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  • 1
    ISSN: 1432-1017
    Keywords: Key words Kinetic folding ; Minimun free energy structures ; RNA secondary structures ; Sequence structure relations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract Algorithms predicting RNA secondary structures based on different folding criteria – minimum free energies (mfe), kinetic folding (kin), maximum matching (mm) – and different parameter sets are studied systematically. Two base pairing alphabets were used: the binary GC and the natural four-letter AUGC alphabet. Computed structures and free energies depend strongly on both the algorithm and the parameter set. Statistical properties, such as mean number of base pairs, mean numbers of stacks, mean loop sizes, etc., are much less sensitive to the choice of parameter set and even of algorithm. Some features of RNA secondary structures, such as structure correlation functions, shape space covering and neutral networks, seem to depend only on the base pairing logic (GC or AUGC alphabet).
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1434-4475
    Keywords: Neutral networks ; Random graphs ; RNA secondary structures ; Zipf's law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: 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.
    Notes: 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).
    Type of Medium: Electronic Resource
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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.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of organic chemistry 44 (1979), S. 374-379 
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper presents a qualitative analysis of the following systems ofn differential equations: $$\dot x_i = x_i x_j - x_i \sum\nolimits_r^n { = 1} x_r x_s {\mathbf{ }}(j = i - 1 + n\delta _{i1} {\mathbf{ }}and{\mathbf{ }}s = r - 1 + n\delta _{r1} )$$ , which show cyclic symmetry. These dynamical systems are of particular interest in the theory of selforganization and biological evolution as well as for application to other fields.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 0030-4921
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The n.m.r. spectra of some 1,2,2-trisubstituted cyclopropanes are reported. Coupling constants and chemical shifts of the cyclopropane protons and their dependence on substituent effects are discussed. Conformations of benzylcyclopropane derivatives are investigated by long range magnetic shielding. The concentration dependence of the n.m.r. spectra of some 1,3-diols is explained by inter- and intramolecular hydrogen bonding.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Publication Date: 2011-08-24
    Description: RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.
    Keywords: Life Sciences (General)
    Type: Journal of theoretical biology (ISSN 0022-5193); Volume 181; 4; 299-310
    Format: text
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