Installation

Install HiCcompare from Bioconductor.

if (!requireNamespace("BiocManager", quietly=TRUE))
    install.packages("BiocManager")
BiocManager::install("HiCcompare")
library(HiCcompare)

Getting Hi-C Data

You will need processed Hi-C data in the form of sparse upper triangular matrices or BEDPE files in order to use HiCcompare. Data is available from several sources and two examples for downloading and extracting data are listed below. If you have full Hi-C contact matrices you can convert them to sparse upper triangular format using the full full2sparse function as shown in additional functions

# read in files
mat <- read.table("hic_1000000.matrix")
bed <- read.table("hic_1000000_abs.bed")
# convert to BEDPE
dat <- hicpro2bedpe(mat, bed)
# NOTE: hicpro2bedpe returns a list of lists. The first list, dat$cis, contains the intrachromosomal contact matrices
# NOTE: dat$trans contains the interchromosomal contact matrix which is not used in HiCcompare.

Detecting Copy Number Variations and Excluding regions

Before you start a HiCcompare analysis, you may want to detect CNV and exclude these regions along with any other regions known to exhibit changes or undesirable sequencing characteristics which could cause false positives. HiCcompare provides a function to perform a CNV detection analysis utilizing the QDNAseq R package. You will need to have your Hi-C data in .bam files. This can be accomplished by downloading the raw sequencing results and aligning them using one of the many Hi-C processing pipelines. Once you have .bam files place them in a specified folder and you can then run get_CNV. Make sure to specify the bin size you will be using in kilobase pairs. The bin size should be the same as the resolution of the Hi-C data that will be used in the HiCcompare analysis. The CNV.level option will allow you to choose which level of CNV you would like to exclude. The CNV calls are defined as -2 = deletion, -1 = loss, 0 = normal, 1 = gain, 2 = amplification. In order to exclude amplifications and deletions set CNV.level = 2. To exclude any amount of CNV set CNV.level = 1.

cnv <- get_CNV(path2bam = 'path/to/bamfiles', out.file = 'path/to/bamfiles/outfile', 
               bin.size = 1000, genome = 'hg19', CNV.level = 2)

This function will run the CNV detection steps provided in QDNAseq and export a .txt file containing the copy number calls and a .bed file containing the regions detected at or above the chosen CNV level. It will also return a data.frame containing the regions at or above the chosen CNV level. It is recommended to exclude regions with scores of -2 or 2, however this decision is left up to the user.

You may want to exclude the regions with CNV along with blacklisted regions from any further analysis. HiCcompare has the ENCODE blacklists for hg19 and hg38 included (available using data("hg19_blacklist") or data("hg38_blacklist")). We can now create a data.frame (or GenomicRanges object) containing all of the regions we want to exclude from any further analysis.

data('hg19_blacklist')

# combine cnv excluded regions with blacklist regions
exclude <- cbind(cnv, hg19_blacklist)

Now that we have a data.frame containing the regions to be excluded we just simply set the exclude.regions options in the create.hic.table function to the exclude data.frame.

Creating the hic.table object

library(`HiCcompare`)
# load the data
data("HMEC.chr22")
data("NHEK.chr22")
head(HMEC.chr22)

##    region1  region2   IF
## 1 16000000 16000000    5
## 2 16000000 16500000    2
## 3 16500000 16500000  297
## 4 16000000 17000000    5
## 5 16500000 17000000   92
## 6 17000000 17000000 5690

