Mathematical Grammar of Biology

  • Michel Eduardo Beleza Yamagishi

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Michel Eduardo Beleza Yamagishi
    Pages 1-8
  3. Michel Eduardo Beleza Yamagishi
    Pages 9-27
  4. Michel Eduardo Beleza Yamagishi
    Pages 29-53
  5. Michel Eduardo Beleza Yamagishi
    Pages 55-70
  6. Back Matter
    Pages 71-82

About this book


This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.


Mathematical DNA rules Intrinsic properties of DNA Bioinformatics Genomics Symmetry Principle Chargaff rules Synthetic Biology

Authors and affiliations

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

Bibliographic information