On limit sets of mixed iterates of commuting mappings

We investigate the limit sets { f^-n °g^m(x) : n, m ? \mathbbN}\{ f^{-n} \circ g^m(x) : n, m \in \mathbb{N}\} of sequences of iterates of commuting continuous injections f and g defined in an interval. As an application of the main result we present theorems describing the problem of the existence and uniqueness of solutions of simultaneous Abel inequalities $\varphi(f(x)) \leq \varphi(x) + 1, \varphi(g(x)) \geq \varphi(x) + s$\varphi(f(x)) \leq \varphi(x) + 1, \varphi(g(x)) \geq \varphi(x) + s in the dependence on the parameter s.     

Distribution of Triterpenoids and Steroids in Developing Rugosa Rose (Rosa rugosa Thunb.) Accessory Fruit

Triterpenoids and steroids are considered to be important for the fruit quality and health-promoting properties for the consumers. The aim of the study was the determination of the changes in triterpenoid and steroid biosynthesis and the accumulation in hypanthium and achenes of rugosa rose (Rosa rugosa Thunb.) hip during fruit development and ripening at three different phenological stages (young fruits, fully developed unripe fruits, and matured fruits). Triterpenoids and steroids were also determined in the peel and the pulp of the matured hips. The obtained results indicated that the distribution of the analyzed compounds in different fruit tissues is a selective process. The increased rate of hydroxylation of triterpenoids, the deposition of hydroxylated acids in fruit surface layer, and the continuous biosynthesis of phytosterols in achenes versus its gradual repression in hypanthium accompanied by the accumulation of their biosynthetic intermediates and ketone derivatives seem to be characteristic metabolic features of maturation of rugosa rose accessory fruit. These observations, apart from providing the important data on metabolic modifications occurring in developing fruits, might have a practical application in defining fruit parts, particularly rich in bioactive constituents, to enable the development of novel functional products.     

Intramolecular Ring-Expansion Reaction (RER) and Intermolecular Coordination of In Situ Generated Cyclic (Amino)(aryl)carbenes (cAArCs)

Cyclic (amino)(aryl)carbenes (cAArCs) based on the isoindoline core were successfully generated in situ by α-elimination of 3-alkoxyisoindolines at high temperatures or by deprotonation of isoindol-2-ium chlorides with sodium or copper(I) acetates at low temperatures. 3-Alkoxy-isoindolines 2 a , b-OR (R=Me, Et, iPr) have been prepared in high yields by the addition of a solution of 2-aryl-1,1-diphenylisoindol-2-ium triflate ( 1 a , b-OTf ; a : aryl=Dipp=2,6-diisopropylphenyl; b : Mesityl-, Mes=2,4,6-trimethylphenyl) to the corresponding alcohol (ROH) with NEt₃ at room temperature. Furthermore, the reaction of 2 a , b-OMe in diethyl ether with a tenfold excess of hydrochloric acid led to the isolation of the isoindol-2-ium chlorides 1 a , b-Cl in high yields. The thermally generated cAArC reacts with sulfur to form the thioamide 3 a . Without any additional trapping reagent, in situ generation of 1,1-diphenylisoidolin-3-ylidenes does not lead to the isolation of these compounds, but to the reaction products of the insertion of the carbene carbon atom into an ortho C−H bond of a phenyl substituent, followed by ring-expansion reaction; namely, anthracene derivatives 9-N(H)aryl-10-Ph-C₁₄H₈ 4 a , b ( a : Dipp; b : Mes). These compounds are conveniently synthesized by deprotonation of the isoindol-2-ium chlorides with sodium acetate in high yields. Deprotonation of 1 a-Cl with copper(I) acetate at low temperatures afforded a mixture of 4 a and the corresponding cAArC copper(I) chloride 5 a , and allowed the isolation and structural characterization of the first example of a cAArC copper complex of general formula [(cAArC)CuCl].     

An efficient molecular docking using conformational space annealing

Molecular docking falls into the general category of global optimization problems because its main purpose is to find the most stable complex consisting of a receptor and its ligand. Conformational space annealing (CSA), a powerful global optimization method, is incorporated with the Tinker molecular modeling package to perform molecular docking simulations of six receptor-ligand complexes (3PTB, 1ULB, 2CPP, 1STP, 3CPA, and 1PPH) from the Protein Data Bank. In parallel, Monte Carlo with the minimization (MCM) method is also incorporated into the Tinker package for comparison. The energy function, consisting of electrostatic interactions, van der Waals interactions, and torsional energy terms, is calculated using the AMBER94 all-atom empirical force field. Rigid docking simulations for all six complexes and flexible docking simulations for three complexes (1STP, 3CPA, and 1PPH) are carried out using the CSA and the MCM methods. The simulation results show that the docking procedures using the CSA method generally find the most stable complexes as well as the native-like complexes more efficiently and accurately than those using the MCM, demonstrating that CSA is a promising search method for molecular docking problems.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. IV. Pairs of different hydrophobic side chains

The potentials of mean force of 21 heterodimers of the molecules modeling hydrophobic amino acid side chains: ethane (for alanine), propane (for proline), isobutane (for valine), isopentane (for leucine and isoleucine), ethylbenzene (for phenylalanine), methyl propyl sulfide (for methionine), and indole (for tryptophane) were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation. Analytical expressions consisting of the Gay-Berne term to represent effective van der Waals interactions and the cavity term proposed in our earlier work were fitted to the potentials of mean force. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules, are well represented by the analytical expressions for all systems; large deviations between the MD-determined PMF and the analytical approximations are observed for pairs involving the least spheroidal solutes: ethylbenzene, indole, and methyl propyl sulfide at short distances at which the PMF is high and, consequently, these regions are rarely visited. When data from the PMF within only 10 kcal/mol above the global minimum are considered, the standard deviation between the MD-determined and the fitted PMF is from 0.25 to 0.55 kcal/mol (the relative standard deviation being from 4% to 8%); it is larger for pairs involving nonspherical solute molecules. The free energies of contact computed from the PMF surfaces are well correlated with those determined from protein-crystal data with a slope close to that relating the free energies of transfer of amino acids (from water to n-octanol) to the average contact free energies determined from protein-crystal data. These observations justify future use of the determined potentials in coarse-grained protein-folding simulations.     

