# Symmetry and Information: a Mathematical Model of the Genetic Code and its Consequences

## Diego Luis González

### CNR-IMM UOS of Bologna

and University of Bologna

Department of Statistical Sciences, Bologna, Italy

The analysis and the interpretation of the huge quantity of complex
experimental data from genetics and molecular biology require a paradigm shift.
Mathematical modelling, as the history of physics demonstrate, is the main way
for coping with such a situation (see, for example, the birth of quantum
mechanics that allowed to explain many different experimental phenomena
observed at the atomic and elementary particle level). Mathematical models
serve as a reference conceptual framework for interpreting experimental data,
suggesting new experiments, and validating predictions. In a dialectic manner,
the cross-fertilization between theory and experiments is the basis for
improving existing models or for replacing them with better ones.

In this spirit we present a mathematical model of the nuclear genetic code
that describes completely its degeneracy distribution. Moreover, the model
uncovers many symmetry properties of the code related to the chemical structure
of genetic information and allows to analyze genetic sequences from a new point
of view. The model can be extended to include the vertebrate mitochondrial
genetic code (tesserae model) providing new insights on the difficult problem
of the origin of protein synthesis and the biological mechanisms devoted to
ensure the quality of genetic coding and decoding.