A Study of Replicators and Hypercycles by Typogenetics

Abstract

A Typogenetics is a formal system designed to study origins of life from a premordial soup of DNA molecules, enzymes and other building materials. It was introduced by Hofstadter in his book Dialogues with Godel, Escher, Bach: An Eternal Golden Braid [17]. Autoreplicating molecules and systems of mutually replicating and catalyzing molecules (hypercycles) were modeled in the present paper in a very simplified way. Abstracted molecules in a form of strands are used in a model of a vessel, where chemical reactions occur. The approach is very similar to evolutionary algorithms. While a small hypercycle of two molecules mutually supporting their reproduction can be created without extreme difficulties, it is nearly impossible to create a hypercycle involving more than 4 autoreplicators at once. This paper demonstrates, that larger hypercycles can be created by an optimization and inclusion of new molecules into a smaller hypercycle. Such a sequential construction of hypercycles can substantially reduce the combinatorial complexity in comparison with a simultaneous optimization of single components of a large hypercycle.