Abstract
Bisulfite sequencing (BSseq) is the gold standard for studying genomewide DNA methylation. We developed MOABS to increase the speed, accuracy, statistical power and biological relevance of BSseq data analysis. MOABS detects differential methylation with 10fold coverage at singleCpG resolution based on a BetaBinomial hierarchical model and is capable of processing two billion reads in 24 CPU hours. Here, using simulated and real BSseq data, we demonstrate that MOABS outperforms other leading algorithms, such as Fisher’s exact test and BSmooth. Furthermore, MOABS analysis can be easily extended to differential 5hmC analysis using RRBS and oxBSseq. MOABS is available at http://code.google.com/p/moabs/.
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Background
DNA methylation, an epigenetic modification affecting organization and function of the genome, plays a critical role in both normal development and disease. Until recently, the only known DNA methylation was 5methylcytosine (5mC) at CpG dinucleotides, which is generally associated with transcriptional repression [1]. In 2009, another form of DNA methylation termed 5hydroxymethylcytosine (5hmC) [2] was found to be involved in active demethylation [3] and gene regulation [4]. Understanding the functional role of DNA methylation requires knowledge of its distribution in the genome [5, 6]. Bisulfite conversion of unmethylated Cs to Ts followed by deep sequencing (BSSeq) has emerged as the gold standard to study genomewide DNA methylation at singlenucleotide resolution. The most popular protocols include RRBS (Reduced Representation Bisulfite Sequencing) [7] and WGBS (Whole Genome Bisulfite Sequencing) [8] for the combination of 5mc and 5hmc, oxBSSeq (Oxidative Bisulfite Sequencing) [9] for 5mc and TABSeq (Tetassisted Bisulfite Sequencing) [10] for 5hmc, respectively. After mapping BSseq reads to the genome, the proportion of unchanged Cs is regarded as the absolute DNA methylation level. Due to random sampling nature of BSseq, deep sequencing (e.g. >30 fold) is usually required to reduce the measurement error. Technological advances and reduced costs have seen a significant increase in interest in BSseq among biologists. Currently, BSseq is widely used by small laboratories to profile cell lines and animal models [11], as well as by large consortiums such as the NIH ENCODE, Roadmap Epigenomics, The Cancer Genome Atlas (TCGA), and European BLUEPRINT to profile thousands of cell populations. Hence, it is expected that BSseq data will continue to grow exponentially. However, despite recent progress [7, 12–14], computational methods designed for issues specific to BSseq are much less developed than those for other sequencing applications such as ChIPSeq and RNAseq.
The most fundamental aspects of BSseq data analysis include read mapping and differential methylation detection. We previously developed one of the most widely used BS mapping programmed BSMAP [15]. After read mapping, the most common task is the identification of differentially methylated regions (DMRs) between samples, such as disease versus normal. Based on the biological question, DMRs can range in size from a single CpG (DMC: differentially methylated CpG) to tens of millions of bases. Although several statistical methods have been applied to DMR detection [12], among which Fisher’s exact test pvalue (FETP) method [16] is the most popular, several challenges remain to be addressed. 1) Statistical Power: most previous methods are very conservative in power and require deep sequencing (e.g. 30 fold). For example, Hansen [13] recently calculated that for single CpG methylation level “even 30× coverage yields standard error as large as 0.09”. As a compromise, many studies assumed that neighboring CpGs have similar methylation levels, thus can be combined together within a genomic region (e.g. 1 kb) to increase the statistical power [17]. For example, BSmooth [13] performs local smoothing followed by ttest for DMR detection. While this strategy may be applicable in many cases, regional average analysis will unfortunately miss lowCpGdensity DMRs that are abundant in the genome and critical for gene expression, such as TFBSs. Most TFBSs are small (i.e. < 50 bp) as implied by highresolution ChIPseq and ChIPexo experiments [18] and contain few or even a single CpG(s) that are in general differentially methylated compared to surrounding ones, thus are very likely to be “overlooked” by the regional average analysis. 2) Biological Significance: previous methods use pvalue for statistical significance of DMR. This pvalue metric only tells whether a region is differentially methylated, but does not directly measure the magnitude of the methylation difference. A similar problem also exists in gene expression profiling, where the pvalue does not directly measure the expression foldchange [19]. Since sequencing depth in BSseq experiments can fluctuate by an order of magnitude in different loci, a very small methylation difference, although not biologically meaningful, can easily return a significant pvalue if the underlying sequencing depth is deep enough. On the other hand, the nominal methylation difference, i.e. direct subtraction of two methylation ratios, suffers significantly from the random sampling error such that a large difference with low sequencing depth is not likely to be statistically meaningful. 3) Biological Variation is an essential feature of DNA methylation [20], and should be handled carefully to detect reproducible DMRs that represent the common characteristics of the sample group. However, most previous methods fail to account for biological variation between replicates, and simply pool the raw data from replicates for DMR detection. Some of the resulting DMRs may have significant differences at the mean level but might not be reproducible between replicates, and hence are “falsepositives”. To our knowledge, BSmooth [13] is the first replicateaware program that accounted for biological variation using a modified ttest.
