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Entropy and long-range correlations in DNA sequences

S.S. Melnik, O.V. Usatenko
2014 Computational biology and chemistry  
Supposing that the correlations are weak we express the conditional probability function of the chain by means of the pair correlation function and represent the entropy as a functional of the pair correlator  ...  We utilize the obtained analytical result for numerical evaluation of the entropy of coarse-grained DNA texts.  ...  Acknowledgments We are grateful for the very helpful and fruitful discussions with A. A. Krokhin, S. V. Denisov, S. S. Apostolov, Z. A. Mayzelis, G. M. Pritula, and Yu. V. Tarasov.  ... 
doi:10.1016/j.compbiolchem.2014.08.006 pmid:25213853 fatcat:idhni4kgp5hfvoqn5qbiwvyjte

Comparative Study of Complexity, Entropy and Correlations of Natural Written Texts Produced by Human Brain and DNA "Texts" that Create Human Being

Melnik SS, Usatenko Usatenko OV
2015 Journal of Theoretical and Computational Science  
Conclusion Thus, DNA and text sequences possess complex long-range correlated behavior.  ...  The powerlaw character of the decrease in long-range correlations in different systems, particularly, in the DNA and literary texts, was mentioned by a number of authors, but it was not associated with  ... 
doi:10.4172/2376-130x.1000139 fatcat:ctln6xuk7bartbabxlxrbsm36q

Dynamic entropies, long-range correlations, and fluctuations in complex linear structures [article]

Werner Ebeling, Alexander Neiman, Thorsten Poeschel
2002 arXiv   pre-print
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected.  ...  The longest correlations found in our analysis comprise a few hundreds or thousands of letters and may be understood as long-wave fluctuations of the composition.  ...  Conclusions Our results show that the dynamic entropies, the low frequency spectra and the scaling of the mean square deviations, are appropriate measures for the long-range correlations in symbolic sequences  ... 
arXiv:cond-mat/0204076v1 fatcat:de77wfqotnbyrgkbsdzevxlddq

Information Measure for Long-Range Correlated Sequences: the Case of the 24 Human Chromosomes

A. Carbone
2013 Scientific Reports  
A new approach to estimate the Shannon entropy of a long-range correlated sequence is proposed.  ...  The entropy is written as the sum of two terms corresponding respectively to power-law (ordered) and exponentially (disordered) distributed blocks (clusters).  ...  In this work, an information measure for long-range correlated sequences, worked out from a partition of the sequence into clusters according to the method proposed in 8, 9 , is put forward.  ... 
doi:10.1038/srep02721 pmid:24056670 pmcid:PMC3779848 fatcat:ywcjae7z35bdtakdxlj5joxq7q

Statistical analysis of the DNA sequence of human chromosome 22

Dirk Holste, Ivo Grosse, Hanspeter Herzel
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We study statistical patterns in the DNA sequence of human chromosome 22, the first completely sequenced human chromosome.  ...  We find that ͑i͒ the 33.4ϫ10 6 nucleotide long human chromosome exhibits long-range power-law correlations over more than four orders of magnitude, ͑ii͒ the entropies H n of the frequency distribution  ...  ACKNOWLEDGMENTS We thank the Institute for Pure and Applied Mathematics ͑University of California, Los Angeles͒ for hospitality and support while part of this work was completed, and the Deutsche Forschungsgemeinschaft  ... 
doi:10.1103/physreve.64.041917 pmid:11690062 fatcat:2kuqrrtswfhzldp4bmsy5oacee

Complexity Estimation of Genetic Sequences Using Information-Theoretic and Frequency Analysis Methods

Robertas Damaševičius
2010 Informatica  
In this paper, the complexity of genetic sequences is estimated using Shannon entropy, Rényi entropy and relative Kolmogorov complexity.  ...  The genetic information in cells is stored in DNA sequences, represented by a string of four letters, each corresponding to a definite type of nucleotides.  ...  The existence of structures at very large scales results in long-range correlations.  ... 
doi:10.15388/informatica.2010.270 fatcat:slc2qqwyhfae7m2xbsoa7tfqim

In the search for the low-complexity sequences in prokaryotic and eukaryotic genomes: how to derive a coherent picture from global and local entropy measures

Claudia Acquisti, Paolo Allegrini, Patrizia Bogani, Marcello Buiatti, Elena Catanese, Leone Fronzoni, Paolo Grigolini, Giuseppe Mersi, Luigi Palatella
2004 Chaos, Solitons & Fractals  
We show that there exists a correlation between changing the amount in LCS and the ratio of long- to short-range correlation.  ...  We investigate on a possible way to connect the presence of Low-Complexity Sequences (LCS) in DNA genomes and the nonstationary properties of base correlations.  ...  The CMM model of DNA In recent years many groups have agreed to consider DNA sequences as a mixture of long-and short-range correlation, the latter blurring the strength of the former.  ... 
doi:10.1016/s0960-0779(03)00435-1 fatcat:jpukcthc55ajvmzwamxzwwbndy

