Original Article

Bulletin of Mathematical Biology

, Volume 70, Issue 3, pp 643-653

First online:

Nucleotide Frequencies in Human Genome and Fibonacci Numbers

  • Michel E. Beleza YamagishiAffiliated withEmbrapa Informática, Laboratório de Bioinformática AplicadaCentro Universitário Salesiano de São Paulo—UNISAL, Curso de Ciência da Computacão Email author 
  • , Alex Itiro ShimabukuroAffiliated withPUC Campinas—CEATEC

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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