In response to these challenges, we developed a powerful differential methylation analysis algorithm termed MOABS: Modelbased Analysis of Bisulfite Sequencing data. Its source code is available as Additional file 1. MOABS uses a BetaBinomial hierarchical model to capture both sampling and biological variations, and accordingly adjusts observed nominal methylation difference by sequencing depth and sample reproducibility. The resulting credible methylation difference (CDIF) is a single metric that combines both biological and statistical significance of differential methylation. Using both simulated and real wholegenome BSseq data from mouse brain tissues and stem cells, we demonstrate the superior performance of MOABS over other leading methods, especially at low sequencing depth. Furthermore, one practical challenge is that BSseq data analysis is usually computational intensive, and requires multiple steps. We therefore seamlessly integrate several major BSseq processing procedures into MOABS, including read mapping, methylation ratio calling, identification of hypo or hyper methylated regions from one sample, and differential methylation from multiple samples. MOABS is implemented in C++ with highly efficient numerical algorithms, and thus is at least 10 times faster than other popular packages. For example, it takes only 24 CPU hours to detect differential methylation from 2 billion aligned reads. Together, MOABS provides a comprehensive, accurate, efficient and userfriendly solution for analyzing largescale BSseq data.
Results and discussion
BetaBinomial hierarchical model for both sampling and biological variations
For a single CpG locus in the jth biological replicate of condition i, we denote the number of total reads, the number of methylated reads and methylation ratio as n_{ ij }, k_{ ij } and p_{ ij }, respectively. For a typical two group comparison, i = 1,2 and j = 1, 2, …, N, where N is the number of replicates in each condition. The n_{ ij } and k_{ ij } are observations from experiments, while the p_{ ij } is unknown with k_{ ij }/n_{ ij } as its nominal estimation. Given p_{ ij }and n_{ ij }, the number of methylated reads k_{ ij } is characterized by the sampling variation from sequencing and can be modeled by a Binomial distribution: k_{ ij } ~ Binomial(n_{ ij }, p_{ ij }). The posterior distribution of the methylation ratio p_{ ij } will then follow a Beta distribution Beta(α_{ ij }, β_{ ij }) and can be estimated using an Empirical Bayes approach. The prior distribution will be estimated from the whole genome, in which most CpGs are either fully methylated or fully unmethylated, resulting in a bimodal distribution. The Empirical Bayes approach will automatically incorporate such bimodal information in the methylation ratio estimation and hence increases the power of our analysis.
When biological replicates are available, we will refine the posterior distribution of p_{ ij } with biological variation from the Bayesian perspective. Specifically, α_{ i } and β_{ i } will be treated as random variables with a prior distribution estimated from all the CpGs in the genome similar to the Empirical Bayes priors. We will then use maximum likelihood approach to generate the posterior distribution of p_{i}. Typical posterior distributions of four CpGs are shown in Figure 1a, in which all CpGs have the same average methylation ratios and the same total number of reads. Their methylation ratios would have identical Beta distributions (black curve on CpG #1) if biological variation was not considered. Our method is able to adjust the posterior distribution of p_{ i } based on observed biological variation. For example, highly variable replicates on CpG #2 results in a bimodal distribution, whereas reproducible replicates on CpG #3 leads to a normallike distribution. Furthermore, increasing the number of reproducible replicates from 2 to 3 on CpG #4 will reduce the variation of the resulting posterior distribution. Taken together, the posterior distribution of the methylation ratio in condition i will be determined by its prior distribution, sequencing depth, and the degree of variation between replicates.
