Combinatorial epigenetic patterns as quantitative predictors of chromatin biology
© Cieślik and Bekiranov; licensee BioMed Central Ltd. 2014
Received: 2 July 2013
Accepted: 15 January 2014
Published: 28 January 2014
Chromatin immunoprecipitation followed by deep sequencing (ChIP-seq) is the most widely used method for characterizing the epigenetic states of chromatin on a genomic scale. With the recent availability of large genome-wide data sets, often comprising several epigenetic marks, novel approaches are required to explore functionally relevant interactions between histone modifications. Computational discovery of "chromatin states" defined by such combinatorial interactions enabled descriptive annotations of genomes, but more quantitative approaches are needed to progress towards predictive models.
We propose non-negative matrix factorization (NMF) as a new unsupervised method to discover combinatorial patterns of epigenetic marks that frequently co-occur in subsets of genomic regions. We show that this small set of combinatorial "codes" can be effectively displayed and interpreted. NMF codes enable dimensionality reduction and have desirable statistical properties for regression and classification tasks. We demonstrate the utility of codes in the quantitative prediction of Pol2-binding and the discrimination between Pol2-bound promoters and enhancers. Finally, we show that specific codes can be linked to molecular pathways and targets of pluripotency genes during differentiation.
We have introduced and evaluated a new computational approach to represent combinatorial patterns of epigenetic marks as quantitative variables suitable for predictive modeling and supervised machine learning. To foster widespread adoption of this method we make it available as an open-source software-package – epicode athttps://github.com/mcieslik-mctp/epicode.
Biochemical and structural properties of chromatin are implicated in the function and maintenance of genomes (e.g.). Chromatin immunoprecipitation followed by deep sequencing (ChIP-seq) is becoming the standard method for the genome-wide mapping of histone modifications and transcription factor (TF) binding sites.
The analysis and interpretation of ChIP-seq data sets is a difficult task. Most of the existing analysis tools are focused on the delineation of enriched sites from a single sample with optional "input control". For histone modifications this task becomes more challenging as their enrichments are often weaker and less localized. A number of groups have extended the peak-calling approach to identify broad domains[5, 6] or analytically represent ChIP-signals beyond read-counts. In order to link epigenetic marks to biological functions and processes, peak calling has also been adapted to paired experimental designs. Individually, each epigenetic mark provides some data towards understanding the structure and biochemistry of the underlying genome. However, it has been argued that the cooperative action of multiple histone modifications, variants, and TFs is functionally most informative[9, 10]. Unfortunately, none of the standard peak-based method deals with multiple marks and the reconciliation of several sets of peaks is an added challenge[11–13].
An alternative, and orthogonal, approach is to integrate individual histone modification maps to discover latent relationships between epigenetic marks. Broadly, these approaches fall into two categories: genome-wide segmentation and locus-based clustering. For example, ChromHMM and Segway[14, 15] partition the genome into epigenetically-similar regions and have been able to reliably associate chromatin profiles with transcription start sites and putative enhancer regions. Similarly, clustering approaches, such as ChromaSig, attempt to identify loci with globally congruent "chromatin signatures". Although the two types of methods differ greatly in the statistical modeling of data, they make the general assumption that a small set of "chromatin states" is sufficient to annotate the genome. Experimental results suggests that these models are too restricted to capture the genome-wide variability of chromatin patterns. The number of global "chromatin states" has been estimated to be in the several hundreds even when only a small set of marks is used to define each pattern.
Both clustering and segmentation results in the hard assignment of a single "chromatin signature" to each locus. This allows for certain types of functional enrichment analyses, but is not, in general, conductive to quantitatively link "chromatin state" to genome biology. Regression and other supervised machine learning technique are needed to move from descriptive annotations to quantitative and predictive models. In most of these approaches, levels of epigenetic signals are linked to a biologically important readout (e.g. transcript level[21, 22] or polymerase occupancy). Unfortunately, histone modifications tend to be highly correlated, which makes it difficult to asses the relative importance of the variables (marks). Since these problems are further exacerbated during stepwise regression, it is difficult to explain how, in terms of direction and strength, combinatorial interactions between marks are linked to the biological readout.
Here, we describe a novel method based on non-negative matrix factorization (NMF) to discover combinatorial patterns of epigenetic marks from integrated epigenetic data sets. Locus-specific weights of these mark co-occurrence patterns are used as quantitative variables, suitable for regression and supervised machine learning. We are able to demonstrate that basis patterns are quantitative predictors of biochemical activity, discriminate between classes of genomic regions, and are associated with molecular pathways. Hence we propose to call these patterns bona fide epigenetic "codes". In the remaining sections we describe the basic algorithm and its extensions (Formulation), investigate important statistical properties of basis patterns (Properties), and show their utility in regression, classification, and gene set analysis (Case Studies). A reference implementation of the method is available athttps://github.com/mcieslik-mctp/epicode and in (Additional file1).
The basic NMF procedure randomly initializes matrices W and H and minimizes the reconstruction error V-W H – difference between the actual and model output values of the epigenetic factor levels – by updating W and H using a projected gradient algorithm. This algorithm finds only local optima that depend on the starting conditions, analogously to the common K-means algorithm. For the initialization of the NMF algorithm we propose to use the deterministic non-negative double singular value decomposition (NNDSVD) technique. The NMF algorithm depends on a single parameter c - the rank of the factor matrices, which is the expected number of basis patterns. As with most unsupervised algorithms the choice of c is not straightforward. A large c results in sparse codes and few combinatorial interactions. Sparsity of the output is a prominent feature of NMF, but is further enhanced by additional constraints. In our implementation the constraints are applied to the matrix H and thus favor combinatorial patterns of only few histone marks. To illustrate the sensitivity of NMF to initialization and the relative performance of NNDSVD for epigenomic data we compared the default factorization with a random initialization approach (Figure2C). We found that this approach has the smallest reconstruction error (the objective function of NMF) and largest sparsity. Further, randomly initialized solutions tend to have a smaller reconstruction error if their H matrix is more similar to the NNDSVD solution (Additional file2: Figure S1). Together, these results show that NMF output is sensitive to initialization. However, the NNDSVD approach yields a solution that outperforms even a large number of random runs.
We develop three complementary approaches which apply the NMF algorithm on epigenomic profile data for distinct tasks of prediction, classification and association: (1) absolute, (2) discriminatory and (3) differential (Figure1). As shown in (Figure1A-B), the absolute algorithm performs NMF on the quantified levels of epigenetic marks at one annotation class (e.g., promoters). The discriminatory algorithm performs NMF on quantified levels of the same set of epigenetic marks at two classes of loci (e.g., promoters and enhancers) (Figure1C). As depicted in Figure1D, the differential algorithm performs NMF on normalized differential epigenetic levels – gains and losses – between two cell lines or cell states (e.g. stem cells vs differentiated cells).
To construct V from genome-wide maps of multiple histone modifications, we individually quantify and scale "absolute" signals of epigenetic marks at each queried locus (Figure1A top). Each row of the input matrix V represents scaled levels of epigenetic marks within a single locus. Some form of column normalization, or scaling, is usually necessary to account for the differences in magnitudes and dynamic ranges of histone modifications, and to reveal the patterns of interest. By default we use a sigmoid function to normalize all signals to 0 to 1 range as this has been shown to accelerate and improve NMF[36, 37].
