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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    European biophysics journal 22 (1993), S. 13-24 
    ISSN: 1432-1017
    Keywords: Fitness landscapes ; Partition function ; Quasispecies ; RNA secondary structures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract Statistical properties of RNA folding landscapes obtained by the partition function algorithm (McCaskill 1990) are investigated in detail. The pair correlation of free energies as a function of the Hamming distance is used as a measure for the ruggedness of the landscape. The calculation of the partition function contains information about the entire ensemble of secondary structures as a function of temperature and opens the door to all quantities of thermodynamic interest, in contrast with the conventional minimal free energy approach. A metric distance of structure ensembles is introduced and pair correlations at the level of the structures themselves are computed. Just as with landscapes based on most stable secondary structure prediction, the landscapes defined on the full biophysical GCAU alphabet are much smoother than the landscapes restricted to pure GC sequences and the correlation lengths are almost constant fractions of the chain lengths. Correlation functions for multi-structure landscapes exhibit an increased correlation length, especially near the melting temperature. However, the main effect on evolution is rather an effective increase in sampling for finite populations where each sequence explores multiple structures.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Chemie 125 (1994), S. 167-188 
    ISSN: 1434-4475
    Keywords: Inverse folding ; parallel computing ; public domain software ; RNA folding ; RNA secondary structures ; tree editing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Die im Vienna RNA package enthaltenen Computer Programme für die Berechnung und den Vergleich von RNA Sekundärstrukturen werden präsentiert. Ihren Kern bilden Algorithmen zur Vorhersage von Strukturen minimaler Energie sowie zur Berechnung von Zustandssumme und Basenpaarungswahrscheinlichkeiten mittels dynamischer Programmierung. Ein effizienter heuristischer Algorithmus für das inverse Faltungsproblem wird vorgestellt. Darüberhinaus präsentieren wir kompakte und effiziente Programme zum Vergleich von RNA Sekundärstrukturen durch Baum-Editierung und Alignierung. Alle Programme sind in ANSI C geschrieben, darunter auch eine Implementation des Faltungs-algorithmus für Parallelrechner mit verteiltem Speicher. Wie Tests auf einem Intel Hypercube zeigen, wird das Parallelrechnen umso effizienter je länger die Sequenzen sind.
    Notes: Summary Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities. An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment. All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.
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  • 3
    ISSN: 1434-4475
    Keywords: Neutral networks ; Percolation of sequence space ; RNA folding ; RNA secondary structures ; Shape space covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Die Beziehungen zwischen RNA-Sequenzen und ihren Sekundärstrukturen werden durch vollständiges Falten allerGC- undAU-Sequenzen mit Kettenlängen bis zun=30 untersucht. Die aus der Informatik bekannte Technik derTries wird zur ökonomischen Datenspeicherung und für rasches Retrieval der gespeicherten Information angewendet. Die berechneten Strukturdaten werden durch vollständiges Abzählen ausgewertet. Sie dienen unter anderem als eine exakte Referenz zum Testen analytischer Resultate aus mathematischen Modellen sowie zur Überprüfung der Ergebnisse statistischer Probennahmen. Verschiedene neuartige Konzepte zur Behandlung der Zusammenhänge zwischen RNA-Sequenzen und Sekundärstrukturen wurden anhand der gewonnenen Daten eingehend untersucht. Unter ihnen befinden sich die Struktur derneutralen Netzwerke (die Gesamtheit der RNA-Sequenzen, die eine bestimmte Struktur ausbilden), diePerkolation des Sequenzraumes durch neutrale Netzwerke sowie das Prinzip derErfassung des Strukturraumes durch einen kleinen Ausschnitt des Sequenzraumes. Die durch vollständiges Abzählen erhaltenen Daten werden mit den analytischen Ergebnissen eines auf der Theorie der Zufallsgraphen aufbauenden Modells verglichen. Dieses Modell gibt die generischen Eigenschaften von Sequenz-Struktur-Relationen wieder, welche lediglich aus der Existenz einer Paarungslogik resultieren. Differenzen zwischen den numerischen und den analytischen Resultaten können als Konsequenzen der spezifischen biophysikalischen Eigenschaften von RNA-Molekülen interpretiert werden.
    Notes: Summary The relations between RNA sequences and secondary structures are investigated by exhaustive folding of allGC andAU sequences with chain lengths up to 30. The technique oftries is used for economic data storage and fast retrieval of information. 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 the structure ofneutral networks (being sets of RNA sequences folding into the same structure),percolation of sequence space by neutral networks, and the principle ofshape space covering. The data of exhaustive enumeration are compared to the analytical results of arandom graph model that reveals the generic properties of sequence to structure mappings based on some base pairing logic. The differences between the numerical and the analytical results are interpreted in terms of specific biophysical properties of RNA molecules.
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