New Results

S3norm: simultaneous normalization of sequencing depth and signal-to-noise ratio in epigenomic data

Guanjue Xiang, Cheryl A. Keller, Belinda Giardine, Lin An, Qunhua Li, Yu Zhang, Ross C. Hardison
doi: https://doi.org/10.1101/506634

ABSTRACT

Quantitative comparison of epigenomic data across multiple cell types or experimental conditions is a promising way to understand the biological functions of epigenetic modifications. However, differences in sequencing depth and signal-to-noise ratios in the results from different experiments can hinder our ability to identify real biological variation from raw epigenomic data. Proper normalization is required prior to data analysis to gain meaningful insights. Most existing methods for data normalization standardize signals by rescaling either background regions or peak regions, assuming that the same scale factor is applicable to both background regions and peak regions. While such methods adjust for differences due to sequencing depths, they do not address differences in the signal-to-noise ratios across different experiments. We developed a new data normalization method, called S3norm, that normalizes the sequencing depths and signal-to-noise ratios across different data sets simultaneously by a monotonic nonlinear transformation. We show empirically that the epigenomic data normalized by our method, compared to existing methods, can better capture real biological variation, such as impact on gene expression regulation.

INTRODUCTION

Epigenetic features of chromatin, such as histone modifications, transcription factor binding, and nuclease accessibility, play an important role in the regulation of gene expression. Advances in biochemical enrichment strategies and high-throughput sequencing technologies have made it possible to determine the landscape of epigenetic features at a genome-wide scale. In recent years, a large collection of genome-wide epigenetic profiles have been acquired in many cell types under different biological contexts (1–4). Quantitative comparison of these epigenetic profiles across different cell types is a powerful approach to study the biological functions of epigenetic modifications and infer functional elements in genomes. Technical heterogeneity across the data sets, such as differences in sequencing depth (SD) and signal-to-noise ratio (SNR), however, can create systematic biases that mask real biological variation (5). Proper data normalization is needed to correct these biases before meaningful insights can be gleaned from the data analyses (6, 7).

A commonly used strategy for data normalization is to calculate a scale factor between two data sets (8, 9), for example between a reference data set and a target data set, and then rescale the target data set according to the scale factor. The simplest scale factor is the ratio of the total signals between the two data sets, which we will refer to as TSnorm hereafter (Figure 1A). This approach is based on the assumption that the signals of a data set is dominated by the background regions and works well when real signals are scarce and take up only a small proportion of reads among the total. For epigenetic profiles, however, signal regions are often abundant, with drastically different number of peaks and reads across different data sets (9–12), whereas the background regions are more uniform across data sets. Recognizing this issue, some recent data normalization methods, such as SES and NCIS (13, 14), took a two-step approach. They first identify the background regions, and then they calculate the scale factor only from the background regions. While these methods can adjust for the scale differences in background regions between data sets, they implicitly assume that the same scale factor can be applied to peak regions as well. In reality, however, the signal-to-noise ratios between data sets are often different, thus the scale factor for the peak regions should be different from that for the background regions.

Figure 1.
Figure 1.

Impacts of different methods of data normalization. Panel (A-C), respectively, shows schematic plots for the signals in two epigenomic data sets normalized by TSnorm, MAnorm, and S3norm. (D-I) The ATAC-seq or DNase-seq read counts at histone gene loci in three cell types (LSK, MEP, and ERY). Panel (D) shows the raw read counts in those three cell types. Panel (E), and (H), respectively, shows the read counts normalized by TSnorm, MAnorm, and S3norm. The scale of tracks is from 0 to 1000. Panel (G) and (I), respectively, shows the zoomed-in version of the same regions in Panel (F) and (H). The scale of tracks is from 0 to 100.

Some normalization methods focus on adjusting SNRs across data sets (15). MAnorm (6), one of the earliest methods to consider SNRs in ChIP-seq normalization, uses the MA plot (16) to fit a curve between signal intensity ratio (M) and average intensity (A) between data sets. The fitting is done using signals in the common peak regions between data sets, under the assumption that the normalized data sets in common peak regions should have the same SNRs. The fitted curve is then applied to adjust signals in peak regions (Figure 1B). MAnorm can adjust signals in peak regions, but not for background regions. It thus is not applicable for applications that utilize signals across the genome, such as genome segmentation (17–20). In segmentations, some epigenetic states are defined by low signals of features, in which case an increase of background noise could result in incorrect assignments to those states. Alternative methods LOWESS normalization and quantile normalization (QTnorm), have been used to adjust both SDs and SNRs by equalizing local signals between two data sets (21–23). When applying these two methods to data sets with substantially different numbers of peaks, they may increase background noise (or decrease peak signals) for data sets with fewer (or more) peaks (21). Finally, rank-based methods have been proposed to normalize data sets with different signal distributions by converting signals into ranks (24). Because they ignore the quantitative spread among signals, they may lose power, and therefore they are not considered in this study.

To illustrate the aforementioned issues encountered by the existing methods (Figure 1), we applied TSnorm and MAnorm to the nuclease accessibility data (ATAC-seq) at a histone gene locus in three hematopoietic cell types, namely, a stem and progenitor cell population (the lineage negative, Sca1 positive, c-kit negative cells or LSK), the megakaryocyte erythroid progenitor cells (MEP), and erythroblasts (ERY) (25). We chose this locus because active production of histones is required for cell replication, and histone genes usually have similar activities across all proliferating cell types. Thus the profiles of nuclease accessibility in the neighborhood are expected to be similar across cell types, but as shown in Figure 1D, the raw ATAC-seq signals in this locus were clearly weaker in LSK and MEP than in ERY. After applying TSnorm, which used a single scale factor, the signals in LSK and MEP were increased but the signals of the peak regions in LSK and MEP were still weaker than in ERY (Figure 1E). This result is expected for a method that cannot match signals in both peak regions and background regions simultaneously. After applying MAnorm, which only used information in common peak regions to estimate a normalization model, the signals of the peak regions in both LSK and MEP were increased to match the level in ERY (Figure 1F), but the background was inflated in LSK (Figure 1G). These results illustrate the need for simultaneous adjustment of both peaks and background.

