Multiple Structural RNA Alignment with Lagrangian Relaxation

In contrast to proteins, many classes of functionally related RNA molecules show a rather weak sequence conservation but instead a fairly well conserved secondary structure. Hence it is clear, that any method that relates RNA sequences in form of (multiple) alignments should take structural features into account. Since multiple alignments are of great importance for subsequent data analysis, research in improving the speed and accuracy of such alignments benefits many other analysis problems. We present a formulation for computing provably optimal, structurebased, multiple RNA alignments and give an algorithm that finds such an optimal solution or at least a very good approximation of it. Our formulation is based on the structural trace formulation of Reinert et al. and uses a recently proposed weighting function of Hofacker et al. that makes use of McCaskill’s approach to compute base pair probability functions. To solve the resulting computational problem we propose an algorithm based on Lagrangian relaxation which already proved useful in the two-sequence case. We compare our implementation, mLARA, to two recent programs (MARNA and pmmulti) and demonstrate that we can compute multiple alignments with consensus structures that have a significant lower minimum free energy term than computed by the other programs. Our prototypical experiments indicate that our new algorithm is the first approach to successfully compute provably optimal multiple structural alignments in reasonable computation time. Further advantages are its applicablity to long sequences where standard dynamic programming approaches must fail and its ability to deal with pseudoknot structures.