A schematic overview of the COALESCE algorithm for regulatory module discovery. COALESCE predicts regulatory modules, each consisting of a gene expression bicluster (co-regulated genes and the conditions under which they are co-regulated) plus zero or more putative regulating motifs. Its primary input data are gene expression microarrays (to form biclusters) and flanking sequences (to predict motifs, although these can be omitted to output only expression biclusters). Additional supporting data types can be flexibly integrated using a Bayesian framework; for example, highly conserved sequence locations may be more likely to contain motifs, and sites occluded by nucleosomes may be less likely. COALESCE is efficient enough to integrate thousands of expression conditions and supporting data for large ( > 20 000 genes) metazoan genomes. 

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... 2. Evaluation of the functional consistency of S.cerevisiae expression biclusters predicted by COALESCE. Precision and recall are over gene pairs co-annotated in the Gene Ontology as described in (Myers et al ., 2006). Unless noted, COALESCE was executed on ∼ 2200 yeast expression conditions using 2 kb of up- and downstream flanking sequence. See Supplementary Figure 1 for a plot with standard scale axes and Supplementary Figure 2 for a comparable evaluation using human data. ( a ) A comparison of COALESCE with the PISA and SAMBA expression- only biclustering systems. This comprises 1870 modules integrating five runs of COALESCE, 428 modules from one run of COALESCE, ∼ 1000 modules integrating ∼ 20 runs of PISA, 492 modules from one run of SAMBA (lower recall results are not available from PISA or SAMBA), and k -means clusters with k ranging from 10 to 5000 for comparison. ( b ) Effects of supporting data types (evolutionary conservation and nucleosome placement) and of dataset correlation structure on COALESCE predictions. While neither supporting data nor prior knowledge of dataset correlation structure (e.g. sets of related conditions such as time courses) significantly influence overall performance, accounting for correlation structure greatly improves conciseness, achieving comparable functional accuracy using < 1/3 as many modules.  ...

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... the genome sequence of an organism describes its complement of potential proteins, it is the controlled expression, translation and modification of these proteins that allows cells to survive and grow. At the level of transcription and mRNA stability, a complex regulatory network of transcription factors (TFs), RNA binding proteins and microRNAs governs the interactions between components of a cell’s internal state and its external environment. Understanding the elements of this regulatory network and the stimuli to which it responds in higher organisms has been of increasing recent interest as a key to metazoan systems biology (Bonneau, 2008; Long et al ., 2008), particularly as genetic misregulation is a major cause of human disease. One means of discovering regulatory modules is the analysis of gene expression data, since a consequence of transcriptional co-regulation is co-expression. While a wealth of assays has also been developed to explore the transcriptional regulatory network under specific experimental conditions, regulatory module prediction from microarray data is a widely studied problem that remains unsurpassed for inference of general regulatory networks, particularly when additional genomic data sources are also integrated (Bussemaker et al ., 2007). Prediction of regulatory relationships has been particularly well-studied in unicellular systems, where regulation often occurs based on well-defined TF binding sites and discrete activation or repression of transcription (Beer and Tavazoie, 2004; Roth et al ., 1998). These assumptions have led to the current motif discovery paradigm, in which microarray data are clustered, each cluster’s promoter sequences tested for enriched motifs, and the resulting consensus sequences matched again known TF binding sites. In many cases, however, and particularly in more complex organisms, these assumptions no longer hold, and predicting regulatory modules from expression data becomes an increasingly difficult problem. It combines the challenges of biclustering [i.e. grouping together co-expressed genes and the subset of conditions where they are co-expressed (Kloster et al ., 2005; Tanay et al ., 2004)] with the difficulty of de novo motif discovery from DNA sequences, where regulatory motifs can be short, degenerate and frequently present without being functional (Hannenhalli, 2008). Note that this is distinct from the related tasks of inferring regulatory networks with prior knowledge of potential regulators or regulatory motifs (e.g. Kundaje et al ., 2008; Lemmens et al ., 2009; Segal et al ., 2003) or while omitting the process of motif discovery (e.g. Margolin et al ., 2006), both of which have also been intensively studied. Most existing approaches to regulatory module discovery break the biclustering and motif discovery tasks into separate stages: first, expression data is clustered or biclustered, and afterwards, each cluster is analyzed for enrichment of sequence motifs (Elemento et al ., 2007). To discover regulatory modules most effectively, though, it would be natural to perform both tasks at the same time, discovering clusters of genes that are both co-expressed and enriched for regulatory motifs. Recent work (Halperin et al ., 2009; Reiss et al ., 2006) has indeed confirmed the intuition that regulatory module discovery by simultaneous analysis of expression and sequence data can be extremely effective, but this has neither been developed to incorporate heterogeneous data integration, nor has it been scaled for application to complex metazoan genomes. Here, we describe a Combinatorial Algorithm for Expression and Sequence-based Cluster Extraction (COALESCE), which allows the discovery of regulatory motifs and modules from large collections of genomic data (Fig. 1). COALESCE takes advantage of Bayesian integration of multiple data types (primarily expression data) on a large scale (Huttenhower and Troyanskaya, 2008) to predict co-expressed gene modules, the conditions under which they are co-regulated, and the consensus binding motifs responsible for their regulation. The algorithm is practical for use with complex metazoan genomes ( > 25 000 genes), analyzes extremely large expression data collections ( > 15 000 conditions), can explicitly model dependencies between related gene expression conditions (e.g. points in a time course) and can integrate heterogeneous supporting data types in order to improve predictions (nucleosome positioning and evolutionary conservation are specifically demonstrated below). An implementation of COALESCE (including C++ source code) is provided as part of the Sleipnir software package at .princeton.edu/sleipnir, and a web interface is available at http:// function.princeton.edu/coalesce. We have validated COALESCE’s ability to discover functionally relevant biclusters and transcriptional motifs in synthetic data and in Saccharomyces cerevisiae , demonstrating improvements over previous methods in both expression biclustering and binding site prediction. We provide further evaluation of TF target predictions using the Yeastract ( S.cerevisiae ; Teixeira et al ., 2006) and RegulonDB ( E.Coli ; Gama- Castro et al ., 2008) motif databases and results including regulatory modules for Caenorhabditis elegans , Drosophila melanogaster , Mus musculus and Homo sapiens ...

