SUMMARY: Codetta is a Python program for predicting the genetic code table of an organism from nucleotide sequences. Codetta can analyze an arbitrary nucleotide sequence and needs no sequence annotation or taxonomic placement. The most likely amino acid decoding for each of the 64 codons is inferred from alignments of profile hidden Markov models of conserved proteins to the input sequence. AVAILABILITY AND IMPLEMENTATION: Codetta 2.0 is implemented as a Python 3 program for MacOS and Linux and is available from http://eddylab.org/software/codetta/codetta2.tar.gz and at http://github.com/kshulgina/codetta. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: In canonical protein translation, ribosomes initiate translation at a specific start codon, maintain a single reading frame throughout elongation, and terminate at the first in-frame stop codon. However, ribosomal behavior can deviate at each of these steps, sometimes in a programmed manner. Certain mRNAs contain sequence and structural elements that cause ribosomes to begin translation at alternative start codons, shift reading frame, read through stop codons, or reinitiate on the same mRNA. These processes represent important translational control mechanisms that can allow an mRNA to encode multiple functional protein products or regulate protein expression. The prevalence of these events remains uncertain, due to the difficulty of systematic detection. RESULTS: We have developed a computational model to infer non-canonical translation events from ribosome profiling data. CONCLUSION: ORFeus identifies known examples of alternative open reading frames and recoding events across different organisms and enables transcriptome-wide searches for novel events.

[This corrects the article DOI: 10.1371/journal.pcbi.1009492.].

Biological sequence families contain many sequences that are very similar to each other because they are related by evolution, so the strategy for splitting data into separate training and test sets is a nontrivial choice in benchmarking sequence analysis methods. A random split is insufficient because it will yield test sequences that are closely related or even identical to training sequences. Adapting ideas from independent set graph algorithms, we describe two new methods for splitting sequence data into dissimilar training and test sets. These algorithms input a sequence family and produce a split in which each test sequence is less than p% identical to any individual training sequence. These algorithms successfully split more families than a previous approach, enabling construction of more diverse benchmark datasets.

Pairwise sequence covariations are a signal of conserved RNA secondary structure. We describe a method for distinguishing when lack of covariation signal can be taken as evidence against a conserved RNA structure, as opposed to when a sequence alignment merely has insufficient variation to detect covariations. We find that alignments for several long non-coding RNAs previously shown to lack covariation support do have adequate covariation detection power, providing additional evidence against their proposed conserved structures. AVAILABILITY AND IMPLEMENTATION: The R-scape web server is at eddylab.org/R-scape, with a link to download the source code. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Most methods for biological sequence homology search and alignment work with primary sequence alone, neglecting higher-order correlations. Recently, statistical physics models called Potts models have been used to infer all-by-all pairwise correlations between sites in deep multiple sequence alignments, and these pairwise couplings have improved 3D structure predictions. Here we extend the use of Potts models from structure prediction to sequence alignment and homology search by developing what we call a hidden Potts model (HPM) that merges a Potts emission process to a generative probability model of insertion and deletion. Because an HPM is incompatible with efficient dynamic programming alignment algorithms, we develop an approximate algorithm based on importance sampling, using simpler probabilistic models as proposal distributions. We test an HPM implementation on RNA structure homology search benchmarks, where we can compare directly to exact alignment methods that capture nested RNA base-pairing correlations (stochastic context-free grammars). HPMs perform promisingly in these proof of principle experiments.

Although convolutional neural networks (CNNs) have been applied to a variety of computational genomics problems, there remains a large gap in our understanding of how they build representations of regulatory genomic sequences. Here we perform systematic experiments on synthetic sequences to reveal how CNN architecture, specifically convolutional filter size and max-pooling, influences the extent that sequence motif representations are learned by first layer filters. We find that CNNs designed to foster hierarchical representation learning of sequence motifs-assembling partial features into whole features in deeper layers-tend to learn distributed representations, i.e. partial motifs. On the other hand, CNNs that are designed to limit the ability to hierarchically build sequence motif representations in deeper layers tend to learn more interpretable localist representations, i.e. whole motifs. We then validate that this representation learning principle established from synthetic sequences generalizes to in vivo sequences.