We developed a new two-factor normalization method, called S3norm, to Simultaneously normalize the Signal in peak regions and the Signal in background regions of epigenomic data sets. Unlike TSnorm or MAnorm, in which either background regions or common peak regions contribute to normalization, our method matches both the mean signals in the common peak regions and the mean signals in the common background regions between two data (Figure 1G), balancing the contribution of common peak and common background regions to data normalization. As a result, S3norm matched the peak signals in our example data sets (ERY, LSK and MEP) without increasing noise the background signals (Figure 1H and I). In this paper, we demonstrate the superior performance of S3norm over existing methods using several epigenomic data sets with a wide range of data quality.

MATERIALS AND METHODS

Data preprocessing and evaluation

We used the data sets compiled by the ValIdated and Systematic integratION of epigenomic data project (VISION: usevision.org), which includes eight epigenetic marks (H3K4me3, H3K4me1, H3K27ac, H3K36me3, H3K27me3, H3K9me3, CTCF occupancy, and nuclease sensitivity) in twenty hematopoietic cell types of mice (20, 26–28). Using the bam files processed by the pipeline of VISION project as the input data (20, 28, 29), we then divided the mm10 mouse genome assembly into ∼13 million 200-bp bins and counted the number of reads mapped to each bin (30). The reads counts per bin comprised the raw signals for each data set. For each data set, the SD was estimated by the number of mapped reads, and the SNR was estimated as the Fraction of Reads in Peaks (FRiP score) (31). The VISION data sets were generated in different laboratories at different time using different technologies, leading to substantial variation in signal quality across data sets (Supplementary Figure 1). Considering H3K4me3 experiments as an example, the total number of mapped reads ranged from <1 million to >10 millions, and the FRiP score ranged from <0.1 to >0.9. This large variability in both SDs and SNRs requires both aspects to be properly normalized to enable meaningful downstream analysis. Indeed, this large variation in both SD and SNR served as a motivating problem to develop our normalization method.

Simultaneous normalization of both peak regions and background regions

S3norm is a normalization model that matches signals in the peak regions between two data sets while avoiding an increase in background (Figure 2). Because the numbers and the signals of the unique peaks can differ between the two data sets, S3norm learns its normalization parameters only from the signals in the common peak regions (6) and the signals in the common background regions. S3norm is built on two assumptions derived from the biological principles of epigenetic events. First, we assumed that epigenetic events shared by multiple cell types tend to regulate processes occurring in all those cell type, such as expression of constitutively active genes, so that the mean signal of common peaks should be the same after normalization. Second, we assumed that the signals in common background regions are technical noise, and thus, they should be equalized after normalization. Based on these two assumptions, S3norm matches the mean signals in the common peak regions and the mean signals in the common background regions between the two data sets. S3norm can also work for more than two data sets, in which case the common peak regions and the common background regions are those shared by all data sets.

Figure 2.
Figure 2.

Overview of the S3norm method. The graphs present scatterplots of read counts (log scale) in 10,000 randomly selected genome locations (200bp) in target cell (x-axis) and reference cell (y-axis). The left figure is the signal before S3norm. The right figure is the signal after S3norm. The S3norm applies a monotonic nonlinear model (log (Ynorm,i) = log(α) + βlog(Yi)) to rotate the target signal so that (1) the mean signals of common peaks (green point, highlighted by black dash circle) and (2) the mean signals of common background (dark blue point, highlighted by black dash circle) can be matched between the two data sets. The original data were split into three groups: the common peak regions (orange), the common background regions (gray), and the remaining bins (blue). The overall mean is represented by a black point.

To match the mean signals, we treat one data set as the reference and the other data set as the target, transforming the signals in the target data set by the following monotonic nonlinear function:

Let Yi and Ynorm,i denote the signal of bin i in the target data set before and after normalization, then Embedded Image where α and β are two positive parameters to be learned from the data. Specifically, α is a scale factor that shifts the signals of the target data set in log scale, and β is a power transformation parameter that rotates the signals of the target data set in log scale (Figure 2). There is one and only one set of values for α and β that can simultaneously match the mean signals in both the common peak regions and the common background regions between the two data sets. In practice, we found matching the arithmetic mean in the original signal space can produce normalized signals with a cleaner background. Thus, our approach solves the values for α and β which satisfy the following two equations, so that the arithmetic mean signals in original signal space in both the common peak regions and the common background regions can be matched between two data sets: Embedded Image where the mean(αYtar,pkβ) and the mean(αYtar,bgβ) are the means of normalized signals in common peak regions and common background region in target data set, the mean(αYref,pk) and the mean(αYref,bg) are the mean of signal in the same common peak regions and the same common background region in reference data set. The values of α and β were estimated by the Newton-Raphson method (32).

Depending on the characteristics of data sets being normalized, users may choose to match the mean signals of non-zero bins or the median signals of all bins rather than matching the mean signals as just described. For example, when the data sets have a very large number of zero bins, matching the mean signals of non-zero bins can generate more consistent background across data sets. For the reference data set, we choose the data set with the best SNR as the reference. In the S3norm package, users can also choose other data set or generate a reference data set by using the median (or mean) signal of all data sets for each genome position.

