper a quantization procedure for these equations is carried out in the Lorentz gauge. It involves two independent variables, corresponding to the number of degrees of freedom of the electromagnetic field in a Hilbert space with a positive-definite metric. Conserved quantities are derived.     

Computation of affinity and selectivity: Binding of 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors to dihydrofolate reductases

Binding energy calculations for complexes of mutant and wild-type human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors are reported. Quantitative insight into binding energetics of these molecules is obtained from calculations based on force field energy evaluation and thermal sampling by molecular dynamics simulations. The calculated affinity of methotrexate for wild-type and mutant enzymes is reasonably well reproduced. Truncation of the methotrexate glutamate tail results in a loss of affinity by several orders of magnitude. No major difference in binding strength is predicted between the pteridines and the quinazolines, while the N-methyl group present in methotrexate appears to confer significantly stronger binding. The recent improvement, which is used here, of our linear interaction energy method for binding affinity prediction, as well as problems with treating charged and flexible ligands are discussed. This approach should be suitable in a drug discovery context for prediction of binding energies of new inhibitors prior to their synthesis, when some information about the binding mode is available.     

Structure and thermodynamics of protein-polymer solutions: effects of spatially distributed hydrophobic surface residues

Protein-polymer association in solution driven by a short-range attraction has been investigated using a simple coarse-grain model solved by Monte Carlo simulations. The effect of the spatial distribution of the hydrophobic surface residues of the protein on the adsorption of weakly hydrophobic polymers at variable polymer concentration, polymer length, and polymer stiffness has been considered. Structural data on the adsorbed polymer layer and thermodynamic properties, such as the free energy, energy, and entropy, related to the protein-polymer interaction were calculated. It was found that a more heterogeneous distribution of the surface residues promotes adsorption and that this also applies for different polymer concentrations, polymer chain lengths, and polymer flexibilities. Furthermore, the polymer adsorption onto proteins with more homogeneous surface distributions displayed larger sensitivity to polymer properties such as chain length and flexibility. Finally, a simple relation between the adsorption probability and the change in the free energy was found and rationalized by a simple two-state adsorption model.     

Ruthenium-manganese complexes for artificial photosynthesis: factors controlling intramolecular electron transfer and excited-state quenching reactions

Continuing our work toward a system mimicking the electron-transfer steps from manganese to P(680)(+) in photosystem II (PS II), we report a series of ruthenium(II)-manganese(II) complexes that display intramolecular electron transfer from manganese(II) to photooxidized ruthenium(III). The electron-transfer rate constant (k(ET)) values span a large range, 1 x 10(5)-2 x 10(7) s(-1), and we have investigated different factors that are responsible for the variation. The reorganization energies determined experimentally (lambda = 1.5-2.0 eV) are larger than expected for solvent reorganization in complexes of similar size in polar solvents (typically lambda approximately 1.0 eV). This result indicates that the inner reorganization energy is relatively large and, consequently, that at moderate driving force values manganese complexes are not fast donors. Both the type of manganese ligand and the link between the two metals are shown to be of great importance to the electron-transfer rate. In contrast, we show that the quenching of the excited state of the ruthenium(II) moiety by manganese(II) in this series of complexes mainly depends on the distance between the metals. However, by synthetically modifying the sensitizer so that the lowest metal-to-ligand charge transfer state was localized on the nonbridging ruthenium(II) ligands, we could reduce the quenching rate constant in one complex by a factor of 700 without changing the bridging ligand. Still, the manganese(II)-ruthenium(III) electron-transfer rate constant was not reduced. Consequently, the modification resulted in a complex with very favorable properties.     

Polynuclear tetrazole-containing amino acid analogs

New analogs of (D,L)-phenylalanine containing tetrazole rings were synthesized. The acidity constants of (D, L)-phenylalanine and (D,L)-tryptophane derivatives containing a tetrazole ring with no substituent on N¹ (pK _a = 3.0–3.1) and of the corresponding carboxylic acids (pK _a = 2.9–3.3) in aqueous methanol were determined by potentiometric titration.Translated from Zhurnal Organicheskoi Khimii, Vol. 40, No. 10, 2004, pp. 1576–1579.Original Russian Text Copyright © 2004 by Morozova, Esikov, Zubarev, Malin, Ostrovskii.