Expanding the Grammar of Biology

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


The Symmetry Principle used to be the only generalization known for Chargaff’s second parity rule. In this chapter, we present the conceptual theoretical framework used to discover four new higher order parity rules.


  1. 3.
    Aristotle: Metaphysics, Book I, 985bGoogle Scholar
  2. 5.
    Baisnée, P.-F., Hampson, S., Baldi, P.: Why are complementary DNA strands symmetric? Bioinformatics 18, 1021–1033 (2002)CrossRefGoogle Scholar
  3. 14.
    Chargaff, E.: Heraclitean Fire: Sketches from a Life Before Nature. The Rockefeller University Press, New York (1978)Google Scholar
  4. 15.
    Chargaff, E.: How genetics got a chemical education. Ann. N. Y. Acad. Sci. 325, 345–360 (1979)CrossRefGoogle Scholar
  5. 19.
    Cohen, J.E.: Mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better. Plos ONE 2(12), e439 (2004)CrossRefGoogle Scholar
  6. 26.
    Dong, Q., Cuticchia, A.J.: Compositional symmetries in complete genomes. Bioinformatics 17(6), 557–559 (2001)CrossRefGoogle Scholar
  7. 33.
    Forsdyke, D.R.: Relative roles of primary sequence and (G+C)% in determining the hierarchy of frequencies of complementary trinucleotide pairs in DNAs of different species. J. Mol. Evol. 41, 573–581 (1995)Google Scholar
  8. 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
  9. 44.
    Gulia-Nuss, M., Nuss, A.B., et al.: Genomic insights into the Ixodes scapularis tick vector of Lyme disease. Nat. Commun. 7, 10507 (2016)CrossRefGoogle Scholar
  10. 48.
    Hilbert, D., Ackermann, W.: Principle of Mathematical Logic. AMS Chelsea Publishing, Providence (1999)Google Scholar
  11. 56.
    Kline, M.: Mathematics for the Nonmathematician. Dover, New York (1967)Google Scholar
  12. 57.
    Kong, S.-G., Fan, W.-L., Chen, H.-D., Hsu, Z.-T., Zhou, N., et al.: Inverse symmetry in complete genomes and whole-genome inverse duplication. PLoS ONE 4(11), e7553 (2009). doi:10.1371/journal.pone.0007553CrossRefGoogle Scholar
  13. 65.
    Lonergan, B.J.F.: Insight: a study of human understanding. Philosophical Library, New York (1965)Google Scholar
  14. 78.
    Prabhu, V.V.: Symmetry observation in long nucleotide sequences. Nucleic Acids Res. 21, 2797–2800 (1993)CrossRefGoogle Scholar
  15. 83.
    Shah, H., Warwick, K., Vallverdú, J., Wu, D.: Can machines talk? comparison of Eliza with modern dialogue systems. Comput. Hum. Behav. 58, 278–295 (2016)CrossRefGoogle Scholar
  16. 93.
    Turing, A.M.: Computing machinery and intelligence. Mind 49, 433–460 (1950)MathSciNetCrossRefGoogle Scholar
  17. 100.
    Wright, A.V., Nuñez, J.K., Doudna, J.A.: Biology and application of CRISPR systems: harnessing natures’s toolbox for genome engineering. Cell 164, 29–44 (2016)CrossRefGoogle Scholar
  18. 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
  19. 103.
    Zinoviev, V.V., Yakishchik, S.I., Evdokimov, A.A., Malygin, E.G., Hattman, S.: Symmetry elements in DNA structure important for recognition/methylation by DNA [amino]-methyltransferases. Nucleic Acids Res. 32(13), 3930–3934 (2004)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

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

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