Different classes of genomic regions, such as promoters and enhancers, show discriminatory epigenetic patterns. Regulatory mechanism operating at distinct classes often have a unique epigenetic component, such as the activity of a specific chromatin remodeling complex (e.g.). Thus, it is reasonable to assume that specific or enriched combinatorial patterns could discriminate between classes of sites. To identify such specific codes we propose the "discriminatory" algorithm (Figure1C). In this mode we first apply the "absolute" algorithm at each set of k genomic regions separately and next reconstruct a single weight matrix. Specifically, we partition input matrix V into k sub-matrices V i , each of these matrices is independently factored V i = W i H i , next we concatenate the k H i matrices into a single matrix H. Finally the matrix W is obtained using non-negative least squares from matrices V and H. Intuitively, we first discover optimal codes for each class of genomic regions and next allow all codes to be used to describe the "chromatin signature" at each locus regardless of its class. If the epigenetic patterns at different classes of sites have the same latent structure, the discovered class-specific codes will be very similar or interchangeable. In both cases codes discovered for one class of sites will be useful to encode the epigenetic features of other classes of loci. On the other hand, if the latent epigenetic structure of the different region types is dissimilar, some of the discovered codes will be discriminatory and not useful to encode epigenetic features of other classes.
Histone modification levels are dynamic and are due to net changes in the activity of modifying enzymes called "writers" and "erasers". Relative to a second sample a locus might show "gain", "loss", or, if it is sufficiently large, both "gain" and "loss" of a histone mark. Although chromatin remodelling complexes often have multiple catalytic activities and substrate cross-reactivities, simultaneous changes to multiple marks at a subset of loci might suggest a shared regulatory mechanisms or function. Therefore, we define basis patterns in the dynamic context as coordinated changes to histone modification levels. Analogously to the "absolute" and "discriminatory" cases, in "differential" mode (Figure1D, Figure1A bottom), mark levels are quantified within each query locus. However, because paired samples are typically sequenced to different depths, the mapped read counts are normalized using the DESeq algorithm. Within each locus absolute signals are transformed into differential "gain-loss" scores (Figure1A bottom). This approach results in twice the number of columns in V –two for each epigenetic mark. Histone modification levels are spatially auto-correlated. In "absolute" and "discriminatory" modes we rely on this property to calculate average enrichment levels within a possibly large locus. Much less is known about the auto-correlation of differential (subtracted) levels. Therefore we divide each locus into adjustable windows (default 100 bp). For each window paired ChIP signals are subtracted resulting in a net "gain" or "loss" of a histone modification. We obtain the final per-locus "gain" score by summing the windows with a net "gain", and the "loss" score by summing windows with a net "loss". If the differential signal is strongly auto-correlated most windows within a locus will show "gains" or "losses" and the whole locus will show only "gain" or "loss". A simple example shows that this is not always the case. If a peak is broadened it results in "losses" at the summit but "gains" at the slopes. Integrating over windows with sizes in the range of ChIP-seq resolution (hundereds of base pairs) allows us to differentiate these two cases. The per-locus columns are likewise scaled to the 0 – 1 range before entering the NMF method. The output is similar (Figure1D): H contains basis "gain-loss" patterns W contains the weights associated with each pattern at each locus. The difference is that now rows in the matrix H correspond to patterns of correlated changes – not patterns of absolute levels.
To illustrate important properties of NMF when applied to epigenomic data we ran the "absolute" algorithm on a relatively simple publicly available ChIP-seq data set. We analyzed 7 histone modifications and one histone variant (H2A.Z) mapped by the ENCODE project in the A549 adenocarcinomic alveolar basal epithelial cell line. We focused on regions of TSS-proximal gene bodies since they contain epigenetic traces of transcription initiation and elongation, and prominently feature all probed marks.
To illustrate the dependence of c on the factorization we ran the "absolute" algorithm with all default parameters and scanned c values from 3 to 8. First, we quantified the average sparsity of matrices H and W using Hoyer’s formula (Figure2A). Hoyer’s sparsity takes on values between 0 (all vector elements equal) and 1 (single non-zero component). We observed that the sparsity of H increases linearly up to a knee-point at c = 6, whereas the sparsity of W is much lower and has a minimum at c = 6. This means that if c is (too) high the H matrix will contain many rows that have only a single mark with positive values. Matrix W contains weights that optimally use all codes to reconstruct the observed "chromatin signature" at each locus (rows of V). The relatively constant sparsity of W suggests that at most loci multiple basis patterns are used and superimposed (Figure2A). An empirical property of NMF is that the higher-rank (large c) solutions are largely consistent with the lower-rank (small c) solutions. For example, in one study involving microarray clustering, higher resolution clusters are in general subsets of lower resolution clusters. To illustrate this for basis patterns, we visualized matrices H for c = (3…6) (Figure2B). This showed that codes obtained for higher c values are, in general terms, obtained by splitting one of the lower resolution codes into two. For example code 1 at c = 4 is split into code 1 and 5 at c = 5 while the latter is further split into code 5 and 6 at c = 6. This suggests that for NMF specifying a c which is (too) small yields a solution which is consistent with a higher (ostensibly correct) rank factorization. This type of stability is particularly useful when analyzing the hierarchical dependencies between histone modifications. The lower-bound of c is determined by the diversity of histone modifications.
Another important feature of the NMF algorithm in absolute mode is the similarity of the H matrices across cell lines. In (Additional file4: Figure S3) we show the H matrices from human embryonic stem (ES) cells (H1ESCs), myoblasts (HSMM blasts), and myotubes (HSMM tubes) derived from a set of 9 common epigenetic marks with c set to 6. In general, rows of each H matrix are in no particular order and equivalent codes obtained from two or more data sets have to be found using (for example) the Munkres assignment algorithm. The NNDSVD approach initializes rows of matrix H using SVD eigenvectors and indirectly ranks basis patterns by their variance. This order is likely to be similar between different cell lines. We observe that the matrices are essentially the same for myotubes and myoblasts and only slightly different for H1ESCs. This suggest that the co-regulation of epigenetic marks is not drastically changing during differentiation. To get further insight on the complexity epigenetic patterns in terms of combinations of the H basis patterns we applied K-means clustering to the W matrix (Additional file5: Figure S4). We clustered the W weight matrix corresponding to the c = 6 factorization from (Figure2B). The majority of clusters (8) is dominated by at most 2 of the 6 codes, which means that for the majority of genes a simple weighted sum of two codes from (rows from H) is (globally) optimal to reconstruct relative levels of epigenetic marks. This should be contrasted with the hypothetical case, where most loci have highly variable and unique code weight patterns and the W matrix displays a second level of combinatorial complexity.
Regression Pol2 binding
In our formulation epigenetic patterns are quantitative i.e. each locus has a specific non-negative weight for each of the basis patterns. This enables us to quantitatively link the weights of codes to functional or biochemical properties of the underlying loci. To illustrate this we tried to predict levels of Pol2 binding at promoters of protein-coding genes in human embryonic stem cells (H1ESC). We compared ridge regression models, which either included basis patterns (code-based) or individual histone marks (mark-based) as independent variables. Levels of histone modifications and Pol2 were calculated within 5k kbp window centered at the TSS.
Parameters and performance of mark-based and code-based ridge regression models
To differentiate active transcription from promoter-proximal Pol2 pausing we assigned each gene to the basis pattern with the highest weight (see Formulation) and plotted genes from select codes in the gene expression – Pol2 level plane. This projection revealed that genes from code 6, featuring most prominently high levels of H3K9ac and H3K27ac, have all moderate to high levels of Pol2. In contrast, genes associated with code 2, which is dominated by H3K27me3, have uniformly low levels of Pol2. Remarkably, high levels of these activating acetylations are not significantly correlated with gene expression, while H3K27 tri-methylated genes tend to be expressed at a low level. This suggests that high levels of H3K27me3 are incompatible with Pol2 binding, and that high levels of Pol2 are associated with K3K9ac and H3K27ac at gene promoters but not necessarily high gene expression.
In this example we have shown that quantitative weights of the "absolute" basis patterns can be used instead of individual histone modifications levels as independent variables in the prediction of Pol2 binding. The code-based model had equal performance to the mark-based regression, but included a smaller number of independent variables and alleviated problems of multicollinearity. Hard assignment of genes to codes allowed visualization of the regulatory differences in Pol2-recruitment and active transcription.
