The Poitiers School of Mathematical and Theoretical Biology: Besson–Gavaudan–Schützenberger’s Conjectures on Genetic Code and RNA Structures

The French school of theoretical biology has been mainly initiated in Poitiers during the sixties by scientists like J. Besson, G. Bouligand, P. Gavaudan, M. P. Schutzenberger and R. Thom, launching many new research domains on the fractal dimension, the combinatorial properties of the genetic code and related amino-acids as well as on the genetic regulation of the biological processes. Presently, the biological science knows that RNA molecules are often involved in the regulation of complex genetic networks as effectors, e.g., activators (small RNAs as transcription factors), inhibitors (micro-RNAs) or hybrids (circular RNAs). Examples of such networks will be given showing that (1) there exist RNA “relics” that have played an important role during evolution and have survived in many genomes, whose probability distribution of their sub-sequences is quantified by the Shannon entropy, and (2) the robustness of the dynamics of the networks they regulate can be characterized by the Kolmogorov–Sinai dynamic entropy and attractor entropy.