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Multifractal analysis of DNA sequences using a novel chaos-game representation

Author

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  • Gutiérrez, J.M.
  • Rodrı́guez, M.A.
  • Abramson, G.

Abstract

We present a generalization of the standard chaos-game representation method introduced by Jeffrey. To this aim, a DNA symbolic sequence is mapped onto a singular measure on the attractor of a particular IFS model, which is a perfect statistical representation of the sequence. A multifractal analysis of the resulting measure is introduced and an interpretation of singularities in terms of mutual information and redundancy (statistical dependence) among subsequence symbols within the DNA sequence is provided. The multifractal spectrum is also shown to be more sensitive for detecting dependence structures within the DNA sequence than the averaged contribution given by redundancy. This method presents several advantages with respect to other representations such as walks or interfaces, which may introduce spurious effects. In contrast with the results obtained by other standard methods, here we note that no general statement can be made on the influence of coding and non-coding content on the correlation length of a given sequence.

Suggested Citation

  • Gutiérrez, J.M. & Rodrı́guez, M.A. & Abramson, G., 2001. "Multifractal analysis of DNA sequences using a novel chaos-game representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 271-284.
    • Handle: RePEc:eee:phsmap:v:300:y:2001:i:1:p:271-284
    DOI: 10.1016/S0378-4371(01)00333-8
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    Cited by:

    1. Meraz, Monica & Carbó, Roxana & Rodriguez, Eduardo & Alvarez-Ramirez, Jose, 2023. "Fractal correlations in the Covid-19 genome sequence via multivariate rescaled range analysis," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Pal, Mayukha & Satish, B. & Srinivas, K. & Rao, P. Madhusudana & Manimaran, P., 2015. "Multifractal detrended cross-correlation analysis of coding and non-coding DNA sequences through chaos-game representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 596-603.
    3. Kosmidis, Kosmas & Hütt, Marc-Thorsten, 2023. "DNA visibility graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    4. Primo, C. & Galván, A. & Sordo, C. & Gutiérrez, J.M., 2007. "Statistical linguistic characterization of variability in observed and synthetic daily precipitation series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 389-402.
    5. Pal, Mayukha & Kiran, V. Satya & Rao, P. Madhusudana & Manimaran, P., 2016. "Multifractal detrended cross-correlation analysis of genome sequences using chaos-game representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 288-293.
    6. Natsuhiro Ichinose & Tetsushi Yada & Osamu Gotoh, 2014. "Tetrahedral Gray Code for Visualization of Genome Information," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-10, January.

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