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... Figure 1; it is summarized in pseudocode in Supplementary Text 1 and described in more detail below. COALESCE receives as input a standard genes-by-conditions expression matrix, DNA sequences for each gene in the regions of interest (e.g. upstream and/or downstream of the coding region), and four parameters: a k -mer length k , maximum P -value cutoffs p e and p m for expression condition and motif significance, respectively, and a minimum probability cutoff p g for inclusion of genes in modules. Each module is then computed beginning with an initial seed of the two genes maximally correlated across all expression conditions. Three steps are then iterated to modify the module until it converges: selection of significant expression conditions, selection of significant motifs and inclusion of probable genes. An expression condition is considered to be significant (and thus included in the module) if the distribution of expression values for genes currently in the module differs below threshhold p e from the genomic background (based on a standard Z -test). Similarly, a motif is significant if its frequency in gene sequences currently in the module differs below threshhold p m from background (based on a Z -test modified to use Cohen’s d ; Supplementary Text 1). Based on these selected features (significant conditions and motifs), each gene’s probability P ( g ∈ G | C , M ) of inclusion in the developing module is calculated using Bayesian data integration of P ( C | g ∈ G ), observed from the expression data, P ( M | g ∈ G ), observed from the sequence data and P ( g ∈ G ), a prior used to stabilize module convergence. Genes above probability p g are included and those below are excluded. When the module converges to a final set of conditions C , motifs M and genes G , its mean expression values and motif frequencies are subtracted from the underlying data and the process is begun again with a new pair of seed genes. C++ source code for the algorithm is available at and a detailed description including pseudocode can be found in Supplementary Text 1. Integration of additional data types modifies the algorithm only minimally and is discussed below. All significance tests involving P -values are Bonferroni corrected for multiple hypotheses. For all experiments in this manuscript, P -value threshholds were fixed at 0.05, probability threshholds at 0.95 and k = 7. 2.1.1 Motifs and DNA sequences COALESCE considers three types of motifs. The pseudocode above describes simple k -mers, each a string of k characters drawn from the alphabet {A, C, G, T}. Our implementation also considers reverse complement pairs (RCs) and probabilistic suffix trees (PSTs) in an equivalent manner. An RC is the equally weighted union of a k -mer and its reverse complement. A PST is the union of two or more arbitrary k -mers and RCs in a weighted (probabilistic) manner; such a structure can be constructed and matched against DNA sequence rapidly at runtime (Pavesi et al ., 2004). Briefly, just as a Position Weight Matrix (PWM) or Position Specific Score Matrix (PSSM) contains a single column per base to be matched, a PST contains a single node in a tree for each base. A PST thus has some depth equivalent to the length of a PWM/PSSM, and the maximal length match against some sequence is thus the depth or the length of the sequence, whichever is shorter. Initially, all possible k -mers and RCs are considered, but no PSTs. During each runtime iteration, a new PST is constructed for any pair of existing motifs m and m for which (i) Z -score ( M m , M m ) is small and (ii) the minimum edit distance between m and m is small (experiments here used gap penalty 1, mismatch penalty 2.1 and threshhold 2.5). Each PST so constructed is treated identically to k -mers and RCs with respect to frequency calculations etc. in all future iterations, subsequent to calculation of gene- specific scores M g , m . For a PST p with depth | p | , maximum length match | p [ s , i ] | for some sequence s beginning at offset i and probability p [ s , i ] of specifically matching position i , these are calculated ...