P-dcfold or How to Predict all Kinds of Pseudoknots in Rna Secondary Structures

Pseudoknots play important roles in many RNAs. But for computational reasons, pseudoknots are usually excluded from the definition of RNA secondary structures. Indeed, prediction of pseudoknots increase very highly the complexities in time of the algorithms, knowing that all existing algorithms for RNA secondary structure prediction have complexities at least of O(n3). Some algorithms have been developed for searching pseudoknots, but all of them have very high complexities, and consider generally particular kinds of pseudoknots. We present an algorithm, called P-DCFold based on the comparative approach, for the prediction of RNA secondary structures including all kinds of pseudoknots. The helices are searched recursively using the "Divide and Conquer" approach, searching the helices from the "most significant" to the "less significant". A selected helix subdivide the sequence into two sub-sequences, the internal one and a concatenation of the two externals. This approach is used to search non-interleaved helices and allows to limit the space of searching. To search for pseudoknots, the processing is reiterated. Therefore, each helix of the pseudoknot is selected in a different step. P-DCFold has been applied to several RNA sequences. In less than two seconds, their respective secondary structures, including their pseudoknots, have been recovered very efficiently.