On Dichotomic Classes and Bijections of the Genetic Code

Elena Fimmel and Lutz Strüngmann

Institute for Applied Mathematics
University of Applied Sciences, Mannheim, Germany

In the talk decompositions of the set of 64 codons in two equal sized subsets, called dichotomic classes, are presented. Dichotomic classes allow to uncover many symmetry properties of the code and mirror biochemical features occurring at discrete base positions in the codon.

A recent mathematical model of the genetic code (see, for instance, [1], [2], [3], [4]), based on non-power representation of integer numbers, provides an original explanation for the structural properties and the degeneracy distribution that naturally occur in the genetic code. In particular, a known biologically meaningful Rumer’s dichotomy (see, for instance, [5]) and a new chemically meaningful parity dichotomy arise based on the model in a natural way. In our work we show that the codon/anticodon complementarity can be understood and obtained in the same algorithmic way as the Rumer’s and the parity dichotomies and present a general algorithm underlying significant dichotomic partitions of the code.

In addition the global framework of bijective transformations of the nucleotide bases is also discussed and we clarify when dichotomic partitions can be generated. Interestingly, the algorithm underlying dichotomic class definition mirrors operations that have a factual biological function in the decoding center of the ribosome.

References

  1. Fimmel, E., Danielli A., Strüngmann L.: On dichotomic classes and bijections of the genetic code. J. Theor. Biol. (2013), http://dx.doi.org/10.1016/j.jtbi.2013.07.027
  2. S. Giannerini, D.L. Gonzalez, R. Rosa: DNA, dichotomic classes and frame syncronization: a quasi-crystal framework., Phil. Trans. R. Soc., 2012, 370, pp. 2987-3006
  3. D.L. Gonzalez, S. Giannerini, R. Rosa: Strong short-range correlations and dichotomic codon classes in coding DNA sequences, Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5 Pt 1):051918. Epub 2008 Nov 19.
  4. D.L. Gonzalez: The Mathematical Structure of the Genetic Code, In Barbieri (Ed.): Codes of Life: The Rules of Microevolution, Springer, 2008
  5. Y.B. Rumer: Systematization of codons in the genetic code, Doklady Akademii nauk SSSR 1969 Aug;187(4):937-8.