The Mathematical Structure of the Genetic Code

Abstract

In this chapter a new mathematical theory of the genetic code is presented, based on a particular kind of number representation: a non-power binary representation. A mathematical model is constructed that allows the description of many known properties of the genetic code, such as the degeneracy distribution and the specific codon-amino acid assignation, and also of some new properties such as, for example, palindromic symmetry (a degeneracy preserving transformation), which is shown to be the highest level of a series of hierarchical symmetries. The role of chemical dichotomy classes, which varies between purine–pyrimidine, amino–keto, and strong–weak following the position of the bases in the codon frame, is shown. A new characterization of codons, obtained through the parity of the corresponding binary strings in the mathematical model, together with the associated symbolic structure acting on the codon space, is also illustrated. Furthermore, it is shown that Rumer’s classes (or degeneracy classes) can be obtained symbolically from the two first letters of a codon by means of an operation, which is identical to that of parity determination from a structural point of view. On this basis, the existence of a third dichotomy class sharing the former properties can be hypothesized.