Classification Pol2-bound enhancers vs. promoters
Polymerase II (Pol2) is known to localize both at promoters and within intragenic regions. In H1ESC preferential association of Pol2 was observed for promoter-distal sites enriched for p300, H3K4me1, and H3K27ac. Genes in the vicinity of these regulatory regions showed increased expression levels, while genes that were activated during differentiation gained Pol2 at close enhancers. In differentiated cells Pol2 levels at enhancers have been shown to change in response to stimuli and to be associated with H3K4me3 and bidirectional transcription. These findings established that enhancers actively engaged in transcription are occupied by the polymerase. The chromatin patterns of this class of enhancers show relatively high levels of H3K4me3 and are more similar to patterns at promoters of protein coding genes. We decided to test whether Pol2-bound enhancers and Pol2-bound promoters can be distinguished based on levels and multivariate patterns of epigenetic modifications.
In the same line of human embryonic cells we divided Pol2-enriched regions into two classes. The promoter-proximal class was defined as 2 kbp regions centered on an Pol2 peak, that overlapped any GENCODE annotated TSS site. All remaining 2 kbp sites centered on an Pol2 peak were classified as promoter-distal. We performed the analysis using all promoter and enhancer regions, but found the classification was relatively trivial because the largest Pol2 peaks are preferentially associated with promoter regions. Thus, we challenged the classification algorithm by rerunning the analysis excluding the top 20 percent of peaks i.e. those with a very high p-value of 1e-25. First, we compared the overall distribution of histone modifications at the promoters and putative enhancers.
We found that some marks showed relatively similar levels (Additional file6: Figure S5). As expected we found substantial H3K4me3 levels at Pol2-bound putative enhancers. Strikingly, levels of H3K4me1 and H3K4me2, which are often associated with poised or active enhancers, were markedly higher in TSS-proximal sites. On the other hand, H3K27ac, which is associated with permissive chromatin, and H4K20me1/H3K79me2, which are associated with transcriptional elongation, had similar levels at both classes of sites. In agreement with recent discoveries, we found that a significant portion of intragenic Pol2 sites occurred within "poised" enhancers that were enriched for H3K27me3 (Additional file6: Figure S5). Notably, while there were some informative level differences, the distributions significantly overlapped for the majority of marks.
To discriminate enhancer from promoter regions we first built a series of logistic regression models. The simplest models ("zero-order" models) included only a single independent variable (i.e. the normalized level of a single histone modification). These zero-order correlations directly measure the shared variance between two variables, since they reflect the amount of variance in the binary outcome variable that is explained by a single continuous predictor. In addition a "multivariate" model was built that included levels of all marks as predictors. An analogous set of zero-order and multivariate models was built using NMF codes. This new set of models differed from the previous in that they used weights from the W matrix rather than levels of individual marks to perform the classification. We applied the "discriminatory" algorithm and discovered optimal codes for enhancers and promoters independently (Figure1C, Formulation). Intuitively, we attempt to identify codes that are useful to encode histone modification levels at enhancers, but not promoters (or vice versa). We combined all codes into matrix H and re-derived the weight matrix W. Therefore, weights for certain codes should discriminate between promoters and enhancers.
To assess the relative importance of independent variables in multivariate regression it is important not to rely only on regression coefficients. One approach is to compare the ranking and signs of variables from zero-order and multivariate models. We found that mark-based logistic regressions have incongruent slope estimates. For example beta coefficients of three marks change signs between the two models. Also the ranking of the beta coefficients are not even approximately maintained and do not track model AUCs (data not shown). In the mark-based case it was difficult to ascertain which histone modifications discriminate enhancers from promoters. In contrast regression on codes yields models that are easier to interpret. Specifically, codes with large zero-order coefficients were also relatively important in the multivariate model, which largely maintained the rank-order of variables (Additional file9: Figure S6). Also, codes with the largest multivariate coefficients consistently showed the best zero-order predictive performance (Figure5B). Several codes have very small zero-order coefficients and AUCs, but relatively large multivariate slopes. Likely, these codes are not important and could be dropped from the multivariate model.
Surprisingly, both enhancers and promoters, are associated with codes dominated by histone modifications associated with transcription elongation. At promoters this code is very sparse and contains non-zero values for H3K36me3, H4K20me1 (both high), and H3K79me2 (low). At putative enhancers the code is slightly different as it does not contain H3K79me2, but includes H3K9ac and H3K27ac at low levels. Recently it was shown that H3K79me2 is most enriched at 5’ ends of genes, slightly downstream of H3K4me3, but before the classic elongation associated mark H3K36me3. Thus, it is expected to occur at promoter proximal Pol2-bound regions. To the contrary, active enhancers are sometimes found in introns of transcribed genes. This dependency between active transcription and activation of enhancers in the gene body appears to be captured via code 7.
In total, these results suggest that the discovered basis patterns capture dependencies between marks that discriminate Pol2-bound enhancers or promoters. The factorization approach successfully de-correlated epigenetic marks, which resulted in an interpretable multivariate classification model. Further, the discovered codes are consistent with known epigenetic mechanisms and features that regulate Pol2-dependent transcription in pluripotent cells.
Gene set enrichment analysis
In the previous analysis we have compared "absolute" levels of histone modifications at multiple classes of loci to discover patterns of co-occurring marks that discriminate among them. Somewhat analogously, histone modification levels can be compared between two experimental conditions. Intuitively, the idea is that patterns of co-occurring changes to mark levels could be used to identify loci that are subjected to coordinated epigenetic regulation. Differentiation is a highly regulated process and specific reprogramming mechanisms could result in similar epigenetic changes at functionally related genes. In other words, genes that share combinatorial patterns of changes could have some common molecular functions or participate in related pathways.
Statistical association of epigenetic remodelling patterns and molecular pathways during myoblast differentiation
Pathway identifier in MSigDB
We have introduced a new computational technique to discover combinatorial patterns of histone modifications. At its core this method relies on non-negative matrix factorization (NMF) to separate the complex "chromatin signatures" at genomic loci into small basis patterns we refer to as codes. These simple parametrizations of the data reveal frequently co-occurring marks, which could potentially be read by multivalent chromatin complexes, or represent differential signatures of coordinated epigenetic reprogramming. Most importantly, the application of NMF results in dimensionality reduction and de-correlation, but maintains the quantitative aspect of epigenetic mark levels.
NMF is one among many matrix factorization algorithms. Results from alternative methods are different due to the difference in the imposed factorization constraints and objectives. Principal component analysis (PCA) constrains H to be a set of orthonormal vectors; vector quantization (VQ), which is equivalent to K-means, constrains W to contain vectors with one non-zero value; while NMF imposes that W and H are non-negative. These constraints result in fundamentally different outputs. PCA favors global reconstruction, which means that every element in V is reconstructed through complex cancellations of positive and negative values in W and H. PCA allows basis vectors (principal component, PC) in H to be ranked by importance. The reconstruction error increases when the least important PC is omitted, but the "coarse" global features of input data are preserved. On the other hand NMF basis vectors cannot be dropped, since it would result in the loss of important parts of (a subset of) the reconstructed vectors.
While PCA dimensions do not resemble any particular data point or combination of data points, NMF basis vectors can be readily interpreted as patterns of frequently co-occurring histone modifications. Only a small number of these codes is sufficient to reliably reconstruct the observed "chromatin signatures" at thousands of loci and, as shown by our analyses, to preserve, or even boost, biological information. Although with respect to the mean squared error (MSE) PCA is theoretically optimal for reconstruction, NMF can perform better for classification or recognition. In some sense NMF returns results that are in between PCA and VQ. In VQ each data point is locally approximated by a single cluster centroid, PCA uses all available components, while in NMF typically few, but not all, basis vectors are required to represent a single data point. If the goal is to assign loci to epigenomic states a form of clustering is preferred as cluster centroids are often intuitively understood. PCA will perform best if the number of histone modifications is large but one desires only few basis vectors (principal components). As illustrated in this paper NMF basis vectors perform well in supervised machine learning. An alternative and analogous approach, known as principal components regression, is to use weights of principal components instead of weights of NMF basis vectors. An advantage of NMF is the physical interpretability of the its basis vectors. Conversely, the optimal reconstruction error of PCA might be important for very simple models.
We have shown that NMF applied to epigenetic marks yield sparse codes with an important nesting property. Further we have demonstrated the benefits of using codes over individual marks in predictive modeling of Pol2-binding. In particular, dimensions obtained from NMF are less correlated than the individual marks, and problems resulting from multicollinearity are alleviated. In addition we developed two variants of the basic algorithm which extended its applicability to multiple classes of genomic regions and paired experimental samples. We have shown the excellent performance of codes for the classification of Pol2-bound enhancers and promoters. The most discriminatory codes highlighted the context-dependence of H2A.Z, which is consistent with current knowledge on the role of this histone variant in the regulation of transcription in ES cells. To showcase the algorithm for paired experimental samples, we analyzed chromatin remodeling during myogenesis. We established that genes from pathways involved in protein synthesis (anabolism), the cell cycle, and signaling from G protein-coupled receptors show unique patterns of chromatin activation or silencing. Finally, we were able to show that target genes of pluripotency factors are also associated with the same chromatin remodeling pattern.
In summary, we have introduced a general NMF-based approach to represent combinatorial patterns of epigenetic marks as quantitative variables. We have shown the utility of this representation for predictive modeling, supervised machine learning and gene set analysis. Hence, this technique is complementary to more descriptive methods aimed at "chromatin pattern" discovery such as genome-wide segmentation and clustering.
All three variants of the presented NMF-based algorithm are provided as the epicode open-source software package. The software provides all that is required to discover basis patterns from aligned sequencing data and sets of user-provided reference regions. Epicode provides three modes of operation: "absolute" and "discriminatory" and "differential". In the "absolute" mode the user is expected to provide a set of genomic loci (in a UCSC Browser Extensible Data (BED) file) of interest and aligned sequencing data for a single experimental condition (in Binary sequence Alignment/Map (BAM) files). The regions can be global such as promoters of protein coding genes or specific subsets e.g. "putative enhancers of expressed miRNAs". The input sequencing data are typically histone modifications mapped in a single cell line and experimental condition. In the "discriminatory" mode the user provides two sets of loci e.g. enhancers and promoters. The "differential" mode requires a single set of genomic regions, but two sets of sequencing data, which correspond to the same marks mapped in two conditions or cell lines.
We have implemented epicode as a Python 2.7 software package, and also provide a command-line executable. The code should run on UNIX-like operating systems and has been tested on Linux (Arch, RHEL 6). Dependencies: several Python packages are required by epicode, including NumPy, SciPy, scikit-learn, and pysam. Input formats: the tool is designed to work with standard file formats. Reference genomic sites are expected in the BED6+ file format. Sequencing data is read from coordinate sorted BAM files. Output: Results are reported in a machine-readable tab-delimited file format. Scripts in the R language are provided to generate publication quality figures from one of the output files. The current implementation of Epicode is IO-bound meaning that the majority of time is spent in reading the BAM files. The factorization takes typically less than 5 minutes on a single Intel(R) Xeon(R) CPU E5-1620 0 3.60 GHz core. Reading the BAM files takes up-to 30 minutes using four cores and strongly depends on the hard-drive speed. 6. URL and license for software should be mentioned in manuscript. The software is freely available (MIT license) athttps://github.com/mcieslik-mctp/epicode.
Throughout the manuscript epicode has been used with all default parameters (as of version 1.0), with the exception of the "differential" algorithm for which a step of 50 was chosen.
Here, u is the 95th percentile of the values in vector x and is the scaled vector. The scaling is done before factorization. In "differential" mode enrichment signals (Figure1D) are windowed and corrected for sequencing-depth (i.e., normalized) using the provided Python implementation of the DESeq algorithm. After subtraction the window scores are summed to overall "gain" (positive integral) and "loss" scores (negative integral) for each locus. "Gain-loss" scores are likewise sigmoid scaled.
Associations of functional gene sets with mark levels and basis pattern weights were done using the random-set method. (an implementation of the random-set method is included in the source-code distribution of epicode). Annotations for Ensembl genes were obtained from MSigDB (msigdb.v3.1.entrez.gmt) and re-mapped from Entrez gene ids (EG) onto GENCODE V14 genes using identifier maps (EG to ENSG) from Ensembl (current as of Apr 20th 2013). Association p-values (obtained from the random-set method) were FDR-corrected (BH-method) over the whole 8513 terms in the MSigDB database (which is more stringent), but we reported on associations from different classes of MSigDB gene sets individually, since different types of gene sets have different distributions of association p-values (experimental gene sets are typically more closely correlated than literature-derived).
All raw sequencing data used in the case studies were downloaded from the ENCODE project website as FASTQ files. We included all available histone modification data sets for four cell lines A549, H1ESC, HSMM, and HSMMT, with the exception of H3K36me3 in A549 because of poor reproducibility of this dataset between replicates. Additional Pol2 (ChIP-seq), expression (RNA-seq), and DNase accessibility (Digital Genomic Footprinting (DGF) and DNase-seq) data sets were downloaded for H1ESC. In the case of histone ChIP-seq and DNase accessibility, reads from multiple replicates (BAM files) were combined into a single BAM file using samtools merge. List of all analyzed files in included in in Additional file12.
We used Bowtie2 with all default settings and indexes for the HG19 genome build (ftp://ftp.ccb.jhu.edu/pub/data/bowtie2_indexes/hg19.zip) for all alignments. To count exonic RNA-seq reads we used the HTSeq tool with default settings on the GENCODE-provided General Transfer Format (GTF) file. To estimate expresssion levels, read-counts for each gene were normalized by total exon length, averaged over replicate samples, and finally scaled to the 0 to 1 range using the same sigmoid function.
Supervised machine learning
Predictive modeling (ridge regression, penalized logistic regression) was done using scikit-learn. All model parameters, including penalty type ('l1’ or 'l2’) and regularization strength C (1, 2, 5, 10, 50, 100, 500), were trained using 10-fold cross-validation. All cross-validated models used 'l2’ penalty and C = 1. Models were evaluated on 20 percent, using scripts included in scikit-learn, on hold-out data which was never used for training or cross-validation.
Evaluation of initialization methods
Three initialization methods were evaluated NNDSVD, random, and randomized NNDSVD (NNDSVDar). In the random initialization both W and H matrices are filled with random uniform numbers (0 to 1 range). In the NNDSVDar only zero elements (after NNDSVD) are set to small (close to 0) random numbers. The NNDSVD approach is deterministic and is described in detail in. To evaluate similarity between two H matrices we use the Munkres algorithm to establish the minimum cost assignment. To find this minimum it is necessary to pair the most similar rows. Similarity of a pair (cost) is evaluated based on the Euclidean distance. The minimum-cost assignment of basis vector pairs is found using the Munkres algorithmi.e. a set of pairs is found that minimizes the global cost. We calculate sparsity using Hoyer’s formula.
Work was supported by the University of Virginia start-up of SB.