# create the `hic.table` object
chr22.table <- create.hic.table(HMEC.chr22, NHEK.chr22, chr = 'chr22')
head(chr22.table)

##     chr1   start1     end1  chr2   start2     end2  IF1         IF2 D          M
## 1: chr22 16000000 16500000 chr22 16000000 16500000    5    5.203323 0 0.05750528
## 2: chr22 16000000 16500000 chr22 16500000 17000000    2    8.672206 1 2.11639897
## 3: chr22 16500000 17000000 chr22 16500000 17000000  297  480.440193 0 0.69389392
## 4: chr22 16000000 16500000 chr22 17000000 17500000    5   14.742750 2 1.56000562
## 5: chr22 16500000 17000000 chr22 17000000 17500000   92  277.510581 1 1.59283701
## 6: chr22 17000000 17500000 chr22 17000000 17500000 5690 9435.359752 0 0.72964887

chr22.table <- create.hic.table(HMEC.chr22, NHEK.chr22, chr = 'chr22', exclude.regions = exclude, exclude.overlap = 0.2)

# create list of `hic.table` objects
data("HMEC.chr10")
data("NHEK.chr10")

# create the `hic.table` object
chr10.table <- create.hic.table(HMEC.chr10, NHEK.chr10, chr = 'chr10')
hic.list <- list(chr10.table, chr22.table)
head(hic.list)

## [[1]]
##         chr1    start1      end1  chr2    start2      end2   IF1          IF2 D          M
##     1: chr10         0    500000 chr10         0    500000 11160 1.491828e+04 0  0.4187441
##     2: chr10         0    500000 chr10    500000   1000000  3339 4.766792e+03 1  0.5136024
##     3: chr10    500000   1000000 chr10    500000   1000000 15871 1.998235e+04 0  0.3323333
##     4: chr10         0    500000 chr10   1000000   1500000  1064 6.501731e+02 2 -0.7106025
##     5: chr10    500000   1000000 chr10   1000000   1500000  2963 2.097443e+03 1 -0.4984269
##    ---                                                                                    
## 35366: chr10 134000000 134500000 chr10 135000000 135500000  1810 1.273570e+03 2 -0.5071112
## 35367: chr10 134500000 135000000 chr10 135000000 135500000  1971 3.634653e+03 1  0.8828898
## 35368: chr10 135000000 135500000 chr10 135000000 135500000 16716 1.188368e+04 0 -0.4922479
## 35369: chr10 134000000 134500000 chr10 135500000 136000000     1 6.865608e-01 3 -0.5425406
## 35370: chr10 135000000 135500000 chr10 135500000 136000000     4 3.432804e+00 1 -0.2206125
## 
## [[2]]
##        chr1   start1     end1  chr2   start2     end2  IF1         IF2 D           M
##    1: chr22 16000000 16500000 chr22 16000000 16500000    5    5.203323 0  0.05750528
##    2: chr22 16000000 16500000 chr22 16500000 17000000    2    8.672206 1  2.11639897
##    3: chr22 16500000 17000000 chr22 16500000 17000000  297  480.440193 0  0.69389392
##    4: chr22 16000000 16500000 chr22 17000000 17500000    5   14.742750 2  1.56000562
##    5: chr22 16500000 17000000 chr22 17000000 17500000   92  277.510581 1  1.59283701
##   ---                                                                               
## 2479: chr22 49000000 49500000 chr22 51000000 51500000   21   54.634896 4  1.37943338
## 2480: chr22 49500000 50000000 chr22 51000000 51500000   35   71.112086 3  1.02273986
## 2481: chr22 50000000 50500000 chr22 51000000 51500000  394  339.083241 2 -0.21655615
## 2482: chr22 50500000 51000000 chr22 51000000 51500000 4066 2741.284207 1 -0.56875831
## 2483: chr22 51000000 51500000 chr22 51000000 51500000 9916 7132.021930 0 -0.47544713

##     chr1   start1     end1  chr2   start2     end2  IF1
## 1: chr22 16000000 16500000 chr22 16000000 16500000    5
## 2: chr22 16000000 16500000 chr22 16500000 17000000    2
## 3: chr22 16500000 17000000 chr22 16500000 17000000  297
## 4: chr22 16000000 16500000 chr22 17000000 17500000    5
## 5: chr22 16500000 17000000 chr22 17000000 17500000   92
## 6: chr22 17000000 17500000 chr22 17000000 17500000 5690

bed.hic.tab <- create.hic.table(HMEC.chr22_BEDPE, NHEK.chr22_BEDPE)
head(bed.hic.tab)

