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1.  Synchronous visual analysis and editing of RNA sequence and secondary structure alignments using 4SALE 
BMC Research Notes  2008;1:91.
Background
The function of a noncoding RNA sequence is mainly determined by its secondary structure and therefore a family of noncoding RNA sequences is much more conserved on the structural level than on the sequence level. Understanding the function of noncoding RNA sequence families requires two things: a hand-crafted or hand-improved alignment and detailed analyses of the secondary structures. There are several tools available that help performing these tasks, but all of them are specialized and focus on only one aspect, editing the alignment or plotting the secondary structure. The problem is both these tasks need to be performed simultaneously.
Findings
4SALE is designed to handle sequence and secondary structure information of RNAs synchronously. By including a complete new method of simultaneous visualization and editing RNA sequences and secondary structure information, 4SALE enables to improve and understand RNA sequence and secondary structure evolution much more easily.
Conclusion
4SALE is a step further for simultaneously handling RNA sequence and secondary structure information. It provides a complete new way of visual monitoring different structural aspects, while editing the alignment. The software is freely available and distributed from its website at
doi:10.1186/1756-0500-1-91
PMCID: PMC2587473  PMID: 18854023
2.  Strategies for measuring evolutionary conservation of RNA secondary structures 
BMC Bioinformatics  2008;9:122.
Background
Evolutionary conservation of RNA secondary structure is a typical feature of many functional non-coding RNAs. Since almost all of the available methods used for prediction and annotation of non-coding RNA genes rely on this evolutionary signature, accurate measures for structural conservation are essential.
Results
We systematically assessed the ability of various measures to detect conserved RNA structures in multiple sequence alignments. We tested three existing and eight novel strategies that are based on metrics of folding energies, metrics of single optimal structure predictions, and metrics of structure ensembles. We find that the folding energy based SCI score used in the RNAz program and a simple base-pair distance metric are by far the most accurate. The use of more complex metrics like for example tree editing does not improve performance. A variant of the SCI performed particularly well on highly conserved alignments and is thus a viable alternative when only little evolutionary information is available. Surprisingly, ensemble based methods that, in principle, could benefit from the additional information contained in sub-optimal structures, perform particularly poorly. As a general trend, we observed that methods that include a consensus structure prediction outperformed equivalent methods that only consider pairwise comparisons.
Conclusion
Structural conservation can be measured accurately with relatively simple and intuitive metrics. They have the potential to form the basis of future RNA gene finders, that face new challenges like finding lineage specific structures or detecting mis-aligned sequences.
doi:10.1186/1471-2105-9-122
PMCID: PMC2335298  PMID: 18302738
3.  LocARNAscan: Incorporating thermodynamic stability in sequence and structure-based RNA homology search 
Background
The search for distant homologs has become an import issue in genome annotation. A particular difficulty is posed by divergent homologs that have lost recognizable sequence similarity. This same problem also arises in the recognition of novel members of large classes of RNAs such as snoRNAs or microRNAs that consist of families unrelated by common descent. Current homology search tools for structured RNAs are either based entirely on sequence similarity (such as blast or hmmer) or combine sequence and secondary structure. The most prominent example of the latter class of tools is Infernal. Alternatives are descriptor-based methods. In most practical applications published to-date, however, the information contained in covariance models or manually prescribed search patterns is dominated by sequence information. Here we ask two related questions: (1) Is secondary structure alone informative for homology search and the detection of novel members of RNA classes? (2) To what extent is the thermodynamic propensity of the target sequence to fold into the correct secondary structure helpful for this task?
Results
Sequence-structure alignment can be used as an alternative search strategy. In this scenario, the query consists of a base pairing probability matrix, which can be derived either from a single sequence or from a multiple alignment representing a set of known representatives. Sequence information can be optionally added to the query. The target sequence is pre-processed to obtain local base pairing probabilities. As a search engine we devised a semi-global scanning variant of LocARNA’s algorithm for sequence-structure alignment. The LocARNAscan tool is optimized for speed and low memory consumption. In benchmarking experiments on artificial data we observe that the inclusion of thermodynamic stability is helpful, albeit only in a regime of extremely low sequence information in the query. We observe, furthermore, that the sensitivity is bounded in particular by the limited accuracy of the predicted local structures of the target sequence.
Conclusions
Although we demonstrate that a purely structure-based homology search is feasible in principle, it is unlikely to outperform tools such as Infernal in most application scenarios, where a substantial amount of sequence information is typically available. The LocARNAscan approach will profit, however, from high throughput methods to determine RNA secondary structure. In transcriptome-wide applications, such methods will provide accurate structure annotations on the target side.
Availability
Source code of the free software LocARNAscan 1.0 and supplementary data are available at http://www.bioinf.uni-leipzig.de/Software/LocARNAscan.
doi:10.1186/1748-7188-8-14
PMCID: PMC3716875  PMID: 23601347
4.  A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures 
BMC Bioinformatics  2011;12(Suppl 1):S13.
Background
Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees.
Results
In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search.
Conclusions
The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request.
doi:10.1186/1471-2105-12-S1-S13
PMCID: PMC3044267  PMID: 21342542
5.  MetaPathways: a modular pipeline for constructing pathway/genome databases from environmental sequence information 
BMC Bioinformatics  2013;14:202.
Background
A central challenge to understanding the ecological and biogeochemical roles of microorganisms in natural and human engineered ecosystems is the reconstruction of metabolic interaction networks from environmental sequence information. The dominant paradigm in metabolic reconstruction is to assign functional annotations using BLAST. Functional annotations are then projected onto symbolic representations of metabolism in the form of KEGG pathways or SEED subsystems.
Results
Here we present MetaPathways, an open source pipeline for pathway inference that uses the PathoLogic algorithm to map functional annotations onto the MetaCyc collection of reactions and pathways, and construct environmental Pathway/Genome Databases (ePGDBs) compatible with the editing and navigation features of Pathway Tools. The pipeline accepts assembled or unassembled nucleotide sequences, performs quality assessment and control, predicts and annotates noncoding genes and open reading frames, and produces inputs to PathoLogic. In addition to constructing ePGDBs, MetaPathways uses MLTreeMap to build phylogenetic trees for selected taxonomic anchor and functional gene markers, converts General Feature Format (GFF) files into concatenated GenBank files for ePGDB construction based on third-party annotations, and generates useful file formats including Sequin files for direct GenBank submission and gene feature tables summarizing annotations, MLTreeMap trees, and ePGDB pathway coverage summaries for statistical comparisons.
