BACKGROUND: The nearest neighbor model and associated dynamic programming algorithms allow for the efficient estimation of the RNA secondary structure Boltzmann ensemble. However because a given RNA secondary structure only contains a fraction of the possible helices that could form from a given sequence, the Boltzmann ensemble is multimodal. Several methods exist for clustering structures and finding those modes. However less focus is given to exploring the underlying reasons for this multimodality: the presence of conflicting basepairs. Information theory, or more specifically mutual information, provides a method to identify those basepairs that are key to the secondary structure. RESULTS: To this end we find most informative basepairs and visualize the effect of these basepairs on the secondary structure. Knowing whether a most informative basepair is present tells us not only the status of the particular pair but also provides a large amount of information about which other pairs are present or not present. We find that a few basepairs account for a large amount of the structural uncertainty. The identification of these pairs indicates small changes to sequence or stability that will have a large effect on structure. CONCLUSION: We provide a novel algorithm that uses mutual information to identify the key basepairs that lead to a multimodal Boltzmann distribution. We then visualize the effect of these pairs on the overall Boltzmann ensemble.

BACKGROUND: Procedures for controlling the false discovery rate (FDR) are widely applied as a solution to the multiple comparisons problem of high-dimensional statistics. Current FDR-controlling procedures require accurately calculated p-values and rely on extrapolation into the unknown and unobserved tails of the null distribution. Both of these intermediate steps are challenging and can compromise the reliability of the results. RESULTS: We present a general method for controlling the FDR that capitalizes on the large amount of control data often found in big data studies to avoid these frequently problematic intermediate steps. The method utilizes control data to empirically construct the distribution of the test statistic under the null hypothesis and directly compares this distribution to the empirical distribution of the test data. By not relying on p-values, our control data-based empirical FDR procedure more closely follows the foundational principles of the scientific method: that inference is drawn by comparing test data to control data. The method is demonstrated through application to a problem in structural genomics. CONCLUSIONS: The method described here provides a general statistical framework for controlling the FDR that is specifically tailored for the big data setting. By relying on empirically constructed distributions and control data, it forgoes potentially problematic modeling steps and extrapolation into the unknown tails of the null distribution. This procedure is broadly applicable insofar as controlled experiments or internal negative controls are available, as is increasingly common in the big data setting.

MOTIVATION: Validation and reproducibility of results is a central and pressing issue in genomics. Several recent embarrassing incidents involving the irreproducibility of high-profile studies have illustrated the importance of this issue and the need for rigorous methods for the assessment of reproducibility. RESULTS: Here, we describe an existing statistical model that is very well suited to this problem. We explain its utility for assessing the reproducibility of validation experiments, and apply it to a genome-scale study of adenosine deaminase acting on RNA (ADAR)-mediated RNA editing in Drosophila. We also introduce a statistical method for planning validation experiments that will obtain the tightest reproducibility confidence limits, which, for a fixed total number of experiments, returns the optimal number of replicates for the study. AVAILABILITY: Downloadable software and a web service for both the analysis of data from a reproducibility study and for the optimal design of these studies is provided at http://ccmbweb.ccv.brown.edu/reproducibility.html .

MOTIVATION: RNA secondary structure plays an important role in the function of many RNAs, and structural features are often key to their interaction with other cellular components. Thus, there has been considerable interest in the prediction of secondary structures for RNA families. In this article, we present a new global structural alignment algorithm, RNAG, to predict consensus secondary structures for unaligned sequences. It uses a blocked Gibbs sampling algorithm, which has a theoretical advantage in convergence time. This algorithm iteratively samples from the conditional probability distributions P(Structure | Alignment) and P(Alignment | Structure). Not surprisingly, there is considerable uncertainly in the high-dimensional space of this difficult problem, which has so far received limited attention in this field. We show how the samples drawn from this algorithm can be used to more fully characterize the posterior space and to assess the uncertainty of predictions. RESULTS: Our analysis of three publically available datasets showed a substantial improvement in RNA structure prediction by RNAG over extant prediction methods. Additionally, our analysis of 17 RNA families showed that the RNAG sampled structures were generally compact around their ensemble centroids, and at least 11 families had at least two well-separated clusters of predicted structures. In general, the distance between a reference structure and our predicted structure was large relative to the variation among structures within an ensemble. AVAILABILITY: The Perl implementation of the RNAG algorithm and the data necessary to reproduce the results described in Sections 3.1 and 3.2 are available at http://ccmbweb.ccv.brown.edu/rnag.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: A recently developed DNaseI assay has given us our first genome-wide view of chromatin structure. In addition to cataloging DNaseI hypersensitive sites, these data allows us to more completely characterize overall features of chromatin accessibility. We employed a Bayesian hierarchical change-point model (CPM), a generalization of a hidden Markov Model (HMM), to characterize tiled microarray DNaseI sensitivity data available from the ENCODE project. RESULTS: Our analysis shows that the accessibility of chromatin to cleavage by DNaseI is well described by a four state model of local segments with each state described by a continuous mixture of Gaussian variables. The CPM produces a better fit to the observed data than the HMM. The large posterior probability for the four-state CPM suggests that the data falls naturally into four classes of regions, which we call major and minor DNaseI hypersensitive sites (DHSs), regions of intermediate sensitivity, and insensitive regions. These classes agree well with a model of chromatin in which local disruptions (DHSs) are concentrated within larger domains of intermediate sensitivity, the accessibility islands. The CPM assigns 92% of the bases within the ENCODE regions to the insensitive regions. The 5.8% of the bases that are in regions of intermediate sensitivity are clearly enriched in functional elements, including genes and activating histone modifications, while the remaining 2.2% of the bases in hypersensitive regions are very strongly enriched in these elements. AVAILABILITY: The CPM software is available upon request from the authors.

