Kinetics of polymerization by activated monomer mechanism

Polymerization of cyclic ethers by activated monomer mechanism involves consecutive additions of protonated monomer molecules to the growing macromolecules fitted with hydroxyl groups at their ends. For oxirane itself and symmetrically substituted oxiranes there is only one kind of hydroxyl groups and one, unique way of ring-opening. Unsymmetrically substituted oxiranes provide however two sites of attack and two different hydroxyls, resulting from these ring-openings. Kinetics of polymerization of epichlorohydrin (chloromethyloxirane) has been studied and all four rate constants determined, namely rate constants of the primary and secondary alcoholate chain ends with a protonated monomer, opening in result of the attack on substituted or unsubstituted carbon atom. These rate constants are (in mol⁻¹·1·s⁻¹ at 25°C, in CH₂Cl₂ solvent): k₁₁ = 0.055, k₁₂ = = 0.41, k₂₂ = 0.135, and k₂₁ = 0.0011 (e.g. k₁₂ is the rate of reaction of the primary alcohol producing the secondary alcohol). Thus, polymerization proceeds almost exclusively on the secondary alcoholate groups, reproducing themselves (k₂₂).     

Direct High-Throughput Screening Assay for mRNA Cap Guanine-N7 Methyltransferase Activity

In eukaryotes, mature mRNA is formed through modifications of precursor mRNA, one of which is 5’ cap biosynthesis, involving RNA cap guanine-N7 methyltransferase (N7-MTase). N7-MTases are also encoded by some eukaryotic viruses and facilitate their replication. N7-MTase inhibitors have therapeutic potential, but their discovery is difficult because long RNA substrates are usually required for activity. Herein, we report a universal N7-MTase activity assay based on small-molecule fluorescent probes. We synthesized 12 fluorescent substrate analogues (GpppA and GpppG derivatives) varying in the dye type, dye attachment site, and linker length. GpppA labeled with pyrene at the 3’-O position of adenosine acted as an artificial substrate with the properties of a turn-off probe for all three tested N7-MTases (human, parasite, and viral). Using this compound, a N7-MTase inhibitor assay adaptable to high-throughput screening was developed and used to screen synthetic substrate analogues and a commercial library. Several inhibitors with nanomolar activities were identified.     

Optimal Stable Nonlinear Approximation

Foundations of Computational Mathematics - While it is well-known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how...     

Star‐Shaped Conjugated Molecules with Oxa‐ or Thiadiazole Bithiophene Side Arms

Star‐shaped conjugated molecules, consisting of a benzene central unit symmetrically trisubstituted with either oxa‐ or thiadiazole bithiophene groups, were synthesized as promising molecules and building blocks for application in (opto)electronics and electrochromic devices. Their optical (E_g(opt)) as well as electrochemical (E_g(electro)) band gaps depended on the type of the side arm and the number of solubilizing alkyl substituents. Oxadiazole derivatives showed E_g(opt) slightly below 3 eV and by 0.2 eV larger than those determined for thiadiazole‐based compounds. The presence of alkyl substituents in the arms additionally lowered the band gap. The obtained compounds were efficient electroluminophores in guest/host‐type light‐emitting diodes. They also showed a strong tendency to self‐organize in monolayers deposited on graphite, as evidenced by scanning tunneling microscopy. The structural studies by X‐ray scattering revealed the formation of supramolecular columnar stacks in which the molecules were organized. Differences in macroscopic alignment in the specimen indicated variations in the self‐assembly mechanism between the molecules. The compounds as trifunctional monomers were electrochemically polymerized to yield the corresponding polymer network. As shown by UV/Vis‐NIR spectroelectrochemical studies, these networks exhibited reversible electrochromic behavior both in the oxidation and in the reduction modes.     

Greedy Algorithms for Reduced Bases in Banach Spaces

Given a Banach space X and one of its compact sets $\mathcal{F}$ , we consider the problem of finding a good n-dimensional space X _n ?X which can be used to approximate the elements of $\mathcal{F}$ . The best possible error we can achieve for such an approximation is given by the Kolmogorov width $d_{n}(\mathcal{F})_{X}$ . However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595–603, 2012) in the case $X=\mathcal{H}$ is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595–603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457–1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces.     

Approaches to the enantioselective synthesis of ferrugine and its analogues

A four-step synthetic route, to ferrugine (2α-benzoyltropane), its methyl analogue (2-acetyltropane) and their N-benzyl analogues is reported. The reaction sequence uses tropinone or N-benzylnortropinone aldols as key intermediates. Reduction of aldol derived N-tosylhydrazones and oxidation of the side chain hydroxyl group followed by spontaneous diastereomer equilibration provides the final products. Relative configuration of the exo,anti N-methyl and N-benzyl aldols was retained during N-tosylhydrazone formation. The relative stereochemistry of N-tosylhydrazones was assigned by single crystal diffraction. The final products, ferrugine and its methyl analogue, were synthesized in enantiomerically pure form via asymmetric deprotonation of tropinone using chiral lithium amide/lithium chloride aggregate prepared in situ from (S,S)-N,N-bis(1-phenylethyl)amine hydrochloride.     

The Study of Derivatization Prior MALDI MSI Analysis—Charge Tagging Based on the Cholesterol and Betaine Aldehyde

Mass spectrometry imaging is a powerful tool for analyzing the different kinds of molecules in tissue sections, but some substances cannot be measured easily, due to their physicochemical properties. In such cases, chemical derivatization could be applied to introduce the charge into the molecule and facilitate its detection. Here, we study cholesterol derivatization with betaine aldehyde from tissue slices and evaluate how different sample preparation methods influence the signal from the derivatization product. In this study, we have tested different solutions for betaine aldehyde, different approaches to betaine aldehyde deposition (number of layers, deposition nozzle height), and different MALDI matrices for its analysis. As a result, we proved that the proposed approach could be used for the analysis of cholesterol in different tissues.     

Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons

We show that a ring of unidirectionally delay-coupled spiking neurons may possess a multitude of stable spiking patterns and provide a constructive algorithm for generating a desired spiking pattern. More specifically, for a given time-periodic pattern, in which each neuron fires once within the pattern period at a predefined time moment, we provide the coupling delays and/or coupling strengths leading to this particular pattern. The considered homogeneous networks demonstrate a great multistability of various travelling time- and space-periodic waves which can propagate either along the direction of coupling or in opposite direction. Such a multistability significantly enhances the variability of possible spatio-temporal patterns and potentially increases the coding capability of oscillatory neuronal loops. We illustrate our results using FitzHugh-Nagumo neurons interacting via excitatory chemical synapses as well as limit-cycle oscillators.