Conclusions
MetaPathways provides users with a modular annotation and analysis pipeline for predicting metabolic interaction networks from environmental sequence information using an alternative to KEGG pathways and SEED subsystems mapping. It is extensible to genomic and transcriptomic datasets from a wide range of sequencing platforms, and generates useful data products for microbial community structure and function analysis. The MetaPathways software package, installation instructions, and example data can be obtained from http://hallam.microbiology.ubc.ca/MetaPathways.
doi:10.1186/1471-2105-14-202
PMCID: PMC3695837  PMID: 23800136
Environmental pathway/Genome Database (ePGDB); Metagenome; Pathway tools; PathoLogic; MetaCyc; Microbial community; Metabolism; Metabolic interaction networks
6.  SSE: a nucleotide and amino acid sequence analysis platform 
BMC Research Notes  2012;5:50.
Background
There is an increasing need to develop bioinformatic tools to organise and analyse the rapidly growing amount of nucleotide and amino acid sequence data in organisms ranging from viruses to eukaryotes.
Finding
A simple sequence editor (SSE) was developed to create an integrated environment where sequences can be aligned, annotated, classified and directly analysed by a number of built-in bioinformatic programs. SSE incorporates a sequence editor for the creation of sequence alignments, a process assisted by integrated CLUSTAL/MUSCLE alignment programs and automated removal of indels. Sequences can be fully annotated and classified into groups and annotated of sequences and sequence groups and access to analytical programs that analyse diversity, recombination and RNA secondary structure. Methods for analysing sequence diversity include measures of divergence and evolutionary distances, identity plots to detect regions of nucleotide or amino acid homology, reconstruction of sequence changes, mono-, di- and higher order nucleotide compositional biases and codon usage.
Association Index calculations, GroupScans, Bootscanning and TreeOrder scans perform phylogenetic analyses that reconcile group membership with tree branching orders and provide powerful methods for examining segregation of alleles and detection of recombination events. Phylogeny changes across alignments and scoring of branching order differences between trees using the Robinson-Fould algorithm allow effective visualisation of the sites of recombination events.
RNA secondary and tertiary structures play important roles in gene expression and RNA virus replication. For the latter, persistence of infection is additionally associated with pervasive RNA secondary structure throughout viral genomic RNA that modulates interactions with innate cell defences. SSE provides several programs to scan alignments for RNA secondary structure through folding energy thermodynamic calculations and phylogenetic methods (detection of co-variant changes, and structure conservation between divergent sequences). These analyses complement methods based on detection of sequence constraints, such as suppression of synonymous site variability.
For each program, results can be plotted in real time during analysis through an integrated graphics package, providing publication quality graphs. Results can be also directed to tabulated datafiles for import into spreadsheet or database programs for further analysis.
Conclusions
SSE combines sequence editor functions with analytical tools in a comprehensive and user-friendly package that assists considerably in bioinformatic and evolution research.
doi:10.1186/1756-0500-5-50
PMCID: PMC3292810  PMID: 22264264
7.  Evolutionary Triplet Models of Structured RNA 
PLoS Computational Biology  2009;5(8):e1000483.
The reconstruction and synthesis of ancestral RNAs is a feasible goal for paleogenetics. This will require new bioinformatics methods, including a robust statistical framework for reconstructing histories of substitutions, indels and structural changes. We describe a “transducer composition” algorithm for extending pairwise probabilistic models of RNA structural evolution to models of multiple sequences related by a phylogenetic tree. This algorithm draws on formal models of computational linguistics as well as the 1985 protosequence algorithm of David Sankoff. The output of the composition algorithm is a multiple-sequence stochastic context-free grammar. We describe dynamic programming algorithms, which are robust to null cycles and empty bifurcations, for parsing this grammar. Example applications include structural alignment of non-coding RNAs, propagation of structural information from an experimentally-characterized sequence to its homologs, and inference of the ancestral structure of a set of diverged RNAs. We implemented the above algorithms for a simple model of pairwise RNA structural evolution; in particular, the algorithms for maximum likelihood (ML) alignment of three known RNA structures and a known phylogeny and inference of the common ancestral structure. We compared this ML algorithm to a variety of related, but simpler, techniques, including ML alignment algorithms for simpler models that omitted various aspects of the full model and also a posterior-decoding alignment algorithm for one of the simpler models. In our tests, incorporation of basepair structure was the most important factor for accurate alignment inference; appropriate use of posterior-decoding was next; and fine details of the model were least important. Posterior-decoding heuristics can be substantially faster than exact phylogenetic inference, so this motivates the use of sum-over-pairs heuristics where possible (and approximate sum-over-pairs). For more exact probabilistic inference, we discuss the use of transducer composition for ML (or MCMC) inference on phylogenies, including possible ways to make the core operations tractable.
Author Summary
A number of leading methods for bioinformatics analysis of structural RNAs use probabilistic grammars as models for pairs of homologous RNAs. We show that any such pairwise grammar can be extended to an entire phylogeny by treating the pairwise grammar as a machine (a “transducer”) that models a single ancestor-descendant relationship in the tree, transforming one RNA structure into another. In addition to phylogenetic enhancement of current applications, such as RNA genefinding, homology detection, alignment and secondary structure prediction, this should enable probabilistic phylogenetic reconstruction of RNA sequences that are ancestral to present-day genes. We describe statistical inference algorithms, software implementations, and a simulation-based comparison of three-taxon maximum likelihood alignment to several other methods for aligning three sibling RNAs. In the Discussion we consider how the three-taxon RNA alignment-reconstruction-folding algorithm, which is currently very computationally-expensive, might be made more efficient so that larger phylogenies could be considered.
doi:10.1371/journal.pcbi.1000483
PMCID: PMC2725318  PMID: 19714212
8.  Efficient pairwise RNA structure prediction using probabilistic alignment constraints in Dynalign 
BMC Bioinformatics  2007;8:130.
Background
Joint alignment and secondary structure prediction of two RNA sequences can significantly improve the accuracy of the structural predictions. Methods addressing this problem, however, are forced to employ constraints that reduce computation by restricting the alignments and/or structures (i.e. folds) that are permissible. In this paper, a new methodology is presented for the purpose of establishing alignment constraints based on nucleotide alignment and insertion posterior probabilities. Using a hidden Markov model, posterior probabilities of alignment and insertion are computed for all possible pairings of nucleotide positions from the two sequences. These alignment and insertion posterior probabilities are additively combined to obtain probabilities of co-incidence for nucleotide position pairs. A suitable alignment constraint is obtained by thresholding the co-incidence probabilities. The constraint is integrated with Dynalign, a free energy minimization algorithm for joint alignment and secondary structure prediction. The resulting method is benchmarked against the previous version of Dynalign and against other programs for pairwise RNA structure prediction.
Results
The proposed technique eliminates manual parameter selection in Dynalign and provides significant computational time savings in comparison to prior constraints in Dynalign while simultaneously providing a small improvement in the structural prediction accuracy. Savings are also realized in memory. In experiments over a 5S RNA dataset with average sequence length of approximately 120 nucleotides, the method reduces computation by a factor of 2. The method performs favorably in comparison to other programs for pairwise RNA structure prediction: yielding better accuracy, on average, and requiring significantly lesser computational resources.
Conclusion
Probabilistic analysis can be utilized in order to automate the determination of alignment constraints for pairwise RNA structure prediction methods in a principled fashion. These constraints can reduce the computational and memory requirements of these methods while maintaining or improving their accuracy of structural prediction. This extends the practical reach of these methods to longer length sequences. The revised Dynalign code is freely available for download.
doi:10.1186/1471-2105-8-130
PMCID: PMC1868766  PMID: 17445273
9.  Fast online and index-based algorithms for approximate search of RNA sequence-structure patterns 
BMC Bioinformatics  2013;14:226.
Background
It is well known that the search for homologous RNAs is more effective if both sequence and structure information is incorporated into the search. However, current tools for searching with RNA sequence-structure patterns cannot fully handle mutations occurring on both these levels or are simply not fast enough for searching large sequence databases because of the high computational costs of the underlying sequence-structure alignment problem.
Results
We present new fast index-based and online algorithms for approximate matching of RNA sequence-structure patterns supporting a full set of edit operations on single bases and base pairs. Our methods efficiently compute semi-global alignments of structural RNA patterns and substrings of the target sequence whose costs satisfy a user-defined sequence-structure edit distance threshold. For this purpose, we introduce a new computing scheme to optimally reuse the entries of the required dynamic programming matrices for all substrings and combine it with a technique for avoiding the alignment computation of non-matching substrings. Our new index-based methods exploit suffix arrays preprocessed from the target database and achieve running times that are sublinear in the size of the searched sequences. To support the description of RNA molecules that fold into complex secondary structures with multiple ordered sequence-structure patterns, we use fast algorithms for the local or global chaining of approximate sequence-structure pattern matches. The chaining step removes spurious matches from the set of intermediate results, in particular of patterns with little specificity. In benchmark experiments on the Rfam database, our improved online algorithm is faster than the best previous method by up to factor 45. Our best new index-based algorithm achieves a speedup of factor 560.
Conclusions
The presented methods achieve considerable speedups compared to the best previous method. This, together with the expected sublinear running time of the presented index-based algorithms, allows for the first time approximate matching of RNA sequence-structure patterns in large sequence databases. Beyond the algorithmic contributions, we provide with RaligNAtor a robust and well documented open-source software package implementing the algorithms presented in this manuscript. The RaligNAtor software is available at http://www.zbh.uni-hamburg.de/ralignator.
doi:10.1186/1471-2105-14-226
PMCID: PMC3765529  PMID: 23865810
10.  Alignment and Prediction of cis-Regulatory Modules Based on a Probabilistic Model of Evolution 
PLoS Computational Biology  2009;5(3):e1000299.
Cross-species comparison has emerged as a powerful paradigm for predicting cis-regulatory modules (CRMs) and understanding their evolution. The comparison requires reliable sequence alignment, which remains a challenging task for less conserved noncoding sequences. Furthermore, the existing models of DNA sequence evolution generally do not explicitly treat the special properties of CRM sequences. To address these limitations, we propose a model of CRM evolution that captures different modes of evolution of functional transcription factor binding sites (TFBSs) and the background sequences. A particularly novel aspect of our work is a probabilistic model of gains and losses of TFBSs, a process being recognized as an important part of regulatory sequence evolution. We present a computational framework that uses this model to solve the problems of CRM alignment and prediction. Our alignment method is similar to existing methods of statistical alignment but uses the conserved binding sites to improve alignment. Our CRM prediction method deals with the inherent uncertainties of binding site annotations and sequence alignment in a probabilistic framework. In simulated as well as real data, we demonstrate that our program is able to improve both alignment and prediction of CRM sequences over several state-of-the-art methods. Finally, we used alignments produced by our program to study binding site conservation in genome-wide binding data of key transcription factors in the Drosophila blastoderm, with two intriguing results: (i) the factor-bound sequences are under strong evolutionary constraints even if their neighboring genes are not expressed in the blastoderm and (ii) binding sites in distal bound sequences (relative to transcription start sites) tend to be more conserved than those in proximal regions. Our approach is implemented as software, EMMA (Evolutionary Model-based cis-regulatory Module Analysis), ready to be applied in a broad biological context.
Author Summary
Comparison of noncoding DNA sequences across species has the potential to significantly improve our understanding of gene regulation and our ability to annotate regulatory regions of the genome. This potential is evident from recent publications analyzing 12 Drosophila genomes for regulatory annotation. However, because noncoding sequences are much less structured than coding sequences, their interspecies comparison presents technical challenges, such as ambiguity about how to align them and how to predict transcription factor binding sites, which are the fundamental units that make up regulatory sequences. This article describes how to build an integrated probabilistic framework that performs alignment and binding site prediction simultaneously, in the process improving the accuracy of both tasks. It defines a stochastic model for the evolution of entire “cis-regulatory modules,” with its highlight being a novel theoretical treatment of the commonly observed loss and gain of binding sites during evolution. This new evolutionary model forms the backbone of newly developed software for the prediction of new cis-regulatory modules, alignment of known modules to elucidate general principles of cis-regulatory evolution, or both. The new software is demonstrated to provide benefits in performance of these two crucial genomics tasks.
doi:10.1371/journal.pcbi.1000299
PMCID: PMC2657044  PMID: 19293946
11.  In silico single strand melting curve: a new approach to identify nucleic acid polymorphisms in Totiviridae 
BMC Bioinformatics  2014;15(1):243.
