Evolution on folding landscapes in combinatorial structures

In this paper the authors investigate the evolution of molecular structures by random point mutations. They will consider two types of molecular structures: (a) (RNA) secondary structures, and (b) random structures. In both cases structure consists of: (1) a contact graph, and (2) a family of relations imposed on its adjacent vertices. The vertex set of the contact graph is simply the set of all indices of a sequence, and its edges are the bonds. The corresponding relations associated with the edges are viewed as secondary base pairing rules and tertiary interaction rules respectively. Mapping of sequences into secondary and random structures are modeled and analyzed. Here, the set of all sequences that map into a particular structure is modeled as a random graph in the sequence space, the so called neutral network and they study how neutral networks are embedded in sequence space. A basic replication of deletion experiment reveals how effective secondary and random structures can be searched by random point mutations and to what extent the structure effects the dynamics of this optimization process. In particular the authors can report a nonlinear relation between the fraction of tertiary interactions in random structures, and the times taken for a population of sequences to find a high fitness target random structure