About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 439089, 13 pages
http://dx.doi.org/10.1155/2012/439089
Research Article

Shannon Information and Power Law Analysis of the Chromosome Code

Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal

Received 8 June 2012; Revised 17 August 2012; Accepted 21 August 2012

Academic Editor: Dumitru Bǎleanu

Copyright © 2012 J. A. Tenreiro Machado. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. T. Schuh and A. V. Z. Brower, Biological Systematics: Principles and Applications, Cornell University Press, 2nd edition, 2009.
  2. H. Seitz, Analytics of Protein-DNA Interactions, Advances in Biochemical Engineering Biotechnology, Springer, 2007.
  3. H. Pearson, “What is a gene?” Nature, vol. 441, no. 7092, pp. 398–401, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. UCSC Genome Bioinformatics, http://hgdownload.cse.ucsc.edu/downloads.html.
  5. G. E. Sims, S. R. Jun, G. A. Wu, and S. H. Kim, “Alignment-free genome comparison with feature frequency profiles (FFP) and optimal resolutions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 8, pp. 2677–2682, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. W. J. Murphy, T. H. Pringle, T. A. Crider, M. S. Springer, and W. Miller, “Using genomic data to unravel the root of the placental mammal phylogeny,” Genome Research, vol. 17, no. 4, pp. 413–421, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Zhao and G. Bourque, “Recovering genome rearrangements in the mammalian phylogeny,” Genome Research, vol. 19, no. 5, pp. 934–942, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. A. B. Prasad, M. W. Allard, and E. D. Green, “Confirming the phylogeny of mammals by use of large comparative sequence data sets,” Molecular Biology and Evolution, vol. 25, no. 9, pp. 1795–1808, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. I. Ebersberger, P. Galgoczy, S. Taudien, S. Taenzer, M. Platzer, and A. Von Haeseler, “Mapping human genetic ancestry,” Molecular Biology and Evolution, vol. 24, no. 10, pp. 2266–2276, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. C. W. Dunn, A. Hejnol, D. Q. Matus et al., “Broad phylogenomic sampling improves resolution of the animal tree of life,” Nature, vol. 452, no. 7188, pp. 745–749, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Fractional dynamics in DNA,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2963–2969, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. A. M. Costa, J. T. Machado, and M. D. Quelhas, “Histogram-based DNA analysis for the visualization of chromosome, genome and species information,” Bioinformatics, vol. 27, no. 9, pp. 1207–1214, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Entropy analysis of the DNA code dynamics in human chromosomes,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1612–1617, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Analysis and visualization of chromosome information,” Gene, vol. 491, no. 1, pp. 81–87, 2012.
  15. M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, Cambridge, Mass, USA, 1983.
  16. P. J. Deschavanne, A. Giron, J. Vilain, G. Fagot, and B. Fertit, “Genomic signature: characterization and classification of species assessed by chaos game representation of sequences,” Molecular Biology and Evolution, vol. 16, no. 10, pp. 1391–1399, 1999. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Lynch, “The frailty of adaptive hypotheses for the origins of organismal complexity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 1, pp. 8597–8604, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. G. Albrecht-Buehler, “Asymptotically increasing compliance of genomes with Chargaff's second parity rules through inversions and inverted transpositions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 47, pp. 17828–17833, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. D. Mitchell and R. Bridge, “A test of Chargaff's second rule,” Biochemical and Biophysical Research Communications, vol. 340, no. 1, pp. 90–94, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. B. R. Powdel, S. S. Satapathy, A. Kumar et al., “A study in entire chromosomes of violations of the intra-strand parity of complementary nucleotides (Chargaff's Second Parity Rule),” DNA Research, vol. 16, no. 6, pp. 325–343, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. C. T. Zhang, R. Zhang, and H. Y. Ou, “The Z curve database: a graphic representation of genome sequences,” Bioinformatics, vol. 19, no. 5, pp. 593–599, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Bak, K. Chen, and C. Tang, “A forest-fire model and some thoughts on turbulence,” Physics Letters A, vol. 147, no. 5-6, pp. 297–300, 1990. View at Publisher · View at Google Scholar · View at Scopus
  23. N. E. Israeloff, M. Kagalenko, and K. Chan, “Can Zipf distinguish language from noise in noncoding DNA?” Physical Review Letters, vol. 76, pp. 1976–1979, 1995.
  24. R. N. Mantegna and H. E. Stanley, “Scaling behaviour in the dynamics of an economic index,” Nature, vol. 376, no. 6535, pp. 46–49, 1995. View at Publisher · View at Google Scholar · View at Scopus
