Modeling Human Nucleotide Frequencies

  • Michel Eduardo Beleza Yamagishi
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


Fibonacci sequence is recurrent in nature. In this chapter, we model the human nucleotide frequencies through an optimization problem in which both the golden ratio and Chargaff’s second parity rule play major roles.


  1. 2.
    Albrecht-Buehler, G.: Asymptotically increasing compliance of genomes with Chargaff’s second parity rules through inversions and inverted transpositions. Proc. Natl. Acad. Sci. U. S. A. 103(47), 17828–17833 (2006)CrossRefGoogle Scholar
  2. 6.
    Bannert, N., Kurth, R.: Retroelements and the human genome: new perspectives on an old relation. Proc. Natl. Acad. Sci. U. S. A. 101, 14572–14579 (2004)CrossRefGoogle Scholar
  3. 20.
    Collins, F.S., Patrinos, A., Jordan, E., Chakravarti, A., Gesteland, R., Walters, L., and the members of the DOE and NIH planning groups: New goals for the U.S. Human Genome Project: 1998–2003. Science 282(5389), 682–689 (1998)Google Scholar
  4. 25.
    Dolgin, E.: The genome finishers. Nature 462, 17 (2009)CrossRefGoogle Scholar
  5. 27.
    Doolittle, W.F.: Is junk DNA bunk? a critique of ENCODE. Proc. Natl. Acad. Sci. U. S. A. 110(14), 5294–5300 (2013)CrossRefGoogle Scholar
  6. 29.
    Eco, U.: On Beauty: A History of a Western Idea. Seeker & Warburg, London (2004)zbMATHGoogle Scholar
  7. 30.
    Eddy, S.R.: Non-coding RNA genes and the modern RNA world. Nat. Rev. Genet. 2(12), 919–929 (2001)CrossRefGoogle Scholar
  8. 31.
    Fibonacci, L., Singler, L.E. (Translator): Fibonacci’s Liber Abaci. Springer, New York (2002)Google Scholar
  9. 32.
    Flintoft, L.: Filling gaps in the human genome. Nat. Rev. Genet. 14, 676 (2013)Google Scholar
  10. 34.
    Forsdyke, D.R., Bell, S.J.: Purine-loading, stem-loops, and Chargaff’s second parity rule: a discussion of the application of elementary principles to early chemical observations. Appl. Bioinformatics 3, 3–8 (2004)CrossRefGoogle Scholar
  11. 40.
    Gerstein, M.B., Bruce, C., Rozowsky, J.S., Zheng, D., Du, J., Korbel, J.O., Emanuelsson, O., Zhang, Z.D., Weissman, S., Snyder, M.: What is a gene, post-ENCODE? history and update definition. Genome Res. 17, 669–681 (2007)CrossRefGoogle Scholar
  12. 42.
    Graur, D., Zheng, Y., Price, N., Azevedo, R.B.R., Zufall, R.A., Elhaik, E.: On the immortality of television sets: “Function” in the human genome according to the evolution-free gospel of ENCODE. Genome Biol. Evol. 5(3), 578–590 (2013)CrossRefGoogle Scholar
  13. 43.
    Gregory, T.R.: The C-value enigma in plants and animals: a review of parallels and an appeal for partnership. Ann. Bot. 95, 133–146 (2005)CrossRefGoogle Scholar
  14. 49.
    Hutchison III, C.A.: DNA sequencing: bench to bedside and beyond. Nucleic Acids Res. 35(18), 6227–6237 (2007)CrossRefGoogle Scholar
  15. 51.
    International Human Genome Sequencing Consortium: Initial sequencing and analysis of the human genome. Nature 409, 860–921 (2001)Google Scholar
  16. 53.
    Jones, M.D., Forn, I., Gadelha, C.M., Egan, M.J., Massana, R., Richards, T.A.: Discovery of novel intermediate forms redefines the fungal tree of life. Nature 474, 200–203 (2011)CrossRefGoogle Scholar
  17. 54.
    Jordan, I.K., Rogozin, I.B., Glazko, G.V., Koonin, E.V.: Origin of a substantial fraction of human regulatory sequences from transposable elements. Trends Genet. 19, 68–72 (2003)CrossRefGoogle Scholar