Generating signal tracks from normalized signal

To facilitate use in downstream analysis, such as peak calling and genome segmentation, we provide a script to generate signal tracks (bigwig format) of the S3norm normalized signals. We followed a similar method as the one adopted in MACS (9) except that the Poisson model used to adjust for fluctuation in the local background (33–36) was replaced by a Negative Binomial (NB) model. In ChIP-seq data, the variance is often greater than the mean (supplementary Figure 2), so NB is preferred as the background model because it estimates the mean and variance separately, whereas the Poisson model has the same mean and variance.

For ChIP-seq, there are usually two data sets for each experiment, one is referred as a immune-precipitation (IP) sample which is a data set generated by sequencing the DNA after immune-precipitation by target-specific antibody, and the other one is the corresponding control sample which is another data set generated by sequencing either the input DNA without immune-precipitation or the DNA after immune-precipitation by non-specific antibody.

The NB background model was defined as follows. Let ri and Embedded Image denote the read counts in bin i in a IP and a control, respectively. Let M and σ2 denote the mean and variance of read counts in the IP in the common background regions, and Mctrl denote the mean read counts in the control in the common background regions. Our dynamic NB background model is defined as: Embedded Image where p denotes the probability of success parameter in the NB model, and slocal denotes a shape parameter of the NB model. For each bin i, slocal is adjusted by Embedded Image to capture any local bias as reflected in the control. The increase of control signal (Embedded Image) is equivalent to the decrease of σ2 which can generate a more significant p-value. The Embedded Image is the local mean read count learned from the control computed in a same way in MACS (9). The ri,wg is the genome mean read count in the control, the ri,1kb, ri,5kb and ri,10kb, are mean read counts of different window sizes centered at the bin i in the control. The local mean read counts are calculated as the maximum of ri,wg, ri,1kb, ri,5kb and ri,10kb. For data sets without a control (i.e. ATAC-seq), the value for Embedded Image can be generated with both of two modifications (9). First, the Embedded Image and Mctrl are estimated from the IP instead of the control. Second, the ri,1kb is not used to estimate Embedded Image.

Finally, −log10 p-value of read count per bin, as derived from the NB background model, is used as the processed signal in the S3norm signal track.

Predicting gene expression from histone modifications

To evaluate whether our new method helped bring out biological meaning from epigenomic data, we used S3norm and several current methods to normalize histone modification datasets, and then compared how well the data normalized by the different methods could predict levels of gene expression. Previous studies showed that a model properly trained to predict gene expression from histone modifications in one cell type can be used to predict gene expression accurately in a different cell type utilizing the histone modification data from the second cell type (37, 38). We thus hypothesized that improvements in normalization of histone modification datasets would enable more accurate prediction of gene expression. We used two histone modifications (H3K4me3 and H3K27ac) that are strong predictors of gene expression (39). Following the study design in Dong et al 2012 (37), we used ten-fold cross validation to evaluate the predictability of gene expression. For each cross validtion, we randomly selected 90% of the genes as training genes and the remaining 10% of the genes as the testing genes. We first trained a regression model to predict expression of training genes in one cell type (training cell type). We then applied the trained model to predict the expression of testing genes in another cell type (testing cell type). The Reads Per Kilobase of transcript per Million mapped reads (RPKM) in log2 scale was used as the estimate of gene expression. The histone modification signal was defined as the mean read counts of the histone modification in a 5kb window centered at transcription start site (TSS). The predictability of gene expression was measured by mean square error (MSE) between the observed gene expression and the predicted gene expression in the testing genes in the testing cell type. To prevent a bias from a specific regression model, we performed this analysis by using four different commonly used regression models, specifically a local regression (loess) model, the 2-step linear regression model (37), a linear regression model, and a support vector machine regression (SVR) model.

Calling peaks from epigenomic data by MACS2

To compare of the influence of data normalization on peak calling, we applied MACS2 to call peaks from CTCF ChIP-seq data normalized by different normalization methods. We first generated the signal tracks in each cell type. For all methods, the signal track was generated by the −log10 p-value (input signal for bdgpeakcall in MACS2 package) of normalized reads count based on the previously described NB background model. We then used the bdgpeakcall in the MACS2 package in the default setting to call peaks from the signal tracks. The threshold was FDR = 1e-2. For each normalization method, the CTCF peaks were first called in 11 cell types that have CTCF occupancy data in VISION project. We used the UpSet method (40) to visualize the number of commonly called peaks from different normalization methods.

To evaluate the type I error (false positive peaks) in these CTCF peak calling results, we compared both the proportion of peaks with a CTCF binding site motif (Jaspar id: MA0139.1) (41) and the signal consistency between the biological replicates in these peaks. We expected that the false positive peaks were generated from the background regions with increased signal, so that they should have lower values for both of these two measurements.

For the proportion of peaks with CTCF binding site motif, we used FIMO in its default setting to scan for the CTCF binding site motif (Jaspar id: MA0139.1) (41) in those peaks.

The signal consistency between the biological replicates was measured by the mean square error (MSE) between the two biological replicates. Embedded Image where signalrep1 and signalrep2 are the signals in two biological replicates. The false positive peaks tend to be the peaks with lower signal. To measure the signal consistency of peak with different signal levels, we calculated the cumulative MSEs. Specifically, we first calculated the MSE of peaks with highest signals (top 1 to 5,000 peaks) and used the MSE as the first MSE in figure 5B. In the second step, we added more peaks (top 1 to 10,000 peaks) and recalculated the MSE. We repeated the second step until all of the peaks were used. All of the MSEs were defined as the cumulative MSEs for each method. We plotted the cumulative MSE for both S3norm peaks and the QTnorm peaks in figure 5B. Since there are more QTnorm peaks than the S3norm peaks, the cumulative MSEs of the QTnorm peaks have more points.

