Molecular Evolution of Catalysis

In this paper we consider evolutionary dynamics of catalytically active species with a distinct genotype-phenotype relationship. Folding landscapes of RNA molecules serve as a paradigm for this relationship with essential neutral properties. This landscape itself is partitioned by phenotypes (realized as secondary structures). To each genotype (represented as sequence) a structure is assigned in a unique way. The set of all sequences which map into a particluar structure is modeled as random graph in sequence space (the so-called neutral network). A catalytic network is realized as a random digraph with maximal out-degree 2 and secondary structures as vertex set. Studying a population of catalytic RNA-molecules shows significantly different behavior compared to a deterministic description: hypercycles are able to coexist and survive resp. a parasite with superior catalytic support. A “switching” between different dynamical organizations of the network can be observed, dynamical stability of hypercyclic organizations against errors and the existence of an error-threshold of catalysis can be reported.