  18. 56.
    Kline, M.: Mathematics for the Nonmathematician. Dover, New York (1967)Google Scholar
  19. 66.
    Martin, J., et al.: The sequence and analysis of duplication-rich human chromosome 16. Nature 432, 988–994 (2004)CrossRefGoogle Scholar
  20. 68.
    McManus, I.C.: The aesthetics of simple figures. Br. J. Psychol. 71, 505–525 (1980)CrossRefGoogle Scholar
  21. 69.
    Metzker, M.L.: Application of next-generation sequencing technologies - the next generation. Nat. Rev. Genet. 11(1), 31–46 (2010)CrossRefGoogle Scholar
  22. 72.
    Newton, I.: The Principia - Mathematical Principles of Natural Philosophy. Snowball Publishing, Dallas (2010)Google Scholar
  23. 73.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research. Springer, New York (2000)zbMATHGoogle Scholar
  24. 74.
    Perez, J.-C.: Chaos, DNA and neuro-computers: a golden link. Specul. Sci. Technol. 14, 336–346 (1991)Google Scholar
  25. 75.
    Pertea, M., Salzberg, S.L.: Between a chicken and a grape: estimating the number of human genes. Genome Biol. 11(5), 206 (2010)CrossRefGoogle Scholar
  26. 76.
    Polya, G.: Mathematics and Plausible Reasoning. Princeton University Press, New Jersey (1954)zbMATHGoogle Scholar
  27. 79.
    Salzberg, S.L., Yorke, J.A.: Beware of mis-assembled genomes. Bioinformatics 21, 4320–4321 (2005)CrossRefGoogle Scholar
  28. 80.
    Sanger, F.: Determination of Nucleotide Sequences in DNA. Nobel Lecture, 8 December 1980Google Scholar
  29. 81.
    Sanger, F., Air, G.M., Barrell, B.G., Brown, N.L., Coulson, A.R., Fiddes, C.A., Hutchinson, C.A., Slocombe, P.M., Smith, M.: Nucleotide sequence of bacteriophage ΦX174 DNA. Nature 265(5596), 687–695 (1977)CrossRefGoogle Scholar
  30. 85.
    Smith, T.F., Waterman, M.S.: Identification of common molecular subsequences. J. Mol. Biol. 147, 195–197 (1981)CrossRefGoogle Scholar
  31. 86.
    Staden, R., Beal, K.F., Bonfield, J.K.: The Staden package. Methods Mol. Biol. 132, 115–130 (2000)Google Scholar
  32. 87.
    Stark, R.: How the West Won: The Neglected Story of the Triumph of Modernity. ISI Books, Delaware (2015)Google Scholar
  33. 91.
    Telenti, A., Pierce, L.C.T., Biggs,W.H., di Iulio, J., Wong, E.H.M., Fabani, M.M., Kirkness, E.F., Moustafa, A., Shah, N., Xie, C., Brewerton, S.C., Bulsara, N., Garner, C., Metzker, G., Sandoval, E., Perkins, B.A., Och, F.J., Turpaz, Y., Venter, J.C.: Deep sequencing of 10,000 human genomes. Proc. Natl. Acad. Sci. U. S. A. 113(42), 11901–11906 (2016)CrossRefGoogle Scholar
  34. 92.
    The ENCODE Project Consortium: An integrated encyclopedia of DNA elements in the human genome. Nature 489, 57–74 (2012)CrossRefGoogle Scholar
  35. 94.
    Venter, J.C., et al.: The sequence of the human genome. Science 291(5507), 1304–1351 (2001)CrossRefGoogle Scholar
  36. 95.
    Vogel, F.: A preliminary estimate of the number of human genes. Nature 201, 847 (1964)CrossRefGoogle Scholar
  37. 96.
    Waterman, M.S.: Introduction to Computational Biology: Maps, Sequences and Genomes. Interdisciplinary Statistics. Chapman & Hall/CRC, Boca Raton (1997)Google Scholar
  38. 102.
    Yamagishi, M.E.B., Shimabukuro, A.I.: Nucleotide frequencies in human genome and Fibonacci numbers. Bull. Math. Biol. 70, 643–653 (2008)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Michel Eduardo Beleza Yamagishi
    • 1
  1. 1.Laboratório de Bioinformática AplicadaEmbrapa Informática AgropecuáriaCampinasBrazil

Personalised recommendations