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Regul. Chaotic Dyn., 2018, том 23, выпуск 2, страницы 135–151 (Mi rcd314)  

Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Pólya Counting to a Physical System

Malcolm Hillebranda, Guy Paterson-Jonesa, George Kalosakasb, Charalampos Skokosa

a Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town 7701, South Africa
b Department of Materials Science, University of Patras, Rio GR-26504, Greece

Аннотация: In modeling DNA chains, the number of alternations between Adenine–Thymine (AT) and Guanine–Cytosine (GC) base pairs can be considered as a measure of the heterogeneity of the chain, which in turn could affect its dynamics. A probability distribution function of the number of these alternations is derived for circular or periodic DNA. Since there are several symmetries to account for in the periodic chain, necklace counting methods are used. In particular, Pólya’s Enumeration Theorem is extended for the case of a group action that preserves partitioned necklaces. This, along with the treatment of generating functions as formal power series, allows for the direct calculation of the number of possible necklaces with a given number of AT base pairs, GC base pairs and alternations. The theoretically obtained probability distribution functions of the number of alternations are accurately reproduced by Monte Carlo simulations and fitted by Gaussians. The effect of the number of base pairs on the characteristics of these distributions is also discussed, as well as the effect of the ratios of the numbers of AT and GC base pairs.

Ключевые слова: DNA models, Pólya’s Counting Theorem, heterogeneity, necklace combinatorics

Финансовая поддержка
M.H. and G.P-J. acknowledge financial assistance from the National Research Foundation (NRF) of South Africa towards this research. G.K. and Ch.S. were supported by the Erasmus+/International Credit Mobility KA107 program. Ch.S. acknowledges support by the NRF of South Africa (IFRR and CPRR Programmes), the UCT (URC Conference Travel Grant) and thanks Hans-Peter Kunzi for useful discussions.


DOI: https://doi.org/10.1134/S1560354718020016

Список литературы: PDF файл   HTML файл

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Тип публикации: Статья
MSC: 05A15, 92D20
Поступила в редакцию: 13.10.2017
Принята в печать:11.12.2017
Язык публикации: английский

Образец цитирования: Malcolm Hillebrand, Guy Paterson-Jones, George Kalosakas, Charalampos Skokos, “Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Pólya Counting to a Physical System”, Regul. Chaotic Dyn., 23:2 (2018), 135–151

Цитирование в формате AMSBIB
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\by Malcolm Hillebrand, Guy Paterson-Jones, George Kalosakas, Charalampos Skokos
\paper Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Pólya Counting to a Physical System
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 2
\pages 135--151
\mathnet{http://mi.mathnet.ru/rcd314}
\crossref{https://doi.org/10.1134/S1560354718020016}
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