Credible methylation difference (CDIF) is a single metric for both statistical and biological significance of differential methylation
We illustrate the idea of CDIF using a simple experimental design, in which only one sample (N = 1) is sequenced for each of the two conditions: k_{ ij } ~ Binomial(n_{ i }, p_{ i }) and p_{ i } ~ Beta(α_{ i }, β_{ i }), i = 1, 2. The Empirical Bayes priors {\mathit{\alpha}}_{\mathit{i}}^{0},{\mathit{\beta}}_{\mathit{i}}^{0} of p_{ i } will be estimated from all the CpGs in the genome by maximizing a marginal likelihood function using the quasiNewton optimization method [21]. In this case, there is no biological variation, so Beta(α_{ i }, β_{ i }) will be only determined by the prior distribution and sequencing depth: {\mathit{\alpha}}_{\mathit{i}}={\mathit{k}}_{\mathit{i}}+{\mathit{\alpha}}_{\mathit{i}}^{0} and {\mathit{\beta}}_{\mathit{i}}={\mathit{n}}_{\mathit{i}}{\mathit{k}}_{\mathit{i}}+{\mathit{\beta}}_{\mathit{i}}^{0}. An example is shown in Figure 1b. Due to low sequencing depth (k_{1} = 9; n_{1} = 10), sample #1′s Beta distribution has higher variance than that of sample #2 with high sequencing depth (k_{2} = 12; n_{2} = 80). The methylation ratio difference between two samples is denoted as t = p_{ 1 }  p_{ 2 }. One immediate question is how to estimate the confidence interval CI(a,b) of t. Many methods have been proposed but their merits have been subject to debate [22]. We therefore propose to use the exact numerical solution [23] to solve CI(a,b). CDIF is then defined as the distance between 0 and the 95% CI(a,b) (Figure 1b):
In practice, CDIF represents the conservative estimation of the true methylation difference, i.e. for 97.5% of chance the absolute value of true methylation difference is greater than or equal to that of CDIF. The CDIF value will be assigned to 0 is there is no significant difference. Constructed in this way, the CDIF value, if greater than the resolution defined as min(1/n_{1}, 1/n_{2}), guarantees a significant pvalue from Fisher’s exact test, and at the same time represents the magnitude of methylation difference. The sequencing depth will largely influence CDIF, since bigger n_{ i } will make a smaller 95% CI of the methylation difference, normally resulting in greater CDIF value.
We believe CDIF is a better metric to capture the methylation difference than statistical pvalue or nominal methylation difference. Three CpG examples are shown in Figure 1c. According to pvalue 1.4e10, CpG #3 is the most significant one. However, this significant pvalue, which is largely driven by the high sequencing depth, does not correctly represent the actual biological difference of 0.3, which is the smallest among three CpGs. On the other hand, if we use nominal difference, CpG #2 would be the most significant. However, its low sequencing depth makes this high nominal difference unreliable. CDIF is able to penalize the nominal difference according to its statistical significance and ranks CpG #1 as the most significant followed by CpGs #2 and #3, although CpG #1 does not have the most significant pvalue or nominal difference. Taken together, CDIF reaches a well balance between statistical and biological significance and gives a more stable and biological meaningful interpretation and ranking of differential methylation.
Functions and performance of the MOABS pipeline
We have implemented MOABS as a comprehensive software pipeline (Figure 2a), including read alignment, quality control (QC), single sample analysis and multiple sample comparative analysis. 1) The read alignment model is a wrapper of popular bisulfite mapping programs, such as BSMAP [15], which allows the trimming of low quality band adaptor sequences, as well as supports parallel computing on a cluster. 2) The QC module adjusts biases in PCR amplification, endrepair, bisulfite conversion failure, and etc. [24]. In addition, it can also estimate bisulfite conversion rate based on cytosines in the nonCpG content. 3) Single sample analysis reports CpG or CpH methylation ratios with corresponding confidence intervals, detects hypo or hyper methylated regions (e.g. Trp53 gene in Figure 2b) in the genome [25], and provides general statistics with descriptive figures (an example of the mouse methylome [25] is shown in Figure 2c). 3) For multiple sample comparative analysis, MOABS detects de novo DMCs, which can be further grouped into DMRs using a Hidden Markov Model. MOABS can also examine the differential methylation levels of predefined regions, such as promoters.
