Numerical solution of the nonlinear Poisson–Boltzmann equation: Developing more robust and efficient methods

We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in an article appearing previously in this journal. A detailed analysis of the resulting method is presented, with comparisons to other methods that have been proposed in the literature, including the classical nonlinear multigrid method, the nonlinear conjugate gradient method, and nonlinear relaxation methods such as successive overrelaxation. Both theoretical and numerical evidence suggests that this method will converge in the case of molecules for which many of the existing methods will not. In addition, for problems which the other methods are able to solve, numerical experiments show that the new method is substantially more efficient, and the superiority of this method grows with the problem size. The method is easy to implement once a linear multilevel solver is available and can also easily be used in conjunction with linear methods other than multigrid. © 1995 by John Wiley & Sons, Inc.     

Spectral and Structural Studies of the Copper(II) Complexes of 3, 4‐Hexanedione Bis(3‐azacyclothiosemicarbazones)

Copper(II) complexes of 3, 4‐hexanedione bis(piperidyl‐ and bis(hexamethyleneiminylthiosemicarbazone), H₂Hxpip and H₂Hxhexim, respectively, have been prepared and studied spectroscopically. The bis(thiosemicarbazones) have been characterized by their melting points, as well as IR, electronic and ¹H NMR spectra. Upon formation of their copper(II) complexes, loss of the hydrazinic hydrogen atoms occurs, and the ligands coordinate as dianionic, tetradentate N₂S₂ ligands. The crystal structures of H₂Hxpip, its 4‐coordinate copper(II) complex, [Cu(Hxpip)], and the related [Cu(Hxhexim)] have been determined by single crystal x‐ray diffraction. The nature of the four‐coordinate copper(II) complexes have also been characterized by ESR, IR, and electronic spectroscopy, as well as magnetic moments and elemental analyses.     

Developing a miniaturized setup for in‐tube simultaneous determination of three alkaloids using electromembrane extraction in combination with ultraviolet spectrophotometry

Herein, electromembrane extraction was combined with ultraviolet spectrophotometry using a customized manifold for preconcentration and simultaneous determination of morphine, codeine, and papaverine in water and human urine samples. Absorption spectra of the extracts were recorded inside the lumen of the hollow fiber using two fiber optics connected to a miniature spectrophotometer. Partial least squares regression was applied to resolve the overlapped spectra of the analytes. Performance of the model was validated by an independent test set. Central composite design was applied to optimize the extraction parameters. The optimized extraction conditions are as follows; supporting liquid membrane: 2‐nitrophenyl octyl ether containing 15% v/v bis(2‐ethylhexyl) phosphate, applied voltage: 80 V, donor pH: 3.0, acceptor pH: 1.0, extraction time: 20 min. Finally, the optimized extraction method was validated for determination of the mentioned alkaloids in human urine samples. The method showed good linearity (R² > 0.995) for all of the mentioned alkaloids. The limits of detection for morphine, codeine, and papaverine in diluted human urine were found to be 0.6, 1.1, and 0.6 ng/mL, respectively with acceptable relative standard deviations. Enrichment factors of 104, 108, and 102 were achieved for morphine, codeine, and papaverine, respectively.     

Quantification of controlled release leuprolide and triptorelin in rabbit plasma using electromembrane extraction coupled with HPLC–UV

An electromembrane extraction followed by HPLC–UV technique was developed and validated for quantification of leuprolide and triptorelin in rabbit plasma. The influencing parameters on the extraction efficiency were optimized using experimental design methodology. The optimized conditions were found to be; supported liquid membrane: a mixture of 1‐octanol and 2‐ethyl hexanol (1:1) containing 10% v/v di(2‐ethylhexyl) phosphate, applied voltage: 5 V, extraction time: 5 min, pH of the donor phase: 4.5 and pH of the acceptor phase: 1.0. The optimized method was validated for linearity, intraday and interday precision, and accuracy in rabbit plasma. The range of quantification for both peptides was 0.5–1000 ng/mL with regression coefficients higher than 0.994. Relative recoveries of leuprolide and triptorelin were found to be 80.3 and 75.5%, respectively. Limits of quantification and detection for both peptides were found to be 0.5 and 0.15 ng/mL, respectively. The validated method was successfully applied to pharmacokinetic study of the 1‐month depot formulations of each peptide after subcutaneous administration to rabbits.     

