DNA Sequences Entropy and Long-Rang Correlated Disorder Beyond the Pair Correlations

Sergey Melnik; Oleg Usatenko

DNA Sequences Entropy and Long-Rang Correlated Disorder Beyond the Pair Correlations

Sergey Melnik, Oleg Usatenko^*

Department of Theoretical Physics, A. Ya. Usikov Institute for Radiophysics and Electronics Ukrainian National Academy of Science, Ukraine

^*Corresponding author: Oleg Usatenko, Department of Theoretical Physics, A. Ya. Usikov Institute for Radiophysics and Electronics Ukrainian National Academy of Science, Ukraine. Tel: +7988532380; Email: olegusatenko@mail.ru

Received Date: 02 May, 2018; Accepted Date: 28 May, 2018; Published Date: 01 June, 2018

Citation: Melnik SS, Usatenko OV (2018) DNA Sequences Entropy and Long-Rang Correlated Disorder Beyond the Pair Correlations. J Biostat Biom: JBSB 104. DOI: 10.29011/JBSB-104.000004

Figure 1: The conditional entropies h per symbol vs length L for R3 chromosome DNA from the Drosophila melanogaster nucleotide sequence translated into a binary file of length M 2:7´10⁷. The low dotted line presents the entropy calculated in the framework of the method of likelihood estimation. The upper dashed line is the entropy calculated in the weak pair correlations approximation, Equation (3). The pair and third order correlation functions, solid line, are taken into account in regions r ≤ 104 and r1 < r2 ≤ 10, respectively.

1. Ebeling W, Nicolis G (1991) Entropy of Symbolic Sequences: The Role of Correlations. Europhys Lett 14: 191.

2. Schurmann T, Grassberger (1996) Entropy estimation of symbol sequences. P Chaos 6: 414-427.

3. Melnik SS, Usatenko OV (2016) Entropy and long-range memory in random symbolic additive Markov chains. Phys Rev E 93: 062144.

4. Melnik SS, Usatenko OV (2017) Entropy of random symbolic high-order bilinear Markov chains. arXiv.org > cond-mat.stat-mech > 1709.06642; to be published in Physica A.

5. Melnik SS, Usatenko OV (2017) Decomposition of conditional probability for high-order symbolic Markov chains. Phys Rev E 96: 012158.

6. Usatenko OV, Yampol'skii VA (2003) Binary N-Step Markov Chains and Long-Range Correlated Systems. Phys Rev Lett 90: 110601.

7. P. C. Shields (1996) The ergodic theory of discrete sample paths (Graduate studies in mathematics, 13).

8. Usatenko OV, Apostolov SS, Mayzelis ZA, Melnik SS (2010) Random Finite-Valued Dynamical Systems: Additive Markov Chain Approach. Cambridge Scientific Publisher 171.

9. https://www.ncbi.nlm.nih.gov/nuccore/NC 004354.1/.

DNA Sequences Entropy and Long-Rang Correlated Disorder Beyond the Pair Correlations

Journal of Biostatistics & Biometrics