All the modules are wrapped in a single master script such that users can specify the input BSseq reads and run all the modules one by one automatically. The MOABS pipeline is developed using C++ with highly efficient numerical algorithms, native multiplethreading and cluster support so that multiple jobs can run in parallel on different computing nodes. Several mathematical and computational optimizations have made MOABS pipeline extremely efficient. For example, it takes only one hour on 24 CPUs (IBM power7 4 Ghz) to detect differential methylation for approximately 30 million CpGs in the human genome based on 2 billion aligned reads. MOABS is significantly faster than other software. For example, a benchmark (Additional file 2: Table S1) based on public BSseq data in mouse hematopoietic stem cell (HSC) [26] reveals that MOABS is roughly 3.3, 1.7, and 1.4 times faster than BSmooth in bisulfite mapping, methylation call and differential methylation analysis, respectively. In summary, MOABS is a comprehensive, accurate, efficient and userfriendly solution for analyzing largescale BSseq data.
Simulated BSseq data reveals the superior performance of MOABS
To assess the performance of MOABS on differentially methylated CpGs (DMCs), we simulated 0.1 million true positive CpGs with large methylation difference and 0.9 million true negative CpGs (Additional file 3: Figure S1) from a H1 methylome [16], and then compared MOABS with FETP at 5% false discovery rate (FDR) (Figure 3). Note that this evaluation is at single CpG resolution without local smoothing, therefore BSmooth [13] cannot be used. The results indicate that MOABS clearly outperforms FETP with the most dramatic difference observed at low sequencing depth. For example, with sequencing depth at 5–10 fold, MOABS can recover 5575% true positives while FETP only predicts 1351% true positives. To further evaluate the performance of MOABS at different methylation levels, we resimulated the 0.1 million true positive CpGs with different baseline methylation levels (0% 100%) and methylation differences (20%  100%). The results (Additional file 3: Figure S2) indicate that MOABS is more accurate than FETP at any sequencing depth and at any methylation difference. Notably, the difference between the two methods is large when sequencing depth is low or when methylation difference is moderate (50% ~ 70%). In contrast, the difference between methods is small when sequencing depth is high or when the methylation difference is either very high (80% ~ 100%) or very low (~20%). Although FETP is well suited for the analysis of discrete data, it has less power for DNA methylation, which by its nature is a continuous rather than discrete random variable. The improved power of MOABS results from the modeling of DNA methylation using a BetaBinomial hierarchical model and the Empirical Bayes approach to borrow information from all the CpGs in the genome. The testing data used for the method validation above is included in Additional file 4.
MOABS improves the detection of allele specific DNA methylation
To assess how MOABS performs on DMRs for real BSseq data, we compared MOABS with FETP and BSmooth [13] using allelespecific mouse methylomes [25], in which a list of wellknown imprinted DMRs can serve as gold standard for method evaluation. Xie et al. [25] used FETP followed by clustering of DMCs for DMR detection. They confirmed 32 known experimentally verified imprinted DMRs (Additional file 5: Table S2) and reported 20 novel ones by pooling two biological replicates without considering sample variation. We noticed that two known DMRs (Ndn and Igf2r) are weak, exhibiting a very small methylation difference of approximately 10%. We also found that 3 novel DMRs they reported (Vwde, Casc1 and Nhlrc1) are differentially methylated in only one of the two replicates, and thus are likely to be false positives (Additional file 3: Figure S3). Since the remaining 17 novel DMRs have yet to be experimentally verified, we decided to remove them from our analysis. In our method evaluation, we used the 32 known DMRs as true positives and the remaining genome (with 17 reproducible novel DMRs removed) as true negatives. To allow for a fair comparison, we used the same method to calculate FDR for all three methods. In addition, we used the same procedure to cluster DMCs into DMRs for MOABS and FETP. The resulting ROClike curves (Figure 4a) clearly indicate that MOABS is superior to the other two methods. MOABS successfully reports all 32 known DMRs including the two weak ones at 11% FDR, and 4 “false positive” new DMRs (Cdh20, Trappc9, Pcdhb20 and Pfdn4). Manual inspection (Additional file 3: Figure S4) confirms that these 4 “false positive” are indeed regions showing differential methylation in both replicates. Hence the 11% FDR of MOABS is significantly over estimated based on incomplete true positives. Interestingly, our FETP analysis predicts 7 new DMRs in addition to 32 known DMRs, suggesting additional filtering steps may have been performed in Xie et al. [25]. Among these 7 DMRs, one greatly overlaps with the new DMR Pcdhb20 reported by MOABS, while the other 6, including Vwde and Casc1 and Nhlc1, show poor correlation between replicates. Finally, the ROClike curve indicates that BSmooth is less accurate than either FETP or MOABS.
