NAOMI: on the almost trivial task of reading molecules from different file formats

In most cheminformatics workflows, chemical information is stored in files which provide the necessary data for subsequent calculations. The correct interpretation of the file formats is an important prerequisite to obtain meaningful results. Consistent reading of molecules from files, however, is not an easy task. Each file format implicitly represents an underlying chemical model, which has to be taken into consideration when the input data is processed. Additionally, many data sources contain invalid molecules. These have to be identified and either corrected or discarded. We present the chemical file format converter NAOMI, which provides efficient procedures for reliable handling of molecules from the common chemical file formats SDF, MOL2, and SMILES. These procedures are based on a consistent chemical model which has been designed for the appropriate representation of molecules relevant in the context of drug discovery. NAOMI's functionality is tested by round robin file IO exercises with public data sets, which we believe should become a standard test for every cheminformatics tool.     

Periodic Traveling Gravity Water Waves with Discontinuous Vorticity

We use elliptic theory to prove the existence of steady two-dimensional periodic waterwaves of large amplitude in a flowwith an arbitrary bounded but discontinuous vorticity. This is achieved by developing a local and global bifurcation construction of weak solutions of the elliptic partial differential equations that are relevant to this hydrodynamical context.     

Pressure Beneath a Solitary Water Wave: Mathematical Theory and Experiments

We study the pressure beneath a solitary water wave propagating in an irrotational flow at the free surface of water with a flat bed. The investigation is divided into two parts. The first part concerns a rigorous nonlinear study of the governing equations for water waves. We prove that the pressure in the fluid beneath a solitary wave strictly increases with depth and strictly decreases horizontally away from the vertical line beneath the crest. The second part of the paper describes an experimental study. Excellent agreement is found to exist between the theoretical predictions and the measurements. Our conclusions are also supported by numerical simulations.     

Addressing the stereochemistry of complex organic molecules by density functional theory-NMR: vannusal B in retrospective

We have employed density functional theory (DFT) protocols to calculate the NMR properties of the vannusals, a class of natural products whose structures have been the subject of recent investigations. The originally assigned structure of vannusal B was revised after a long synthetic journey which generated a series of closely related diastereomers. In this work we show how DFT calculations based on density functionals and basis sets designed for the prediction of NMR spectra (M06/pcS-2 level of theory) can be used to reproduce the observed parameters, thereby offering to the synthetic chemist a useful tool to discard or accept putative structures of unknown organic molecules.     

Does compound I vary significantly between isoforms of cytochrome P450?

The cytochrome P450 (CYP) enzymes are important in many areas, including pharmaceutical development. Subtle changes in the electronic structure of the active species, Compound I, have been postulated previously to account partly for the experimentally observed differences in reactivity between isoforms. Current predictive models of CYP metabolism typically assume an identical Compound I in all isoforms. Here we present a method to calculate the electronic structure and to estimate the Fe-O bond enthalpy of Compound I, and apply it to several human and bacterial CYP isoforms. Conformational flexibility is accounted for by sampling large numbers of structures from molecular dynamics simulations, which are subsequently optimized with density functional theory (B3LYP) based quantum mechanics/molecular mechanics. The observed differences in Compound I between human isoforms are small: They are generally smaller than the spread of values obtained for the same isoform starting from different initial structures. Hence, it is unlikely that the variation in activity between human isoforms is due to differences in the electronic structure of Compound I. A larger difference in electronic structure is observed between the human isoforms and P450(cam) and may be explained by the slightly different hydrogen-bonding environment surrounding the cysteinyl sulfur. The presence of substrate in the active site of all isoforms studied appears to cause a slight decrease in the Fe-O bond enthalpy, apparently due to displacement of water out of the active site, suggesting that Compound I is less stable in the presence of substrate.     

Regiochemistry in cobalt-mediated intermolecular Pauson-Khand reactions of unsymmetrical internal heteroaromatic alkynes with norbornene