- Kharchenko PV, Alekseyenko AA, Schwartz YB, Minoda A, Riddle NC, Ernst J, Sabo PJ, Larschan E, Gorchakov AA, Gu T, Linder-Basso D, Plachetka A, Shanower G, Tolstorukov MY, Luquette LJ, Xi R, Jung YL, Park RW, Bishop EP, Canfield TK, Sandstrom R, Thurman RE, MacAlpine DM, Stamatoyannopoulos JA, Kellis M, Elgin SCR, Kuroda MI, Pirrotta V, Karpen GH, Park PJ: Comprehensive analysis of the chromatin landscape in Drosophila melanogaster. Nature. 2011, 471 (7339): 480-485. 10.1038/nature09725. [http://dx.doi.org/10.1038/nature09725],PubMed CentralPubMedView ArticleGoogle Scholar
- Mikkelsen TS, Ku M, Jaffe DB, Issac B, Lieberman E, Giannoukos G, Alvarez P, Brockman W, Kim TK, Koche RP, Lee W, Mendenhall E, O’Donovan A, Presser A, Russ C, Xie X, Meissner A, Wernig M, Jaenisch R, Nusbaum C, Lander ES, Bernstein BE: Genome-wide maps of chromatin state in pluripotent and lineage-committed cells. Nature. 2007, 448 (7153): 553-560. 10.1038/nature06008. [PMID: 17603471 PMCID: 2921165]PubMed CentralPubMedView ArticleGoogle Scholar
- Landt SG, Marinov GK, Kundaje A, Kheradpour P, Pauli F, Batzoglou S, Bernstein BE, Bickel P, Brown JB, Cayting P, Chen Y, DeSalvo G, Epstein C, Fisher-Aylor KI, Euskirchen G, Gerstein M, Gertz J, Hartemink AJ, Hoffman MM, Iyer VR, Jung YL, Karmakar S, Kellis M, Kharchenko PV, Li Q, Liu T, Liu XS, Ma L, Milosavljevic A, Myers RM, et al: ChIP-seq guidelines and practices of the ENCODE and modENCODE consortia. Genome Res. 2012, 22 (9): 1813-1831. 10.1101/gr.136184.111. [http://genome.cshlp.org/content/22/9/1813],PubMed CentralPubMedView ArticleGoogle Scholar
- Wilbanks EG, Facciotti MT: Evaluation of algorithm performance in ChIP-Seq peak detection. PLoS ONE. 2010, 5 (7): e11471-10.1371/journal.pone.0011471. [http://dx.doi.org/10.1371/journal.pone.0011471],PubMed CentralPubMedView ArticleGoogle Scholar
- Zang C, Schones DE, Zeng C, Cui K, Zhao K, Peng W: A clustering approach for identification of enriched domains from histone modification ChIP-Seq data. Bioinformatics. 2009, 25 (15): 1952-1958. 10.1093/bioinformatics/btp340. [PMID: 19505939]PubMed CentralPubMedView ArticleGoogle Scholar
- Song Q, Smith A: Identifying dispersed epigenomic domains from ChIP-Seq data. Bioinformatics. 2011, 27 (6): 870-10.1093/bioinformatics/btr030.PubMed CentralPubMedView ArticleGoogle Scholar
- Hoang SA, Xu X, Bekiranov S: Quantification of histone modification ChIP-seq enrichment for data mining and machine learning applications. BMC Res Notes. 2011, 4: 288-10.1186/1756-0500-4-288. [PMID: 21834981]PubMed CentralPubMedView ArticleGoogle Scholar
- Xu H, Wei CL, Lin F, Sung WK: An HMM approach to genome-wide identification of differential histone modification sites from ChIP-seq data. Bioinformatics. 2008, 24 (20): 2344-2349. 10.1093/bioinformatics/btn402. [http://bioinformatics.oxfordjournals.org/content/24/20/2344.abstract],PubMedView ArticleGoogle Scholar
- Strahl BD, Allis CD: The language of covalent histone modifications. Nature. 2000, 403 (6765): 41-45. 10.1038/47412. [http://www.nature.com/nature/journal/v403/n6765/full/403041a0.html],PubMedView ArticleGoogle Scholar
- Wang Z, Zang C, Rosenfeld JA, Schones DE, Barski A, Cuddapah S, Cui K, Roh TY, Peng W, Zhang MQ, Zhao K: Combinatorial patterns of histone acetylations and methylations in the human genome. Nature Genet. 2008, 40 (7): 897-903. 10.1038/ng.154. [PMID: 18552846]PubMed CentralPubMedView ArticleGoogle Scholar
- Ye T, Krebs AR, Choukrallah MA, Keime C, Plewniak F, Davidson I, Tora L: seqMINER: an integrated ChIP-seq data interpretation platform. Nucleic Acids Res. 2011, 39 (6): e35-e35. 10.1093/nar/gkq1287. [http://nar.oxfordjournals.org/content/39/6/e35],PubMed CentralPubMedView ArticleGoogle Scholar
- Liu Y, Han JDJ: Application of Bayesian networks on large-scale biological data. Front Biol. 2010, 5 (2): 98-104. 10.1007/s11515-010-0023-8. [http://link.springer.com/article/10.1007/s11515-010-0023-8],View ArticleGoogle Scholar
- Santoni FA: EMdeCODE: a novel algorithm capable of reading words of epigenetic code to predict enhancers and retroviral integration sites and to identify H3R2me1 as a distinctive mark of coding versus non-coding genes. Nucleic Acids Res. 2013, 41 (3): e48-e48. 10.1093/nar/gks1214. [http://nar.oxfordjournals.org/content/41/3/e48] [PMID: 23234700],PubMed CentralPubMedView ArticleGoogle Scholar
- Ernst J, Kellis M: ChromHMM: automating chromatin-state discovery and characterization. Nature Methods. 2012, 9 (3): 215-216. 10.1038/nmeth.1906. [http://www.nature.com/nmeth/journal/v9/n3/abs/nmeth.1906.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Hoffman MM, Buske OJ, Bilmes JA, Noble WS: Segway: simultaneous segmentation of multiple functional genomics data sets with heterogeneous patterns of missing data. 2011, [http://noble.gs.washington.edu/proj/segway/manuscript/temposegment.nips09.hoffman.pdf],Google Scholar
- Hoffman MM, Buske OJ, Wang J, Weng Z, Bilmes JA, Noble WS: Unsupervised pattern discovery in human chromatin structure through genomic segmentation. Nature Methods. 2012, 9 (5): 473-476. 10.1038/nmeth.1937. [http://www.nature.com/nmeth/journal/v9/n5/full/nmeth.1937.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Hon G, Ren B, Wang W: ChromaSig: a probabilistic approach to finding common chromatin signatures in the human genome. PLoS Comput Biol. 2008, 4 (10): e1000201-10.1371/journal.pcbi.1000201. [http://dx.doi.org/10.1371/journal.pcbi.1000201],PubMed CentralPubMedView ArticleGoogle Scholar
- Ucar D, Hu Q, Tan K: Combinatorial chromatin modification patterns in the human genome revealed by subspace clustering. Nucleic Acids Res. 2011, 39 (10): 4063-4075. 10.1093/nar/gkr016. [http://nar.oxfordjournals.org/content/39/10/4063],PubMed CentralPubMedView ArticleGoogle Scholar
- Ernst J, Kheradpour P, Mikkelsen TS, Shoresh N, Ward LD, Epstein CB, Zhang X, Wang L, Issner R, Coyne M, Ku M, Durham T, Kellis M, Bernstein BE: Mapping and analysis of chromatin state dynamics in nine human cell types. Nature. 2011, 473 (7345): 43-49. 10.1038/nature09906. [http://www.nature.com/nature/journal/v473/n7345/full/nature09906.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Chen Y, Jørgensen M, Kolde R, Zhao X, Parker B, Valen E, Wen J, Sandelin A: Prediction of RNA Polymerase II recruitment, elongation and stalling from histone modification data. BMC Genomics. 2011, 12: 544-10.1186/1471-2164-12-544. [http://www.biomedcentral.com/1471-2164/12/544/abstract] [PMID: 22047616],PubMed CentralPubMedView ArticleGoogle Scholar