BACKGROUND: Inference of sequence homology is inherently an evolutionary question, dependent upon evolutionary divergence. However, the insertion and deletion penalties in the most widely used methods for inferring homology by sequence alignment, including BLAST and profile hidden Markov models (profile HMMs), are not based on any explicitly time-dependent evolutionary model. Using one fixed score system (BLOSUM62 with some gap open/extend costs, for example) corresponds to making an unrealistic assumption that all sequence relationships have diverged by the same time. Adoption of explicit time-dependent evolutionary models for scoring insertions and deletions in sequence alignments has been hindered by algorithmic complexity and technical difficulty. RESULTS: We identify and implement several probabilistic evolutionary models compatible with the affine-cost insertion/deletion model used in standard pairwise sequence alignment. Assuming an affine gap cost imposes important restrictions on the realism of the evolutionary models compatible with it, as single insertion events with geometrically distributed lengths do not result in geometrically distributed insert lengths at finite times. Nevertheless, we identify one evolutionary model compatible with symmetric pair HMMs that are the basis for Smith-Waterman pairwise alignment, and two evolutionary models compatible with standard profile-based alignment. We test different aspects of the performance of these "optimized branch length" models, including alignment accuracy and homology coverage (discrimination of residues in a homologous region from nonhomologous flanking residues). We test on benchmarks of both global homologies (full length sequence homologs) and local homologies (homologous subsequences embedded in nonhomologous sequence). CONCLUSIONS: Contrary to our expectations, we find that for global homologies a single long branch parameterization suffices both for distant and close homologous relationships. In contrast, we do see an advantage in using explicit evolutionary models for local homologies. Optimal branch parameterization reduces a known artifact called "homologous overextension", in which local alignments erroneously extend through flanking nonhomologous residues.

SUMMARY: Infernal builds probabilistic profiles of the sequence and secondary structure of an RNA family called covariance models (CMs) from structurally annotated multiple sequence alignments given as input. Infernal uses CMs to search for new family members in sequence databases and to create potentially large multiple sequence alignments. Version 1.1 of Infernal introduces a new filter pipeline for RNA homology search based on accelerated profile hidden Markov model (HMM) methods and HMM-banded CM alignment methods. This enables ∼100-fold acceleration over the previous version and ∼10 000-fold acceleration over exhaustive non-filtered CM searches. AVAILABILITY: Source code, documentation and the benchmark are downloadable from http://infernal.janelia.org. Infernal is freely licensed under the GNU GPLv3 and should be portable to any POSIX-compliant operating system, including Linux and Mac OS/X. Documentation includes a user's guide with a tutorial, a discussion of file formats and user options and additional details on methods implemented in the software. CONTACT: [email protected]

SUMMARY: Sequence database searches are an essential part of molecular biology, providing information about the function and evolutionary history of proteins, RNA molecules and DNA sequence elements. We present a tool for DNA/DNA sequence comparison that is built on the HMMER framework, which applies probabilistic inference methods based on hidden Markov models to the problem of homology search. This tool, called nhmmer, enables improved detection of remote DNA homologs, and has been used in combination with Dfam and RepeatMasker to improve annotation of transposable elements in the human genome. AVAILABILITY: nhmmer is a part of the new HMMER3.1 release. Source code and documentation can be downloaded from http://hmmer.org. HMMER3.1 is freely licensed under the GNU GPLv3 and should be portable to any POSIX-compliant operating system, including Linux and Mac OS/X.

MOTIVATION: Homology search for RNAs can use secondary structure information to increase power by modeling base pairs, as in covariance models, but the resulting computational costs are high. Typical acceleration strategies rely on at least one filtering stage using sequence-only search. RESULTS: Here we present the multi-segment CYK (MSCYK) filter, which implements a heuristic of ungapped structural alignment for RNA homology search. Compared to gapped alignment, this approximation has lower computation time requirements (O(N⁴) reduced to O(N³), and space requirements (O(N³) reduced to O(N²). A vector-parallel implementation of this method gives up to 100-fold speed-up; vector-parallel implementations of standard gapped alignment at two levels of precision give 3- and 6-fold speed-ups. These approaches are combined to create a filtering pipeline that scores RNA secondary structure at all stages, with results that are synergistic with existing methods.

