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  • 1
    ISSN: 1434-4475
    Keywords: RNA secondary structures ; RNA free energies ; Value landscapes ; Autocorrelation functions ; Correlation lengths
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung RNA-Sekundärstrukturen werden aus den Primärsequenzen mit Hilfe eines Computeralgorithmus berechnet, welcher einem Kriterium minimaler freier Energien folgt. Freie Energien, Replikations- oder Abbaugeschwindigkeitskonstanten werden aus den Sekundärstrukturen berechnet. Man kann daher diese Eigenschaften als komplizierte Funktionen der Sequenzen auffassen, deren Zahlenwerte durch Vermittlung der Sekundärstrukturen erhalten werden. Diese Funktionen induzieren hochkomplexe Bewertungslandschaften im Raum der Sequenzen. Die Landschaften werden mit Hilfe von Irrflugtechniken analysiert. Im einzelnen werden Autokorrelationsfunktionen und Korrelationslängen berechnet. Die freien Energie-Landschaften sind vom AR(1) Typ. Die von den Reaktionsgeschwindigkeitskonstanten abgeleiteten Landschaften stellten sich hingegen als komplexer heraus. Zusätzlich werden die Bewertungslandschaften auch noch mit Hilfe vonGradient undAdaptive Walks untersucht, um mehr Einblick in ihre komplexe Struktur zu gewinnen.
    Notes: Summary RNA secondary structures are computed from primary sequences by means of a folding algorithm which uses a minimum free energy criterion. Free energies as well as replication and degradation rate constants are derived from secondary structures. These properties can be understood as highly sophisticated functions of the individual sequences whose values are mediated by the secondary structures. Such functions induce complex value landscapes on the space of sequences. The landscapes are analysed by random walk techniques, in particular autocorrelation functions and correlation lengths are computed. Free energy landscapes were found to be of AR(1) type. The rate constant landscapes, however, turned out to be more complex. In addition, gradient and adaptive walks are performed in order to get more insight into the complex structure of the landscapes.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2234
    Keywords: (HF)n-chains ; (H2O)n-chains ; Hydrogen bond energies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Energy band structures of one-dimensional (HF)n- and (H2O)n-chains have been calculated (1) by extrapolation of CNDO/2-MO levels to infinite chain length and (2) by the CNDO/2 crystal orbital (CO) method. In the CO-calculations interactions up to fifth neighbours have been taken into account. Both types of calculations were performed using experimental geometries and CNDO/2 minimum geometries of the corresponding dimers (HF)2 and (H2O)2. With the same geometries CO calculations on two-dimensional sheets of hydrogen bonded chains were performed too. Due to end-effects the extrapolated MO bands are much broader than the bands obtained by the CO method. In the CO calculations further neighbour interactions play a non-negligible role and hence the nearest neighbour approximation is not sufficient for an accurate description of crystals containing hydrogen bonds. MO calculations on one-dimensional chains of both systems show that the hydrogen bond energies increase with the number of monomers indicating the presence of cooperative effects. The hydrogen bond energies calculated with the CO method are usually somewhat larger than those extrapolated from the MO results. In three-dimensional networks of (H2O)n, however, the additional stabilization of clusters with respect to dimers is drastically diminished.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 30 (1992), S. 597-632 
    ISSN: 1432-1416
    Keywords: Autocatalysis ; Mutation ; Perturbation theory ; Qualitative analysis ; Replication dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A class of kinetic equations describing catalysed and template induced replication, and mutation is introduced. This ODE in its most general form is split into two vector fields, a replication and a mutation field. The mutation field is considered as a perturbation of the replicator equation. The perturbation expansion is a Taylor series in a mutation parameter λ. First, second and higher order contributions are computed by means of the conventional Rayleigh-Schrödinger approach. Qualitative shifts in the positions of rest points and limit cycles on the boundary of the physically meaningful part of concentration space are predicted from flow topologies. The results of the topological analysis are summarized in two theorems which turned out to be useful in applications: the rest point migration theorem (RPM) and the limit cycle migration theorem (LCM). Quantitative expressions for the shifts of rest points are computed directly from the perturbation expansion. The concept is applied to a collection of selected examples from biophysical chemistry and biology.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 30 (1992), S. 597-631 
    ISSN: 1432-1416
    Keywords: Autocatalysis ; Mutation ; Perturbation theory ; Qualitative analysis ; Replication dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A class of kinetic equations describing catalysed and template induced replication, and mutation is introduced. This ODE in its most general form is split into two vector fields, a replication and a mutation field. The mutation field is considered as a perturbation of the replicator equation. The perturbation expansion is a Taylor series in a mutation parameter λ. First, second and higher order contributions are computed by means of the conventional Rayleigh-Schrödinger approach. Qualitative shifts in the positions of rest points and limit cycles on the boundary of the physically meaningful part of concentration space are predicted from flow topologies. The results of the topological analysis are summarized in two theorems which turned out to be useful in applications: the rest point migration theorem (RPM) and the limit cycle migration theorem (LCM). Quantitative expressions for the shifts of rest points are computed directly from the perturbation expansion. The concept is applied to a collection of selected examples from biophysical chemistry and biology.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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