Solutions of nonlinear differential equations

We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions. The solution of such an equation is a new generalized function. In this article we formulate necessary and sufficient conditions for when the solution of the given equation in the algebra of new generalized functions is associated with an ordinary function. Moreover, a class of all possible associated functions is described.     

Efficient implementation of periodic boundary conditions in Monte Carlo simulation

Determination of the shortest distances between particles is one of the most time-consuming parts of molecular simulation by the Monte Carlo method. In this work, we demonstrate that the use of signed-integer storage of coordinates in a scaled box allows one to skip multiple conditional statements in realization of periodic boundary conditions in cubic and rectangular boxes, which, in turn, increases the performance. Performance of the improved procedure was tested in NVT Monte Carlo simulations for liquid krypton and water. © 2018 Wiley Periodicals, Inc.     

Oligomerization of indole derivatives with incorporation of thiols

Two molecules of indole derivative, e.g. indole-5-carboxylic acid, reacted with one molecule of thiol, e.g. 1,2-ethanedithiol, in the presence of trifluoroacetic acid to yield adducts such as 3-[2-(2-amino-5-carboxyphenyl)-1-(2-mercaptoethylthio)ethyl]-1Hindole-5-carboxylic acid. Parallel formation of dimers, such as 2,3-dihydro-1H,1'H-2,3'-biindole-5,5'-dicarboxylic acid and trimers, such as 3,3'-[2-(2-amino-5-carboxyphenyl) ethane-1,1-diyl]bis(1H-indole-5-carboxylic acid) of the indole derivatives was also observed. Reaction of a mixture of indole and indole-5-carboxylic acid with 2-phenylethanethiol proceeded in a regioselective way, affording 3-[2-(2-aminophenyl)-1-(phenethylthio)ethyl]-1H-indole-5-carboxylic acid. An additional product of this reaction was 3-[2-(2-aminophenyl)-1-(phenethylthio)ethyl]-2,3-dihydro-1H,1'H-2,3'-biindole-5'-carboxylic acid, which upon standing in DMSO-d6 solution gave 3-[2-(2-aminophenyl)-1-(phenethylthio)ethyl]-1H,1'H-2,3'-biindole-5'-carboxylic acid. Structures of all compounds were elucidated by NMR, and a mechanism for their formation was suggested.     

Analysis of side chain rotational restrictions of membrane-embedded proteins by spin-label ESR spectroscopy

Site-directed spin-labeling electron spin resonance (SDSL-ESR) is a promising tool for membrane protein structure determination. Here we propose a novel way to translate the local structural constraints gained by SDSL-ESR data into a low-resolution structure of a protein by simulating the restrictions of the local conformational spaces of the spin label attached at different protein sites along the primary structure of the membrane-embedded protein. We test the sensitivity of this approach for membrane-embedded M13 major coat protein decorated with a limited number of strategically placed spin labels employing high-throughput site-directed mutagenesis. We find a reasonably good agreement of the simulated and the experimental data taking a protein conformation close to the one determined by fluorescence resonance energy transfer analysis [P.V. Nazarov, R.B.M. Koehorst, W.L. Vos, V.V. Apanasovich, M.A. Hemminga, FRET study of membrane proteins: determination of the tilt and orientation of the N-terminal domain of M13 major coat protein, Biophys. J. 92 (2007) 1296–1305].     

Speeding up a genetic algorithm for EPR-based spin label characterization of biosystem complexity

Complexity of biological systems is one of the toughest problems for any experimental technique. Complex biochemical composition and a variety of biophysical interactions governing the evolution of a state of a biological system imply that the experimental response of the system would be superimposed of many different responses. To obtain a reliable characterization of such a system based on spin-label Electron Paramagnetic Resonance (EPR) spectroscopy, multiple Hybrid Evolutionary Optimization (HEO) combined with spectral simulation can be applied. Implemented as the GHOST algorithm this approach is capable of handling the huge solution space and provides an insight into the "quasicontinuous" distribution of parameters that describe the biophysical properties of an experimental system. However, the analysis procedure requires several hundreds of runs of the evolutionary optimization routine making this algorithm extremely computationally demanding. As only the best parameter sets from each run are assumed to contribute into the final solution, this algorithm appears far from being optimized. The goal of this study is to modify the optimization routine in a way that 20-40 runs would be enough to obtain qualitatively the same characterization. However, to keep the solution diversity throughout the HEO run, fitness sharing and newly developed shaking mechanisms are applied and tested on various test EPR spectra. In addition, other evolutionary optimization parameters such as population size and probability of genetic operators were also varied to tune the algorithm. According to the testing examples a speed-up factor of 5-7 was achieved.