On Mincʼs sheltered middle path

This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a “sheltered middle path”, can in the case of general (non-PL) paths result in the topologist?s sine curve.     

Molecular Dynamics Simulation of Ester‐Linked Hen Egg White Lysozyme Reveals the Effect of Missing Backbone Hydrogen Bond Donors on the Protein Structure

The three‐dimensional structure of a protein is stabilized by a number of different atomic interactions. One of these is hydrogen bonding. Its influence on the spatial structure of the hen egg white lysozyme is investigated by replacing peptide bonds (except those of the two proline residues) by ester bonds. Molecular dynamics simulations of native and ester‐linked lysozyme are compared with the native crystal structure and with NOE distance bounds derived from solution NMR experiments. The ester‐linked protein shows a slight compaction while losing its native structure. However, it does not unfold completely. The structure remains compact due to its hydrophobic core and a changed network of hydrogen bonds involving side chains.     

An adaptive algorithm for simulation of stochastic reaction–diffusion processes

We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction–diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie’s stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.     

Cyclization of Propargylic Amides: Mild Access to Oxazole Derivatives

The substrate scope, the mechanistic aspects of the gold‐catalyzed oxazole synthesis, and substrates with different aliphatic, aromatic, and functional groups in the side chain were investigated. Even molecules with several propargyl amide groups could easily be converted, delivering di‐ and trioxazoles with interesting optical properties. Furthermore, the scope of the gold(I)‐catalyzed alkylidene synthesis was investigated. Further functionalizations of these isolable intermediates of the oxazole synthesis were developed and chelate ligands can be obtained. The use of Barluenga’s reagent offers a new and mild access to the synthetically valuable iodoalkylideneoxazoles from propargylic amides, this reagent being superior to other sources of halogens.     

Sulfonation of polystyrene: Toward the “ideal” polyelectrolyte

Sulfonation of narrow polydispersity polystyrene, PS, standards remains the method of choice for generating polystyrene sulfonate, PSS, samples with defined composition. Although a variety of sulfonation techniques have been described, relatively little is reported on the material obtained, which is used for so many studies on the fundamental behavior of polyelectrolytes. Here, we show that powdered polystyrene treated with concentrated sulfuric acid (96%) at 90 °C without catalyst yields fully sulfonated PSS. Extensive characterization with ¹H and ¹³C NMR as well as size exclusion chromatography coupled with static and dynamic light scattering shows no evidence of sulfone crosslinking or chain degradation under the conditions used. Though mono‐sulfonated as soon as it dissolves in the acid, the PSS contains about 6% meta substitution. Sulfonation kinetics for this heterogeneous reaction depend strongly on particle size, sulfuric acid content and temperature. For preparing perdeuterated PSS from the corresponding PS it is essential to employ D₂SO₄, as about half of the aromatic units undergo H/D exchange during sulfonation. The remaining ortho H/D may be exchanged with extended exposure to the concentrated sulfuric acid, but the meta site is deactivated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2416–2624