The 32 known DMRs can be easily detected by both MOABS and FETP mainly because they have large methylation differences and high read depth (54fold in DMR regions), which is consistent with our simulation study. However, deep bisulfite sequencing of the mammalian genome is still quite expensive. This reality motivated us to test to what extent these known DMRs can still be recovered at a lower sequencing depth. The same previous procedure was applied to compare all three methods. The number of recovered known DMRs at 5% FDR is plotted at each sequencing depth from random sampling (Figure 4b). We observe that the lower sequencing depth, the greater performance difference between MOABS and FETP. For example, when the depth is at 11fold, MOABS recovers roughly 90% of known DMRs, while FETP only detects 78% of DMRs. When the depth is further lowed to 3.1fold, MOABS can still recover roughly 70% of known DMRs, while FETP detects 44% DMRs. Interestingly, BSmooth’s performance is largely independent of sequencing depth, probably because it was designed mainly for low sequencing depth. Indeed, at a low depth of 3.1fold, BSmooth outperforms FETP. However, at sequencing depth higher than 3.1fold, BSmooth has a lower sensitivity than the other two methods. Collectively, we conclude that MOABS is superior in DMR detection, especially at low sequencing depth.
MOABS reliably reveals differential methylation underlying TFBSs
Since the previous benchmark is based on a small number of experimentally verified DMRs, we sought to further evaluate the performance of MOABS based on larger scale datasets. The link between differential methylation and TFBSs provides such a good system. TFBSs are usually hypomethylated compared to surrounding genome background; therefore, a tissue specific TFBS is expected to be a tissue specific hypomethylatedDMR (hypoDMR). To test this hypothesis, we performed deep (46fold) WGBS of the mouse hematopoietic stem cell (HSC), and compared the HSC methylome with that of a publically available mouse embryonic stem cell (ESC) [27]. The HSC methylome data is accessible at NCBI GEO Accession GSE47815. The HSCspecific hypoDMR were then compared with approximately 58,000 in vivo ChIPseq TFBSs of 10 major HSC specific TFs [28], including Erg, Fli1, Gata2, Gfi1b, Lmo2, Lyl1, Meis1, Pu.1, Runx1 and Scl. Figure 5a illustrates the hypomethylation of a TFBS in Runx2 gene. At the center of the TFBS cobound by Runx1, Gata2 and Scl, there are 2 CpGs fully methylated in mouse ESC but unmethylated in HSC, while the surrounding regions are almost fully methylated in both HSC and ESC. Additional file 3: Figure S5 shows more examples of tissue specific hypoDMR coupled with tissue specific TFBSs. Such TFBS associated hypomethylated regions are usually very small and abundant in the genome. Using Runx1 as an example, 71% of the 4793 Runx1 TFBSs show hypomethylation, while the remaining TFBSs are either fully methylated or have no underlying CpGs. Together, ~34% of TFBS associated hypomethylated regions contain no more than 3 CpGs with a median length of 51 bp (Figure 5b). Furthermore, 14% of such regions even have a single CpG. For such small DMRs, single CpG level differential analysis is essential since regional averaging is very likely to overlook most of them.
We then used TFBSs to evaluate DMC detection assuming tissuespecific TF binding is associated with tissuespecific hypomethylation. For a fair comparison, we calculated FDR for each method based on a methodspecific null distribution obtained through permutation of read sample labels. At FDR of 5%, MOABS, FETP and BSmooth predicted 32,867, 32,047 and 18,021 differentially methylated TFBSs respectively (Figure 5c). We also used a method similar to Gene Set Enrichment Analysis (GSEA [29]) to test enrichment of TFBS moving down the lists of DMCs ranked by different methods. MOABS shows the highest enrichment score (Figure 5d) of TFBS. For example, with the same 4,000 most significant DMCs, MOABS recovers 1,000 TFBSs while FETP only predicts ~600 TFBSs (i.e., 40% less).
