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).

---

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.

     

X-ray coherence and ultra small angle resolution at grazing incidence and exit angles

We measure the nonspecular x-ray scattering at grazing incidence and exit angles from a GaAs surface, modulated by an one-dimensional lateral grating of effectively variable periodicity 1 md60 m. Due to the projection onto the sample surface, the lateral coherence length is enlarged by a factor of more than 100. The line broadening of the diffraction maxima is used to deduce the number of periods that add up coherently for a given periodd and given angle of incidence. We demonstrate that the scattering geometry used allows for large coherently illuminated lengths on the sample and ultra small angle resolution of one- or two-dimensional objects. Thus structures of m size and larger will be accessible by coherent x-ray scattering.     

Internal dynamics of flexible molecules: Cyclohexane

Summary The international motions of a single cyclohexane molecule are studied by molecular dynamics calculations. Classical trajectories are calculated by integrating Newton's equation of motion. The potential functions used are essentially the same as in Allinger's MM2 program which is widely applied for calculations on conformational energies of organic molecules.Geometries and relative energies are reported for all stable low energy conformers and some transition states of cyclohexane. Vibrational frequencies of classical oscillations of individual bonds — computed for ethane as reference system — are close to the experimental values.Two trajectories of the molecular dynamics of cyclohexane were simulated. In the first we were able to follow the process of ring inversion: chair twisted forms inverted chair. The reaction path is analysed in detail and compared with static approaches. The second trajectory shows the correlated reorientation of the possible twisted forms alone. This process is known as pseudorotation.Dedicated to Prof. Dr. Karl Schlögl     

Synthesis of fluorous fullerene adducts: reversible solubilization of fullerenes in perfluorinated solvents

Fullerene (C60) Diels-Alder adducts with perfluoroalkylated 1,3-cyclopentadiene (1a,b) were synthesized and studied. The perfluoroalkylated cyclopentadiene was found to be less reactive toward C60 than cyclopentadiene itself, possibly because of the electron-withdrawing effect of the side chain. Because of the same effect, the temperature of the retro-Diels-Alder reaction for the fluorinated adducts was lower (70 degrees C) than the reported value (95 degrees C) for the cyclopentadiene adducts of C60. Higher adducts of the fluorous diene and C60 were found to be soluble in perfluorohexane and to show visible partitioning between organic (toluene) and fluorous phases. Also, the Diels-Alder addition of the fluorous diene was accompanied by extensive oxidation of the fullerene core, as revealed by MALDI-TOF data.