On a factorization of homeomorphisms of the circle possessing periodic points

We prove that for every orientation-preserving homeomorphism possessing periodic points of order n there exist a homeomorphism such that Tn=id and a homeomorphism without periodic points except fixed points such that

F=Tq○G     

Silicon Carbide Modified Carbon Materials. Formation of Nanocrystalline SiC from Thermochemical Processes in the System Coal Tar Pitch/Poly(carbosilane)

Poly(carbosilane) or PCS, {–CH₂–SiH(CH₃)–} _n , is used as a Si-bearing precursor in combination with a coal tar pitch to study thermally induced transformations toward SiC-modified carbon composites. Following mixing of the components in the molten pitch at 160°C, the mixture is heated under argon atmosphere at 500°C yielding a solid carbonizate that is further subjected to separate pyrolysis experiments at 1300°C or 1650°C. At temperatures up to 500°C, the PCS reacts with suitable pitch components as well as undergoing decomposition reactions. At higher temperatures, clusters of prevailingly nanocrystalline -SiC are confirmed after the 1650°C pyrolysis step with indications that the formation of the compound starts at 1300°C. ²⁹Si MAS NMR, XRD, FT-IR, XPS, and elemental analysis are used to characterize each pyrolysis step, especially, from the viewpoint of transformation of silicon species to silicon carbide in the carbon matrix evolved from the pitch.     

Technology aspects of GaN-based diodes for high-field operation

This work reports important aspects of technology development and characterization for GaN based diodes operating at high electric fields. The considered operation conditions result, in comparison to III–V semiconductor devices, from the higher values of threshold field for intervalley transfer of electrons. This lies above 150 kV/cm and requires correspondingly higher biasing voltages and currents through semiconducting layers of transferred electron devices, switches or NDR (negative differential resistance) diodes. Mesa-based vertical and lateral devices using GaN layers on sapphire substrate were considered for current–voltage characteristics under very high electric field conditions. A systematic investigation of MOCVD-grown diode structures with regular, tapered mesa designs and variable dimensions was carried out under pulsed-bias condition. The current–voltage characteristics showed threshold voltages for saturation corresponding to electric fields well above the critical value of 150 kV/cm in the active layer. Self-heating and electromigration effects have been addressed in relation with biasing and metallization conditions.     

Simulation of the opening and closing of Hsp70 chaperones by coarse-grained molecular dynamics

Heat-shock proteins 70 (Hsp70s) are key molecular chaperones which assist in the folding and refolding/disaggregation of proteins. Hsp70s, which consist of a nucleotide-binding domain (NBD, consisting of NBD-I and NBD-II subdomains) and a substrate-binding domain [SBD, further split into the β-sheet (SBD-β) and α-helical (SBD-α) subdomains], occur in two major conformations having (a) a closed SBD, in which the SBD and NBD domains do not interact, (b) an open SBD, in which SBD-α interacts with NBD-I and SBD-β interacts with the top parts of NBD-I and NBD-II. In the SBD-closed conformation, SBD is bound to a substrate protein, with release occurring after transition to the open conformation. While the transition from the closed to the open conformation is triggered efficiently by binding of adenosine triphosphate (ATP) to the NBD, it also occurs, although less frequently, in the absence of ATP. The reverse transition occurs after ATP hydrolysis. Here, we report canonical and multiplexed replica exchange simulations of the conformational dynamics of Hsp70s using a coarse-grained molecular dynamics approach with the UNRES force field. The simulations were run in the following three modes: (i) with the two halves of the NBD unrestrained relative to each other, (ii) with the two halves of the NBD restrained in an "open" geometry as in the SBD-closed form of DnaK (2KHO), and (iii) the two halves of NBD restrained in a "closed" geometry as in known experimental structures of ATP-bound NBD forms of Hsp70. Open conformations, in which the SBD interacted strongly with the NBD, formed spontaneously during all simulations; the number of transitions was largest in simulations carried out with the "closed" NBD domain, and smallest in those carried out with the "open" NBD domain; this observation is in agreement with the experimentally-observed influence of ATP-binding on the transition of Hsp70's from the SBD-closed to the SBD-open form. Two kinds of open conformations were observed: one in which SBD-α interacts with NBD-I and SBD-β interacts with the top parts of NBD-I and NBD-II (as observed in the structures of nucleotide exchange factors), and another one in which this interaction pattern is swapped. A third type of motion, in which SBD-α binds to NBD without dissociating from SBD-β was also observed. It was found that the first stage of interdomain communication (approach of SBD-β, to NBD) is coupled with the rotation of the long axes of NBD-I and NBD-II towards each other. To the best of our knowledge, this is the first successful simulation of the full transition of an Hsp70 from the SBD-closed to the SBD-open conformation.