Prediction and statistics of pseudoknots in RNA structures using exactly clustered stochastic simulations

Ab initio RNA secondary structure predictions have long dismissed helices interior to loops, so-called pseudoknots, despite their structural importance. Here we report that many pseudoknots can be predicted through long-time-scale RNA-folding simulations, which follow the stochastic closing and opening of individual RNA helices. The numerical efficacy of these stochastic simulations relies on an 𝒪( n 2 ) clustering algorithm that computes time averages over a continuously updated set of n reference structures. Applying this exact stochastic clustering approach, we typically obtain a 5- to 100-fold simulation speed-up for RNA sequences up to 400 bases, while the effective acceleration can be as high as 10 5 -fold for short, multistable molecules (≤150 bases). We performed extensive folding statistics on random and natural RNA sequences and found that pseudoknots are distributed unevenly among RNA structures and account for up to 30% of base pairs in G+C-rich RNA sequences (online RNA-folding kinetics server including pseudoknots: http://kinefold.u-strasbg.fr ).