RESULTS

S3norm overview

We introduce a new data normalization method called S3norm that uses a nonlinear transformation to normalize signals in both peak regions and background regions simultaneously. The goal of the S3norm method is to match both the mean signal in the common peak regions and the mean signal in the common background regions between a target data set and a reference data set, which is the data set with the best SNR (Figure 2). The method employs a nonlinear transformation model with parameters learned from the signal in both common peaks and common background regions. As shown in the scatterplot between signal of target data set and signal of reference data set, this nonlinear transformation can rotate the target signal in log scale so that both the mean signal in the common peak regions and the mean signal in the common background regions between a target data set and a reference data set can are matched. As a result, the method can boost signals in peak regions in the target data set without increasing the background noise, thereby increasing the SNR in the target data sets (see Materials and Methods for details). This makes S3norm a more desirable method for genome-wide normalization across multiple data sets than existing methods.

Evaluation by ATAC-seq

We first compared S3norm with other normalization methods in terms of their abilities to match the signal in both peak regions and background regions. We used the ATAC-seq data sets in megakaryocyte (iMK) cells (∼92 million reads for replicate 1 and ∼74 million reads for replicate 2) and LSK cells (∼53 million reads for replicate 1 and ∼59 million reads for replicate 2) for illustration. We chose these two data sets because they have different SNRs (Figure 3A). We used the iMK as the reference because it has a higher SNR than the LSK data set. For all normalization methods, the signal of the target data set was matched to the signal of the reference data set.

Figure 3.
Figure 3.

Comparison of normalization methods on peaks and background in ATAC-seq experiments. The scatterplots of ATAC-seq signal in iMK (reference data set) and LSK (target data set) are shown on a log scale. (A) The scatterplot of the raw signal between reference data set and target data set. Panel (B) to (E), respectively, shows the scatterplot of the signal after TSnorm, MAnorm, QTnorm, and S3norm. (F) The boxplot of the mean signals in common peak regions (P) and the mean signals in the common background regions (B) in the biological replicates of different cell types.

Because the two data sets had similar signal in background regions, the TSnorm method had little impact on the results (Figure 3B), i.e., the peak signals in iMK remained consistently higher than the peak signals in LSK after TSnorm normalization. The MAnorm method did normalize the signals in peak regions so that the peak signals in the LSK data set became similar to the peak signals in the iMK data set (Figure 3C). However, MAnorm increased the noise in the background regions in the LSK data set. The poor performance of TSnorm and MAnorm was expected, as they either used background regions or peak regions to calculate scale factors, but not considering both types of regions simultaneously. In contrast, the QTnorm and S3norm normalized the signals in both peak regions and background regions. After their normalization, the mean signals of the common peak regions (green point) and the mean signals in the common background regions (dark blue point) were both matched between the two data sets (Figure 3D and E).

We further systematically used the four methods to normalize all ATAC-seq data sets in the VISION project that have biological replicates. We used the data set with the highest SNR as the reference, which is the iMK data set. As shown in Figure 3F, the signals in the common peak regions retained substantial differences both between replicates and across all data sets after TSnorm, illustrating the limitation of single factor normalization. On the other hand, though MAnorm can adjust the signal in common peak regions appropriately (as deduced from similarities in distributions between replicates), the signals in the background regions became more heterogeneous across all data sets than before normalization. In comparison, S3norm and QTnorm effectively adjusted the signals in both types of regions so that the normalized signals became much more comparable both between replicates and across data sets.

Evaluation by gene expression

Modeling approaches have been used to predict gene expression from histone modifications, and the quantitative relationships learned from one cell type can be applied to predict gene expression in other cell types (37, 38). The predictability, however, will be reduced if the epigenomic data across cell types are not properly normalized. We thus use the predictability of gene expression from different normalized epigenetic data to evalute their ability to reflect real biological variation.

Specifically, we randomly selected 90% of genes (Training Genes) to train four commonly used regression models to predict a gene expression from H3K4me3 and H3K27ac normalized signals around a gene TSS. We then evaluated the performance of these regression models on the remaining 10% of genes (Testing Genes). We first trained the regression models using the Training Genes in one cell type (Training Cell type) and then evaluated the models using the Testing Genes in both Training Cell type and a different cell type (Testing Cell type).

The evaluation in the Training Cell type is to see if these regression models can successfully learn robust quantative relationships between gene expression and histone modifications. As expected for performance in the Training Cell types, the MSEs of the models were similarly good across all normalization methods (Figure 4A and Supplementary figure 3A-C). It thus indicated the regression models can successfully learn the quantitative relationships between the gene expression and histone modications with different normalizations.

Figure 4.
Figure 4.

Comparing S3norm and other methods by their ability to predict gene expression. (A) The MSE of the observed RNA-seq signal and the predicted RNA-seq in ten-fold cross validation in the Training Cell Type by using a loess regression model. (B) The MSE of the observed RNA-seq signal and the predicted RNA-seq in ten-fold cross validation in the Testing Cell Type. The p-values above the boxes come from the Wilcoxon test that tests if the MSE of S3norm are significantly better than the other methods.

Figure 5.
Figure 5.