##     chr1   start1     end1  chr2   start2     end2  IF1         IF2 D          M
## 1: chr22 16000000 16500000 chr22 16000000 16500000    5    5.203323 0 0.05750528
## 2: chr22 16000000 16500000 chr22 16500000 17000000    2    8.672206 1 2.11639897
## 3: chr22 16500000 17000000 chr22 16500000 17000000  297  480.440193 0 0.69389392
## 4: chr22 16000000 16500000 chr22 17000000 17500000    5   14.742750 2 1.56000562
## 5: chr22 16500000 17000000 chr22 17000000 17500000   92  277.510581 1 1.59283701
## 6: chr22 17000000 17500000 chr22 17000000 17500000 5690 9435.359752 0 0.72964887

# first dataset
mat1 <- read.table("hic1_1000000.matrix")
bed1 <- read.table("hic1_1000000_abs.bed")
dat1 <- hicpro2bedpe(mat, bed)
dat1 <- dat1$cis # extract intrachromosomal matrices
# second dataset
mat2 <- read.table("hic2_1000000.matrix")
bed2 <- read.table("hic2_1000000_abs.bed")
dat2 <- hicpro2bedpe(mat, bed)
dat2 <- dat2$cis # extract intrachromosomal matrices

# for chr1
hic.table <- create.hic.table(dat1[[1]], dat2[[1]])

# for all chromosomes
hic.list <- mapply(create.hic.table, dat1, dat2, SIMPLIFY = FALSE)

data("hmec.IS")
data("nhek.IS")
head(hmec.IS)

## GInteractions object with 6 interactions and 1 metadata column:
##       seqnames1           ranges1     seqnames2           ranges2 |        IF
##           <Rle>         <IRanges>         <Rle>         <IRanges> | <numeric>
##   [1]     chr22 16000000-16499999 ---     chr22 16000000-16499999 |         5
##   [2]     chr22 16000000-16499999 ---     chr22 16500000-16999999 |         2
##   [3]     chr22 16500000-16999999 ---     chr22 16500000-16999999 |       297
##   [4]     chr22 16000000-16499999 ---     chr22 17000000-17499999 |         5
##   [5]     chr22 16500000-16999999 ---     chr22 17000000-17499999 |        92
##   [6]     chr22 17000000-17499999 ---     chr22 17000000-17499999 |      5690
##   -------
##   regions: 71 ranges and 0 metadata columns
##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

IS.hic.tab <- create.hic.table(hmec.IS, nhek.IS)

Total Sum Scaling

If you are performing your HiCcompare analysis on the entire genome you can perform total sum scaling on the data before performing loess normalization. This requires the use of a list of hic.table objects, one for each chromosome. Additionally, when you create these hic.table objects you must set scale = FALSE. Once you have your list of hic.table objects you can then perform total sum scaling.

hic.list <- total_sum(hic.list)

It is recommended to use total sum scaling when performing a HiCcompare analysis on the entire genome. If you are only using data for a single chromosome then total sum scaling should be equivalent to the scale option in the create.hic.table function.

Joint Normalization

Now that you have created a hic.table object you can jointly normalize your two Hi-C matrices. The hic_loess function has many options and can accept a single hic.table or a list of hic.tables. If for example you wish to perform joint normalization for every chromosome on two cell lines while utilizing parallel computing you can create a list containing the hic.tables for each chromosome.