Computational biology is replete with high-dimensional (high-D) discrete prediction and inference problems, including sequence alignment, RNA structure prediction, phylogenetic inference, motif finding, prediction of pathways, and model selection problems in statistical genetics. Even though prediction and inference in these settings are uncertain, little attention has been focused on the development of global measures of uncertainty. Regardless of the procedure employed to produce a prediction, when a procedure delivers a single answer, that answer is a point estimate selected from the solution ensemble, the set of all possible solutions. For high-D discrete space, these ensembles are immense, and thus there is considerable uncertainty. We recommend the use of Bayesian credibility limits to describe this uncertainty, where a (1-alpha)%, 0< or =alpha< or =1, credibility limit is the minimum Hamming distance radius of a hyper-sphere containing (1-alpha)% of the posterior distribution. Because sequence alignment is arguably the most extensively used procedure in computational biology, we employ it here to make these general concepts more concrete. The maximum similarity estimator (i.e., the alignment that maximizes the likelihood) and the centroid estimator (i.e., the alignment that minimizes the mean Hamming distance from the posterior weighted ensemble of alignments) are used to demonstrate the application of Bayesian credibility limits to alignment estimators. Application of Bayesian credibility limits to the alignment of 20 human/rodent orthologous sequence pairs and 125 orthologous sequence pairs from six Shewanella species shows that credibility limits of the alignments of promoter sequences of these species vary widely, and that centroid alignments dependably have tighter credibility limits than traditional maximum similarity alignments.

MOTIVATION: Identification of functionally conserved regulatory elements in sequence data from closely related organisms is becoming feasible, due to the rapid growth of public sequence databases. Closely related organisms are most likely to have common regulatory motifs; however, the recent speciation of such organisms results in the high degree of correlation in their genome sequences, confounding the detection of functional elements. Additionally, alignment algorithms that use optimization techniques are limited to the detection of a single alignment that may not be representative. Comparative-genomics studies must be able to address the phylogenetic correlation in the data and efficiently explore the alignment space, in order to make specific and biologically relevant predictions. RESULTS: We describe here a Gibbs sampler that employs a full phylogenetic model and reports an ensemble centroid solution. We describe regulatory motif detection using both simulated and real data, and demonstrate that this approach achieves improved specificity, sensitivity, and positive predictive value over non-phylogenetic algorithms, and over phylogenetic algorithms that report a maximum likelihood solution. AVAILABILITY: The software is freely available at http://bayesweb.wadsworth.org/gibbs/gibbs.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

UNLABELLED: The energy landscape of RNA secondary structures is often complex, and the Boltzmann-weighted ensemble usually contains distinct clusters. Furthermore, the minimum free energy structure often lies outside of the cluster containing the structure determined by comparative sequence analysis. We have developed procedures to characterize and visualize the Boltzmann-weighted ensemble, and have made them available on the Sfold Web server. The new features on the Web server include clustering statistics, ensemble and cluster centroids, multi-dimensional scaling display and energy landscape representation of the Boltzmann-weighted ensemble. AVAILABILITY: http://sfold.wadsworth.org; http://www.bioinfo.rpi.edu/applications/sfold CONTACT: [email protected].

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/

The selection of a scoring matrix and gap penalty parameters continues to be an important problem in sequence alignment. We describe here an algorithm, the 'Bayes block aligner, which bypasses this requirement. Instead of requiring a fixed set of parameter settings, this algorithm returns the Bayesian posterior probability for the number of gaps and for the scoring matrices in any series of interest. Furthermore, instead of returning the single best alignment for the chosen parameter settings, this algorithm returns the posterior distribution of all alignments considering the full range of gapping and scoring matrices selected, weighing each in proportion to its probability based on the data. We compared the Bayes aligner with the popular Smith-Waterman algorithm with parameter settings from the literature which had been optimized for the identification of structural neighbors, and found that the Bayes aligner correctly identified more structural neighbors. In a detailed examination of the alignment of a pair of kinase and a pair of GTPase sequences, we illustrate the algorithm's potential to identify subsequences that are conserved to different degrees. In addition, this example shows that the Bayes aligner returns an alignment-free assessment of the distance between a pair of sequences.