Entropy and Long-Range Correlations in Literary English

W Ebeling, T Pöschel
1994 Europhysics letters  
We investigated long range correlations in two literary texts, Moby Dick by H. Melville and Grimm's tales.  ...  Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters.  ...  Nicolis and A. Schmitt for fruitful discussions. Further we thank the Project Gutenberg Etext at Illinois Benedictine College for providing the ASCII-files of the investigated literature.  ... 
doi:10.1209/0295-5075/26/4/001 fatcat:pzfyfij3lveh5ea3kpmalrpaiy

Aκ-statistical analysis of the Y-chromosome

N. T. C. M. Souza, D. H. A. L. Anselmo, R. Silva, M. S. Vasconcelos, V. D. Mello
2014 Europhysics letters  
An analysis of the coding sequence for the Y-chromosome (Homo sapiens) has been performed, embedded in the formalism of κ-statistics, which naturally encompasses long-range correlations.  ...  contained on the DNA increases monotonically linearly with the sample size, and also depicts an internal order.  ...  Indeed, the κ-statistics is suitable to analyze the long-range correlations of the DNA molecules.  ... 
doi:10.1209/0295-5075/108/38004 fatcat:nou6bwyvazcaxeviwdj77krr44

A Stochastic Phylogenetic Algorithm for Mitochondrial DNA Analysis

M. Corona-Ruiz, Francisco Hernandez-Cabrera, José Roberto Cantú-González, O. González-Amezcua, Francisco Javier Almaguer
2019 Frontiers in Genetics  
These new functions incorporate the long-range correlations, the probability of occurrence of nucleic bases, and the ratio of pyrimidines-to-purines.  ...  Multiple stochastic parameters, such as the Hurst and detrended fluctuation analysis (DFA) exponents, Shannon entropy, and Chargaff ratio are computed for each DNA sequence.  ...  These DNA-walk studies find differences in the long-range correlation between coding and non-coding DNA sequences (Peng et al., 1994) .  ... 
doi:10.3389/fgene.2019.00066 pmid:30906309 pmcid:PMC6418022 fatcat:hdgwyjfzabg5joquxi6ggiy4gm

The Lack of Long Range Correlations is a Necessary Condition for a Functional Biologically Active Protein [article]

E.Sh.Mamasakhlisov, V.F.Morozov & M.S.Shahinian
1998 arXiv   pre-print
The long-range correlations between kinds of monomers were introduce.  ...  The relationship between our results and some early obtained results for the DNA intrones sequences are discussed.  ...  are some reasons about existence of the scale-invariant long range correlations in the DNA sequences only in non-coding regions of DNA (intrones) (see, e.g  ... 
arXiv:cond-mat/9802225v3 fatcat:yducwphmsredfhtg4fco2dgq7a

Application of information theory to DNA sequence analysis: A review

Ramón Román-Roldán, Pedro Bernaola-Galván, JoséL Oliver
1996 Pattern Recognition  
The emerging interest concerning long-range correlations and the mosaic structure of DNA sequences is considered from our own point of view.  ...  The analysis of DNA sequences through information theory methods is reviewed from the beginning in the 70s.  ...  Acknowledgements--This work was partially supported by grants TIC91-646 to R.R.R. and PB93-1152-CO2-01 to J.L.O. from the DGICYT of the Spanish Government.  ... 
doi:10.1016/0031-3203(95)00145-x fatcat:7b3vw2gvsrg63nsrmcxhawzyku

Entropy of finite random binary sequences with weak long-range correlations

S. S. Melnik, O. V. Usatenko
2014 Physical Review E  
Application of the theory to the DNA sequence of the R3 chromosome of Drosophila melanogaster is presented.  ...  Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator  ...  Acknowledgments We are grateful for the very helpful and fruitful discussions with A. A. Krokhin, G. M. Pritula, S. V. Denisov, S. S. Apostolov, and Z. A. Mayzelis.  ... 
doi:10.1103/physreve.90.052106 pmid:25493739 fatcat:ojnukf2b4jhp5pxpl6zr4o4m3u

Compositional segmentation and long-range fractal correlations in DNA sequences

Pedro Bernaola-Galván, Ramón Román-Roldán, José L. Oliver
1996 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
are arranged in the sequence is critical; therefore, long-range correlations in nucleotide sequences seem to rely only on the power-law distribution of patch lengths.  ...  Some of the identified DNA domains were uncorrelated, but most of them continued to display long-range correlations even after several steps of recursive segmentation, thus indicating a complex multi-length-scaled  ...  Monitoring long-range correlations DNA walks were constructed as described in ͓2͔.  ... 
doi:10.1103/physreve.53.5181 pmid:9964850 fatcat:adekqmbbpbheniuzk3hdltmao4

Entropy and long-range correlations in random symbolic sequences [article]

S.S. Melnik, O.V. Usatenko
2014 arXiv   pre-print
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet.  ...  The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences.  ...  Acknowledgments We are grateful for the helpful and fruitful discussions with G. M. Pritula, S. S. Apostolov, and Z. A. Maizelis.  ... 
arXiv:1412.3692v1 fatcat:zzrzrkxuqfdjhmqyon7luis46m
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