Synthesis of some novel imidazolidine derivatives and their metal complexes with biological and antitumor activity

Halogenated imidazo(pyrazine,[1,4]diazocine and quinoxaline), 9,10‐anthraquinone‐ [6,7‐e], phenanthroline[5,6‐e] {imidazo[4,5‐b]pyrazine}, and naphtho[1,8‐ef]imidazo[4,5‐b][1,4] diazipen were obtained through interaction of imidazolidineiminothiones with the corresponding diamino compounds. Imidazo[4,5‐e] triazine and pyrrolo[2,3‐d]imidazole were prepared when the iminothiones were reacted with thiocarbohydrazide and with ethylphenyl acetate, separately. Some of the synthesized compounds exhibited better biological and antitumor activities. © 2006 Wiley Periodicals, Inc. Heteroatom Chem 17:634–647, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20244     

Submaximal interpenetration and bicontinuous three-dimensional channels in porous molecular networks

Crystallization of tetrakis(3,5-dihydroxyphenyl)silane (1) from various solvents produces structures built from interpenetrated hydrogen-bonded diamondoid networks. Crystals grown from hexane/methyl propiolate show 5-fold interpenetration, with no volume remaining for the inclusion of guests. In contrast, crystals grown from mixtures of hexane with ethyl acrylate, ethyl acetate, THF, or dioxolane all exhibit submaximal 3-fold interpenetration. Approximately 50% of the volumes are accessible to guests, which occupy regions of diamondoid topology that replace missing networks of tetraresorcinol 1. Of particular interest are crystals containing THF or dioxolane, in which guests occupy two independent systems of interpenetrating diamondoid channels. The submaximally interpenetrated structures of tetraresorcinol 1 provide detailed models of complex topologies adopted by block copolymers and amphiphilic assemblies to optimize interfacial contact.     

Deformation of porous molecular networks induced by the exchange of guests in single crystals

A strategy for making molecular networks that are porous and deformable is revealed by the behavior of compound 1, in which groups that form hydrogen bonds are attached to a nominally tetrahedral Si core. Compound 1 crystallizes from various carboxylic acids to produce a porous hydrogen-bonded diamondoid network, with up to 65% of the volume available for including guests. Changing the guests expands or contracts the network up to 30% in one direction, and single crystals can accommodate these exchange-induced deformations without loss of crystallinity. This resilience appears to result in part from the incorporation of flexible Si nodes in an otherwise robust network maintained by multiple hydrogen bonds. In certain cases, exchange is faster than deformation of the network, allowing the isolation of metastable structures with a new guest included in an otherwise unchanged network. Such processes can provide new materials that would be difficult or impossible to obtain in other ways.     

Classification of the similarity solutions of free Kramers equation

We obtain, a complete classification of all possible nontrivial similarity solutions of the free Kramers equations, together with a necessary and sufficient condition for each type to be reducible to the heat equation. A confluent hypergeometric solution of the free Kramers equation is derived for some classes of similarity solutions.     

Hydrolysis of Sucrose by Heterogeneous Catalysts

A kinetic study of the hydrolysis of sucrose by solid catalysts has been carried out using a polarimetric technique. V₂O₅/-Al₂O₃ was selected as appropriate catalyst. At the optimum conditions the activation parameters have been evaluated using the Arrhenius and Eyring plots.     

On the Brazil Nuts Problem: Is It of Relevance to Hydrodynamics?

A recent advance in understanding the Brazil nuts phenomenon together with insight into the relative motion of different-size particles in a lattice fluid makes this phenomenon amenable to an approach based on hydrodynamic concept. Here we use this conjecture as a stimulus for solving the equation describing asymmetric transport of particles in a medium moving with constant velocity. We also consider a method for constructing invariant solutions, which enables us to study the dependence of the probability density function on the parameters controlling the asymmetry of the flow. Physical realizations of the invariant solutions are in agreement with recent computer simulations by Alexander and Lebowitz.