A rewinding model for replicons with DNA-links
DOI:
https://doi.org/10.11145/j.biomath.2020.01.047Keywords:
DNA, Replication, Link, Topological model, RepliconAbstract
A double strand DNA has a double helical structure and it is modeled by a thin long twisted ribbon fixed at the both ends. A DNA-linkВ is a topological model of such a DNA segment in the nuclear of a eukaryotic cell. In the cell cycle, the DNA is replicated and distributedВ into new cells. The complicated replication process follows the semi-conservative scheme in which each backbone string is preserved in theВ replicated DNA. This is interpreted in terms of splitting process ofВ the DNA-link. In order to split the DNA-link, unknotting operationsВ are required. This paper presents a recursive unknotting operations,В which efficiently reduce the number of twistings.
References
M. Barbi, J. Mozziconacci, H. Wong, and J. Victor, DNA topology in chromosomes: a quantitative survey and its physiological implication, J. Math. Biol. 68 (2014), 145–179.
A. Bates and A. Maxwell, DNA topology, Oxford University Press, 2005.
A. Kornberg and T. A. Baker, DNA replication, second edition, University Science Book, 2005.
S. D. Levene, C. Donahue, T. C. Boles, and N. R. Cozzarelli, Analysis of the structure of dimeric DNA catenanes by electron microscopy, Biophysical Journal 69 (1995), 1036–1045.
A. A. Mohamad and T. Yashiro, A topological model of DNA replication with DNA-links, Far East J. Mathematical Sciences 107 (2018), 241–255.
K. Murasugi, Knot theory and its applications, Modern Birkhäuser Classics, Birkhäuser, 2008.
H. Nakamura, T. Morita, and C. Sato, Exp. Cell Res. 165 (1986), 291.
S. V. Razin, A. A. Gavrilov, E. S. Ioudinkova, and O. V. Iarovaia, Communication of genome regulatory elements in a folded chromosome, FEBS Letters 587 (2013), 1840–1847.
J. C. Rivera-Mlia, R. Henandez-Munoz, F. Matinez, and A. Aranda-Anzaldo, DNA moves sequentially towards the nuclear matrix during DNA replication in vivo, BMC Cell Biology 12:3 (2011), 16 pages.
V. V. Rybenkov, N. R. Cozzarelli, and A. V. Volgodskii, Propability of DNA knotting and the effective diameter of the DNA double helix, Natl. Acad. Sci. USA 90 (1993), 5307–5311.
R. R. Sinden, DNA structure and function, Academic Press, 1994.
A. Vologodskii, Bridged DNA circles: A new model system to study DNA topology, Macromolecules 45 (2012), 4333–4336.
J. H. White, Self-linking and gauss integral in higher dimensions, Amer. J. of Math. 91 (1969), 693–728.
R. H. C. Wilson and D. Coverley, Relationship between DNA replication and the nuclear matrix, Gens to Cells 18 (2013), 17–31.
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