A mathematical model of the genetic code, the origin of protein coding, and the ribosome as a dynamical molecular machine

A paradigm shift is needed in order to interpret the huge quantity of complex experimental data arriving mainly from genetics and molecular biology. Mathematical modelling, as the history of physics demonstrate, is the main way for coping with such a situation. Mathematical models serve as a reference conceptual framework for interpreting experimental data and allow to suggest new experiments. In a dialectic manner, comparison between theory and experiments allows the optimization of existing models or their replacement with more accurate ones when optimization is not more possible. In this contribution we present a mathematical model of the nuclear genetic code that describes completely its degeneracy distribution. Moreover, it allows the uncovering of many symmetry properties of the code that are related with the structure of genetic information. In such a way the statistical study of actual coding sequences becomes feasible from a new theoretical point of view. The model can be extended to include the vertebrate mitochondrial genetic code (tesserae model) allowing new insight on the difficult problem of the origin of protein synthesis and the biological mechanisms which are devoted to ensure the quality of genetic coding and decoding (mutation robustness and error detection/correction, circular and comma-free coding for frame maintenance, etc.). The possibility that error correction should be implemented by taking profit of the dynamics of the synthesis apparatus is also briefly explored.