The relations between RNA sequences and structures are understood as mappings from the space of sequences into a space of structures. Mathematical analysis of these maps is currently possible only for secondary structures. There, the mapping between sequences and structures is highly redundant in the sense that many sequences form identical secondary structures under the minimum free energy (mfe) criterium. We approached RNA sequence-structure relations in four different ways: (i) A mathematical model derived from random graph theory has been conceived and used to derive generic properties of sequence-structure maps. (ii) Exhaustive folding, implying that all sequences of given chain length were folded to yield mfe structures and evaluated by enumeration, has been used to study RNA molecules of short chain lengths. (iii) Statistical methods were used to evaluate structural properties from random or correlated samples of sequences. (iv) Evolutionarily relevant features of sequence to structure mappings were derived from computer simulations of populations evolving on RNA based fitness landscapes.
An overview of the results derived from the various approaches will be given and then the secondary structure model will be discussed in the light of several generalizations: (i) three-dimensional structures, (ii) contribution of suboptimal configurations to mfe structures (in particular the use of partition functions), and (iii) kinetic folding criteria.