In this instance, the sequencing depth is sufficient to enable MOABS and FETP to recover very similar number of TFBSs. However, when we randomly sampled reads to a depth of 4fold, MOABS recovered many more TFBS (15,349) than FETP (7,520) and BSmooth (4,028) (Figure 5e). Again, at this low sequencing depth, MOABS not only recovers 2–3 fold more TFBSs, but also exhibit more significant score of TFBS enrichment in the most significant DMCs. In both high and low sequencing depths, BSmooth recovers fewer TFBSs mainly because its smoothing function easily ignores small region with a few CpGs. Together, using tissue specific in vivo TFBSs, we demonstrate that MOABS can better recover differential methylation in small regulatory regions with a few CpGs, especially at low sequencing depth (e.g. 4fold).
MOABS detects differential 5hmc in ES cells using RRBS and oxBSSeq
To demonstrate the broad utility of MOABS, we analyzed 5hmc data using RRBS and oxBSseq [9]. RRBS measures both 5mc and 5hmc together while oxBSSeq [9] detects 5mc directly. The 5hmc level can then be inferred by the difference between RRBS and oxBSSeq of the same sample. The 5hmc level is often very small (e.g. at 5%) and hence its detection requires hundreds of fold coverage using FETP [9]. Our simulation study indicates that MOABS can significantly reduce the depth requirement (Figure 6a). For example, to detect 5hmc at 5% when 5mc is at 0%, MOABS requires 80fold coverage while FETP needs ~200fold. However, when the 5mc level is close to 50%, significantly more reads will be needed for both methods (~120fold for MOABS and >500fold for FETP). The differential 5hmc between two samples can be inferred by the difference of two CDIF values, each of which is the difference between RRBS and oxBSSeq of the same sample. The similar numerical approach can then be used to infer the distribution of the difference of the difference between two Beta distributions, which are used to model BSseq data. Figure 6b shows an example, in which 5hmc is measured by both RRBS and oxBSSeq in two samples. FETP shows more significant pvalue for 5hmc in sample #1 than in #2, whereas MOABS CDIF is bigger in sample #2 than in #1. However, the significance of FETP on sample #1 is largely driven by the high sequencing depth, thus does not correctly represent the actual biological difference. In contrast, MOABS CDIF reaches a balance between statistical and biological significance and gives a biologically meaningful differential 5hmc at CDIF value of 0.06 (0.290.23).
When applied to RRBS and oxBSseq data derived from ES cell lines with different passages [9], MOABS reported 299 genes with decreased 5hmc and 125 genes with increased 5hmc (Additional file 6: Table S3) in promoters in the later passage P20, which is consistent with the mass spectrometry data [9] that shows overall reduced 5hmc in later passage. This result implies that the epigenetic stability of ES cells is impacted by prolonged in vitro culture. This is an important issue for both the safety and efficacy of stem cellderived tissues in cellreplacement therapies as well as the appropriate interpretation of experimental models. Monoallelic gene expression, including genomic imprinting, is primarily regulated through epigenetic mechanisms and thus can serve as a useful model of epigenetic stability. As expected, our analysis identified five imprinted genes with decreased 5hmc: Plagl1, Sfmbt2, Gpr1, Kcnq1 and Kcnq1ot1, as well as one imprinted gene with increased 5hmc, Pcdha4g.
The role of 5hmc in disease remains unclear. A recent study suggests that genomewide loss of 5hmc is an epigenetic feature of neurodegenerative Huntington’s disease [30]. The authors identified 559 genes with decreased 5hmc in the diseased mice compared to healthy controls. A considerable fraction of these diseasespecific genes were uncovered in our differential 5hmc analysis in ES cells. This included 26 of 299 and 11 of 125 genes (overlapping pvalue < 8e5) with decreased and increased 5hmc, respectively. These results suggest that one potential consequence of decreased epigenetic stability over time in ES cells is the acquisition of pathological epimutations.
