Predicting RNA Secondary Structures with Arbitrary Pseudoknots by Maximizing the Number of Stacking Pairs

TL;DR

This paper develops approximation algorithms for predicting RNA secondary structures with arbitrary pseudoknots by maximizing stacking pairs, providing theoretical guarantees and analyzing computational complexity.

Contribution

It introduces the first approximation algorithms with proven ratios for RNA secondary structure prediction with pseudoknots, and establishes NP-hardness results.

Findings

Approximation algorithms with ratios 1/2 and 1/3 for planar and general structures.

Algorithms run in O(n^3) and linear time respectively.

Maximizing stacking pairs with pseudoknots is NP-hard.

Abstract

The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no performance guarantee and can only handle limited types of pseudoknots. In this paper we initiate the study of predicting RNA secondary structures with a maximum number of stacking pairs while allowing arbitrary pseudoknots. We obtain two approximation algorithms with worst-case approximation ratios of 1/2 and 1/3 for planar and general secondary structures,respectively. For an RNA sequence of $n$ bases, the approximation algorithm for planar secondary structures runs in $O(n^3)$ time while that for the general case runs in linear time. Furthermore, we prove that allowing pseudoknots makes it NP-hard to maximize the number of stacking pairs in a planar secondary structure. This result is in contrast with the recent NP-hard results on psuedoknots which are based on optimizing some general and complicated energy functions.