  25. L. A. Adamic and B. A. Huberman, “Zipfs law and the Internet,” Glottometrics, vol. 3, pp. 143–150, 2002.
  26. H. Aoyama, Y. Fujiwara, and W. Souma, “Kinematics and dynamics of pareto-zipf's law and gibrat's law,” Physica A, vol. 344, no. 1-2, pp. 117–121, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. C. Andersson, A. Hellervik, and K. Lindgren, “A spatial network explanation for a hierarchy of urban power laws,” Physica A, vol. 345, no. 1-2, pp. 227–244, 2005. View at Publisher · View at Google Scholar · View at Scopus
  28. A. L. Barabási, “The origin of bursts and heavy tails in human dynamics,” Nature, vol. 435, no. 7039, pp. 207–211, 2005. View at Publisher · View at Google Scholar · View at Scopus
  29. W. Dahui, L. Menghui, and D. Zengru, “True reason for Zipf's law in language,” Physica A, vol. 358, no. 2–4, pp. 545–550, 2005. View at Publisher · View at Google Scholar · View at Scopus
  30. J. M. Sarabia and F. Prieto, “The Pareto-positive stable distribution: a new descriptive model for city size data,” Physica A, vol. 388, no. 19, pp. 4179–4191, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. T. Fenner, M. Levene, and G. Loizou, “Predicting the long tail of book sales: unearthing the power-law exponent,” Physica A, vol. 389, no. 12, pp. 2416–2421, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Shannon, Rényie and Tsallis entropy analysis of DNA using phase plane,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3135–3144, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  33. J. A. T. Machado and S. Entropy, “Analysis of the Genome Code,” Mathematical Problems in Engineering, vol. 2012, Article ID 132625, 12 pages, 2012. View at Publisher · View at Google Scholar
  34. J. T. Machado, “Accessing complexity from genome information,” Communications in Nonlinear Science and Numerical Simulations, vol. 17, no. 6, pp. 2237–2243, 2012.
  35. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. View at Publisher · View at Google Scholar
  36. D. Baleanu and S. I. Vacaru, “Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics,” Journal of Mathematical Physics, vol. 52, no. 5, Article ID 053514, 15 pages, 2011. View at Publisher · View at Google Scholar
  37. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Complexity, Nonlinearity and Chaos, World Scientific Publishing, 2012. View at Publisher · View at Google Scholar
  38. C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, pp. 379–423, 1948. View at Zentralblatt MATH
  39. E. T. Jaynes, “Information Theory and Statistical Mechanics,” vol. 106, pp. 620–630, 1957. View at Zentralblatt MATH
  40. A. I. Khinchin, Mathematical foundations of information theory, Dover Publications, New York, NY, USA, 1957.
  41. A. Plastino and A. R. Plastino, “Tsallis Entropy and Jaynes' information theory formalism,” Brazilian Journal of Physics, vol. 29, no. 1, pp. 50–60, 1999. View at Publisher · View at Google Scholar · View at Scopus
  42. H. J. Haubold, A. M. Mathai, and R. K. Saxena, “Boltzmann-Gibbs entropy versus Tsallis entropy: recent contributions to resolving the argument of Einstein concerning “neither Herr Boltzmann nor Herr Planck has given a definition of W”? Essay review,” Astrophysics and Space Science, vol. 290, no. 3-4, pp. 241–245, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  43. A. M. Mathai and H. J. Haubold, “Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy,” Physica A, vol. 375, no. 1, pp. 110–122, 2007. View at Publisher · View at Google Scholar
  44. T. Carter, An Introduction to Information Theory and Entropy, Complex Systems Summer School, Santa Fe, Mexico, 2007.
  45. P. N. Rathie and S. Da Silva, “Shannon, Lévy, and Tsallis: a note,” Applied Mathematical Sciences, vol. 2, no. 25–28, pp. 1359–1363, 2008. View at Zentralblatt MATH
  46. C. Beck, “Generalised information and entropy measures in physics,” Contemporary Physics, vol. 50, no. 4, pp. 495–510, 2009. View at Publisher · View at Google Scholar · View at Scopus
  47. I. J. Taneja, “On measures of information and inaccuracy,” Journal of Statistical Physics, vol. 14, no. 3, pp. 263–270, 1976. View at Publisher · View at Google Scholar
  48. B. D. Sharma and I. J. Taneja, “Three generalized-additive measures of entropy,” Elektronische Informationsverarbeitung und Kybernetik, vol. 13, no. 7-8, pp. 419–433, 1977. View at Zentralblatt MATH
  49. A. Wehrl, “General properties of entropy,” Reviews of Modern Physics, vol. 50, no. 2, pp. 221–260, 1978. View at Publisher · View at Google Scholar
  50. H. D. Chen, C. H. Chang, L. C. Hsieh, and H. C. Lee, “Divergence and Shannon information in genomes,” Physical Review Letters, vol. 94, no. 17, Article ID 178103, 2005. View at Publisher · View at Google Scholar · View at Scopus
  51. R. M. Gray, Entropy and Information Theory, Springer, New York, NY, USA, 1990.
  52. M. R. Ubriaco, “Entropies based on fractional calculus,” Physics Letters A, vol. 373, no. 30, pp. 2516–2519, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH