Evolutionary rate variation and RNA secondary structure prediction

Hierarchical folding of multiple sequence alignments for the prediction of structures and RNA-RNA interactions

BACKGROUND

Many regulatory non-coding RNAs (ncRNAs) function through complementary binding with mRNAs or other ncRNAs, e.g., microRNAs, snoRNAs and bacterial sRNAs. Predicting these RNA interactions is essential for functional studies of putative ncRNAs or for the design of artificial RNAs. Many ncRNAs show clear signs of undergoing compensating base changes over evolutionary time. Here, we postulate that a non-negligible part of the existing RNA-RNA interactions contain preserved but covarying patterns of interactions.

METHODS

We present a novel method that takes compensating base changes across the binding sites into account. The algorithm works in two steps on two pre-generated multiple alignments. In the first step, individual base pairs with high reliability are found using the PETfold algorithm, which includes evolutionary and thermodynamic properties. In step two (where high reliability base pairs from step one are constrained as unpaired), the principle of cofolding is combined with hierarchical folding. The final prediction of intra- and inter-molecular base pairs consists of the reliabilities computed from the constrained expected accuracy scoring, which is an extended version of that used for individual multiple alignments.

RESULTS

We derived a rather extensive algorithm. One of the advantages of our approach (in contrast to other RNA-RNA interaction prediction methods) is the application of covariance detection and prediction of pseudoknots between intra- and inter-molecular base pairs. As a proof of concept, we show an example and discuss the strengths and weaknesses of the approach.

Probabilistic phylogenetic inference with insertions and deletions

A fundamental task in sequence analysis is to calculate the probability of a multiple alignment given a phylogenetic tree relating the sequences and an evolutionary model describing how sequences change over time. However, the most widely used phylogenetic models only account for residue substitution events. We describe a probabilistic model of a multiple sequence alignment that accounts for insertion and deletion events in addition to substitutions, given a phylogenetic tree, using a rate matrix augmented by the gap character. Starting from a continuous Markov process, we construct a non-reversible generative (birth-death) evolutionary model for insertions and deletions. The model assumes that insertion and deletion events occur one residue at a time. We apply this model to phylogenetic tree inference by extending the program dnaml in phylip. Using standard benchmarking methods on simulated data and a new "concordance test" benchmark on real ribosomal RNA alignments, we show that the extended program dnamlepsilon improves accuracy relative to the usual approach of ignoring gaps, while retaining the computational efficiency of the Felsenstein peeling algorithm.

Semiautomated improvement of RNA alignments

We have developed a semiautomated RNA sequence editor (SARSE) that integrates tools for analyzing RNA alignments. The editor highlights different properties of the alignment by color, and its integrated analysis tools prevent the introduction of errors when doing alignment editing. SARSE readily connects to external tools to provide a flexible semiautomatic editing environment. A new method, Pcluster, is introduced for dividing the sequences of an RNA alignment into subgroups with secondary structure differences. Pcluster was used to evaluate 574 seed alignments obtained from the Rfam database and we identified 71 alignments with significant prediction of inconsistent base pairs and 102 alignments with significant prediction of novel base pairs. Four RNA families were used to illustrate how SARSE can be used to manually or automatically correct the inconsistent base pairs detected by Pcluster: the mir-399 RNA, vertebrate telomase RNA (vert-TR), bacterial transfer-messenger RNA (tmRNA), and the signal recognition particle (SRP) RNA. The general use of the method is illustrated by the ability to accommodate pseudoknots and handle even large and divergent RNA families. The open architecture of the SARSE editor makes it a flexible tool to improve all RNA alignments with relatively little human intervention. Online documentation and software are available at (http://sarse.ku.dk).

Evolutionary models for insertions and deletions in a probabilistic modeling framework

BACKGROUND

Probabilistic models for sequence comparison (such as hidden Markov models and pair hidden Markov models for proteins and mRNAs, or their context-free grammar counterparts for structural RNAs) often assume a fixed degree of divergence. Ideally we would like these models to be conditional on evolutionary divergence time. Probabilistic models of substitution events are well established, but there has not been a completely satisfactory theoretical framework for modeling insertion and deletion events.

RESULTS

I have developed a method for extending standard Markov substitution models to include gap characters, and another method for the evolution of state transition probabilities in a probabilistic model. These methods use instantaneous rate matrices in a way that is more general than those used for substitution processes, and are sufficient to provide time-dependent models for standard linear and affine gap penalties, respectively. Given a probabilistic model, we can make all of its emission probabilities (including gap characters) and all its transition probabilities conditional on a chosen divergence time. To do this, we only need to know the parameters of the model at one particular divergence time instance, as well as the parameters of the model at the two extremes of zero and infinite divergence. I have implemented these methods in a new generation of the RNA genefinder QRNA (eQRNA).

CONCLUSION

These methods can be applied to incorporate evolutionary models of insertions and deletions into any hidden Markov model or stochastic context-free grammar, in a pair or profile form, for sequence modeling.

Comparing two K-category assignments by a K-category correlation coefficient

Predicted assignments of biological sequences are often evaluated by Matthews correlation coefficient. However, Matthews correlation coefficient applies only to cases where the assignments belong to two categories, and cases with more than two categories are often artificially forced into two categories by considering what belongs and what does not belong to one of the categories, leading to the loss of information. Here, an extended correlation coefficient that applies to K-categories is proposed, and this measure is shown to be highly applicable for evaluating prediction of RNA secondary structure in cases where some predicted pairs go into the category "unknown" due to lack of reliability in predicted pairs or unpaired residues. Hence, predicting base pairs of RNA secondary structure can be a three-category problem. The measure is further shown to be well in agreement with existing performance measures used for ranking protein secondary structure predictions. Server and software is available at http://rk.kvl.dk/.

Pairwise local structural alignment of RNA sequences with sequence similarity less than 40%

MOTIVATION

Searching for non-coding RNA (ncRNA) genes and structural RNA elements (eleRNA) are major challenges in gene finding today as these often are conserved in structure rather than in sequence. Even though the number of available methods is growing, it is still of interest to pairwise detect two genes with low sequence similarity, where the genes are part of a larger genomic region.

RESULTS

Here we present such an approach for pairwise local alignment which is based on foldalign and the Sankoff algorithm for simultaneous structural alignment of multiple sequences. We include the ability to conduct mutual scans of two sequences of arbitrary length while searching for common local structural motifs of some maximum length. This drastically reduces the complexity of the algorithm. The scoring scheme includes structural parameters corresponding to those available for free energy as well as for substitution matrices similar to RIBOSUM. The new foldalign implementation is tested on a dataset where the ncRNAs and eleRNAs have sequence similarity <40% and where the ncRNAs and eleRNAs are energetically indistinguishable from the surrounding genomic sequence context. The method is tested in two ways: (1) its ability to find the common structure between the genes only and (2) its ability to locate ncRNAs and eleRNAs in a genomic context. In case (1), it makes sense to compare with methods like Dynalign, and the performances are very similar, but foldalign is substantially faster. The structure prediction performance for a family is typically around 0.7 using Matthews correlation coefficient. In case (2), the algorithm is successful at locating RNA families with an average sensitivity of 0.8 and a positive predictive value of 0.9 using a BLAST-like hit selection scheme.

AVAILABILITY

The program is available online at http://foldalign.kvl.dk/