Evaluation of the protein solvent-accessible surface using reduced representations in terms of critical points of the electron density

The aim of our study is the development of a method for calculating the interface of dimerization of protein-protein complexes based on simplified medium-resolution structures. In particular, we wished to evaluate if the existing concepts for the computation of the Solvent-Accessible Surface Area (SASA) of macromolecules could be applied to medium-resolution models. Therefore, we selected a set of 140 protein chains and computed their reduced representations by topological analysis of their electron density maps at 2.85 A crystallographic resolution. This procedure leads to a limited number of critical points (CPs) that can be identified and associated to backbone and side-chain parts. To evaluate the SASA and interfaces of dimerization of the reduced representations, we chose and modified two existing programs that calculate the SASA of atomic representations, and tested (1) several radii tables of amino acids, (2) the influence of the backbone and side-chain points, and (3) the radius of the solvent molecule, which rolls over the surface. The results are shown in terms of relative error compared to the values calculated on the corresponding atomic representations of the proteins.     

One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model

We consider the Skyrme model using the explicit parameterization of the rotation group through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of is . We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces .     

Regular Ordering and Existence of Minimum Points in Uniform Spaces and Topological Groups

It is defined the locally order convexity of an ordered uniform space and an ordered topological group and is investigated its relation to the existence of minimum points of denumerable, complete lower bounded sets.     

The Problem of Subrayleigh Resolution in Interference Microscopy

A method allowing subwavelength resolution within the framework of optical interferometric microscopy is proposed. It is shown that overcoming the diffraction limit is not a necessary requirement. Generally speaking, subrayleigh resolution and overcoming the diffraction limit are basically different concepts. The method developed uses the all-parameter modulation of the light source and separation of the phase shifts generated due to different reasons. In this method, a topological phase technique is used to separate the phases and therefore determine the corresponding characteristics of an object. The approach developed provides for a way to create a new type of optical devices. Within the framework of a uniform measuring procedure these devices make possible determining both geometrical and material parameters of the object under study.     

Electron density investigation of a push-pull ethylene (C14H24N2O2.H2O) by X-ray diffraction at T = 21 K

The electron charge distribution in a strongly twisted push-pull ethylene [PPE, 3-(1,3-diisopropyl-2-imidazolidinylidene)-2,4-pentanedione] has been determined by low temperature (T = 21 K) single-crystal X-ray diffraction analysis. The derived electronic properties are consistent with a zwitterionic molecule, as indicated by a charge transfer of 0.82(16) e from the push to the pull moieties and a charge polarization of 0.29(7) e on the olefinic bond. A dipole moment of 12(3) D has been determined, which compares well with ab initio theoretical results in terms of both modulus and orientation. The second moments, which have also been obtained with good precision, characterize PPE as a highly quadrupolar molecule. The special electronic features of the molecule confer particular topological properties to the electron density distribution, as evidenced by comparison with "standard" organic molecules. The crystallographic asymmetric unit of the present system includes one water molecule, which is hydrogen bonded to PPE. Its topological properties have also been investigated, together with an analysis of the hydrogen bonds involved.