The observed bias toward loss of 5hmc in ES cells upon longterm culture may also suggest stem cell properties, such as pluripotency, are affected. Ficz and colleagues [31] showed that knockdown of Tet1/Tet2 in mouse ES cells down regulates epigenetic reprogramming and pluripotencyrelated genes such as Esrrb, Klf2, Tcl1, Zfp42, Dppa3, Ecat1 and Prdm14. Decreased expression was concomitant with both decreased 5hmC and increased 5mC at the gene promoters. In our differential 5hmc analysis in ES cells, we observed decreased 5hmc at three of these genes: Ecat1, Esrrb, and Zfp42. Together, we conclude that MOABS can be used effectively to infer differential 5hmc using RRBS and oxBSSeq.
Conclusions
While progress in nextgeneration sequencing allows increasingly affordable BSseq experiments, the resulting data generated poses significant and unique bioinformatics challenges. The lack of efficient computational methods is the major bottleneck that prevents a broad adoption of such powerful technologies. In response to this challenge, we developed MAOBS, an accurate, comprehensive, efficient, and userfriendly pipeline for BSseq data analysis. The MOABS analysis is novel and significant in two major aspects: 1) MOABS CDIF value provides an innovative strategy to combine statistical pvalue and biological difference into a single metric, which will bring biological relevance to the interpretation of the DNA methylation data. 2) MOABS does not sacrifice resolution with low sequencing depth. By relying on the BetaBinomial Hierarchical Model and Empirical Bayes approach, MOABS has enough power to detect singleCpGresolution differential methylation in lowCpGdensity regulatory regions, such as TFBSs, with as low as 10fold. The lowdepth BSseq experimental design enables remarkable cost reduction per sample. In Figure 3 simulated data, we showed that MOABS achieved roughly 80% sensitivity with 5% FDR at 10fold sequencing depth. In Figure 4b real data, we showed that as sequencing depth decreased to 11fold by sampling, MOABS recovered roughly 90% of known DMRs. The MOABS sensitivity starts to drop dramatically when sequencing depth is further reduced. Based on the above two observations, we would recommend lowdepth (e.g. 10fold) BSseq on more biological samples with the same limited budget, which in most scenarios will provide greater biological insights than highdepth BSseq on fewer samples.
Copy Number Variation (CNV) is a common issue in many disease related bisulfite sequencing. The sequencing depth is normally higher or lower in high (or low) copynumber regions and this depth bias has an impact on our CDIF calculation. To correct this bias, we have included a separate script ‘redepth.pl’ in the MOABS package. Users can select their favorite CNV detection tools [32], such as CNVSeq, ControlFREEC and VarScan, to predict the CNV region from genome sequencing or bisulfite sequencing. Nearly all these tools output a bed file of CNV regions with predicted copy number based on a pvalue cutoff. The script ‘redepth.pl’ manipulates the read alignment BAM files according to the CNV prediction. If a read is located in a CNV region with a predicted copy number of X in a diploid genome, the read will have a probability of 2/X to be kept in the new BAM files. Reads in the nonCNV regions will keep unchanged. This process will result in CNV bias free BAM files for downstream analysis.
Largescale case–control epigenomewide association study (EWAS) is a powerful strategy to identify diseaseassociated epigenetic biomarkers. Currently, most studies use Illumina bisulfite arrays (e.g. 450 K) mainly due to the cost constraint. MOABS in theory can also be applied to such studies when EWAS bisulfite sequencing data are publicly available.
In summary, as DNA methylation is increasingly recognized as a key regulator of genomic function, deciphering its genomewide distribution using BSseq in numerous samples and conditions will continue to be a major research interest. MOABS significantly increase the speed, accuracy, statistical power and biological relevance of the BSseq data analysis. We believe that MOABS’s superior performance will greatly facilitate the study of epigenetic regulation in numerous biological systems and disease models.
Materials and methods
The major portions of the methods for the model are described here. In the Additional file 7, we provide more details and additional methods to make the model complete.
Distribution for difference of two Binomial proportions
In the Additional method section (Additional file 7) we show that a methylation ratio p inferred from k methylated cytosines out of n total reads, follows a Beta distribution from the Bayesian perspective. The probability density function is
where α = k + α_{0}, β = nk + β_{0}, if Be(α_{0}, β_{0}) is priori distribution for p. We also give formulas to numerically calculate the confidence interval for the single Binomial proportional p under observed (n, k).