Profile hidden Markov models (profile HMMs) and probabilistic inference methods have made important contributions to the theory of sequence database homology search. However, practical use of profile HMM methods has been hindered by the computational expense of existing software implementations. Here I describe an acceleration heuristic for profile HMMs, the "multiple segment Viterbi" (MSV) algorithm. The MSV algorithm computes an optimal sum of multiple ungapped local alignment segments using a striped vector-parallel approach previously described for fast Smith/Waterman alignment. MSV scores follow the same statistical distribution as gapped optimal local alignment scores, allowing rapid evaluation of significance of an MSV score and thus facilitating its use as a heuristic filter. I also describe a 20-fold acceleration of the standard profile HMM Forward/Backward algorithms using a method I call "sparse rescaling". These methods are assembled in a pipeline in which high-scoring MSV hits are passed on for reanalysis with the full HMM Forward/Backward algorithm. This accelerated pipeline is implemented in the freely available HMMER3 software package. Performance benchmarks show that the use of the heuristic MSV filter sacrifices negligible sensitivity compared to unaccelerated profile HMM searches. HMMER3 is substantially more sensitive and 100- to 1000-fold faster than HMMER2. HMMER3 is now about as fast as BLAST for protein searches.

BACKGROUND: Profile hidden Markov models (profile-HMMs) are sensitive tools for remote protein homology detection, but the main scoring algorithms, Viterbi or Forward, require considerable time to search large sequence databases. RESULTS: We have designed a series of database filtering steps, HMMERHEAD, that are applied prior to the scoring algorithms, as implemented in the HMMER package, in an effort to reduce search time. Using this heuristic, we obtain a 20-fold decrease in Forward and a 6-fold decrease in Viterbi search time with a minimal loss in sensitivity relative to the unfiltered approaches. We then implemented an iterative profile-HMM search method, JackHMMER, which employs the HMMERHEAD heuristic. Due to our search heuristic, we eliminated the subdatabase creation that is common in current iterative profile-HMM approaches. On our benchmark, JackHMMER detects 14% more remote protein homologs than SAM's iterative method T2K. CONCLUSIONS: Our search heuristic, HMMERHEAD, significantly reduces the time needed to score a profile-HMM against large sequence databases. This search heuristic allowed us to implement an iterative profile-HMM search method, JackHMMER, which detects significantly more remote protein homologs than SAM's T2K and NCBI's PSI-BLAST.

MOTIVATION: Gene expression patterns can be useful in understanding the structural organization of the brain and the regulatory logic that governs its myriad cell types. A particularly rich source of spatial expression data is the Allen Brain Atlas (ABA), a comprehensive genome-wide in situ hybridization study of the adult mouse brain. Here, we present an open-source program, ALLENMINER, that searches the ABA for genes that are expressed, enriched, patterned or graded in a user-specified region of interest. RESULTS: Regionally enriched genes identified by ALLENMINER accurately reflect the in situ data (95-99% concordance with manual curation) and compare with regional microarray studies as expected from previous comparisons (61-80% concordance). We demonstrate the utility of ALLENMINER by identifying genes that exhibit patterned expression in the caudoputamen and neocortex. We discuss general characteristics of gene expression in the mouse brain and the potential application of ALLENMINER to design strategies for specific genetic access to brain regions and cell types. AVAILABILITY: ALLENMINER is freely available on the Internet at http://research.janelia.org/davis/allenminer.

MOTIVATION: Accuracy of automated structural RNA alignment is improved by using models that consider not only primary sequence but also secondary structure information. However, current RNA structural alignment approaches tend to perform poorly on incomplete sequence fragments, such as single reads from metagenomic environmental surveys, because nucleotides that are expected to be base paired are missing. RESULTS: We present a local RNA structural alignment algorithm, trCYK, for aligning and scoring incomplete sequences under a model using primary sequence conservation and secondary structure information when possible. The trCYK algorithm improves alignment accuracy and coverage of sequence fragments of structural RNAs in simulated metagenomic shotgun datasets. AVAILABILITY: The source code for Infernal 1.0, which includes trCYK, is available at http://infernal.janelia.org.