To change the degree of the polynomial for the loess joint normalization you can utilize the degree option, default is 1 (linear regression). A user-defined span, or the amount of data used to build the loess model, can also be set with the span option. However if span = NA (the default) the automatic smoothing parameter selection process will run and determine the optimal span for the data. The type of selection process can be changed using the loess.criterion option. Available settings are gcv (the default) for generalized cross-validation or aicc for Akaike information criterion. The loess automatic smoothing parameter selection uses a customized version of the fANCOVA::loess.as function. For more information on parameter selection please see the fANCOVA reference manual. It is recommended to use the default settings. If you have already run hic_loess on a dataset and know the span or would like to use a specific span then manually setting the span to a value can significantly reduce computation time especially for high resolution data.

hic_loess can utilize the BiocParallel package to perform parallel computing and lower computation time. The parallel option (FALSE by default) will only speed up computation if a list of hic.tables is entered into the function, i.e., it parallelizes processing of several chromosome-specific matrices. This is useful for performing joint normalization for every chromosome between two Hi-C datasets. For more information on BiocParallel see the reference manual here.

The basis of HiCcompare rests on the novel concept termed the MD plot. The MD plot is similar to the MA plot or the Bland-Altman plot. \(M\) is the log2 difference between the interaction frequencies from the two datasets. \(D\) is the unit distance between the two interacting regions. Loess is performed on the data after it is represented in the MD coordinate system. To visualize the MD plot the Plot option can be set to TRUE.

If you wish to detect differences between the two Hi-C datasets immediately following joint normalization you can set the check.differences option to TRUE. However, if you only want to jointly normalize the data for now keep this option set to FALSE. The difference detection process will be covered in the next section.

# Jointly normalize data for a single chromosome
hic.table <- hic_loess(chr22.table, Plot = TRUE, Plot.smooth = FALSE)

## Span for loess: 0.219052588777294

## GCV for loess: 0.000118686898199309

## AIC for loess: -0.212037314500057

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

knitr::kable(head(hic.table))

# Multiple hic.tables can be processed in parallel by entering a list of hic.tables
hic.list <- hic_loess(hic.list, parallel = TRUE)

The hic_loess joint normalization function extends the hic.table with the adjusted interaction frequencies, adjusted “M”, the “mc” correction factor, and the average expression “A”.

Difference Detection

the MD plot is used to represent the differences \(M\) between two normalized datasets at a distance \(D\). Normalized \(M\) values are centered around 0 and the distribution at each distance remains fairly consistent. The \(M\) values are approximately normally distributed. \(M\) values are converted to Z-scores using the standard approach:

\[ Z_i = \frac{M_i - \bar{M}}{\sigma_M} \] where \(\bar{M}\) is the mean value of all \(M\)’s on the chromosome and \(\sigma_M\) is the standard deviation of all \(M\) values on the chromosome and \(i\) is the \(i\)th interacting pair on the chromosome.

During Z-score conversion the average expression of each interacting pair is considered. Due to the nature of \(M\), a difference represented by an interacting pair with IFs 1 and 10 is equivalent to an interacting pair of IFs 10 and 100 with both differences having an \(M\) value of 3.32. However the average expression of these two differences is 5.5 and 55, respectively. Differences with higher average expression are more trustworthy than those with low average expression due to the fact that a relatively small difference on the raw scale can lead to a large log2 fold change. Additionally since the IFs represent Hi-C sequencing reads, lower average numbers of reads are also less trustworthy. Thus we filter out differences with low average expression before calculating Z-scores when average expression (\(A\)) is less than a user set quantile (typically 5-20%) or a user set specific value of \(A\). The Z-scores can then be converted to p-values using the standard normal distribution.

To determine how to filter your data you can use the filter_params() function. This will produce a plot of the Matthews Correlation Coefficient (MCC) vs. the A minimum value filtered out. This plot should help you determine a reasonable value to set your filtering parameter in hic_compare. You may need to adjust the numChanges option and the FC option depending on the resolution of the data and how noisy it is.

