Lifting prediction to alignment of RNA pseudoknots

Prediction and alignment of RNA pseudoknot structures are NP-hard. Nevertheless, several efficient prediction algorithms by dynamic programming have been proposed for restricted classes of pseudoknots. We present a general scheme that yields an efficient alignment algorithm for arbitrary such classes. Moreover, we show that such an alignment algorithm benefits from the class restriction in the same way as the corresponding structure prediction algorithm does. We look at five of these classes in greater detail. The time and space complexity of the alignment algorithm is increased by only a linear factor over the respective prediction algorithm. For four of the classes, no efficient alignment algorithms were known. For the fifth, most general class, we improve the previously best complexity of O(n⁵m⁵) time to O(nm⁶), where n and m denote sequence lengths. Finally, we apply our fastest algorithm with O(nm⁴) time and O(nm²) space to comparative de-novo pseudoknot prediction.