On Circular Coding Properties of Gene and Protein Sequences

Abstract

The algorithms and equations that define and link circular coding properties of the genetic code and amino acid structural properties are derived according to the model of Canter dynamics based automaton. It is shown that the model defines a unifying concept of the genetic code, which incorporates Crick's code without comma and the evolutionary code concept. Arithmetic for codes is defined via the number theory results in coding theory, Smale's horseshoe map and the dynamics on fractal lattices. The method has been denoted SCA (Symbolic Canter Algorithm) and defined with respect to the principles of Molecular Recognition Theory, Grafstein's hypothesis of the stereochemical origin of the genetic code and Siemion's mutation ring. Underlying Fibonacci dynamics is extracted and mathematically defined considering the Canter set and Farey tree codon and amino acid projections. Two digit specification of the codon positions, by means of the binary group subdivision, is particularly analysed with respect to octal coding and defined according to the purine-pyrimidine, amino-keto and strong-week H bonding discrimination principles.