Comparing S3norm and other methods by CTCF ChIP-seq peak calling results. (A) The UpSet figure of the peak calling results using different normalization signals in all 11 cell types in VISION project. The top black barplot represents the number of peaks present in the peak calling results by using different normalized signals. The black points below each bar represent the combinations of normalization methods. The left barplot represents the total number of peaks called by using a specific normalization method. For the bars with the substantial number of peaks, the number of the peaks are shown on the top of the bar. The percentage of those peaks that include the CTCF motif are shown in the parentheses. (B) The cumulative mean square errors (MSE) of CTCF-seq signal between two biological replicates. Each point represents the MSE calculated from signals of two biological replicates in top 1 to N+5000 peaks with the highest mean signals. For examples, the first blue point on the left indicates the MSE of top 1 to 5,000 S3norm peaks is 0.74 and the second blue point on the left indicates the MSE of top 1 to 10,000 S3norm peaks is 0.70. The vertical lines with different colors represent the proportion of the pooled peak list was called by a specific normalization method. Panel (C) and (D) shows the normalized peak signals in two biological replicates. Panel (C) is the signals normalized by QTnorm. Panel (D) is the signals normalized by S3norm.

To further evaluate if the learned quantitative relationships can be applied to different cell types, we compared the performances of the trained models on the Testing Genes in the Testing Cell Type. As shown in figure 4B and Supplementary figure 3D-F, the models trained on S3norm signals and QTnorm signals were always better (Wilcoxon test p-value < 1e-4) than the models trained on the TSnorm signals and MAnorm signals. This result shows that the quantitative relationships learned from the histone modification signals normalized by the latter two methods did not transfer to other cell types as effectively as those normalized by QTnorm and S3norm.

Evaluation by peak calling

So far we have observed superior performance of S3norm and QTnorm than some other normalization methods. Like S3norm, QTnorm matches the signal in both peak regions and background regions simultaneously. However, QTnorm assumes normalized signals have the same distribution across data sets. This assumption is particularly questionable for epigenomic data, because the number of epigenetic peaks usually differs substantially across cell types. If two data sets have different numbers of peaks, QTnorm would force some background signals in the data set with fewer peaks to match the peak signals with the same rank in the data set with more peaks, potentially creating false positive peaks.

To evaluate the effect of normalization on peak calling, we called peaks on CTCF ChIP-seq data in VISION project using the signal normalized by different normalization methods. We first compared the number of peaks overlapping between sets by using the UpSet figure (Figure 5A) (40). While almost 80,000 peaks were called consistently on the data normalized by all methods, 71,472 peaks were only called from the QTnorm signal. These peak calls that were unique to normalization by QTnorm could be false positive peaks created by forcing identical distributions across data sets and thereby inflating the background such peaks are called erroneously.

To further estimate the false positive peaks in these peaks, we first compared the proportion of the peaks with a match to the CTCF binding site motif in the peaks obtained from the different normalization methods. Given that the ∼80% of CTCF binding site contain the CTCF motif (42, 43), we expect the false positive peaks should be less likely to have CTCF motif. Among the QTnorm specific peaks, only 8.7% of the peaks had CTCF binding site motif, whereas 80.8% of the peaks that shared by all methods had CTCF motif. These results suggest that many of the QTnorm CTCF peaks are likely to be false positive peaks.

Furthermore, we examined the consistency of signal strengths in biological replicates of CTCF in G1E-ER4 cells. We first pooled and merged the peaks called by different normalized methods into one master peak list. The mean square error (MSE) between the two biological replicates of these peaks was used to measure the signal consistency (Figure 5B) (see Materials and Methods section for more details). The number of peaks in the pooled peak list that was called by each normalization method was shown as a vertical line with specifc color. Compared with S3norm, QTnorm called ∼42% more peaks. The peaks called in both S3norm signals and QTnorm signals were highly consistent, with similarly low MSEs between the biological replicates. For the QTnorm specific peaks, however, the MSEs between biological replicates increased substantially. That is, the signals were less consistent between replicates in those peaks. This is also confirmed by the scatterplot showing the signal of two biological replicates normalized by QTnorm and S3norm. The replicates normalized by QTnorm show much more between-replicate variance, especially for the peaks with weaker signals (Figure 5C) relative to S3norm (Figure 5D). All of these results suggest the large number of QTnorm specific peaks are false positive peaks.

The evaluation of both CTCF motif occurrence and the signal consitency indicate the S3norm has a substantial advantage over QTnorm in reducing false positive peaks in peak calling results.

DISCUSSION

We introduce a simple and robust method to normalize the signals across multiple epigenomic data sets. The essence of this method is to use a nonlinear transformation to rotate the signal of the target data set to that of the reference data set, so that the mean signals of both common peak regions and common background regions are matched simultaneously between the two data sets. The S3norm method achieves several notable improvements over existing normalization methods. First, the inclusion of background regions is a particular advantage when data across the entire genome needs to be normalized. As an example, this method was developed to facilitate our work on genomic segmentations that assign every genomic interval to an epigenetic state, which is a common combination of epigenetic features (20). An inflation of background noise could result in assigning regions with increased noise to low signal-containing states. Second, in contrast to the TSnorm and QTnorm methods, S3norm is robust to biases resulting from the substantial proportion of background regions in the genome. Third, S3norm can be trained on data sets with small numbers of peaks, such as data sets that include spike-in controls (44). Finally, S3norm has only two parameters to be trained from the data, which makes the method robust across a wide variety of data sets.

A key assumption of the S3norm method is that true biological signals should have the same means in common peak regions and in common background regions between data sets. For some data sets in which different signal strengths in common peak regions are expected, the S3norm method may not be directly applicable. For example, for ChIP-seq data sets of transcription factors whose abundance is changing over the course of a targeted degradation protocol, we expect the mean signals in peak regions (which are common peak regions across the time course) to deteriorate over time. In such cases, one should not use any of the data sets in the time course as a reference for S3norm normalization. Instead, a spike-in control or a small number of unchanged peak regions identified by other techniques should be paired with the background regions at each time point in order for S3norm to work properly.

