Self-organization of Genetic Coding

The self-organization of genetic coding is studied in a simple model system which uses the products of translation as catalysts for the process. The system studied contains protein molecules chosen from a sequence space of high dimension. Catalysts which assign amino acids to codons are chosen in such a way that a random selection of proteins synthesizes further proteins randomly. Under some circumstances, dictated by the genetic information supplied to the system and the manner in which protein function depends on protein sequence, the state of random synthesis is unstable. The system then evolves spontaneously to a new state in which proteins synthesize further proteins in an ordered fashion, typically executing the rules of a simple code for the assignment of amino acids to codons. For some embeddings of protein functions in the protein sequence space, the domains of stability of the ordered and disordered states are calculated. Computer simulations verify that coding self-organization occurs in a variety of systems of the sort studied. Coding self-organization among catalysts which recognize genetic information is a high order co-operative selection process which provides the link between genotype and phenotype needed for the Darwinian evolution of complex biochemical systems.