SUMMARY: INFERNAL builds consensus RNA secondary structure profiles called covariance models (CMs), and uses them to search nucleic acid sequence databases for homologous RNAs, or to create new sequence- and structure-based multiple sequence alignments. AVAILABILITY: Source code, documentation and benchmark downloadable from http://infernal.janelia.org. INFERNAL is freely licensed under the GNU GPLv3 and should be portable to any POSIX-compliant operating system, including Linux and Mac OS/X.

Bioinformatics (2009) 25(10), 1335–1337 We regret that the above paper was published with the wrong copyright line. The correct copyright line for this Open Access paper should have been: The Author 2009. Published by Oxford University Press. All rights reserved.

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (lambda) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty ("Forward" scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores ("Viterbi" scores) are Gumbel-distributed with constant lambda = log 2, and the high scoring tail of Forward scores is exponential with the same constant lambda. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments.

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.

When searching sequence databases for RNAs, it is desirable to score both primary sequence and RNA secondary structure similarity. Covariance models (CMs) are probabilistic models well-suited for RNA similarity search applications. However, the computational complexity of CM dynamic programming alignment algorithms has limited their practical application. Here we describe an acceleration method called query-dependent banding (QDB), which uses the probabilistic query CM to precalculate regions of the dynamic programming lattice that have negligible probability, independently of the target database. We have implemented QDB in the freely available Infernal software package. QDB reduces the average case time complexity of CM alignment from LN(2.4) to LN(1.3) for a query RNA of N residues and a target database of L residues, resulting in a 4-fold speedup for typical RNA queries. Combined with other improvements to Infernal, including informative mixture Dirichlet priors on model parameters, benchmarks also show increased sensitivity and specificity resulting from improved parameterization.

BACKGROUND: We are interested in the problem of predicting secondary structure for small sets of homologous RNAs, by incorporating limited comparative sequence information into an RNA folding model. The Sankoff algorithm for simultaneous RNA folding and alignment is a basis for approaches to this problem. There are two open problems in applying a Sankoff algorithm: development of a good unified scoring system for alignment and folding and development of practical heuristics for dealing with the computational complexity of the algorithm. RESULTS: We use probabilistic models (pair stochastic context-free grammars, pairSCFGs) as a unifying framework for scoring pairwise alignment and folding. A constrained version of the pairSCFG structural alignment algorithm was developed which assumes knowledge of a few confidently aligned positions (pins). These pins are selected based on the posterior probabilities of a probabilistic pairwise sequence alignment. CONCLUSION: Pairwise RNA structural alignment improves on structure prediction accuracy relative to single sequence folding. Constraining on alignment is a straightforward method of reducing the runtime and memory requirements of the algorithm. Five practical implementations of the pairwise Sankoff algorithm - this work (Consan), David Mathews' Dynalign, Ian Holmes' Stemloc, Ivo Hofacker's PMcomp, and Jan Gorodkin's FOLDALIGN - have comparable overall performance with different strengths and weaknesses.

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BACKGROUND: RNA secondary structure prediction methods based on probabilistic modeling can be developed using stochastic context-free grammars (SCFGs). Such methods can readily combine different sources of information that can be expressed probabilistically, such as an evolutionary model of comparative RNA sequence analysis and a biophysical model of structure plausibility. However, the number of free parameters in an integrated model for consensus RNA structure prediction can become untenable if the underlying SCFG design is too complex. Thus a key question is, what small, simple SCFG designs perform best for RNA secondary structure prediction? RESULTS: Nine different small SCFGs were implemented to explore the tradeoffs between model complexity and prediction accuracy. Each model was tested for single sequence structure prediction accuracy on a benchmark set of RNA secondary structures. CONCLUSIONS: Four SCFG designs had prediction accuracies near the performance of current energy minimization programs. One of these designs, introduced by Knudsen and Hein in their PFOLD algorithm, has only 21 free parameters and is significantly simpler than the others.

