How to search for RNA structures. Theoretical concepts in evolutionary biotechnology.

The relation between RNA sequences and minimum free energy secondary structures is viewed as a mapping from sequence space into shape space. The properties of such mappings depend strongly on the ratios of the numbers of sequences and structures and, hence, substantial differences are observed between samples of structures derived from AUGC, pure AU or pure GC sequences. Statistical analysis of large samples is used to demonstrate that structures from AUGC sequences are much less sensitive to point mutations than those from sequences containing exclusively AU or GC. The frequency with which a structure is realized in sequence space is inversely proportional to some power c > 1 of the structure's frequency rank, thus following a (generalized) Zipf law. For long sequences the exponent approaches c = 1. An inverse folding algorithm is used to compute samples of sequences folding into the same secondary structure. These sequences are distributed randomly in sequence space. Common structures form extended neutral networks along which populations can migrate through the entire sequence space without changing structure. In this migration, moves of Hamming distance d = 1 and d = 2 are accepted in order to allow for base and base pair exchanges, respectively. Around any arbitrarily chosen sequence a ball that contains sequences folding into all common structures can be drawn. This ball has a diameter that is much smaller than the diameter of sequence space. Hence, only a small fraction of sequence space needs to be searched in order to find a given structure. The results derived from the mapping of sequences into structures are used to suggest a rationale for evolutionary searches on RNA structures: selection cycles with high and low mutation rates applied in alternation. Generalizations of the results to RNA 3-D structures and protein structures are discussed.