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Investigating Some Attributes of Periodicity in DNA Sequences via Semi-Markov Modelling

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Stochastic Processes, Statistical Methods, and Engineering Mathematics (SPAS 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 408))

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Abstract

Periodicity of DNA segments and sequences have been studied thoroughly during the past decades. One of the main problems is the identification of protein coding and non-coding regions inside genes, using mathematical techniques. Periodicity plays an important role in the structure of DNA, as specific regions have been shown to have periodic patterns. In this paper, we consider that a DNA sequence is described by a semi-Markov chain (SMC), with discrete state space consisting of the four nucleotides. Equations in closed analytic form are derived, in order to characterize strong or weak d-periodic and quasiperiodic behaviour of our model for both the homogeneous and non-homogeneous case. The model is applied to 3-base periodic sequences, which characterize the protein-coding regions of the gene. The related probabilities and the corresponding indexes are provided, which yield a description of the underlying periodic pattern. Last, the previous theoretical results are illustrated with data from synthetic and real DNA sequences.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Pavlos Kolias & Alexandra Papadopoulou

Authors
  1. Pavlos Kolias
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  2. Alexandra Papadopoulou
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Corresponding author

Correspondence to Pavlos Kolias .

Editor information

Editors and Affiliations

  1. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  2. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Ying Ni

  3. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Milica Rančić

  4. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

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Kolias, P., Papadopoulou, A. (2022). Investigating Some Attributes of Periodicity in DNA Sequences via Semi-Markov Modelling. In: Malyarenko, A., Ni, Y., Rančić, M., Silvestrov, S. (eds) Stochastic Processes, Statistical Methods, and Engineering Mathematics . SPAS 2019. Springer Proceedings in Mathematics & Statistics, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-031-17820-7_9

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