In summary, S3norm is a simple and robust method to normalize multiple data sets. The results of applying S3norm to epigenomic data sets show that it is more effective in bringing out real biological differences than existing methods. As more epigenomic data continue to be generated, S3norm will be useful to normalize signals across these diverse and heterogeneous epigenomic data sets to allow downstream analyses to capture true epigenetic changes rather than technical bias. Improved normalization will aide studies that analyze data sets across multiple experiments, such as differential gene regulation, genome segmentation (17, 19), joint peak calling (45), predicting gene expression (46), and detecting transcription factor binding events (47).

DATA AVAILABILITY

Files for raw signals, p-value converted signals, and signals from S3norm are available both for download and for viewing from the VISION website (http://usevision.org). The S3norm normalization package is available at GitHub (https://github.com/guanjue/S3norm).

FUNDING

The work is supported by National Institutes of Health grants [GM121613 to Y.Z.], [DK106766 to Y.Z. R.C.H., and Q.L.], [GM109453 to Q.L.] and [CA178393 to R.C.H.].

ACKNOWLEDGEMENT

We thank Dr. Alexander Q. Wixom and Tiffany Wang for their help to test S3norm package.

References

  1. 1.↵
    ENCODE Project Consortium (2012) An integrated encyclopedia of DNA elements in the human genome. Nature, doi:10.1038/nature11247.
    OpenUrlCrossRefPubMedWeb of Science
  2. 2.↵
    Bernstein, B.E., Stamatoyannopoulos, J.A., Costello, J.F., Ren, B., Milosavljevic, A., Meissner, A., Kellis, M., Marra, M.A., Beaudet, A.L., Ecker, J.R., et al. (2010) The NIH roadmap epigenomics mapping consortium. Nat. Biotechnol., doi:10.1038/nbt1010-1045.
    OpenUrlCrossRefPubMedWeb of Science
  3. 3.
    Stunnenberg, H.G., Abrignani, S., Adams, D., de Almeida, M., Altucci, L., Amin, V., Amit, I., Antonarakis, S.E., Aparicio, S., Arima, T., et al. (2016) The International Human Epigenome Consortium: A Blueprint for Scientific Collaboration and Discovery. Cell, doi:10.1016/j.cell.2016.11.007.
    OpenUrlCrossRef
  4. 4.↵
    Martens, J.H.A. and Stunnenberg, H.G. (2013) BLUEPRINT: Mapping human blood cell epigenomes. Haematologica, doi:10.3324/haematol.2013.094243.
    OpenUrlFREE Full Text
  5. 5.↵
    Kidder, B.L., Hu, G. and Zhao, K. (2011) ChIP-Seq: Technical considerations for obtaining high-quality data. Nat. Immunol., doi:10.1038/ni.2117.
    OpenUrlCrossRefPubMed
  6. 6.↵
    Shao, Z., Zhang, Y., Yuan, G.-C., Orkin, S.H. and Waxman, D.J. (2012) MAnorm: a robust model for quantitative comparison of ChIP-Seq data sets. Genome Biol., doi:10.1186/gb-2012-13-3-r16.
    OpenUrlCrossRefPubMed
  7. 7.↵
    Meyer, C.A. and Liu, X.S. (2014) Identifying and mitigating bias in next-generation sequencing methods for chromatin biology. Nat. Rev. Genet., doi:10.1038/nrg3788.
    OpenUrlCrossRefPubMed
  8. 8.↵
    Marioni, J.C., Mason, C.E., Mane, S.M., Stephens, M. and Gilad, Y. (2008) RNA-seq: An assessment of technical reproducibility and comparison with gene expression arrays. Genome Res., doi:10.1101/gr.079558.108.
    OpenUrlAbstract/FREE Full Text
  9. 9.↵
    Zhang, Y., Liu, T., Meyer, C.A., Eeckhoute, J., Johnson, D.S., Bernstein, B.E., Nussbaum, C., Myers, R.M., Brown, M., Li, W., et al. (2008) Model-based analysis of ChIP-Seq (MACS). Genome Biol., doi:10.1186/gb-2008-9-9-r137.
    OpenUrlCrossRefPubMed
  10. 10.
    John, S., Sabo, P.J., Thurman, R.E., Sung, M.H., Biddie, S.C., Johnson, T.A., Hager, G.L. and Stamatoyannopoulos, J.A. (2011) Chromatin accessibility pre-determines glucocorticoid receptor binding patterns. Nat. Genet., doi:10.1038/ng.759.
    OpenUrlCrossRefPubMedWeb of Science
  11. 11.
    Heinz, S., Benner, C., Spann, N., Bertolino, E., Lin, Y.C., Laslo, P., Cheng, J.X., Murre, C., Singh, H. and Glass, C.K. (2010) Simple Combinations of Lineage-Determining Transcription Factors Prime cis-Regulatory Elements Required for Macrophage and B Cell Identities. Mol. Cell, doi:10.1016/j.molcel.2010.05.004.
    OpenUrlCrossRefPubMedWeb of Science
  12. 12.↵
    Boyle, A.P., Guinney, J., Crawford, G.E. and Furey, T.S. (2008) F-Seq: A feature density estimator for high-throughput sequence tags. Bioinformatics, doi:10.1093/bioinformatics/btn480.
    OpenUrlCrossRefPubMedWeb of Science
