The Unconventionality of Nature: Biology from Noise to Morphogenesis

(joint work with Barbara Bravi)

Computability Theory has been invented to … prove incomputability. After Gödel’s theory of computable functions, invented in order to define rigorously decidability and give an undecidable statement of first order Arithmetic, Turing proposed a Logical Computing Machine, for the purpose of the definition of an incomputable function and to discriminate between computable and incomputable real numbers. By further work, in 1952, he gave a non-linear frame for a material dynamics where forms could emerge with no predefined design (no software), triggered and guided by &lquot;symmetry breaking&rquot;, &lquot;catastrophic instabilities&rquot;, &lquot;exponential drifts&rquot;. These are incomputable/unpredictable physical processes in continua where randomness is far from being noise to be contrasted, but positively contributes to the shaping of forms. Present models of morphogenesis rely significantly on non-linear intracellular and intercellular dynamics, thus on randomness. Recent work on phenotype variability in connection to stochastic gene expression and extrinsic fluctuations stresses the fundamental role of stochasticity in the historicity of developmental paths and its constructive contribution towards robustness. Extrinsic and intrinsic fluctuations may be inserted in biochemical differential equations as probabilistic terms, in conjunction to diffusion (Fokker-Planck) or path integrals (Wiener). This may help to understand the role of proper biological &lquot;resonance&rquot; (interactions between different levels of organisation and their unpredictable dynamics), in a highly unconventional frame for biological processes.

Giuseppe Longo is a mathematician, Directeur de Recherche (DRE) CNRS at Ecole Normale Supérieure, Paris. He is a former Professor of Logic and Computing at the University of Pisa. He spent three years in the USA (Berkeley, MIT, Carnegie Mellon) as researcher and Visiting Professor. He worked at applications of Mathematics to Computer Science, and he recently extended his research interests to Theoretical Biology. Web page: http://www.di.ens.fr/users/longo/