Multifractal detrended cross-correlation analysis of coding and non-coding DNA sequences through chaos-game representation

We propose a new approach combining the chaos game representation and the two dimensional multifractal detrended cross correlation analysis methods to examine multifractal behavior in power law cross correlation between any pair of nucleotide sequences of unequal lengths. In this work, we analyzed the characteristic behavior of coding and non-coding DNA sequences of eight prokaryotes. The results show the presence of strong multifractal nature between coding and non-coding sequences of all data sets. We found that this integrative approach helps us to consider complete DNA sequences for characterization, and further it may be useful for classification, clustering, identification of class affiliation of nucleotide sequences etc. with high precision.

[1]  V. Plerou,et al.  Scaling of the distribution of price fluctuations of individual companies. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Guangxi Cao,et al.  Multifractal detrended cross-correlations between the Chinese exchange market and stock market , 2012 .

[3]  Han Jia-Jing,et al.  Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation , 2010 .

[4]  Revealing the surface interface correlations in a-Si:H films by 2D detrended fluctuation analysis , 2013 .

[5]  P. Manimaran,et al.  Characterizing multi-scale self-similar behavior and non-statistical properties of fluctuations in financial time series , 2010, 1003.2539.

[6]  H. Hurst,et al.  A Suggested Statistical Model of some Time Series which occur in Nature , 1957, Nature.

[7]  P. Manimaran,et al.  Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series , 2014 .

[8]  Alain Giron,et al.  A genomic schism in birds revealed by phylogenetic analysis of DNA strings. , 2002, Systematic biology.

[9]  J. Preinhaelter,et al.  Penetration of high-frequency waves into a weakly inhomogeneous magnetized plasma at oblique incidence and their transformation to Bernstein modes , 1973, Journal of Plasma Physics.

[10]  H. Stanley,et al.  Multifractal properties of price fluctuations of stocks and commodities , 2003, cond-mat/0308012.

[11]  V. Plerou,et al.  Scaling of the distribution of fluctuations of financial market indices. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  H. Stanley,et al.  Cross-correlations between volume change and price change , 2009, Proceedings of the National Academy of Sciences.

[13]  E. Bacry,et al.  Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Wei‐Xing Zhou Multifractal detrended cross-correlation analysis for two nonstationary signals. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Prasanta K. Panigrahi,et al.  Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets , 2006 .

[16]  Feng Ma,et al.  Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets , 2013 .

[17]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  P. Manimaran,et al.  Features in the Primordial Spectrum from WMAP: A Wavelet Analysis , 2007 .

[19]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[20]  Harvard Medical School,et al.  Effect of nonstationarities on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[22]  The MDF technique for the analysis of tokamak edge plasma fluctuations , 2014 .

[23]  S Karlin,et al.  Genome-scale compositional comparisons in eukaryotes. , 2001, Genome research.

[24]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[25]  H. Stanley,et al.  Quantifying cross-correlations using local and global detrending approaches , 2009 .

[26]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[27]  G. A. Hunt Random Fourier transforms , 1951 .

[28]  Prasanta K Panigrahi,et al.  Wavelet analysis and scaling properties of time series. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  I. Simonsen,et al.  Determination of the Hurst exponent by use of wavelet transforms , 1997, cond-mat/9707153.

[30]  A. Arneodo,et al.  Wavelet transform of multifractals. , 1988, Physical review letters.

[31]  José Manuel Gutiérrez,et al.  Multifractal analysis of DNA sequences using a novel chaos-game representation , 2001 .

[32]  A. Carbone,et al.  Second-order moving average and scaling of stochastic time series , 2002 .

[33]  Boris Podobnik,et al.  Statistical tests for power-law cross-correlated processes. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Apostolos Serletis,et al.  The Hurst exponent in energy futures prices , 2007 .

[35]  Sergio Arianos,et al.  Self-similarity of higher-order moving averages. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  C. Cristescu,et al.  Investigation on series of length of coding and non-coding DNA sequences of bacteria using multifractal detrended cross-correlation analysis. , 2013, Journal of theoretical biology.

[37]  P. Manimaran,et al.  Difference in nature of correlation between NASDAQ and BSE indices , 2006 .

[38]  Cristina Stan,et al.  Similarity analysis for DNA sequences based on chaos game representation. Case study: the albumin. , 2010, Journal of theoretical biology.

[39]  E. Bacry,et al.  Wavelets and multifractal formalism for singular signals: Application to turbulence data. , 1991, Physical review letters.

[40]  S. Karlin,et al.  Genome signature comparisons among prokaryote, plasmid, and mitochondrial DNA. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Zhi-Qiang Jiang,et al.  Multifractal detrending moving-average cross-correlation analysis. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Ling-Yun He,et al.  Multifractal Detrended Cross-Correlation Analysis of agricultural futures markets , 2011 .

[43]  Wei-Xing Zhou,et al.  Detrended fluctuation analysis for fractals and multifractals in higher dimensions. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  R. Sandberg,et al.  Capturing whole-genome characteristics in short sequences using a naïve Bayesian classifier. , 2001, Genome research.

[45]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Zu-Guo Yu,et al.  Relationships of exponents in two-dimensional multifractal detrended fluctuation analysis. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Jiunn-Jong Wu Structure function and spectral density of fractal profiles , 2001 .

[48]  P. Manimaran,et al.  Statistics of event by event fluctuations , 2010 .

[49]  Prasanta K. Panigrahi,et al.  LETTER TO THE EDITOR: Spectral fluctuation characterization of random matrix ensembles through wavelets , 2006 .

[50]  Jonas S. Almeida,et al.  Analysis of genomic sequences by Chaos Game Representation , 2001, Bioinform..

[51]  D. Noever,et al.  New method of structural functions for analysing fractal scaling properties of natural processes , 1994 .

[52]  Pengjian Shang,et al.  Multifractal Detrended Cross-Correlation Analysis of BVP model time series , 2011, Nonlinear Dynamics.

[53]  Xinsheng Lu,et al.  Cross-correlations between agricultural commodity futures markets in the US and China , 2012 .

[54]  Kyoko Ohashi,et al.  Asymmetrical singularities in real-world signals. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  P. Deschavanne,et al.  Genomic signature: characterization and classification of species assessed by chaos game representation of sequences. , 1999, Molecular biology and evolution.

[56]  H. J. Jeffrey Chaos game representation of gene structure. , 1990, Nucleic acids research.

[57]  Wen Shi,et al.  Multifractal detrended cross-correlation analysis for power markets , 2013, Nonlinear Dynamics.

[58]  Wei-Xing Zhou,et al.  Detrending moving average algorithm for multifractals. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.