Title : Quantum theory concepts and biological evolution paths from structure waves in biopolymers
Abstract:
The Lamarckian theory of biological evolution assumed that changes induced by the environ- ment on what we now call a ‘phenotype’ could be transferred to its ‘genotype’, while the Darwinian the- ory was based on natural and sexual selection of those ‘genotypes’ which showed up in fit ‘phenotypes’. Darwinian mechanisms have proven quite efficient in explaining microevolution processes, but not suf- ficient to understand such macroevolution phenomena as speciation, radiation, and punctuated equilibria, which involve highly coordinated, structural and functional biological changes.
The fact that nucleic acids bearing the genetic material are amenable to quantum theory, as was foreseen by Schrödinger, suggests that the physico-chemical dynamics of these biomolecules and of their coded proteins over extended time scales could play a role in these coordinated changes. As wave mechanics took its roots in the de Broglie analysis of the Maupertuis and Fermat principles, one may go further and wonder if an integral formulation involving a extremum principle may not be derived for the biological evolution as well, which would make its finalist flavour compatible with the determinist views.
In the present talk, we propose to define a ‘biological extremal principle’ which could be used to uncover phylum evolution paths by maximizing the convolution of a complexity functional involving Clausius and
/ or Kolmogorov entropies and a fitness functional to be defined from former evolution theories:
E [q] º (G * V) [q] º òòG (q - qa, v - va, t) V (qa, va, t) dqa dt ; dE / dq = 0.
As the Hamilton principle could be derived by the Feynman path-integral formulation, which involved constructive / destructive interferences of quantum waves, such an biological extremal principle may be derived from the structure waves expressing nucleic-acid and related protein structures. We propose an elaborated code for expressing such structure waves in nucleic acids and related proteins, and illustrate our code on a velvet-tobacco mottle-virus satellite RNA.