Background
The PCR technique and its variations have been increasingly used in the clinical laboratory and recent advances in this field generated new higher resolution techniques based on nucleic acid denaturation dynamics. The principle of these new molecular tools is based on the comparison of melting profiles, after denaturation of a DNA double strand. Until now, the secondary structure of single-stranded nucleic acids has not been exploited to develop identification systems based on PCR. To test the potential of single-strand RNA denaturation as a new alternative to detect specific nucleic acid variations, sequences from viruses of the Totiviridae family were compared using a new in silico melting curve approach. This family comprises double-stranded RNA virus, with a genome constituted by two ORFs, ORF1 and ORF2, which encodes the capsid/RNA binding proteins and an RNA-dependent RNA polymerase (RdRp), respectively.
Results
A phylogenetic tree based on RdRp amino acid sequences was constructed, and eight monophyletic groups were defined. Alignments of RdRp RNA sequences from each group were screened to identify RNA regions with conserved secondary structure. One region in the second half of ORF2 was identified and individually modeled using the RNAfold tool. Afterwards, each DNA or RNA sequence was denatured in silico using the softwares MELTSIM and RNAheat that generate melting curves considering the denaturation of a double stranded DNA and single stranded RNA, respectively. The same groups identified in the RdRp phylogenetic tree were retrieved by a clustering analysis of the melting curves data obtained from RNAheat. Moreover, the same approach was used to successfully discriminate different variants of Trichomonas vaginalis virus, which was not possible by the visual comparison of the double stranded melting curves generated by MELTSIM.
Conclusion
In silico analysis indicate that ssRNA melting curves are more informative than dsDNA melting curves. Furthermore, conserved RNA structures may be determined from analysis of individuals that are phylogenetically related, and these regions may be used to support the reconstitution of their phylogenetic groups. These findings are a robust basis for the development of in vitro systems to ssRNA melting curves detection.
Electronic supplementary material
The online version of this article (doi:10.1186/1471-2105-15-243) contains supplementary material, which is available to authorized users.
doi:10.1186/1471-2105-15-243
PMCID: PMC4119202  PMID: 25030031
RNA secondary structure; Infectious Myonecrosis Virus; high resolution melting curve; Virus detection; IHHNV, WSSV, Trichomonas
12.  4SALE – A tool for synchronous RNA sequence and secondary structure alignment and editing 
BMC Bioinformatics  2006;7:498.
Background
In sequence analysis the multiple alignment builds the fundament of all proceeding analyses. Errors in an alignment could strongly influence all succeeding analyses and therefore could lead to wrong predictions. Hand-crafted and hand-improved alignments are necessary and meanwhile good common practice. For RNA sequences often the primary sequence as well as a secondary structure consensus is well known, e.g., the cloverleaf structure of the t-RNA. Recently, some alignment editors are proposed that are able to include and model both kinds of information. However, with the advent of a large amount of reliable RNA sequences together with their solved secondary structures (available from e.g. the ITS2 Database), we are faced with the problem to handle sequences and their associated secondary structures synchronously.
Results
4SALE fills this gap. The application allows a fast sequence and synchronous secondary structure alignment for large data sets and for the first time synchronous manual editing of aligned sequences and their secondary structures. This study describes an algorithm for the synchronous alignment of sequences and their associated secondary structures as well as the main features of 4SALE used for further analyses and editing. 4SALE builds an optimal and unique starting point for every RNA sequence and structure analysis.
Conclusion
4SALE, which provides an user-friendly and intuitive interface, is a comprehensive toolbox for RNA analysis based on sequence and secondary structure information. The program connects sequence and structure databases like the ITS2 Database to phylogeny programs as for example the CBCAnalyzer. 4SALE is written in JAVA and therefore platform independent. The software is freely available and distributed from the website at
doi:10.1186/1471-2105-7-498
PMCID: PMC1637121  PMID: 17101042
13.  Benchmarking tools for the alignment of functional noncoding DNA 
BMC Bioinformatics  2004;5:6.
Background
Numerous tools have been developed to align genomic sequences. However, their relative performance in specific applications remains poorly characterized. Alignments of protein-coding sequences typically have been benchmarked against "correct" alignments inferred from structural data. For noncoding sequences, where such independent validation is lacking, simulation provides an effective means to generate "correct" alignments with which to benchmark alignment tools.
Results
Using rates of noncoding sequence evolution estimated from the genus Drosophila, we simulated alignments over a range of divergence times under varying models incorporating point substitution, insertion/deletion events, and short blocks of constrained sequences such as those found in cis-regulatory regions. We then compared "correct" alignments generated by a modified version of the ROSE simulation platform to alignments of the simulated derived sequences produced by eight pairwise alignment tools (Avid, BlastZ, Chaos, ClustalW, DiAlign, Lagan, Needle, and WABA) to determine the off-the-shelf performance of each tool. As expected, the ability to align noncoding sequences accurately decreases with increasing divergence for all tools, and declines faster in the presence of insertion/deletion evolution. Global alignment tools (Avid, ClustalW, Lagan, and Needle) typically have higher sensitivity over entire noncoding sequences as well as in constrained sequences. Local tools (BlastZ, Chaos, and WABA) have lower overall sensitivity as a consequence of incomplete coverage, but have high specificity to detect constrained sequences as well as high sensitivity within the subset of sequences they align. Tools such as DiAlign, which generate both local and global outputs, produce alignments of constrained sequences with both high sensitivity and specificity for divergence distances in the range of 1.25–3.0 substitutions per site.