  13. 13.↵
    Diaz, A., Nellore, A. and Song, J.S. (2012) CHANCE: comprehensive software for quality control and validation of ChIP-seq data. Genome Biol., doi:10.1186/gb-2012-13-10-r98.
    OpenUrlCrossRefPubMed
  14. 14.↵
    Liang, K. and Keles, S. (2012) Normalization of ChIP-seq data with control. BMC Bioinformatics, doi:10.1186/1471-2105-13-199.
    OpenUrlCrossRefPubMed
  15. 15.↵
    Tu, S. and Shao, Z. (2017) An introduction to computational tools for differential binding analysis with ChIP-seq data. Quant. Biol., doi:10.1007/s40484-017-0111-8.
    OpenUrlCrossRef
  16. 16.↵
    Smyth, G.K. and Speed, T. (2003) Normalization of cDNA microarray data. Methods, doi:10.1016/S1046-2023(03)00155-5.
    OpenUrlCrossRefPubMedWeb of Science
  17. 17.↵
    Ernst, J. and Kellis, M. (2012) ChromHMM: Automating chromatin-state discovery and characterization. Nat. Methods, doi:10.1038/nmeth.1906.
    OpenUrlCrossRefPubMedWeb of Science
  18. 18.
    Hoffman, M.M., Buske, O.J., Wang, J., Weng, Z., Bilmes, J.A. and Noble, W.S. (2012) Unsupervised pattern discovery in human chromatin structure through genomic segmentation. Nat. Methods, doi:10.1038/nmeth.1937.
    OpenUrlCrossRefPubMedWeb of Science
  19. 19.↵
    Zhang, Y., An, L., Yue, F. and Hardison, R.C. (2016) Jointly characterizing epigenetic dynamics across multiple human cell types. Nucleic Acids Res., doi:10.1093/nar/gkw278.
    OpenUrlCrossRefPubMed
  20. 20.↵
    Xiang, G., Keller, C.A., Heuston, E., Giardine, B.M., An, L., Wixom, A.Q., Miller, A., Cockburn, A., Lichtenberg, J., Göttgens, B., et al. (2019) An integrative view of the regulatory and transcriptional landscapes in mouse hematopoiesis. https://doi.org/10.1101/731729.
  21. 21.↵
    Bolstad, B.M., Irizarry, R. a, Astrand, M. and Speed, T.P. (2003) A comparison of normalization methods for high density oligonucleotide array data based on variance and bias. Bioinformatics, doi:10.1093/bioinformatics/19.2.185.
    OpenUrlCrossRefPubMedWeb of Science
  22. 22.
    Nair, N.U., Das Sahu, A., Bucher, P. and Moret, B.M.E. (2012) Chipnorm: A statistical method for normalizing and identifying differential regions in histone modification chip-seq libraries. PLoS One, doi:10.1371/journal.pone.0039573.
    OpenUrlCrossRefPubMed
  23. 23.↵
    Taslim, C., Wu, J., Yan, P., Singer, G., Parvin, J., Huang, T., Lin, S. and Huang, K. (2009) Comparative study on ChIP-seq data: Normalization and binding pattern characterization. Bioinformatics, doi:10.1093/bioinformatics/btp384.
    OpenUrlCrossRefPubMedWeb of Science
  24. 24.↵
    Lyu, Y. and Li, Q. (2016) A semi-parametric statistical model for integrating gene expression profiles across different platforms. BMC Bioinformatics, doi:10.1186/s12859-015-0847-y.
    OpenUrlCrossRef
  25. 25.↵
    Buenrostro, J.D., Giresi, P.G., Zaba, L.C., Chang, H.Y. and Greenleaf, W.J. (2013) Transposition of native chromatin for fast and sensitive epigenomic profiling of open chromatin, DNA-binding proteins and nucleosome position. Nat. Methods, doi:10.1038/nmeth.2688.
    OpenUrlCrossRefPubMedWeb of Science
  26. 26.↵
    Oudelaar, A.M., Hanssen, L.L.P., Hardison, R.C., Kassouf, M.T., Hughes, J.R. and Higgs, D.R. (2017) Between form and function: The complexity of genome folding. Hum. Mol. Genet., doi:10.1093/hmg/ddx306.
    OpenUrlCrossRef
  27. 27.
    Philipsen, S. and Hardison, R.C. (2018) Evolution of hemoglobin loci and their regulatory elements. Blood Cells, Mol. Dis., doi:10.1016/j.bcmd.2017.08.001.
    OpenUrlCrossRef
  28. 28.↵
    Heuston, E.F., Keller, C.A., Lichtenberg, J., Giardine, B., Anderson, S.M., Hardison, R.C. and Bodine, D.M. (2018) Establishment of regulatory elements during erythro-megakaryopoiesis identifies hematopoietic lineage-commitment points. Epigenetics and Chromatin, doi:10.1186/s13072-018-0195-z.
    OpenUrlCrossRef
  29. 29.↵
    Langmead, B., Trapnell, C., Pop, M. and Salzberg, S.L. (2009) Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biol., doi:10.1186/gb-2009-10-3-r25.
    OpenUrlCrossRefPubMed
  30. 30.↵
    Quinlan, A.R. (2014) BEDTools: The Swiss-Army tool for genome feature analysis. Curr. Protoc. Bioinforma., doi:10.1002/0471250953.bi1112s47.
    OpenUrlCrossRefPubMed
  31. 31.↵
