We shall try to assign mathematical meaning to the language used by biologists for describing basic structures and processes in living organisms, from the (sub)cellular level up to evolutionary dynamics of populations.
In particular, we shall elucidate the mathematical as well as biological meaning of the following concepts.
● biological (non-Shannon) information,
● descriptional (non-Kolmogorov) complexity,
● biological structure,
● biological function (performed by a particular structure),
● biological purpose (of a function),
● information/program encoded and stored by a material structure (DNA, RNA),
● information/signal transmitted by a matter/energy process/flow,
● information/program, which controls such a "flow",
● biological structures build by (networks of) matter/energy flows, e.g transcription --> translation --> protein folding.
Also we indicate a potential use of formalisation of biological language in genetic engineering, e.g. in the analysis/applications of CRISPR and of phage assisted continuous evolution.
Emmanuel Ullmo