Conclusion
For species with genomic properties similar to Drosophila, we conclude that a single pair of optimally diverged species analyzed with a high performance alignment tool can yield accurate and specific alignments of functionally constrained noncoding sequences. Further algorithm development, optimization of alignment parameters, and benchmarking studies will be necessary to extract the maximal biological information from alignments of functional noncoding DNA.
doi:10.1186/1471-2105-5-6
PMCID: PMC344529  PMID: 14736341
14.  Computational annotation of genes differentially expressed along olive fruit development 
BMC Plant Biology  2009;9:128.
Background
Olea europaea L. is a traditional tree crop of the Mediterranean basin with a worldwide economical high impact. Differently from other fruit tree species, little is known about the physiological and molecular basis of the olive fruit development and a few sequences of genes and gene products are available for olive in public databases. This study deals with the identification of large sets of differentially expressed genes in developing olive fruits and the subsequent computational annotation by means of different software.
Results
mRNA from fruits of the cv. Leccino sampled at three different stages [i.e., initial fruit set (stage 1), completed pit hardening (stage 2) and veraison (stage 3)] was used for the identification of differentially expressed genes putatively involved in main processes along fruit development. Four subtractive hybridization libraries were constructed: forward and reverse between stage 1 and 2 (libraries A and B), and 2 and 3 (libraries C and D). All sequenced clones (1,132 in total) were analyzed through BlastX against non-redundant NCBI databases and about 60% of them showed similarity to known proteins. A total of 89 out of 642 differentially expressed unique sequences was further investigated by Real-Time PCR, showing a validation of the SSH results as high as 69%. Library-specific cDNA repertories were annotated according to the three main vocabularies of the gene ontology (GO): cellular component, biological process and molecular function. BlastX analysis, GO terms mapping and annotation analysis were performed using the Blast2GO software, a research tool designed with the main purpose of enabling GO based data mining on sequence sets for which no GO annotation is yet available. Bioinformatic analysis pointed out a significantly different distribution of the annotated sequences for each GO category, when comparing the three fruit developmental stages. The olive fruit-specific transcriptome dataset was used to query all known KEGG (Kyoto Encyclopaedia of Genes and Genomes) metabolic pathways for characterizing and positioning retrieved EST records. The integration of the olive sequence datasets within the MapMan platform for microarray analysis allowed the identification of specific biosynthetic pathways useful for the definition of key functional categories in time course analyses for gene groups.
Conclusion
The bioinformatic annotation of all gene sequences was useful to shed light on metabolic pathways and transcriptional aspects related to carbohydrates, fatty acids, secondary metabolites, transcription factors and hormones as well as response to biotic and abiotic stresses throughout olive drupe development. These results represent a first step toward both functional genomics and systems biology research for understanding the gene functions and regulatory networks in olive fruit growth and ripening.
doi:10.1186/1471-2229-9-128
PMCID: PMC2774695  PMID: 19852839
15.  Query-Dependent Banding (QDB) for Faster RNA Similarity Searches 
PLoS Computational Biology  2007;3(3):e56.
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 LN2.4 to LN1.3 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.
Author Summary
Database similarity searching is the sine qua non of computational molecular biology. Well-known and powerful methods exist for primary sequence searches, such as Blast and profile hidden Markov models. However, for RNA analysis, biologists rely not only on primary sequence but also on conserved RNA secondary structure to manually align and compare RNAs, and most computational tools for identifying RNA structural homologs remain too slow for large-scale use. We describe a new algorithm for accelerating one of the most general and powerful classes of methods for RNA sequence and structure analysis, so-called profile SCFG (stochastic context-free grammar) RNA similarity search methods. We describe this approach, called query-dependent banding, in the context of this and other improvements in a practical implementation, the freely available Infernal software package, the basis of the Rfam RNA family database for genome annotation. Infernal is now a faster, more sensitive, and more specific software tool for identifying homologs of structural RNAs.
doi:10.1371/journal.pcbi.0030056
PMCID: PMC1847999  PMID: 17397253
16.  Inferring Noncoding RNA Families and Classes by Means of Genome-Scale Structure-Based Clustering 
PLoS Computational Biology  2007;3(4):e65.
The RFAM database defines families of ncRNAs by means of sequence similarities that are sufficient to establish homology. In some cases, such as microRNAs and box H/ACA snoRNAs, functional commonalities define classes of RNAs that are characterized by structural similarities, and typically consist of multiple RNA families. Recent advances in high-throughput transcriptomics and comparative genomics have produced very large sets of putative noncoding RNAs and regulatory RNA signals. For many of them, evidence for stabilizing selection acting on their secondary structures has been derived, and at least approximate models of their structures have been computed. The overwhelming majority of these hypothetical RNAs cannot be assigned to established families or classes. We present here a structure-based clustering approach that is capable of extracting putative RNA classes from genome-wide surveys for structured RNAs. The LocARNA (local alignment of RNA) tool implements a novel variant of the Sankoff algorithm that is sufficiently fast to deal with several thousand candidate sequences. The method is also robust against false positive predictions, i.e., a contamination of the input data with unstructured or nonconserved sequences. We have successfully tested the LocARNA-based clustering approach on the sequences of the RFAM-seed alignments. Furthermore, we have applied it to a previously published set of 3,332 predicted structured elements in the Ciona intestinalis genome (Missal K, Rose D, Stadler PF (2005) Noncoding RNAs in Ciona intestinalis. Bioinformatics 21 (Supplement 2): i77–i78). In addition to recovering, e.g., tRNAs as a structure-based class, the method identifies several RNA families, including microRNA and snoRNA candidates, and suggests several novel classes of ncRNAs for which to date no representative has been experimentally characterized.
