The language of RNA: a formal grammar that includes pseudoknots

In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However, a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking.

Here we show a one-to-one correspondence between that algorithm and a formal transformational grammar. This grammar class encompasses the context-free grammars and goes beyond to generate pseudoknotted structures. The pseudoknot grammar avoids the use of general context-sensitive rules by introducing a small number of auxiliary symbols used to reorder the strings generated by an otherwise context-free grammar. This formal representation of the residue correlations in RNA structure is important because it means we can build full probabilistic models of RNA secondary structure, including pseudoknots, and use them to optimally parse sequences in polynomial time.