Sequence-Structure Relationships in Nucleic Acids

The secondary structures of nucleic acids provide a unique computer model for investigating the most important aspects of their structural and evolutionary biology. Secondary structures, defined as the lists of base pairing contacts in RNA or DNA molecules, are a coarse-grained representation of the 3D structures; nevertheless they capture many important features of the molecules. The existence of efficient algorithms for solving the folding problem, i.e., for predicting the secondary structure given only the sequence, allows a detailed analysis of the model by means of computer simulations. The notion of a "landscape" underlies both the structure formation (folding) and the (in vitro) evolution of RNA.

Evolutionary adaptation may be seen as hill climbing process on a fitness landscape which is determined by the phenotype of the RNA molecule (within the model this is its secondary structure) and the selection constraints acting on the molecules. We find that a substantial fraction of point mutations do not change an RNA secondary structure. On the other hand, a comparable fraction of mutations leads to very different structures. This interplay of smoothness and ruggedness (or robustness and sensitivity) is a generic feature of both RNA and protein sequence-structure maps. Its consequences, "shape space covering" and "neutral networks" are inherited by the fitness landscapes and determine the dynamics of RNA evolution. Punctuated equilibria at phenotype level and a diffusion-like evolution of the underlying genotypes are a characteristic feature of such models.

The folding dynamics of particular RNA molecule can also be studied in a meaningful way based on secondary structures. Given an RNA sequence, we consider the energy landscape formed by all possible conformations (secondary structures). A straight-forward implementation of the Metropolis algorithm is sufficient to produce a quite realistic folding kinetics, allowing to identify meta-stable states and folding pathways. Just as in the protein case there are good and bad folders which can be distinguished by the properties of their energy landscapes.