Abstract
The prediction of RNA structure with pseudoknots is a nondeterministic polynomial-time hard (NP-hard) problem; according to minimum free energy models and computational methods, we investigate the RNA-pseudoknotted structure. Our paper presents an efficient algorithm for predicting RNA structure with pseudoknots, and the algorithm takes O([Formula: see text]) time and O([Formula: see text]) space, the experimental tests in Rfam10.1 and PseudoBase indicate that the algorithm is more effective and precise. The predicting accuracy, the time complexity and space complexity outperform existing algorithms, such as Maximum Weight Matching (MWM) algorithm, PKNOTS algorithm and Inner Limiting Layer (ILM) algorithm, and the algorithm can predict arbitrary pseudoknots. And there exists a [Formula: see text] ([Formula: see text]) polynomial time approximation scheme in searching maximum number of stackings, and we give the proof of the approximation scheme in RNA-pseudoknotted structure. We have improved several types of pseudoknots considered in RNA folding structure, and analyze their possible transitions between types of pseudoknots.
Highlights
RNA is an important biomacromolecule which performs a wide range of functions in biological systems
There exists a 1 þ " (" > 0) polynomial time approximation scheme in searching maximum number of stackings, and we give the proof of the approximation scheme in RNA-pseudoknotted structure
E±cient algorithm fornding optimal folding of an RNA structure has beenrstly known by Michael Zuker[35]; Pknots algorithm for RNA-pseudoknotted structure of predigesting model based on minimum free energy (MFE) has been presented by Rivas and Eddy,[28] in which time complexity and space complexity are O(n6) and O(n4), respectively
Summary
RNA is an important biomacromolecule which performs a wide range of functions in biological systems. Cross of base pairs form pseudoknots, and cross of stems can form pseudoknotted structure It is di±cult to compute large RNA molecules including pseudoknots for existing polynomial time-predicting algorithms. For predicting secondary structures with pseudoknots, Nussinov has studied the case where the energy function is minimized when the number of base pairs is maximized, and has obtained an O(n3) time algorithm for predicting RNA secondary structures,[22] but Nussinov algorithm cannot predict pseudoknotted structures. The problem for predicting RNA secondary structure including pseudoknots is NP-complete,[21] and maximizing the number of stacking pairs allowing pseudoknots in a planar secondary structure makes it NP-hard,[10] so naturally people seek for approximation algorithms in the past. This paper presents several types of pseudoknots considered in RNA folding structures, and analyzes their possible transitions between types of pseudoknots
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