    Landt, S.G., Marinov, G.K., Kundaje, A., Kheradpour, P., Pauli, F., Batzoglou, S., Bernstein, B.E., Bickel, P., Brown, J.B., Cayting, P., et al. (2012) ChIP-seq guidelines and practices of the ENCODE and modENCODE consortia. Genome Res., doi:10.1101/gr.136184.111.
    OpenUrlAbstract/FREE Full Text
  32. 32.↵
    Ypma, T.J. (1995) Historical Development of the Newton–Raphson Method. SIAM Rev., doi:10.1137/1037125.
    OpenUrlCrossRefWeb of Science
  33. 33.↵
    Dohm, J.C., Lottaz, C., Borodina, T. and Himmelbauer, H. (2008) Substantial biases in ultra-short read data sets from high-throughput DNA sequencing. Nucleic Acids Res., doi:10.1093/nar/gkn425.
    OpenUrlCrossRefPubMed
  34. 34.
    Kuan, P.F., Chung, D., Pan, G., Thomson, J.A., Stewart, R. and Keles, S. (2011) A statistical framework for the analysis of ChIP-Seq data. J. Am. Stat. Assoc., doi:10.1198/jasa.2011.ap09706.
    OpenUrlCrossRefPubMed
  35. 35.
    Rozowsky, J., Euskirchen, G., Auerbach, R.K., Zhang, Z.D., Gibson, T., Bjornson, R., Carriero, N., Snyder, M. and Gerstein, M.B. (2009) PeakSeq enables systematic scoring of ChIP-seq experiments relative to controls. Nat. Biotechnol., doi:10.1038/nbt.1518.
    OpenUrlCrossRefPubMedWeb of Science
  36. 36.↵
    Vega, V.B., Cheung, E., Palanisamy, N. and Sung, W.K. (2009) Inherent signals in sequencing-based Chromatin-ImmunoPrecipitation control libraries. PLoS One, doi:10.1371/journal.pone.0005241.
    OpenUrlCrossRefPubMed
  37. 37.↵
    Dong, X., Greven, M.C., Kundaje, A., Djebali, S., Brown, J.B., Cheng, C., Gingeras, T.R., Gerstein, M., Guigó, R., Birney, E., et al. (2012) Modeling gene expression using chromatin features in various cellular contexts. Genome Biol., doi:10.1186/gb-2012-13-9-r53.
    OpenUrlCrossRefPubMed
  38. 38.↵
    Karlic, R., Chung, H.-R., Lasserre, J., Vlahovicek, K. and Vingron, M. (2010) Histone modification levels are predictive for gene expression. Proc. Natl. Acad. Sci., doi:10.1073/pnas.0909344107.
    OpenUrlAbstract/FREE Full Text
  39. 39.↵
    Jones, P.A. (2012) Functions of DNA methylation: Islands, start sites, gene bodies and beyond. Nat. Rev. Genet., doi:10.1038/nrg3230.
    OpenUrlCrossRefPubMed
  40. 40.↵
    Lex, A., Gehlenborg, N., Strobelt, H., Vuillemot, R. and Pfister, H. (2014) UpSet: Visualization of intersecting sets. IEEE Trans. Vis. Comput. Graph., doi:10.1109/TVCG.2014.2346248.
    OpenUrlCrossRefPubMed
  41. 41.↵
    Mathelier, A., Zhao, X., Zhang, A.W., Parcy, F., Worsley-Hunt, R., Arenillas, D.J., Buchman, S., Chen, C.Y., Chou, A., Ienasescu, H., et al. (2014) JASPAR 2014: An extensively expanded and updated open-access database of transcription factor binding profiles. Nucleic Acids Res., doi:10.1093/nar/gkt997.
    OpenUrlCrossRefPubMedWeb of Science
  42. 42.↵
    Ghirlando, R. and Felsenfeld, G. (2016) CTCF: Making the right connections. Genes Dev., doi:10.1101/gad.277863.116.
    OpenUrlAbstract/FREE Full Text
  43. 43.↵
    Nakahashi, H., Kwon, K.R.K., Resch, W., Vian, L., Dose, M., Stavreva, D., Hakim, O., Pruett, N., Nelson, S., Yamane, A., et al. (2013) A Genome-wide Map of CTCF Multivalency Redefines the CTCF Code. Cell Rep., doi:10.1016/j.celrep.2013.04.024.
    OpenUrlCrossRefPubMedWeb of Science
  44. 44.↵
    Jiang, L., Schlesinger, F., Davis, C.A., Zhang, Y., Li, R., Salit, M., Gingeras, T.R. and Oliver, B. (2011) Synthetic spike-in standards for RNA-seq experiments. Genome Res., doi:10.1101/gr.121095.111.
    OpenUrlAbstract/FREE Full Text
  45. 45.↵
    Stark, R. and Brown, G. (2011) DiffBind: differential binding analysis of ChIP-Seq peak data. Bioconductor, doi:10.1093/nar/gkv1191.
    OpenUrlCrossRefPubMed
  46. 46.↵
    Singh, R., Lanchantin, J., Robins, G. and Qi, Y. (2016) DeepChrome: Deep-learning for predicting gene expression from histone modifications. In Bioinformatics.
  47. 47.↵
    Alipanahi, B., Delong, A., Weirauch, M.T. and Frey, B.J. (2015) Predicting the sequence specificities of DNA- and RNA-binding proteins by deep learning. Nat. Biotechnol., doi:10.1038/nbt.3300.
    OpenUrlCrossRefPubMed
Back to top
Posted August 28, 2019.
Download PDF

Supplementary Material

Email
S3norm: simultaneous normalization of sequencing depth and signal-to-noise ratio in epigenomic data
Guanjue Xiang, Cheryl A. Keller, Belinda Giardine, Lin An, Qunhua Li, Yu Zhang, Ross C. Hardison
bioRxiv 506634; doi: https://doi.org/10.1101/506634
Reddit logo Twitter logo Facebook logo LinkedIn logo Mendeley logo
Citation Tools

Subject Area