The methylation ratio difference at a defined genomic locus from two biological samples is the difference of two Binomial proportions p_{1}p_{2}. Many methods have been proposed to estimate the confidence interval p_{1}p_{2} of and their merits have been subject to decades of considerable debate [22, 33–38]. No comprehensive comparison of currently available methods is available. This motivated us to turn to the direct and exact numerical calculation of confidence interval from Bayesian perspective.
Let t = p_{1}p_{2}, where p_{ i } is the proportion for the sample i with observation n_{ i } and k_{ i }. Since the joint probability density of such observation is f(p_{1}, n_{1}, k_{1}) f(p_{2}, n_{2}, k_{2}), the PDF for t is
where f_{ i }(p_{ i }) ≡ f(p_{ i }; n_{ i }, k_{ i }). Boundary conditions like the proportional area condition, minimal length condition can be applied to get unique solutions for (a, b).
Distribution for difference of difference
Let t = p_{1}  p_{2}, where p_{ i } is the proportion for the assay i with observation n_{ i } and k_{ i }. In the oxBS experiments, p_{ 2 } is the oxBS methylation ratio and p_{1} is the RRBS methylation ratio, and t is the 5hmc methylation ratio. Since the joint probability density of such observation is f(p_{1}; n_{1}; k_{1})f(p_{2}; n_{2}; k_{2}), the PDF for t is
where f_{ i }(p_{ i }) ≡ f(p_{ i }; n_{ i }, k_{ i }).
Let {\mathit{t}}^{\text{'}}={\mathit{p}}_{1}^{\text{'}}{\mathit{p}}_{2}^{\text{'}}, where ′ denotes the other sample. To be clear, call the two samples S and S′. In general we want to know the difference of the two 5hmc ratios, i.e., tt′. Let x = t–t′, we can immediately obtain the distribution of difference of 5hmc ratio between two samples by
where f(t) and f′(t′) are the distributions of 5hmc ratio for sample S and S′ respectively. After distribution of difference of 5hmc ratio between two samples is obtained, similarly confidence interval, credible difference and similarity test pvalue can be calculated.
Distribution for measurements with replicates
Here we use the exact numerical approach to calculate the distribution of p at observance (m_{ i }, l_{ i }) of with m_{ i } as total count for replicate i and l_{ i } as methylated count for replicate i. Let us start with 2 replicates. We try to fit this unknown distribution of p at observance (m_{1}, l_{1}) and (m_{2}, l_{2}) into a Beta distribution f(p; α,β). The parameter estimation is based on the following formula
where P(k_{ i }; n_{ i }, α, β) is the probability to observe (n_{ i }, k_{ i }) under the Beta distribution f(p; α, β), and f(k_{ i }; n_{ i }, p) is the Binomial distribution, i.e., the probability to observe (n_{ i }, k_{ i }) under a specific true ratio p. For N number of replicates, (α, β) may be estimated by maximizing the log likelihood function
where the expression inside log is the probability P(k_{ i }; n_{ i }, α, β) defined in equation (5) and B (α, β)is the Beta function.
Abbreviations
 CDIF:

Credible difference
 DMC:

Differentially methylated cytosine
 DMR:

Differentially methylated region
 FETP:

Fisher’s exact test Pvalue
 TFBS:

Transcription factor binding site.
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Acknowledgements
We are grateful to Wei Xie for sharing the mouse methylome data, and Grant A. Challen for critical reading of this manuscript. This work was supported by CPRIT RP110471C3 and NIH R01HG007538 (to WL).
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DS and WL conceived the project, designed the algorithms, analyzed the data, and wrote the manuscript. DS developed the software package with the help of YX, TP and HJP; MM and MAG contributed the HSC methylome. All authors participated in the discussion and edited the manuscript. All authors read and approved the final manuscript.
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Additional file 1: The source code for the software MOABS. This version is for archive purpose only. Please download the latest version from website. (ZIP 708 KB)
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Additional file 2: Table S1: Benchmark for performance of MOABS and BSmooth for reads alignment, methylation call, and differential methylation. (XLSX 51 KB)
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Sun, D., Xi, Y., Rodriguez, B. et al. MOABS: model based analysis of bisulfite sequencing data. Genome Biol 15, R38 (2014). https://doi.org/10.1186/gb2014152r38
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DOI: https://doi.org/10.1186/gb2014152r38