Analysis of RNA sequence structure maps by exhaustive enumeration I. Neutral networks

Summary Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of allGC andAU sequences with chain lengths up to 30. The computed structural data are evaluated through exhaustive enumeration and used as an exact reference for testing analytical results derived from mathematical models and sampling based on statistical methods. Several new concepts of RNA sequence to secondary structure mappings are investigated, among them that ofneutral networks (being sets of sequences folding into the same structure). Exhaustive enumeration allows to test several previously suggested relations: the number of (minimum free energy) secondary structures as a function of the chain length as well as the frequency distribution of structures at constant chain length (commonly resulting in generalized forms ofZipf's law).

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Analyse der Beziehungen zwischen RNA-Sequenzen und Sekundärstrukturen durch vollständige Faltung, 1. Mitt. Faltung, Neutrale Netzwerke

Zusammenfassung Die globalen Benziehungen zwischen RNA-Sequenzen und Sekundärstrukturen werden als Abbildungen aus einem Raum aller Sequenzen in einen Raum aller Strukturen aufgefaßt. Diese Abbildungen werden durch Falten aller binären Sequenzen desGC-undAU-Alphabets mit Kettenlängen bis zun=30 untersucht. Die berechneten Strukturdaten werden durch vollständiges Abzählen ausgewertet und als eine exakte Referenz zum Überprüfen analytischer Resultate aus mathematischen Modellen sowie zum Testen statistisch erhobener Proben verwendet. Einige neuartige Konzepte zur Beschreibung der Beziehungen zwischen Sequenzen und Strukturen werden eingehend untersucht, unter ihnen der Begriff derneutralen Netzwerke. Ein neutrales Netzwerk besteht aus allen Sequenzen, die eine bestimmte Struktur ausbilden. Vollständiges Abzählen ermöglicht beispielsweise die Bestimmung aller Strukturen minimaler freier Energie in Abhängigkeit von der Kettenlänge ebenso wie die Bestimmung der Häufigkeitsverteilungen der Strukturen bei konstanten Kettenlängen. Die letzteren folgen einer verallgemeinerten FormZipfschen Gesetzes.

     

Critical Points in a Crystal and Procrystal

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, –1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.     

Interaction between poly(ethylene oxide) and sodium dodecyl sulfonate as studied by surface tension, conductivity, viscosity, electron spin resonance and nuclear magnetic resonance

The aggregation of sodium dodecyl sulfonate (AS) in aqueous solution containing various amounts of poly(ethylene oxide) (PEO) has been investigated by different experimental techniques. The experimental techniques include surface tension, conductivity, viscosity, electron spin resonance (ESR) and nuclear magnetic resonance (NMR). The critical aggregate concentration of AS on polymer strands as well as the concentration where the polymer becomes saturated with surfactant has been determined. Both ESR and NMR results indicate that the AS–PEO complex forms a more “open” structure and that PEO may penetrate into the interior of the micelles. Received: 22 October 1998 Accepted in revised form: 1 April 1999     

Advances in two-dimensional GC with glass capillary columns

A versatile two-dimensional gas chromatograph is described, consisting of 2 separate ovens, one intermediate trap, an auxiliary inlet, and the necessary hardware to effect off-line switching according to the principle of Deans. The unit has been designed for use with high resolution glass capillary columns. The performance of individual instrumental components was critically evaluated. Results showed that low dead volume glass to metal connections were required in the manifold and detector lines to minimize extra-column effects. The mass of the intermediate trap must be low to allow rapid heating. Operational parameters are discussed and examples of some applications are shown.     

Phase Equilibria and Critical Curves of Binary Ammonia–Hydrocarbon Mixtures

Liquid or dense supercritical ammonia has been suggested as an extraction fluid. It is indeed good solvent for very different classes of compounds, as can be seen from phase diagrams. Such diagrams for binary systems of ammonia and hydrocarbons are presented and discussed on the basis of their critical curves. Apparatus and methods for the measurement of phase equilibria and equation of state data of fluid mixtures at high pressure are described.     

Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

Critical micelle concentrations for alkyltrimethylammonium bromides in water from 25 to 160°C

Critical micelle concentrations were determined by conductance measurements for decyl-, dodecyl-, tetradecyl- and hexadecyltrimethylammonium bromide in water at 25, 60, 95, 130, and 160°C. The results are discussed in terms of the equilibrium model and the nonlinear Poisson-Boltzmann model for micelle formation. The free energies of transferring a methylene group from water to the oil-like interior of the micelle are found to be –781 at 25°C, –796 at 60°C, –819 at 95°C, –815 at 130°C, and –787 at 160°C cal-mol^–1.     

A graph-theoretic approach to modeling metabolic pathways

Summary The metabolic pathways of medazepam, oxazepam, and diazepam were modeled using graph-theoretic transforms which are incorporable into computer-assisted metabolic analysis programs. The information, represented in the form of a graph-theoretic transform kit, which was obtained from these pathways was then used to predict the metabolites of other benzodiazepine compounds. The transform kits gave statistically significant predictions with respect to a statistical method for evaluating the performance of the transform kits.