Bulletin of Mathematical Biology

, Volume 70, Issue 3, pp 643–653 | Cite as

Nucleotide Frequencies in Human Genome and Fibonacci Numbers

  • Michel E. Beleza Yamagishi
  • Alex Itiro Shimabukuro
Original Article


This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci’s numbers. The model relies on two assumptions. First, Chargaff’s second parity rule should be valid, and second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. This result may be used as evidence to the Fibonacci string model that was proposed to the sequence growth of DNA repetitive sequences. It is noteworthy that the predicted values are solutions of an optimization problem, which is commonplace in many of nature’s phenomena.


Chargaff’s parity rules Nucleotide frequencies Fibonacci numbers Golden ratio Repetitive sequences Optimization problem 


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  1. Bannert, N., Kurth, R., 2004. Retroelements and the human genome: new perspectives on an old relation. Proc. Natl. Acad. Sci. 101, 14572–14579. CrossRefGoogle Scholar
  2. Chargaff, E., 1951. Structure and function of nucleic acids as cell constituents. Fed. Proc. 10, 654–659. Google Scholar
  3. Dress, A., Giegerich, R., Grunewald, S., Wagner, H., 2003. Fibonacci-Cayley numbers and repetition patterns in genomic DNA. Ann. Comb. 7, 259–279. zbMATHCrossRefMathSciNetGoogle Scholar
  4. Do, J.H., Choi, D.-K., 2006. Computational approaches to gene prediction. J. Microbiol. 44, 137–144. Google Scholar
  5. Fibonacci, L., Singler, L.E., 2002. Fibonacci’s Liber Abaci. Springer, New York. Google Scholar
  6. Forsdyke, D.R., Bell, S.J., 2004. A discussion of the application of elementary principles to early chemical observations. Appl. Bioinform. 3, 3–8. CrossRefGoogle Scholar
  7. Gregory, T.R., 2005. The C-value enigma in plants and animals: a review of parallels and an appeal for partnership. Ann. Bot. 95, 133–146. CrossRefGoogle Scholar
  8. Jordan, I.K., Rogozin, I.B., Glazko, G.V., Koonin, E.V., 2003. Origin of a substantial fraction of human regulatory sequences from transposable elements. Trends Genet. 19, 68–72. CrossRefGoogle Scholar
  9. Mitchell, D., Bridge, R., 2006. A test of Chargaff’s second rule. BBRC 340, 90–94. Google Scholar
  10. Nocedal, J., Wright, S.J., 2000. Numerical Optimization. Springer Series in Operations Research. New York, Springer. Google Scholar
  11. Salzberg, S.L., Yorke, J.A., 2005. Beware of mis-assembled genomes. Bioinformatics 21, 4320–4321. CrossRefGoogle Scholar
  12. Schwartz, S., Alazzouzi, H., Perucho, M., 2006. Mutational dynamics in human tumors confirm the neutral intrinsic instability of the mitochondrial D-loop poly-cytidine repeat. Genes Chromosom. Cancer 8, 770–780. CrossRefGoogle Scholar
  13. Watson, J.D., Crick, F.H.C., 1953. Molecular structure of nucleic acids. Nature 4356, 737. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  • Michel E. Beleza Yamagishi
    • 1
    • 2
  • Alex Itiro Shimabukuro
    • 3
  1. 1.Embrapa InformáticaLaboratório de Bioinformática AplicadaCampinasBrazil
  2. 2.Centro Universitário Salesiano de São Paulo—UNISALCurso de Ciência da ComputacãoCampinasBrazil
  3. 3.PUC Campinas—CEATECCampinasBrazil

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