Here we check the filtering:

filter_params(hic.table)

Difference detection can be performed using the hic_compare() function. Before difference detection you will need to decide how you would like to filter out interactions with low average expression. You can filter based on a specific value of A. Once you have a normalized hic.table or list of hic.tables detect differences with an A filter as follows:

hic.table <- hic_compare(hic.table, A.min = 15, adjust.dist = TRUE, p.method = 'fdr', Plot = TRUE)

## Filtering out interactions with A < 15

If you leave the A.min = NA then the 10th percentile of A will be calculated and used for filtering by default. The resulting table will display the results as shown below:

knitr::kable(head(hic.table))

Where Z is the Z-score calculated for the interaction (Z-scores with NA values result from filtering based on A), p.value is the un-adjusted p-value based on the standard normal distribution, and p.adj is the p-value after the multiple testing correction specified was applied.

Converting HiCcompare results to InteractionSet objects

If after running hic_loess or hic_compare on your data you wish to perform additional analyses which require the GRanges object class you can convert the results using the make_InteractionSet function. This function will produce an InteractionSet object with the genomic ranges contained in the hic.table along with several metadata files containing the additional information produced by hic_loess or hic_compare.

IntSet <- make_InteractionSet(hic.table)

Simulating Hi-C Data

HiCcompare includes functions for simulating Hi-C data. The hic_simulate function allows you to simulate two Hi-C matrices with added bias and true differences at a specified fold change. As an example we will simulate two matrices with 250 true differences added at a fold change of 4.

number_of_unitdistances <- 100 # The dimensions of the square matrix to be simualted
number_of_changes       <- 250 # How many cells in the matrix will have changes
i.range <- sample(1:number_of_unitdistances, number_of_changes, replace = TRUE) # Indexes of cells to have controlled changes
j.range <- sample(1:number_of_unitdistances, number_of_changes, replace = TRUE) # Indexes of cells to have controlled changes

sim_results <- hic_simulate(nrow = number_of_unitdistances, medianIF = 50000, sdIF = 14000, powerlaw.alpha = 1.8, fold.change = 4, i.range = i.range, j.range = j.range, Plot = TRUE, alpha = 0.1)

## Span for loess: 0.176604456256237

## GCV for loess: 0.000109316686262945

## AIC for loess: 0.347184003433046

## Filtering out interactions with A < 102

## True Positives: 198 Total added differences: 202 True Negatives: 4464

## TPR: 0.98019801980198

## SPC: 0.985212977267711

The results of the simulation are saved in a list.

names(sim_results)

## [1] "TPR"       "SPC"       "pvals"     "hic.table" "true.diff" "truth"     "sim.table"

TPR is the true positive rate, SPC is the specificity, pvals is a vector of the p-values for every cell in the matrices, hic.table is the resulting hic.table object after hic_loess and hic_compare have been applied to the simulated data, true.diff is a table for the cells that had the specified fold change applied to them, truth is a vector of 0’s and 1’s indicating if a cell had a true difference applied - this is useful for input into ROC packages, sim.table is the simulated data in a hic.table object before being scaled, normalized, and analyzed for differences.

The sim_matrix function will produce two simulated Hi-C matrices without performing any analysis.

sims <- sim_matrix(nrow = number_of_unitdistances, medianIF = 50000, sdIF = 14000, powerlaw.alpha = 1.8, fold.change = 4, 
                   i.range = i.range, j.range = j.range)

Additional Functions

HiCcompare contains some additional functions that may be useful.

If you do not choose to show the MD plots when you initially run hic_loess or hic_compare you can use the MD.plot1 or MD.plot2 functions. MD.plot1 will create a side by side MD plot showing before and after loess normalization. Enter your original M and D vectors along with the M correction factor, mc, calculated by hic_loess. The smooth option controls if the plot is plotted using smoothScatter or as a ggplot2 scatter plot.

MD.plot1(M = hic.table$M, D = hic.table$D, mc = hic.table$mc, smooth = TRUE)

MD.plot2 will create a standard MD plot with optional coloring based on p-value. Just enter an M and D vector and a p-value vector if desired.

