Synthesis of substituted 3-acyl-1-hydroxyindoles and azoles on their basis

A general approach to the synthesis of new 3-acetyl-substituted pyrrolo[3,4-f]indole-5,7-diones, 3-[3-(dimethylamino)acryloyl]-1-methoxypyrrolo[3,4-f]indole-5,7-diones and similar indole-5,6-dicarbonitriles has been developed. Dimethylaminoacryloyl derivatives synthesized on their basis regioselectively reacted with hydrazine hydrochlorides and hydroxylamine with the formation of the corresponding 5-substituted azoles.     

<Emphasis Type="Italic">N</Emphasis>-Allyl-substituted aminomethylene-1,1-bisphosphonates in 1,3-dipolar cycloaddition reaction with aromatic nitrile <Emphasis Type="Italic">N</Emphasis>-oxides

A reaction of N-allyl-substituted aminomethylene-1,1-bisphosphonates with aromatic nitrile N-oxides was used to obtain new aminomethylenebisphosphonates with one or two 3-arylisoxazoline rings at the nitrogen atom. NMR spectroscopy studies showed that the bisphosphonates with two isoxazoline fragments in the molecule exist in solution as a mixture of two diastereomers.     

TMDIM: an improved algorithm for the structure prediction of transmembrane domains of bitopic dimers

\(\alpha\)-Helical transmembrane proteins are the most important drug targets in rational drug development. However, solving the experimental structures of these proteins remains difficult, therefore computational methods to accurately and efficiently predict the structures are in great demand. We present an improved structure prediction method TMDIM based on Park et al. (Proteins 57:577–585, 2004) for predicting bitopic transmembrane protein dimers. Three major algorithmic improvements are introduction of the packing type classification, the multiple-condition decoy filtering, and the cluster-based candidate selection. In a test of predicting nine known bitopic dimers, approximately 78% of our predictions achieved a successful fit (RMSD <2.0 Å) and 78% of the cases are better predicted than the two other methods compared. Our method provides an alternative for modeling TM bitopic dimers of unknown structures for further computational studies. TMDIM is freely available on the web at https://cbbio.cis.umac.mo/TMDIM. Website is implemented in PHP, MySQL and Apache, with all major browsers supported.     

Optical activity of films based on chitosan of various molecular masses and modifications

The effect of chemical (polysalt → polybase reaction) and physicochemical (heat and vapor processing) modifications of the films of chitosan of various molecular masses and prehistories on the optical activity of the polysaccharide is studied. For both of the chitosan chemical modifications, the following dependence that is nontrivial for high-molecular compounds is established: [α] = f(log\({\bar M_\eta }\)); as the degree of polymerization decreases, the modulus of [α] of the films increases. The X-ray diffraction study shows that the differences in the optical activity of the samples with different \({\bar M_\eta }\) are caused by a restriction in the mobility of the macromolecular sections upon formation of the films of high-molecular chitosan and incompleteness of the relaxation processes of the film systems to the state with energetically favorable conformations. The comparison of humidity and optical and biological activities of the initial and dehydrated chitosan films is performed. The chitosan films in the salt modification feature moderate bactericidal activity, which decreases with an increase in \({\bar M_\eta }\) of the polymer. The thermal processing of the salt modification reduces the antibacterial action; a conversion to the base form is accompanied by the loss of bactericidal activity.     

Structural properties of star-shaped polyions: Entropic sampling

The method of entropic sampling within the Wang–Landau algorithm (a modern variant of the Monte Carlo method) is used to determine the densities of energy states of a strongly charged star-shaped polyelectrolyte within the framework of the lattice model. The equilibrium thermal and structural properties of the polyelectrolyte with the number of arms f ≤ 6 and the length of arms N _arm ≤ 73 in a wide temperature range are determined from the density of states. Such characteristics as the free energy, the mean-squared radius of gyration, its components, and the parameters characterizing the shape of a polyion are calculated. It is found that the concentration, length, and number of arms affect the thermal and structural properties. The main attention is focused on the effect of temperature on these properties. The coil-to-globule transition is detected, while for the polyion with the highest length of arms (N _arm = 24) the transition from the liquid globule to the crystal-like one is observed. Differences in the properties of the star-shaped and corresponding linear polyions are characterized.     

Qualitative behaviour of incompressible two-phase flows with phase transitions: The isothermal case

A thermodynamically consistent model for incompressible two-phase flows with phase transitions is considered mathematically. The model is based on first principles, i.e., balance of mass, momentum and energy. In the isothermal case, this problem is analysed to obtain local well-posedness, stability of non-degenerate equilibria, and global existence and convergence to equilibria of solutions which do not develop singularities.     

Some asymptotically optimal one-sided embeddings of trees of similar formulas into rectangular lattices

We consider the problem of optimally placing trees of formulas in rectangular lattices. We construct and study two types of these trees and corresponding ways of placing (embedding) them into such lattices. The first is based on perfect binary trees, while the second is based on special binary trees. For the second type of tree embeddings, we prove asymptotic optimality among the trees of all formulas similar to the initial formula of no greater depth.     

Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems

A convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. All constraints involve parameters. The close relation of the instability of this problem and, hence, the instability of the classical Lagrange principle for it to its regularity properties and the subdifferentiability of the value function in the problem is discussed. An iterative nondifferential Lagrange principle with a stopping rule is proved for the indicated problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimization problems is discussed. The capabilities of this principle are illustrated by numerically solving the classical ill-posed problem of finding the normal solution of a Fredholm integral equation of the first kind.     

Approximation algorithm for the problem of partitioning a sequence into clusters

We consider the problem of partitioning a finite sequence of Euclidean points into a given number of clusters (subsequences) using the criterion of the minimal sum (over all clusters) of intercluster sums of squared distances from the elements of the clusters to their centers. It is assumed that the center of one of the desired clusters is at the origin, while the center of each of the other clusters is unknown and determined as the mean value over all elements in this cluster. Additionally, the partition obeys two structural constraints on the indices of sequence elements contained in the clusters with unknown centers: (1) the concatenation of the indices of elements in these clusters is an increasing sequence, and (2) the difference between an index and the preceding one is bounded above and below by prescribed constants. It is shown that this problem is strongly NP-hard. A 2-approximation algorithm is constructed that is polynomial-time for a fixed number of clusters.