An adaptive stepsize method for the chemical Langevin equation

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.     

Mineral composition of fruit by-products evaluated by neutron activation analysis

Brazil is one of the largest producers of fruits cropping 40 million tons per year. In agro-food processing, approximately 50 % of raw material is discarded generating large amounts of by-products. The lack of information on the nutritional quality of agroindustrial by-products precludes their potential use in the manufacture of food products accessible to all. In this context, the objective of this work was to investigate the nutritional quality of by-products of the industrial processing of fruits. Samples of bagasse, peel and seeds of several fruits (banana, camu camu, coconut, cupuaçu, guava, jackfruit, mango, orange, papaya, pineapple, and soursop) were analysed by neutron activation analysis for the determination of Br, Ca, Co, Cr, Cs, Fe, K, La, Na, Rb, Sc and Zn. In general, higher levels of minerals were found in the by-products rather than in the pulps of fruits. This indicates that the use of the by-products should be encouraged, thereby reducing the economic and environmental impact of waste generated by agroindustrial processing.     

Utilization of deuterium labelling and 13C NMR spectroscopy in the investigation of the condensation of 1-Methyl-5-nitroimidazole-2-aldehyde and 2-Amino-4-methylpyrimidine

The product obtained condensing l-methyl-5-nitroimidazole-2-aldehyde with 2-amino-4-trideuteriomethyl-pyrimidine and showing total deuterium incorporation at one of the olefinic carbons and partial deuterium incorporation para to the amino group, served to assign ¹³C and ¹H resonances in the condensation products 3. The nature of the species undergoing condensation has been inferred from labelling experiments and from ¹H and ¹³C nmr spectra of precursors and products in dimethylsulfoxide and trifluoroacetic acid.     

Inter‐ and intramolecular hydrogen bonds in polyamines: variable‐concentration 1H‐NMR studies

Inter‐ and intramolecular hydrogen bonding play an important role in determining the arrangement, physical properties, and reactivity of a great diversity of structures in chemical and biological systems. Several aromatic nucleophilic substitutions (ANS) in nonpolar aprotic, (non‐HBD), solvents recently studied in our laboratory have demonstrated the importance of self‐association of amines by hydrogen‐bond interactions. In this paper, we describe ¹H‐NMR studies carried out at room temperature on bi‐ and polyfunctionalized amines, namely: N‐(3‐amino‐1‐propyl)morpholine (3‐APMo), histamine, 2‐guanidinobenzimidazole (2‐GB), 1,2‐diaminoethane (EDA), 3‐dimethylamino‐l‐propylamine (DMPA), and 1‐(2‐aminoethyl)piperidine (2‐AEPip). By ¹H‐NMR measurements of amine solutions at variable concentrations we have shown that 3‐APMo, histamine and 2‐GB are able to form a six‐membered ring by intramolecular hydrogen bonding, while EDA, DMPA, and 2‐AEPip form dimers by intermolecular hydrogen bonds. Likewise, variable concentration ¹H‐NMR studies allowed estimation of the corresponding equilibrium constants for the dimerization. These results are correlated with experimental kinetic results of ANS, confirming hereto the relevance of the “dimer mechanism” in reactions involving these amines. Copyright © 2011 John Wiley & Sons, Ltd.     

Pharmacophore modeling as an efficient tool in the discovery of novel noncompetitive AMPA receptor antagonists

A three-dimensional pharmacophore model for the binding of noncompetitive AMPA receptor antagonists was developed in order to map common structural features of highly active compounds. This hypothesis, which consists of two hydrophobic regions, one hydrogen bond acceptor and one aromatic region, was successfully used as framework for the design of a new class of allosteric modulators containing a tetrahydroisoquinoline skeleton and for in silico screening. The promising biological results suggested that the identified molecules might be useful "lead compounds" for future drug development.     

Stereoelectronic and inductive effects on 1H and 13C NMR chemical shifts of some cis-1,3-disubstituted cyclohexanes

This work presents the substituent effects on the 1H and 13C NMR chemical shifts in the cis-isomer of 3-Y-cyclohexanols (Y = Cl, Br, I, CH3, N(CH3)2 and OCH3) and 3-Y-1-methoxycyclohexanes (Y = F, Cl, Br, I, CH3, N(CH3)2 and OCH3). It was observed that the H-3 chemical shift, due to the substituent alpha-effect, increases with the increase of substituent electronegativity when Y is from the second row of the periodic table of elements, (CH3 *sigma(C3--H3a) interaction energy. This interaction energy, for the halogenated compounds, decreases with an increase in size of the halogen, and this is a possible reason for the largest measured chemical shift for H-3 of the iodo-derivatives. The beta-effect of the analyzed compounds showed that the chemical shift of hydrogens at C-2 and C-4 increases with the decrease of n(Y) --> *sigma(C2-C3) and n(Y) --> *sigma(C3-C4) interaction energies, respectively, showing a behavior similar to H-3. The alpha-effect on 13C chemical shifts correlates well with substituent electronegativity, while the beta-effect is inversely related to electronegativity in halogenated compounds. NBO analysis indicated that the substituent inductive effect is the predominant effect on 13C NMR chemical shift changes for the alpha-carbon. It was also observed that C-2 and C-4 chemical shifts for compounds with N(CH3)2, OCH3 and F are more shielded in comparison to the compounds having a halogen, most probably because of the larger interaction of the lone pair of more electronegative atoms (n(N) > n(O) > n(F)) with *sigma(C2-C3), *sigma(C3-C4) and *sigma(C3-H3a) in comparison with the same type of interaction with the lone pair of the other halogens.     

Chemical composition and antimicrobial activity of Anthriscus nemorosa root essential oil

The essential oil obtained by hydrodistillation from the roots of Anthriscus nemorosa (Bieb.) Sprengel (Umbelliferae) was analyzed by GC and GC-MS. Among sixty-two compounds identified (representing 89.0% of the total oil), the main components were: n-nonane (12.1%), n-hexadecanol (6.9%), delta-cadinene (6.4%), beta-pinene (6.0%) and germacrene D (5.4%). Furthermore, the antimicrobial activity of the oil was evaluated against the Gram-positive bacteria Staphylococcus epidermidis (ATCC 12228) and Bacillus subtilis (ATCC 6633), the Gram-negative bacterium Escherichia coli (ATCC 25922), and a yeast Candida albicans (ATCC 10259 and ATCC 24433) using the broth microdilution method.