On the local asymptotics of Faber polynomials

We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.

     

A class of dimension-skipping graphs

Forn≧6 there exists a graphG with dimG=n, dimG*≧n+2, whereG* isG with a certain edge added.     

High-frequency 263 GHz PELDOR

Pulsed electron–electron double resonance (PELDOR/DEER) at high frequencies can provide information on the relative orientation of paramagnetic centres or spin labels, if those are rigidly oriented in a host biomolecule and experiments are performed with sufficient orientation selectivity. We present the first comparative PELDOR study at 263 and 94 GHz on a model RNA system containing rigid nitroxides. We show that at 263 GHz still considerable modulation depth is observed and orientation selectivity is significant, particularly in g _x–g _y plane of the nitroxides.     

Removability of isolated singularity for anisotropic parabolic equations with absorption

We study the problem of removability of isolated singularity for general quasilinear anisotropic parabolic equations with absorption. The precise conditions on the behaviour of the absorption term that ensure the non-existence of solutions with point singularities are established.     

Practical synthesis of 1,4-dioxane derivative of the closo-dodecaborate anion and its ring opening with acetylenic alkoxides

Practical method of synthesis of the 1,4-dioxane derivative of the closo-dodecaborate anion was developed. The cleavage of the dioxonium ring in [B₁₂H₁₁O(CH₂CH₂)₂O]⁻ with acetylenic alcohols gave rise to the preparation of closo-dodecaborate derivatives with terminal acetylene group. These compounds can be introduced into click reactions with phenylazide leading to the corresponding triazoles. The structures of (Bu₄N)[B₁₂H₁₁O(CH₂CH₂)₂O] and (Bu₄N)₂[B₁₂H₁₁(OCH₂CH₂)₂OCH₂CCH] · 0.5HOCH₂CCH were determined by single-crystal X-ray diffraction.     

Computation of hydration free energies of organic solutes with an implicit water model

A new approach for computing hydration free energies DeltaG(solv) of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component DeltaG(el) of DeltaG(solv) and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (DeltaG(nel)). The novel features include the following: (a) two different cavities are used for treating DeltaG(el) and DeltaG(nel). For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of DeltaG(nel) is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed.     

Heat capacity of methacetin in a temperature range of 6 to 300 K

Heat capacity of methacetin (N-(4-methoxyphenyl)-acetamide) has been measured in the temperature range 5.8–300 K. No anomalies in the C _p(T) dependence were observed. Thermodynamic functions were calculated. At 298.15 K, the values of entropy and enthalpy are equal to 243.1 J K⁻¹ mol⁻¹ and 36360 J mol⁻¹, respectively. The heat capacity of methacetin in the temperature range 6–10 K is well fitted by Debye equation C _p = AT ³. The thermodynamic data obtained for methacetin are compared with those for the monoclinic and orthorhombic polymorphs of paracetamol.     

Mesoporous silica nanoparticles for intracellular delivery of membrane-impermeable proteins

An MCM-41-type mesoporous silica nanoparticle (MSN) material with a large average pore diameter (5.4 nm) is synthesized and characterized. The in vitro uptake and release profiles of cytochrome c by the MSN were investigated. The enzymatic activity of the released protein was quantitatively analyzed and compared with that of the native cytochrome c in physiological buffer solutions. We found that the enzymes released from the MSNs are still functional and highly active in catalyzing the oxidation of 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulfonate) (ABTS) by hydrogen peroxide. In contrast to the fact that cytochrome c is a cell-membrane-impermeable protein, we discovered that the cytochrome c-encapsulated MSNs could be internalized by live human cervical cancer cells (HeLa) and the protein could be released into the cytoplasm. We envision that these MSNs with large pores could serve as a transmembrane delivery vehicle for controlled release of membrane-impermeable proteins in live cells, which may lead to many important biotechnological applications including therapeutics and metabolic manipulation of cells.