BACKGROUND: For many RNA molecules, secondary structure rather than primary sequence is the evolutionarily conserved feature. No programs have yet been published that allow searching a sequence database for homologs of a single RNA molecule on the basis of secondary structure. RESULTS: We have developed a program, RSEARCH, that takes a single RNA sequence with its secondary structure and utilizes a local alignment algorithm to search a database for homologous RNAs. For this purpose, we have developed a series of base pair and single nucleotide substitution matrices for RNA sequences called RIBOSUM matrices. RSEARCH reports the statistical confidence for each hit as well as the structural alignment of the hit. We show several examples in which RSEARCH outperforms the primary sequence search programs BLAST and SSEARCH. The primary drawback of the program is that it is slow. The C code for RSEARCH is freely available from our lab's website. CONCLUSION: RSEARCH outperforms primary sequence programs in finding homologs of structured RNA sequences.

BACKGROUND: Covariance models (CMs) are probabilistic models of RNA secondary structure, analogous to profile hidden Markov models of linear sequence. The dynamic programming algorithm for aligning a CM to an RNA sequence of length N is O(N3) in memory. This is only practical for small RNAs. RESULTS: I describe a divide and conquer variant of the alignment algorithm that is analogous to memory-efficient Myers/Miller dynamic programming algorithms for linear sequence alignment. The new algorithm has an O(N2 log N) memory complexity, at the expense of a small constant factor in time. CONCLUSIONS: Optimal ribosomal RNA structural alignments that previously required up to 150 GB of memory now require less than 270 MB.

BACKGROUND: When analyzing protein sequences using sequence similarity searches, orthologous sequences (that diverged by speciation) are more reliable predictors of a new protein's function than paralogous sequences (that diverged by gene duplication). The utility of phylogenetic information in high-throughput genome annotation ("phylogenomics") is widely recognized, but existing approaches are either manual or not explicitly based on phylogenetic trees. RESULTS: Here we present RIO (Resampled Inference of Orthologs), a procedure for automated phylogenomics using explicit phylogenetic inference. RIO analyses are performed over bootstrap resampled phylogenetic trees to estimate the reliability of orthology assignments. We also introduce supplementary concepts that are helpful for functional inference. RIO has been implemented as Perl pipeline connecting several C and Java programs. It is available at http://www.genetics.wustl.edu/eddy/forester/. A web server is at http://www.rio.wustl.edu/. RIO was tested on the Arabidopsis thaliana and Caenorhabditis elegans proteomes. CONCLUSION: The RIO procedure is particularly useful for the automated detection of first representatives of novel protein subfamilies. We also describe how some orthologies can be misleading for functional inference.

Abstract Motivation: When analyzing protein sequences using sequence similarity searches, orthologous sequences (that diverged by speciation) are more reliable predictors of a new protein’s function than paralogous sequences (that diverged by gene duplication), because duplication enables functional diversification. The utility of phylogenetic information in high-throughput genome annotation (‘phylogenomics’) is widely recognized, but existing approaches are either manual or indirect (e.g. not based on phylogenetic trees). Our goal is to automate phylogenomics using explicit phylogenetic inference. A necessary component is an algorithm to infer speciation and duplication events in a given gene tree. Results: We give an algorithm to infer speciation and duplication events on a gene tree by comparison to a trusted species tree. This algorithm has a worst-case running time of O(\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(n^{2}\) \end{document}) which is inferior to two previous algorithms that are \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\sim}\) \end{document}O(\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(n\) \end{document}) for a gene tree of \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(n\) \end{document}sequences. However, our algorithm is extremely simple, and its asymptotic worst case behavior is only realized on pathological data sets. We show empirically, using 1750 gene trees constructed from the Pfam protein family database, that it appears to be a practical (and often superior) algorithm for analyzing real gene trees. Availability: http://www.genetics.wustl.edu/eddy/forester Contact: [email protected]; [email protected]

Abstract Summary: A Tree Viewer (ATV) is a Java tool for the display and manipulation of annotated phylogenetic trees. It can be utilized both as a standalone application and as an applet in a web browser. Availability: ATV is available via WWW at http://www.genetics.wustl.edu/eddy/atv/ and via FTP at ftp://ftp.genetics.wustl.edu/pub/eddy/software/forester.tar.Z Contact: [email protected]

