An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids

Abstract

It has been shown that minimum free-energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble-based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble-based approaches is the computational complexity of the partition function and base-pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is O(n4) and the time complexity is O(n6), which is prohibitively large. Our goal in this article is to present a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola (2012). The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is O(MFE(n)ℓ) for single RNA and O(MFE(m, n)ℓ) for RNA-RNA interaction in practice, in which MFE is the running time of sparse folding and ℓ≤n (ℓ≤n+m) is a sequence-dependent parameter.

LinearPartition: linear-time approximation of RNA folding partition function and base-pairing probabilities

“…There are other algorithmic efforts to speed up RNA folding and partition function calculation, including sparsification ( Backofen et al , 2011 ; Chitsaz et al , 2013 ). But our work differs from those efforts in the following ways: (i) our dynamic programming is left-to-right and theirs are bottom-up; (ii) our work guarantees linear runtime while theirs cannot; (iii) our search is inexact while theirs are exact.…”