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

TL;DR

This paper introduces a fast, sparse folding-based algorithm to compute an upper bound on the partition function of nucleic acids, improving efficiency over traditional methods and aiding ensemble-based RNA structure predictions.

Contribution

The authors develop a novel algorithm that efficiently computes an upper bound on the partition function using sparse folding, reducing computational complexity for RNA and RNA-RNA interaction analysis.

Findings

Algorithm has same space complexity as sparse folding methods.

Time complexity is practical, O(MFE(n)ℓ) for single RNA.

Provides a computationally feasible way to estimate partition functions.

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 [7] 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 $O(n^4)$ and the time complexity is $O(n^6)$ which are prohibitively large [4,12]. Our goal in this paper is to give 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 [10]. The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is $O(MFE(n)\ell)$ for single RNA and $O(MFE(m, n)\ell)$ for RNA-RNA interaction in practice, in which $MFE$ is the running time of sparse folding and $\ell \leq n$ ($\ell \leq n + m$) is a sequence dependent parameter.