Author Summary
For a long time, it was believed that the control of processes in living organisms is almost only performed by proteins. Only recently, scientists learned that a further class of molecules, namely special RNAs, plays an important role in cell control. In consequence, research on such RNAs enjoys increasing attention over the last few years. These RNAs were called noncoding RNAs (ncRNA), because, unlike most other RNAs, these molecules do not code for proteins. Due to recent research successes, one can predict a lot of potential new ncRNAs by comparing the genomes of related organisms. Technically, comparing such RNAs is challenging and computationally expensive, since related ncRNAs often show only weak similarity on the sequence level, but share similar structures. In the paper, we present the new method LocARNA for fast and accurate comparison of RNAs with respect to their sequence and structure. Using this method, we define a distance measure between pairs of ncRNAs based on sequence and structure. This is then used for combining RNAs into a cluster for identifying groups of similar RNAs in large unorganized sets of RNA. The final aim of such a comparison is to identify new classes of ncRNAs. We applied our clustering procedure to a previously published set of 3,332 predicted ncRNAs in the C. intestinalis genomes. In addition to rediscovering known classes of RNAs, e.g., tRNAs, the method predicts microRNA candidates, and suggests several novel, experimentally uncharacterized classes of ncRNAs. For verification, we clustered about 4,000 RNAs of RFAM, which is a large database that contains RNAs with an already known classification into families. Our results show good performance of the presented structure-based clustering approach.
doi:10.1371/journal.pcbi.0030065
PMCID: PMC1851984  PMID: 17432929
17.  Fast Statistical Alignment 
PLoS Computational Biology  2009;5(5):e1000392.
We describe a new program for the alignment of multiple biological sequences that is both statistically motivated and fast enough for problem sizes that arise in practice. Our Fast Statistical Alignment program is based on pair hidden Markov models which approximate an insertion/deletion process on a tree and uses a sequence annealing algorithm to combine the posterior probabilities estimated from these models into a multiple alignment. FSA uses its explicit statistical model to produce multiple alignments which are accompanied by estimates of the alignment accuracy and uncertainty for every column and character of the alignment—previously available only with alignment programs which use computationally-expensive Markov Chain Monte Carlo approaches—yet can align thousands of long sequences. Moreover, FSA utilizes an unsupervised query-specific learning procedure for parameter estimation which leads to improved accuracy on benchmark reference alignments in comparison to existing programs. The centroid alignment approach taken by FSA, in combination with its learning procedure, drastically reduces the amount of false-positive alignment on biological data in comparison to that given by other methods. The FSA program and a companion visualization tool for exploring uncertainty in alignments can be used via a web interface at http://orangutan.math.berkeley.edu/fsa/, and the source code is available at http://fsa.sourceforge.net/.
Author Summary
Biological sequence alignment is one of the fundamental problems in comparative genomics, yet it remains unsolved. Over sixty sequence alignment programs are listed on Wikipedia, and many new programs are published every year. However, many popular programs suffer from pathologies such as aligning unrelated sequences and producing discordant alignments in protein (amino acid) and codon (nucleotide) space, casting doubt on the accuracy of the inferred alignments. Inaccurate alignments can introduce large and unknown systematic biases into downstream analyses such as phylogenetic tree reconstruction and substitution rate estimation. We describe a new program for multiple sequence alignment which can align protein, RNA and DNA sequence and improves on the accuracy of existing approaches on benchmarks of protein and RNA structural alignments and simulated mammalian and fly genomic alignments. Our approach, which seeks to find the alignment which is closest to the truth under our statistical model, leaves unrelated sequences largely unaligned and produces concordant alignments in protein and codon space. It is fast enough for difficult problems such as aligning orthologous genomic regions or aligning hundreds or thousands of proteins. It furthermore has a companion GUI for visualizing the estimated alignment reliability.
doi:10.1371/journal.pcbi.1000392
PMCID: PMC2684580  PMID: 19478997
18.  Bioinformatics resource manager v2.3: an integrated software environment for systems biology with microRNA and cross-species analysis tools 
BMC Bioinformatics  2012;13:311.
Background
MicroRNAs (miRNAs) are noncoding RNAs that direct post-transcriptional regulation of protein coding genes. Recent studies have shown miRNAs are important for controlling many biological processes, including nervous system development, and are highly conserved across species. Given their importance, computational tools are necessary for analysis, interpretation and integration of high-throughput (HTP) miRNA data in an increasing number of model species. The Bioinformatics Resource Manager (BRM) v2.3 is a software environment for data management, mining, integration and functional annotation of HTP biological data. In this study, we report recent updates to BRM for miRNA data analysis and cross-species comparisons across datasets.
Results
BRM v2.3 has the capability to query predicted miRNA targets from multiple databases, retrieve potential regulatory miRNAs for known genes, integrate experimentally derived miRNA and mRNA datasets, perform ortholog mapping across species, and retrieve annotation and cross-reference identifiers for an expanded number of species. Here we use BRM to show that developmental exposure of zebrafish to 30 uM nicotine from 6–48 hours post fertilization (hpf) results in behavioral hyperactivity in larval zebrafish and alteration of putative miRNA gene targets in whole embryos at developmental stages that encompass early neurogenesis. We show typical workflows for using BRM to integrate experimental zebrafish miRNA and mRNA microarray datasets with example retrievals for zebrafish, including pathway annotation and mapping to human ortholog. Functional analysis of differentially regulated (p<0.05) gene targets in BRM indicates that nicotine exposure disrupts genes involved in neurogenesis, possibly through misregulation of nicotine-sensitive miRNAs.
Conclusions
BRM provides the ability to mine complex data for identification of candidate miRNAs or pathways that drive phenotypic outcome and, therefore, is a useful hypothesis generation tool for systems biology. The miRNA workflow in BRM allows for efficient processing of multiple miRNA and mRNA datasets in a single software environment with the added capability to interact with public data sources and visual analytic tools for HTP data analysis at a systems level. BRM is developed using Java™ and other open-source technologies for free distribution (http://www.sysbio.org/dataresources/brm.stm).
doi:10.1186/1471-2105-13-311
PMCID: PMC3534564  PMID: 23174015
Systems biology; Genomics; MicroRNA; Bioinformatics; Zebrafish
19.  R-Coffee: a web server for accurately aligning noncoding RNA sequences 
Nucleic Acids Research  2008;36(Web Server issue):W10-W13.