- Xu X, Hoang S, Mayo MW, Bekiranov S: Application of machine learning methods to histone methylation ChIP-Seq data reveals H4R3me2 globally represses gene expression. BMC Bioinformatics. 2010, 11: 396-[http://www.biomedcentral.com/1471-2105/11/396/abstract] [PMID: 20653935],PubMed CentralPubMedGoogle Scholar
- Karlić R, Chung HR, Lasserre J, Vlahoviček K, Vingron M: Histone modification levels are predictive for gene expression. Proc Natl Acad Sci. 2010, 107 (7): 2926-2931. 10.1073/pnas.0909344107. [http://www.pnas.org/content/107/7/2926],PubMed CentralPubMedView ArticleGoogle Scholar
- Nathans LL, Oswald FL, Nimon K: Interpreting multiple linear regression: a guidebook of variable importance. Pract Assessment, Res Eval. 2012, 17 (9): 2-[http://pareonline.net/pdf/v17n9.pdf],Google Scholar
- Chong IG, Jun CH: Performance of some variable selection methods when multicollinearity is present. Chemometrics Intell Lab Syst. 2005, 78 (1–2): 103-112. [http://www.sciencedirect.com/science/article/pii/S0169743905000031],View ArticleGoogle Scholar
- Ernst J, Kellis M: Discovery and characterization of chromatin states for systematic annotation of the human genome. Nat Biotech. 2010, 28 (8): 817-825. 10.1038/nbt.1662. [http://dx.doi.org/10.1038/nbt.1662],View ArticleGoogle Scholar
- Ruthenburg AJ, Li H, Patel DJ, David Allis C: Multivalent engagement of chromatin modifications by linked binding modules. Nature Rev Mol Cell Biol. 2007, 8 (12): 983-994. 10.1038/nrm2298. [http://www.nature.com/nrm/journal/v8/n12/full/nrm2298.html],View ArticleGoogle Scholar
- Heinz S, Benner C, Spann N, Bertolino E, Lin YC, Laslo P, Cheng JX, Murre C, Singh H, Glass CK: Simple combinations of lineage-determining transcription factors prime cis-regulatory elements required for macrophage and B cell identities. Mol Cell. 2010, 38 (4): 576-589. 10.1016/j.molcel.2010.05.004. [http://www.sciencedirect.com/science/article/pii/S1097276510003667],PubMed CentralPubMedView ArticleGoogle Scholar
- Bonn S, Zinzen RP, Girardot C, Gustafson EH, Perez-Gonzalez A, Delhomme N, Ghavi-Helm Y, Wilczyéski B, Riddell A, Furlong EEM: Tissue-specific analysis of chromatin state identifies temporal signatures of enhancer activity during embryonic development. Nature Genet. 2012, 44 (2): 148-156. 10.1038/ng.1064. [http://www.nature.com/ng/journal/v44/n2/full/ng.1064.html],PubMedView ArticleGoogle Scholar
- Lee DD, Seung HS: Learning the parts of objects by non-negative matrix factorization. Nature. 1999, 401 (6755): 788-791. 10.1038/44565. [http://www.nature.com/nature/journal/v401/n6755/abs/401788a0.html],PubMedView ArticleGoogle Scholar
- Brunet JP, Tamayo P, Golub TR, Mesirov JP: Metagenes and molecular pattern discovery using matrix factorization. Proc Natl Acad Sci. 2004, 101 (12): 4164-4169. 10.1073/pnas.0308531101. [http://www.pnas.org/content/101/12/4164] [PMID: 15016911],PubMed CentralPubMedView ArticleGoogle Scholar
- Pascual-Montano A, Carmona-Saez P, Chagoyen M, Tirado F, Carazo JM, Pascual-Marqui RD: bioNMF: a versatile tool for non-negative matrix factorization in biology. BMC Bioinformatics. 2006, 7: 366-10.1186/1471-2105-7-366. [http://www.biomedcentral.com/1471-2105/7/366/abstract] [PMID: 16875499],PubMed CentralPubMedView ArticleGoogle Scholar
- Lin CJ: Projected gradient methods for nonnegative matrix factorization. Neural Comput. 2007, 19 (10): 2756-2779. 10.1162/neco.2007.19.10.2756. [http://dx.doi.org/10.1162/neco.2007.19.10.2756],PubMedView ArticleGoogle Scholar
- Boutsidis C, Gallopoulos E: SVD based initialization: A head start for nonnegative matrix factorization. Pattern Recognit. 2008, 41 (4): 1350-1362. 10.1016/j.patcog.2007.09.010. [http://www.sciencedirect.com/science/article/pii/S0031320307004359],View ArticleGoogle Scholar
- Hoyer PO: Non-negative matrix factorization with sparseness constraints. J Mach Learn Res. 2004, 5: 1457-1469. [http://dl.acm.org/citation.cfm?id=10053321044709],Google Scholar
- Devarajan K: Nonnegative matrix factorization: an analytical and interpretive tool in computational biology. PLoS Comput Biol. 2008, 4 (7): e1000029-10.1371/journal.pcbi.1000029. [http://dx.doi.org/10.1371/journal.pcbi.1000029],PubMed CentralPubMedView ArticleGoogle Scholar
- Jain A, Nandakumar K, Ross A: Score normalization in multimodal biometric systems. Pattern Recognit. 2005, 38 (12): 2270-2285. 10.1016/j.patcog.2005.01.012. [http://www.sciencedirect.com/science/article/pii/S0031320305000592],View ArticleGoogle Scholar
- Okun O, Priisalu H: Nonnegative matrix factorization for pattern recognition. Pattern Recognition. 2005, ACTA Press, [http://www.actapress.com/Abstract.aspx?paperId=21730],Google Scholar
- Wong MM, Cox LK, Chrivia JC: The chromatin remodeling protein, SRCAP, is critical for deposition of the histone variant H2A.Z at promoters. J Biol Chem. 2007, 282 (36): 26132-26139. 10.1074/jbc.M703418200. [http://www.jbc.org/content/282/36/26132] [PMID: 17617668],PubMedView ArticleGoogle Scholar
- Calo E, Wysocka J: Modification of enhancer chromatin: what, how, and why?. Mol Cell. 2013, 49 (5): 825-837. 10.1016/j.molcel.2013.01.038. [http://www.sciencedirect.com/science/article/pii/S1097276513001020],PubMedView ArticleGoogle Scholar
- Bannister AJ, Kouzarides T: Regulation of chromatin by histone modifications. Cell Res. 2011, 21 (3): 381-395. 10.1038/cr.2011.22. [http://www.nature.com/cr/journal/v21/n3/full/cr201122a.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Papp B, Plath K: Reprogramming to pluripotency: stepwise resetting of the epigenetic landscape. Cell Res. 2011, 21 (3): 486-501. 10.1038/cr.2011.28. [http://www.nature.com/cr/journal/v21/n3/abs/cr201128a.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Anders S, Huber W: Differential expression analysis for sequence count data. Genome Biol. 2010, 11 (10): R106-10.1186/gb-2010-11-10-r106. [http://genomebiology.com/2010/11/10/R106],PubMed CentralPubMedView ArticleGoogle Scholar
- Lieber M, Smith B, Szakal A, Nelson-Rees W, Todaro G: A continuous tumor-cell line from a human lung carcinoma with properties of type II alveolar epithelial cells. Int J Cancer. Journal International Du Cancer. 1976, 17: 62-70. 10.1002/ijc.2910170110. [http://www.ncbi.nlm.nih.gov/pubmed/175022] [PMID: 175022],View ArticleGoogle Scholar
