Information Complexity and Biology

Abstract

Kolmogorov contributed directly to Biology in essentially three problems: the analysis of population dynamics (Lotka-Volterra equations), the reaction-diffusion formulation of gene spreading (FKPP equation), and some discussions about Mendel’s laws. However, the widely recognized importance of his contribution arises from his work on algorithmic complexity. In fact, the limited direct intervention in Biology reflects the generally slow growth of interest of mathematicians towards biological issues. From the early work of Vito Volterra on species competition, to the slow growth of dynamical systems theory, contributions to the study of matter and the physiology of the nervous system, the first 50–60 years have witnessed important contributions, but as scattered pieces apparently uncorrelated, and in branches often far away from Biology. Up to the 40’ it is hard to see the initial loose build up of a convergence, for those theories that will become mainstream research by the end of the century, and connected by the study of biological systems per-se.

The initial intuitions of L. Pauling and E. Schrödinger on life and matter date from this period, and will gave the first initial full fledged results only ten years later, with the discovery of the structure of DNA by J. Watson and F. Crick, and the initial applications of molecular structures to the study of human diseases few years earlier by Pauling. Thus, as a result of scientific developments in Biology that took place after the 50’, the work of Kolmogorov on Information Theory is much more fundamental than his direct contributions would suggest. For scientist working in Molecular Biology and Genetics, Information Theory has increasingly become, during the last fifty years, one of the mayor tools in dissecting and understanding basic Biological problems.

After an introductory presentation on algorithmic complexity and information theory, in relation to biological evolution and control, we discuss those aspects relevant for a rational approach to problems arising on different scales. The processes of transcription and replication of DNA which are at the basis of life, can be recasted into an Information theory problem. Proteins and enzymes with their biological functionality contribute to the cellular life and activity. The cell offers an extraordinary example of a highly complex system that is able to regulate its own activity through metabolic network. Then we present an example on the formation of complex structures through cellular division and differentiation in a model organism (C. elegans). Finally we discuss the essential principles that are thought to rule evolution through natural selection (theory of fitness landscapes).