The intermolecular Pauson-Khand (PK) reactions of sterically comparable (2-phenylethynyl)heteroaromatic compounds with norbornene, mediated by Co(2)(CO)(8) to give cyclopentenone products, were examined in this study. A synthetic protocol utilizing focused-microwave dielectric heating proved indispensable in the efficient synthesis of the PK cyclopentenone products. "π-Deficient" heteroaromatic substrates, e.g., 2-pyrones, and some "π-excessive" heteroaromatics such as 2- and 3-thiophene and 2-furan favor the β-position in the newly formed cyclopentenone ring. Other π-excessive heteroaromatics such as 2-pyrrole or 2-indole favor the α-position. A π-excessive 3-indole derivative gave a nearly equal mixture of regioisomers. The position of the nitrogen in pyridyl-containing alkyne substrates also affects the regiochemical outcome of the PK reaction. A 2-pyridyl alkyne, possessing a proximal nitrogen, influences the regioselectivity relative to a 4-pyridyl variant quite dramatically, favoring the β-position in the newly formed cyclopentenone ring. A 2-pyrimidylalkyne exhibits similar behavior to the 2-pyridylalkyne. Compounds that do not participate in PK reactions with norbornene include (2-phenylethynyl)imidazoles and the related benzimidazoles, which promote rapid decomposition of the in situ generated (μ(2)-alkyne)Co(2)(CO)(6) complexes. This stands in contrast with other nitrogen-containing heteroaromatics, e.g., pyrrole-, indole-, and pyrimidine-derived compounds, which effectively undergo PK reactions. Overall, the type of heteroaromatic group dramatically influences PK regioselectivity, which can in part be explained by rationalization of the current reaction mechanism, but not fully.     

Preparative separation of 1,3,6-pyrenetrisulfonic acid trisodium salt from the color additive D&C Green No. 8 (pyranine) by pH-zone-refining counter-current chromatography

In developing analytical methods for batch certification of the color additive D&C Green No. 8 (G8), the U.S. Food and Drug Administration needed the trisodium salt of 1,3,6-pyrenetrisulfonic acid (P3S) for use as a reference material. Since P3S was not commercially available, preparative quantities of it were separated from portions of a sample of G8 that contained ～3.5% P3S. The separations were performed by pH-zone-refining counter-current chromatography using dodecylamine (DA) as the hydrophobic counterion. The added DA enabled partitioning of the polysulfonated components into the organic stationary phase of the two-phase solvent system used, 1-butanol-water (1:1). Thus, a typical separation that involved 20.3g of G8, using sulfuric acid as the retainer acid and 20% DA in the stationary phase and 0.1M sodium hydroxide as the mobile phase, resulted in ～0.58 g of P3S of greater than 99% purity. The identification and characterization of the separated P3S were performed by elemental analyses, proton nuclear magnetic resonance, high-resolution mass spectrometry, ultra-violet spectra, and high-performance liquid chromatography.     

Thermodynamic parameters and counterion binding to the micelle in binary anionic surfactant systems

Competitive counterion binding of sodium and calcium to micelles, and mixed micellization have been investigated in the systems sodium dodecylsulfate (NaDS)/sodium decylsulfate (NaDeS) and NaDS/sodium 4-octylbenzenesulfonate (NaOBS) in order to accurately model the activity of the relevant species in solution. The critical micelle concentration (CMC) and equilibrium micelle compositions of mixtures of these anionic surfactants, which is necessary for determining fractional counterion binding measurements, is thermodynamically modeled by regular solution theory. The mixed micelle is ideal (the regular solution parameter β(M)=0) for the NaDS/NaOBS system, while the mixed micelle for NaDS/NaDeS has β(M)=-1.05 indicating a slight synergistic interaction. Counterion binding of sodium to the micelle is influenced by the calcium ion concentration, and vice versa. However, the total degree of counterion binding is essentially constant at approximately 0.65 charge negation at the micelle's surface. The counterion binding coefficients can be quantitatively modeled using a simple equilibrium model relating concentrations of bound and unbound counterions.     

New bounds on the average distance from the Fermat–Weber center of a planar convex body

The Fermat–Weber center of a planar body Q is a point in the plane from which the average distance to the points in Q is minimal. We first show that for any convex body Q in the plane, the average distance from the Fermat–Weber center of Q to the points in Q is larger than , where Δ(Q) is the diameter of Q. This proves a conjecture of Carmi, Har-Peled and Katz. From the other direction, we prove that the same average distance is at most . The new bound substantially improves the previous bound of due to Abu-Affash and Katz, and brings us closer to the conjectured value of . We also confirm the upper bound conjecture for centrally symmetric planar convex bodies.     

Corrector-predictor methods for sufficient linear complementarity problems

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has \(O((1+\kappa)\sqrt{n}L)\)-iteration complexity, the same as Miao’s method, but our error estimates are sightly better. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also present a family of infeasible higher order corrector-predictor methods that are superlinearly convergent even in the absence of strict complementarity. The algorithms of this class are globally convergent for general positive starting points. They have \(O((1+\kappa)\sqrt{n}L)\)-iteration complexity for feasible, or “almost feasible”, starting points and O((1+κ)² nL)-iteration complexity for “sufficiently large” infeasible starting points.