- Liokatis S, Stützer A, Elsüsser SJ, Theillet FX, Klingberg R, van Rossum B, Schwarzer D, Allis CD, Fischle W, Selenko P: Phosphorylation of histone H3 Ser10 establishes a hierarchy for subsequent intramolecular modification events. Nature Struct Mol Biol. 2012, 19 (8): 819-823. 10.1038/nsmb.2310. [http://www.nature.com/nsmb/journal/v19/n8/full/nsmb.2310.html],View ArticleGoogle Scholar
- Guccione E, Martinato F, Finocchiaro G, Luzi L, Tizzoni L, Dall’ Olio V, Zardo G, Nervi C, Bernard L, Amati B: Myc-binding-site recognition in the human genome is determined by chromatin context. Nature Cell Biol. 2006, 8 (7): 764-770. 10.1038/ncb1434. [http://www.nature.com/ncb/journal/v8/n7/full/ncb1434.html],PubMedView ArticleGoogle Scholar
- Schuster-Böckler B, Lehner B: Chromatin organization is a major influence on regional mutation rates in human cancer cells. Nature. 2012, [http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature11273.html],Google Scholar
- Kiang MY: A comparative assessment of classification methods. Decis Support Syst. 2003, 35 (4): 441-454. 10.1016/S0167-9236(02)00110-0. [http://www.sciencedirect.com/science/article/pii/S0167923602001100],View ArticleGoogle Scholar
- Park MY, Hastie T: Penalized logistic regression for detecting gene interactions. Biostatistics. 2008, 9: 30-50. 10.1093/biostatistics/kxm010. [http://biostatistics.oxfordjournals.org/content/9/1/30] [PMID: 17429103],PubMedView ArticleGoogle Scholar
- Farrar DE, Glauber RR: Multicollinearity in regression analysis: the problem revisited. Rev Econ Stat. 1967, 49: 92-107. 10.2307/1937887. [http://www.jstor.org/stable/1937887] [ArticleType: research-article/Full publication date: Feb., 1967/CopyrightⒸ1967 The MIT Press],View ArticleGoogle Scholar
- Ward JH: Hierarchical grouping to optimize an objective function. J Am Stat Assoc. 1963, 58 (301): 236-244. 10.1080/01621459.1963.10500845. [http://www.tandfonline.com/doi/abs/10.1080/01621459.1963.10500845],View ArticleGoogle Scholar
- Cosine similarity. 2013, [http://en.wikipedia.org/w/index.php?title=Cosine_similarity&oldid=572823419] [Page Version ID: 572823419],
- Munkres J: Algorithms for the assignment and transportation problems. J Soc Ind Appl Math. 1957, 5: 32-38. 10.1137/0105003. [http://www.jstor.org/stable/2098689] [ArticleType: research-article/Full publication date: Mar., 1957/CopyrightⒸ1957 Society for Industrial and Applied Mathematics],View ArticleGoogle Scholar
- Dong X, Greven MC, Kundaje A, Djebali S, Brown JB, Cheng C, Gingeras TR, Gerstein M, Guigó R, Birney E, Weng Z: Modeling gene expression using chromatin features in various cellular contexts. Genome Biology. 2012, 13 (9): R53-10.1186/gb-2012-13-9-r53. [http://genomebiology.com/2012/13/9/R53/abstract] [PMID: 22950368],PubMed CentralPubMedView ArticleGoogle Scholar
- Guenther MG, Levine SS, Boyer LA, Jaenisch R, Young RA: A chromatin landmark and transcription initiation at most promoters in human cells. Cell. 2007, 130: 77-88. 10.1016/j.cell.2007.05.042. [http://www.sciencedirect.com/science/article/pii/S0092867407006812],PubMed CentralPubMedView ArticleGoogle Scholar
- De Santa F, Barozzi I, Mietton F, Ghisletti S, Polletti S, Tusi BK, Muller H, Ragoussis J, Wei CL, Natoli G: A large fraction of extragenic RNA pol II transcription sites overlap enhancers. PLoS Biol. 2010, 8 (5): e1000384-10.1371/journal.pbio.1000384. [http://dx.doi.org/10.1371/journal.pbio.1000384],PubMed CentralPubMedView ArticleGoogle Scholar
- Rada-Iglesias A, Bajpai R, Swigut T, Brugmann SA, Flynn RA, Wysocka J: A unique chromatin signature uncovers early developmental enhancers in humans. Nature. 2011, 470 (7333): 279-283. 10.1038/nature09692. [http://www.nature.com/nature/journal/v470/n7333/abs/nature09692.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Pekowska A, Benoukraf T, Zacarias-Cabeza J, Belhocine M, Koch F, Holota H, Imbert J, Andrau JC, Ferrier P, Spicuglia S: H3K4 tri-methylation provides an epigenetic signature of active enhancers. EMBO J. 2011, 30 (20): 4198-4210. 10.1038/emboj.2011.295. [http://www.nature.com/emboj/journal/v30/n20/full/emboj2011295a.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Bargaje R, Alam MP, Patowary A, Sarkar M, Ali T, Gupta S, Garg M, Singh M, Purkanti R, Scaria V, Sivasubbu S, Brahmachari V, Pillai B: Proximity of H2A.Z containing nucleosome to the transcription start site influences gene expression levels in the mammalian liver and brain. Nucleic Acids Res. 2012, 40 (18): 8965-8978. 10.1093/nar/gks665. [http://nar.oxfordjournals.org/content/40/18/8965],PubMed CentralPubMedView ArticleGoogle Scholar
- Hu G, Cui K, Northrup D, Liu C, Wang C, Tang Q, Ge K, Levens D, Crane-Robinson C, Zhao K: H2A.Z facilitates access of active and repressive complexes to chromatin in embryonic stem cell self-renewal and differentiation. Cell Stem Cell. 2013, 12 (2): 180-192. 10.1016/j.stem.2012.11.003. [http://www.sciencedirect.com/science/article/pii/S1934590912006376],PubMed CentralPubMedView ArticleGoogle Scholar
- Meissner A, Mikkelsen TS, Gu H, Wernig M, Hanna J, Sivachenko A, Zhang X, Bernstein BE, Nusbaum C, Jaffe DB, Gnirke A, Jaenisch R, Lander ES: Genome-scale DNA methylation maps of pluripotent and differentiated cells. Nature. 2008, 454 (7205): 766-770. [http://www.ncbi.nlm.nih.gov/pubmed/18600261] [PMID: 18600261],PubMed CentralPubMedGoogle Scholar
- Wang Y, Zhang XS, Xia Y: Predicting eukaryotic transcriptional cooperativity by Bayesian network integration of genome-wide data. Nucleic Acids Res. 2009, 37 (18): 5943-5958. 10.1093/nar/gkp625. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2764433/] [PMID: 19661283 PMCID: PMC2764433],PubMed CentralPubMedView ArticleGoogle Scholar
- Hon GC, Hawkins RD, Ren B: Predictive chromatin signatures in the mammalian genome. Human Mol Genet. 2009, 18 (R2): R195-R201. 10.1093/hmg/ddp409. [http://hmg.oxfordjournals.org/content/18/R2/R195.abstract],View ArticleGoogle Scholar
- Asp P, Blum R, Vethantham V, Parisi F, Micsinai M, Cheng J, Bowman C, Kluger Y, Dynlacht BD: Genome-wide remodeling of the epigenetic landscape during myogenic differentiation. Proc Natl Acad Sci. 2011, 108 (22): E149-E158. 10.1073/pnas.1102223108. [http://www.pnas.org/content/108/22/E149] [PMID: 21551099],PubMed CentralPubMedView ArticleGoogle Scholar
- Liberzon A, Subramanian A, Pinchback R, Thorvaldsdóttir H, Tamayo P, Mesirov JP: Molecular signatures database (MSigDB) 3.0. Bioinformatics. 2011, 27 (12): 1739-1740. 10.1093/bioinformatics/btr260. [http://bioinformatics.oxfordjournals.org/content/27/12/1739],PubMed CentralPubMedView ArticleGoogle Scholar