BACKGROUND: Currently, most genome annotation is curated by centralized groups with limited resources. Efforts to share annotations transparently among multiple groups have not yet been satisfactory. RESULTS: Here we introduce a concept called the Distributed Annotation System (DAS). DAS allows sequence annotations to be decentralized among multiple third-party annotators and integrated on an as-needed basis by client-side software. The communication between client and servers in DAS is defined by the DAS XML specification. Annotations are displayed in layers, one per server. Any client or server adhering to the DAS XML specification can participate in the system; we describe a simple prototype client and server example. CONCLUSIONS: The DAS specification is being used experimentally by Ensembl, WormBase, and the Berkeley Drosophila Genome Project. Continued success will depend on the readiness of the research community to adopt DAS and provide annotations. All components are freely available from the project website http://www.biodas.org/.

BACKGROUND: Noncoding RNA genes produce transcripts that exert their function without ever producing proteins. Noncoding RNA gene sequences do not have strong statistical signals, unlike protein coding genes. A reliable general purpose computational genefinder for noncoding RNA genes has been elusive. RESULTS: We describe a comparative sequence analysis algorithm for detecting novel structural RNA genes. The key idea is to test the pattern of substitutions observed in a pairwise alignment of two homologous sequences. A conserved coding region tends to show a pattern of synonymous substitutions, whereas a conserved structural RNA tends to show a pattern of compensatory mutations consistent with some base-paired secondary structure. We formalize this intuition using three probabilistic "pair-grammars": a pair stochastic context free grammar modeling alignments constrained by structural RNA evolution, a pair hidden Markov model modeling alignments constrained by coding sequence evolution, and a pair hidden Markov model modeling a null hypothesis of position-independent evolution. Given an input pairwise sequence alignment (e.g. from a BLASTN comparison of two related genomes) we classify the alignment into the coding, RNA, or null class according to the posterior probability of each class. CONCLUSIONS: We have implemented this approach as a program, QRNA, which we consider to be a prototype structural noncoding RNA genefinder. Tests suggest that this approach detects noncoding RNA genes with a fair degree of reliability.

MOTIVATION: Several results in the literature suggest that biologically interesting RNAs have secondary structures that are more stable than expected by chance. Based on these observations, we developed a scanning algorithm for detecting noncoding RNA genes in genome sequences, using a fully probabilistic version of the Zuker minimum-energy folding algorithm. RESULTS: Preliminary results were encouraging, but certain anomalies led us to do a carefully controlled investigation of this class of methods. Ultimately, our results argue that for the probabilistic model there is indeed a statistical effect, but it comes mostly from local base-composition bias and not from RNA secondary structure. For the thermodynamic implementation (which evaluates statistical significance by doing Monte Carlo shuffling in fixed-length sequence windows, thus eliminating the base-composition effect) the signals for noncoding RNAs are still usually indistinguishable from noise, especially when certain statistical artifacts resulting from local base-composition inhomogeneity are taken into account. We conclude that although a distinct, stable secondary structure is undoubtedly important in most noncoding RNAs, the stability of most noncoding RNA secondary structures is not sufficiently different from the predicted stability of a random sequence to be useful as a general genefinding approach.

MOTIVATION: In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However, a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking. RESULTS: Here we show a one-to-one correspondence between that algorithm and a formal transformational grammar. This grammar class encompasses the context-free grammars and goes beyond to generate pseudoknotted structures. The pseudoknot grammar avoids the use of general context-sensitive rules by introducing a small number of auxiliary symbols used to reorder the strings generated by an otherwise context-free grammar. This formal representation of the residue correlations in RNA structure is important because it means we can build full probabilistic models of RNA secondary structure, including pseudoknots, and use them to optimally parse sequences in polynomial time.

The recent literature on profile hidden Markov model (profile HMM) methods and software is reviewed. Profile HMMs turn a multiple sequence alignment into a position-specific scoring system suitable for searching databases for remotely homologous sequences. Profile HMM analyses complement standard pairwise comparison methods for large-scale sequence analysis. Several software implementations and two large libraries of profile HMMs of common protein domains are available. HMM methods performed comparably to threading methods in the CASP2 structure prediction exercise.