Modeling the Dynamics of Nonenzymatic and Enzymatic Nucleotide Processes by Fractal Dimension View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1998

AUTHORS

Z. Földes-Papp , B. Angerer , W. Ankenbauer , G. Baumann , E. Birch-Hirschfeld , S. Björling , S. Conrad , M. Hinz , R. Rigler , H. Seliger , P. Thyberg , A. K. Kleinschmidt

ABSTRACT

We introduce here D as a fractal dimension according to Mandelbrot [5] for multicyclic nucleotide processes producing variabilities, where M (l,N) is the probability density of truncated, deleted and point-mutated sequence variabilities (l) as net term of the deterministic processes in the two-dimensional embedding space. The very generality of this result holds for all fractal sets of cumulative sequence variabilities. The minimal requirements sufficient to produce, or to degrade, a target DNA sequence N are multistep additions, recombinations or degradations of some monomeric or oligomeric building blocks with the propagation probability function d = di at cycle i. Our fractal dimension D can be obtained from the scaling with respect to the largest nucleotide lengths of interest, N. The scaling behaviour of suitable examples of quantified experiments is experimentally analysed for the first time in the following systems, ordered by increasing complexity: (i) chemical, solid-phase oligodeoxyribonucleotide synthesis, (ii) incorporation of fluorescently-labeled deoxyuri-dine 5′-triphosphate by different DNA polymerases and reverse transcriptases, and (iii) characteristic restriction endonuclease patterns for a few typical genes within the genome of herpes simplex virus type 1. Under different experimental conditions, D extends the interpretation to a short-term synthesis pattern of variability of oligonucleotide populations, to characteristics of DNA polymerase and reverse transcriptase activities, and to typical intrinsic long-term variability as shown by enzymatic degradation of viral DNA strains studied. More... »

PAGES

238-254

Book

TITLE

Fractals in Biology and Medicine

ISBN

978-3-0348-9834-8
978-3-0348-8936-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-8936-0_19

DOI

http://dx.doi.org/10.1007/978-3-0348-8936-0_19

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020433844


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26 schema:description We introduce here D as a fractal dimension according to Mandelbrot [5] for multicyclic nucleotide processes producing variabilities, where M (l,N) is the probability density of truncated, deleted and point-mutated sequence variabilities (l) as net term of the deterministic processes in the two-dimensional embedding space. The very generality of this result holds for all fractal sets of cumulative sequence variabilities. The minimal requirements sufficient to produce, or to degrade, a target DNA sequence N are multistep additions, recombinations or degradations of some monomeric or oligomeric building blocks with the propagation probability function d = di at cycle i. Our fractal dimension D can be obtained from the scaling with respect to the largest nucleotide lengths of interest, N. The scaling behaviour of suitable examples of quantified experiments is experimentally analysed for the first time in the following systems, ordered by increasing complexity: (i) chemical, solid-phase oligodeoxyribonucleotide synthesis, (ii) incorporation of fluorescently-labeled deoxyuri-dine 5′-triphosphate by different DNA polymerases and reverse transcriptases, and (iii) characteristic restriction endonuclease patterns for a few typical genes within the genome of herpes simplex virus type 1. Under different experimental conditions, D extends the interpretation to a short-term synthesis pattern of variability of oligonucleotide populations, to characteristics of DNA polymerase and reverse transcriptase activities, and to typical intrinsic long-term variability as shown by enzymatic degradation of viral DNA strains studied.
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