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

Abstract

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.

Keywords

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

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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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