Accurate SHAPE-directed RNA secondary structure modeling, including pseudoknots

Abstract

A pseudoknot forms in an RNA when nucleotides in a loop pair with a region outside the helices that close the loop. Pseudoknots occur relatively rarely in RNA but are highly overrepresented in functionally critical motifs in large catalytic RNAs, in riboswitches, and in regulatory elements of viruses. Pseudoknots are usually excluded from RNA structure prediction algorithms. When included, these pairings are difficult to model accurately, especially in large RNAs, because allowing this structure dramatically increases the number of possible incorrect folds and because it is difficult to search the fold space for an optimal structure. We have developed a concise secondary structure modeling approach that combines SHAPE (selective 2′-hydroxyl acylation analyzed by primer extension) experimental chemical probing information and a simple, but robust, energy model for the entropic cost of single pseudoknot formation. Structures are predicted with iterative refinement, using a dynamic programming algorithm. This melded experimental and thermodynamic energy function predicted the secondary structures and the pseudoknots for a set of 21 challenging RNAs of known structure ranging in size from 34 to 530 nt. On average, 93% of known base pairs were predicted, and all pseudoknots in wellfolded RNAs were identified. Information is encoded in an RNA molecule at two levels: in its primary sequence and in its ability to form higher-order secondary and tertiary structures. Nearly all RNAs can fold to form some secondary structure and, in many RNAs, highly structured regions encode important regulatory motifs. Such structured regulatory elements can be composed of canonical base pairs but may also feature specialized and distinctive RNA structures. Among the best characterized of these specialized structures are RNA pseudoknots. Pseudoknots are relatively rare but occur overwhelmingly in functionally important regions of RNA (2-4). For example, all of the large catalytic RNAs contain pseudoknots (5, 6); roughly two-thirds of the known classes of riboswitches contain pseudoknots that appear to be essential for ligand binding and gene regulatory functions (7); and pseudoknots occur prominently in the regulatory elements that viruses use to usurp cellular metabolism (3). Pseudoknots are thus harbingers of biological function. An important and challenging goal is to identify these structures reliably.Pseudoknots are excluded from the most widely used algorithms that model RNA secondary structure (8). This exclusion is based on the challenge of incorporating the pseudoknot structure into the efficient dynamic programming algorithm used in the most popular secondary structure prediction approaches and because of the additional computational effort required. The prediction of lowest free energy structures with pseudoknots is NP-complete (9), which means that lowest free energy structure cannot be solved as a function of sequence length in polynomial time. In addition, allowing pseudoknots greatly increases the number of (incorrect) hel...

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