Abstract
BackgroundSoon after the first algorithms for RNA folding became available, it was recognised that the prediction of only one energetically optimal structure is insufficient to achieve reliable results. An in-depth analysis of the folding space as a whole appeared necessary to deduce the structural properties of a given RNA molecule reliably. Folding space analysis comprises various methods such as suboptimal folding, computation of base pair probabilities, sampling procedures and abstract shape analysis. Common to many approaches is the idea of partitioning the folding space into classes of structures, for which certain properties can be derived.ResultsIn this paper we extend the approach of abstract shape analysis. We show how to compute the accumulated probabilities of all structures that share the same shape. While this implies a complete (non-heuristic) analysis of the folding space, the computational effort depends only on the size of the shape space, which is much smaller. This approach has been integrated into the tool RNAshapes, and we apply it to various RNAs.ConclusionAnalyses of conformational switches show the existence of two shapes with probabilities approximately vs. , whereas the analysis of a microRNA precursor reveals one shape with a probability near to 1.0. Furthermore, it is shown that a shape can outperform an energetically more favourable one by achieving a higher probability. From these results, and the fact that we use a complete and exact analysis of the folding space, we conclude that this approach opens up new and promising routes for investigating and understanding RNA secondary structure.
Highlights
Soon after the first algorithms for RNA folding became available, it was recognised that the prediction of only one energetically optimal structure is insufficient to achieve reliable results
Analyses of conformational switches show the existence of two shapes with probabilities approximately 2 vs. 1, whereas the analysis of a microRNA precursor reveals one 33 shape with a probability near to 1.0
In the first three subsections, we explain the mathematical model underlying our new type of analysis. (Algorithmic details and efficiency concerns are deferred to the Methods section.) Subsequently, we report on the findings of various applications of the method
Summary
Soon after the first algorithms for RNA folding became available, it was recognised that the prediction of only one energetically optimal structure is insufficient to achieve reliable results. The first algorithm capable of computing the structure with minimum free energy (MFE) based on the nearest neighbour energy model was introduced in [1]. The challenge of folding space analysis is to determine whether there is some family of structures in this ensemble that is internally similar, distinct from the rest, and collectively dominates the probabilities of all other families. In [6] Zuker introduced an extended version of his algorithm, which was capable of predicting certain suboptimal structures. This allows a researcher to check different predictions for correspondence to experimental results. The most recent version of the algorithm [2,7] is implemented in the MFOLD package [8]
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