- Newton MA, Quintana FA, Boon JAd, Sengupta S, Ahlquist P: Random-set methods identify distinct aspects of the enrichment signal in gene-set analysis. Ann Appl Stat. 2007, 1: 85-106. 10.1214/07-AOAS104. [http://www.jstor.org/stable/4537423] [ArticleType: research-article/Full publication date: Jun., 2007/CopyrightⒸ2007 Institute of Mathematical Statistics],View ArticleGoogle Scholar
- Subramanian A, Kuehn H, Gould J, Tamayo P, Mesirov JP: GSEA-P: a desktop application for gene set enrichment analysis. Bioinformatics. 2007, 23 (23): 3251-3253. 10.1093/bioinformatics/btm369. [http://bioinformatics.oxfordjournals.org/content/23/23/3251] [PMID: 17644558],PubMedView ArticleGoogle Scholar
- Moran JL, Li Y, Hill AA, Mounts WM, Miller CP: Gene expression changes during mouse skeletal myoblast differentiation revealed by transcriptional profiling. Physiolo Genomics. 2002, 10 (2): 103-111. [http://physiolgenomics.physiology.org/content/10/2/103] [PMID: 12181367],View ArticleGoogle Scholar
- Jean-Baptiste G, Yang Z, Khoury C, Gaudio S, Greenwood MT: Peptide and non-peptide G-protein coupled receptors (GPCRs) in skeletal muscle. Peptides. 2005, 26 (8): 1528-1536. 10.1016/j.peptides.2005.03.011. [http://www.sciencedirect.com/science/article/pii/S0196978105001245],PubMedView ArticleGoogle Scholar
- Rayman JB, Takahashi Y, Indjeian VB, Dannenberg JH, Catchpole S, Watson RJ, te Riele H, Dynlacht BD: E2F mediates cell cycle-dependent transcriptional repression in vivo by recruitment of an HDAC1/mSin3B corepressor complex. Genes Dev. 2002, 16 (8): 933-947. 10.1101/gad.969202. [http://genesdev.cshlp.org/content/16/8/933] [PMID: 11959842],PubMed CentralPubMedView ArticleGoogle Scholar
- Kennedy PJ, Feng J, Robison AJ, Maze I, Badimon A, Mouzon E, Chaudhury D, Damez-Werno DM, Haggarty SJ, Han MH, Bassel-Duby R, Olson EN, Nestler EJ: Class I HDAC inhibition blocks cocaine-induced plasticity by targeted changes in histone methylation. Nature Neurosci. 2013, 16 (4): 434-440. 10.1038/nn.3354. [http://www.nature.com/neuro/journal/v16/n4/full/nn.3354.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Lang KC, Lin IH, Teng HF, Huang YC, Li CL, Tang KT, Chen SL: Simultaneous overexpression of Oct4 and Nanog abrogates terminal myogenesis. Am J Physiol - Cell Physiol. 2009, 297: C43-C54. 10.1152/ajpcell.00468.2008. [http://ajpcell.physiology.org/content/297/1/C43] [PMID: 19403798],PubMedView ArticleGoogle Scholar
- Tan KY, Eminli S, Hettmer S, Hochedlinger K, Wagers AJ: Efficient generation of iPS cells from skeletal muscle stem cells. PLoS ONE. 2011, 6 (10): e26406-10.1371/journal.pone.0026406. [http://dx.doi.org/10.1371/journal.pone.0026406],PubMed CentralPubMedView ArticleGoogle Scholar
- Müller FJ, Laurent LC, Kostka D, Ulitsky I, Williams R, Lu C, Park IH, Rao MS, Shamir R, Schwartz PH, Schmidt NO, Loring JF: Regulatory networks define phenotypic classes of human stem cell lines. Nature. 2008, 455 (7211): 401-405. 10.1038/nature07213. [http://www.nature.com/nature/journal/v455/n7211/full/nature07213.html],PubMed CentralPubMedView ArticleGoogle Scholar
- Wong DJ, Liu H, Ridky TW, Cassarino D, Segal E, Chang HY: Module map of stem cell genes guides creation of epithelial cancer stem cells. Cell Stem Cell. 2008, 2 (4): 333-344. 10.1016/j.stem.2008.02.009. [http://www.sciencedirect.com/science/article/pii/S1934590908000738],PubMed CentralPubMedView ArticleGoogle Scholar
- Guillamet D, Vitrià J, Schiele B: Introducing a weighted non-negative matrix factorization for image classification. Pattern Recognit Lett. 2003, 24 (14): 2447-2454. 10.1016/S0167-8655(03)00089-8. [http://www.sciencedirect.com/science/article/pii/S0167865503000898],View ArticleGoogle Scholar
- Li SZ, Hou X, Zhang H, Cheng Q: Learning spatially localized, parts-based representation. Proceedings of the. 2001, 2001:I–207–I–212 vol.1. doi:10.1109/CVPR.2001.990477, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001. CVPR 2001, Volume 1Google Scholar
- Orkin S, Hochedlinger K: Chromatin connections to pluripotency and cellular reprogramming. Cell. 2011, 145 (6): 835-850. 10.1016/j.cell.2011.05.019. [http://www.sciencedirect.com/science/article/pii/S0092867411005769],PubMedView ArticleGoogle Scholar
- van der Walt S, Colbert S, Varoquaux G: The NumPy array: a structure for efficient numerical computation. Comput Sci Eng. 2011, 13 (2): 22-30.View ArticleGoogle Scholar
- Jones E, Oliphant T, Peterson P: SciPy: Open source scientific tools for Python. 2001, [http://www.scipy.org/Citing_SciPy],Google Scholar
- Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E: Scikit-learn: machine learning in Python. J Mach Learn Res. 2011, 12: 2825-2830. [http://dl.acm.org/citation.cfm?id=19530482078195],Google Scholar
- Quinlan AR, Hall IM: BEDTools: a flexible suite of utilities for comparing genomic features. Bioinformatics. 2010, 26 (6): 841-842. 10.1093/bioinformatics/btq033. [http://bioinformatics.oxfordjournals.org/content/26/6/841] [PMID: 20110278],PubMed CentralPubMedView ArticleGoogle Scholar
- Li H, Handsaker B, Wysoker A, Fennell T, Ruan J, Homer N, Marth G, Abecasis G, Durbin R: The sequence alignment/map format and SAMtools. Bioinformatics. 2009, 25 (16): 2078-2079. 10.1093/bioinformatics/btp352. [http://bioinformatics.oxfordjournals.org/content/25/16/2078] [PMID: 19505943],PubMed CentralPubMedView ArticleGoogle Scholar
- Harrow J, Frankish A, Gonzalez JM, Tapanari E, Diekhans M, Kokocinski F, Aken BL, Barrell D, Zadissa A, Searle S, Barnes I, Bignell A, Boychenko V, Hunt T, Kay M, Mukherjee G, Rajan J, Despacio-Reyes G, Saunders G, Steward C, Harte R, Lin M, Howald C, Tanzer A, Derrien T, Chrast J, Walters N, Balasubramanian S, Pei B, Tress M, et al: GENCODE: The reference human genome annotation for The ENCODE Project. Genome Res. 2012, 22 (9): 1760-1774. 10.1101/gr.135350.111. [http://genome.cshlp.org/content/22/9/1760],PubMed CentralPubMedView ArticleGoogle Scholar
- Benjamini Y, Hochberg Y: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J Royal Stat Soc. Ser B (Methodological). 1995, 57: 289-300. [http://www.jstor.org/stable/2346101] [ArticleType: research-article/Full publication date: 1995/CopyrightⒸ1995 Royal Statistical Society],Google Scholar
- Langmead B, Salzberg SL: Fast gapped-read alignment with Bowtie 2. Nature Methods. 2012, 9 (4): 357-359. 10.1038/nmeth.1923. [http://www.nature.com/nmeth/journal/v9/n4/abs/nmeth.1923.html],PubMed CentralPubMedView ArticleGoogle Scholar
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