The R-Coffee web server produces highly accurate multiple alignments of noncoding RNA (ncRNA) sequences, taking into account predicted secondary structures. R-Coffee uses a novel algorithm recently incorporated in the T-Coffee package. R-Coffee works along the same lines as T-Coffee: it uses pairwise or multiple sequence alignment (MSA) methods to compute a primary library of input alignments. The program then computes an MSA highly consistent with both the alignments contained in the library and the secondary structures associated with the sequences. The secondary structures are predicted using RNAplfold. The server provides two modes. The slow/accurate mode is restricted to small datasets (less than 5 sequences less than 150 nucleotides) and combines R-Coffee with Consan, a very accurate pairwise RNA alignment method. For larger datasets a fast method can be used (RM-Coffee mode), that uses R-Coffee to combine the output of the three packages which combines the outputs from programs found to perform best on RNA (MUSCLE, MAFFT and ProbConsRNA). Our BRAliBase benchmarks indicate that the R-Coffee/Consan combination is one of the best ncRNA alignment methods for short sequences, while the RM-Coffee gives comparable results on longer sequences. The R-Coffee web server is available at http://www.tcoffee.org.
doi:10.1093/nar/gkn278
PMCID: PMC2447777  PMID: 18483080
20.  A probabilistic model for the evolution of RNA structure 
BMC Bioinformatics  2004;5:166.
Background
For the purposes of finding and aligning noncoding RNA gene- and cis-regulatory elements in multiple-genome datasets, it is useful to be able to derive multi-sequence stochastic grammars (and hence multiple alignment algorithms) systematically, starting from hypotheses about the various kinds of random mutation event and their rates.
Results
Here, we consider a highly simplified evolutionary model for RNA, called "The TKF91 Structure Tree" (following Thorne, Kishino and Felsenstein's 1991 model of sequence evolution with indels), which we have implemented for pairwise alignment as proof of principle for such an approach. The model, its strengths and its weaknesses are discussed with reference to four examples of functional ncRNA sequences: a riboswitch (guanine), a zipcode (nanos), a splicing factor (U4) and a ribozyme (RNase P). As shown by our visualisations of posterior probability matrices, the selected examples illustrate three different signatures of natural selection that are highly characteristic of ncRNA: (i) co-ordinated basepair substitutions, (ii) co-ordinated basepair indels and (iii) whole-stem indels.
Conclusions
Although all three types of mutation "event" are built into our model, events of type (i) and (ii) are found to be better modeled than events of type (iii). Nevertheless, we hypothesise from the model's performance on pairwise alignments that it would form an adequate basis for a prototype multiple alignment and genefinding tool.
doi:10.1186/1471-2105-5-166
PMCID: PMC534097  PMID: 15507142
21.  Self Containment, a Property of Modular RNA Structures, Distinguishes microRNAs 
PLoS Computational Biology  2008;4(8):e1000150.
RNA molecules will tend to adopt a folded conformation through the pairing of bases on a single strand; the resulting so-called secondary structure is critical to the function of many types of RNA. The secondary structure of a particular substring of functional RNA may depend on its surrounding sequence. Yet, some RNAs such as microRNAs retain their specific structures during biogenesis, which involves extraction of the substructure from a larger structural context, while other functional RNAs may be composed of a fusion of independent substructures. Such observations raise the question of whether particular functional RNA substructures may be selected for invariance of secondary structure to their surrounding nucleotide context. We define the property of self containment to be the tendency for an RNA sequence to robustly adopt the same optimal secondary structure regardless of whether it exists in isolation or is a substring of a longer sequence of arbitrary nucleotide content. We measured degree of self containment using a scoring method we call the self-containment index and found that miRNA stem loops exhibit high self containment, consistent with the requirement for structural invariance imposed by the miRNA biogenesis pathway, while most other structured RNAs do not. Further analysis revealed a trend toward higher self containment among clustered and conserved miRNAs, suggesting that high self containment may be a characteristic of novel miRNAs acquiring new genomic contexts. We found that miRNAs display significantly enhanced self containment compared to other functional RNAs, but we also found a trend toward natural selection for self containment in most functional RNA classes. We suggest that self containment arises out of selection for robustness against perturbations, invariance during biogenesis, and modular composition of structural function. Analysis of self containment will be important for both annotation and design of functional RNAs. A Python implementation and Web interface to calculate the self-containment index are available at http://kim.bio.upenn.edu/software/.
Author Summary
An RNA molecule is made up of a linear sequence of nucleotides, which form pairwise interactions that define its folded three-dimensional structure; the particular structure largely depends on the specific sequence. These base-pairing interactions are stabilizing, and the RNA will tend to fold in a particular way to maximize stability. Consider some nucleotide sequence that optimally folds into some structure in isolation; if this sequence is now embedded inside a larger sequence, then either the original structure will be a robust subcomponent of the larger folded structure, or it will be disrupted due to new interactions between the original sequence and the surrounding sequence. We explore this property of context robustness of structure and in particular define the property of “self containment” to describe intrinsic context robustness—i.e., the tendency for certain sequences to be structurally robust in many different sequence contexts. Self containment turns out to be a strong characteristic of a class of RNAs called microRNAs, whose biogenesis process depends on the maintenance of structural robustness. This finding will be useful in future efforts to characterize novel miRNAs, as well as in understanding the regulation and evolution of noncoding functional RNAs as modular units.
doi:10.1371/journal.pcbi.1000150
PMCID: PMC2517099  PMID: 18725951
22.  An optimized TOPS+ comparison method for enhanced TOPS models 
BMC Bioinformatics  2010;11:138.
Background
Although methods based on highly abstract descriptions of protein structures, such as VAST and TOPS, can perform very fast protein structure comparison, the results can lack a high degree of biological significance. Previously we have discussed the basic mechanisms of our novel method for structure comparison based on our TOPS+ model (Topological descriptions of Protein Structures Enhanced with Ligand Information). In this paper we show how these results can be significantly improved using parameter optimization, and we call the resulting optimised TOPS+ method as advanced TOPS+ comparison method i.e. advTOPS+.
Results
We have developed a TOPS+ string model as an improvement to the TOPS [1-3] graph model by considering loops as secondary structure elements (SSEs) in addition to helices and strands, representing ligands as first class objects, and describing interactions between SSEs, and SSEs and ligands, by incoming and outgoing arcs, annotating SSEs with the interaction direction and type. Benchmarking results of an all-against-all pairwise comparison using a large dataset of 2,620 non-redundant structures from the PDB40 dataset [4] demonstrate the biological significance, in terms of SCOP classification at the superfamily level, of our TOPS+ comparison method.