# no p-value coloring
MD.plot2(M = hic.table$adj.M, D = hic.table$D, smooth = FALSE)

# p-value coloring
MD.plot2(M = hic.table$adj.M, D = hic.table$D, hic.table$p.value, smooth = FALSE)

There are two matrix transformation functions included. sparse2full will transform a sparse upper triangular matrix to a full Hi-C matrix. full2sparse will transform a full Hi-C matrix to sparse upper triangular format.

full.NHEK <- sparse2full(NHEK.chr22)

## Matrix dimensions: 71x71

full.NHEK[1:5, 1:5]

##          1.6e+07 16500000 1.7e+07 17500000 1.8e+07
## 1.6e+07        6       10      17       13       1
## 16500000      10      554     320      118      23
## 1.7e+07       17      320   10880     2922     576
## 17500000      13      118    2922    27545    3693
## 1.8e+07        1       23     576     3693   25794

sparse.NHEK <- full2sparse(full.NHEK)
head(sparse.NHEK)

##     region1  region2    IF
## 1: 16000000 16000000     6
## 2: 16000000 16500000    10
## 3: 16500000 16500000   554
## 4: 16000000 17000000    17
## 5: 16500000 17000000   320
## 6: 17000000 17000000 10880

KRnorm will perform Knight-Ruiz normalization on a Hi-C matrix. Just enter the full Hi-C matrix to be normalized.

KR.NHEK <- KRnorm(full.NHEK)

SCN will perform Sequential Component Normalization on a Hi-C matrix. Just enter the full Hi-C matrix to be normalized.

SCN.NHEK <- SCN(full.NHEK)

MA_norm will perform MA normalization on a hic.table object.

result <- MA_norm(hic.table, Plot = TRUE)

Using HiCcompare on a cluster

Below is an example script for using HiCcompare on a computing cluster. The data was concatenated into a single sparse matrix for each group, containing information for all the chromosomes.

library(HiCcompare)
library(BiocParallel)

args = commandArgs(trailingOnly=TRUE)

dat1 <- read.table(args[1], header=FALSE, col.names=c("chr1", "start1", "end1", "chr2", "start2", "end2", "IF"))
dat2 <- read.table(args[2], header=FALSE, col.names=c("chr1", "start1", "end1", "chr2", "start2", "end2", "IF"))

dat1 <- dat1[dat1$chr1==dat1$chr2, ]
dat2 <- dat2[dat2$chr1==dat2$chr2, ]

dat1 <- split(dat1, dat1$chr1)
dat2 <- split(dat2, dat2$chr1)

hic.list <- mapply(create.hic.table, dat1, dat2, SIMPLIFY = FALSE, scale=FALSE)

hic.list <- total_sum(hic.list)

register(MulticoreParam(workers = 10), default = TRUE)

hic.list <- hic_loess(hic.list, Plot=TRUE, parallel=TRUE)
hic.list <- hic_compare(hic.list, A.min = NA, adjust.dist = TRUE, p.method = 'fdr', Plot = TRUE, parallel=TRUE)

hic.list <- do.call(rbind, hic.list)

hic.list <- hic.list[hic.list$p.adj<0.05,]

write.table(hic.list, args[3])

The above can be saved as an R script and then submitted to a cluster using the following submission script.

#!/bin/sh
# Sun Grid Engine options (lines prefixed with #$)
#$ -cwd
#$ -N HiCCompare
#$ -l h_rt=06:00:00
#$ -l h_vmem=32G
#$ -pe sharedmem 11
#$ -V

Rscript 01_HiCcompare.R $1 $2 $3

qsub 01_launch_HiCcompare.sh dat1.1000000.pixels.tsv dat2.1000000.pixels.tsv hiccompare_1Mb.tsv

Credit to Ilya Flyamer (@Phlya on GitHub) for this example of using HiCcompare on a cluster.