Conclusions
Our advanced TOPS+ comparison shows better performance on the PDB40 dataset [4] compared to our basic TOPS+ method, giving 90% accuracy for SCOP alpha+beta; a 6% increase in accuracy compared to the TOPS and basic TOPS+ methods. It also outperforms the TOPS, basic TOPS+ and SSAP comparison methods on the Chew-Kedem dataset [5], achieving 98% accuracy.
Software Availability
The TOPS+ comparison server is available at http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/.
doi:10.1186/1471-2105-11-138
PMCID: PMC2858036  PMID: 20236520
23.  PFAAT version 2.0: A tool for editing, annotating, and analyzing multiple sequence alignments 
BMC Bioinformatics  2007;8:381.
Background
By virtue of their shared ancestry, homologous sequences are similar in their structure and function. Consequently, multiple sequence alignments are routinely used to identify trends that relate to function. This type of analysis is particularly productive when it is combined with structural and phylogenetic analysis.
Results
Here we describe the release of PFAAT version 2.0, a tool for editing, analyzing, and annotating multiple sequence alignments. Support for multiple annotations is a key component of this release as it provides a framework for most of the new functionalities. The sequence annotations are accessible from the alignment and tree, where they are typically used to label sequences or hyperlink them to related databases. Sequence annotations can be created manually or extracted automatically from UniProt entries. Once a multiple sequence alignment is populated with sequence annotations, sequences can be easily selected and sorted through a sophisticated search dialog. The selected sequences can be further analyzed using statistical methods that explicitly model relationships between the sequence annotations and residue properties. Residue annotations are accessible from the alignment viewer and are typically used to designate binding sites or properties for a particular residue.
Residue annotations are also searchable, and allow one to quickly select alignment columns for further sequence analysis, e.g. computing percent identities. Other features include: novel algorithms to compute sequence conservation, mapping conservation scores to a 3D structure in Jmol, displaying secondary structure elements, and sorting sequences by residue composition.
Conclusion
PFAAT provides a framework whereby end-users can specify knowledge for a protein family in the form of annotation. The annotations can be combined with sophisticated analysis to test hypothesis that relate to sequence, structure and function.
doi:10.1186/1471-2105-8-381
PMCID: PMC2092438  PMID: 17931421
24.  Searching for evolutionary distant RNA homologs within genomic sequences using partition function posterior probabilities 
BMC Bioinformatics  2008;9:61.
Background
Identification of RNA homologs within genomic stretches is difficult when pairwise sequence identity is low or unalignable flanking residues are present. In both cases structure-sequence or profile/family-sequence alignment programs become difficult to apply because of unreliable RNA structures or family alignments. As such, local sequence-sequence alignment programs are frequently used instead. We have recently demonstrated that maximal expected accuracy alignments using partition function match probabilities (implemented in Probalign) are significantly better than contemporary methods on heterogeneous length protein sequence datasets, thus suggesting an affinity for local alignment.
Results
We create a pairwise RNA-genome alignment benchmark from RFAM families with average pairwise sequence identity up to 60%. Each dataset contains a query RNA aligned to a target RNA (of the same family) embedded in a genomic sequence at least 5K nucleotides long. To simulate common conditions when exact ends of an ncRNA are unknown, each query RNA has 5' and 3' genomic flanks of size 50, 100, and 150 nucleotides. We subsequently compare the error of the Probalign program (adjusted for local alignment) to the commonly used local alignment programs HMMER, SSEARCH, and BLAST, and the popular ClustalW program with zero end-gap penalties. Parameters were optimized for each program on a small subset of the benchmark. Probalign has overall highest accuracies on the full benchmark. It leads by 10% accuracy over SSEARCH (the next best method) on 5 out of 22 families. On datasets restricted to maximum of 30% sequence identity, Probalign's overall median error is 71.2% vs. 83.4% for SSEARCH (P-value < 0.05). Furthermore, on these datasets Probalign leads SSEARCH by at least 10% on five families; SSEARCH leads Probalign by the same margin on two of the fourteen families. We also demonstrate that the Probalign mean posterior probability, compared to the normalized SSEARCH Z-score, is a better discriminator of alignment quality. All datasets and software are available online.
Conclusion
We demonstrate, for the first time, that partition function match probabilities used for expected accuracy alignment, as done in Probalign, provide statistically significant improvement over current approaches for identifying distantly related RNA sequences in larger genomic segments.
doi:10.1186/1471-2105-9-61
PMCID: PMC2248559  PMID: 18226231
25.  DAMBE5: A Comprehensive Software Package for Data Analysis in Molecular Biology and Evolution 
Molecular Biology and Evolution  2013;30(7):1720-1728.
Since its first release in 2001 as mainly a software package for phylogenetic analysis, data analysis for molecular biology and evolution (DAMBE) has gained many new functions that may be classified into six categories: 1) sequence retrieval, editing, manipulation, and conversion among more than 20 standard sequence formats including MEGA, NEXUS, PHYLIP, GenBank, and the new NeXML format for interoperability, 2) motif characterization and discovery functions such as position weight matrix and Gibbs sampler, 3) descriptive genomic analysis tools with improved versions of codon adaptation index, effective number of codons, protein isoelectric point profiling, RNA and protein secondary structure prediction and calculation of minimum folding energy, and genomic skew plots with optimized window size, 4) molecular phylogenetics including sequence alignment, testing substitution saturation, distance-based, maximum parsimony, and maximum-likelihood methods for tree reconstructions, testing the molecular clock hypothesis with either a phylogeny or with relative-rate tests, dating gene duplication and speciation events, choosing the best-fit substitution models, and estimating rate heterogeneity over sites, 5) phylogeny-based comparative methods for continuous and discrete variables, and 6) graphic functions including secondary structure display, optimized skew plot, hydrophobicity plot, and many other plots of amino acid properties along a protein sequence, tree display and drawing by dragging nodes to each other, and visual searching of the maximum parsimony tree. DAMBE features a graphic, user-friendly, and intuitive interface and is freely available from http://dambe.bio.uottawa.ca (last accessed April 16, 2013).
doi:10.1093/molbev/mst064
PMCID: PMC3684854  PMID: 23564938
bioinformatics; phylogenetics; dating; Gibbs sampler; motif discovery; secondary structure; codon usage; hidden Markov model; genomic analysis

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