SpectralTAD is a package designed to allow for fast
hierarchical TAD calling on a wide-variety of chromatin conformation
capture (Hi-C) data. SpectralTAD takes a contact matrix as
an input and outputs a list of data frames or GRange objects in BED
format containing coordinates corresponding to TAD locations. The
package contains two functions, SpectralTAD() and
SpectralTAD_Par() with SpectralTAD being a single-CPU
TAD-caller and SpectralTAD_Par being the parallelized
version. This package provides flexibility in the data it accepts,
allowing for n × n
(square numerical matrix), n × (n + 3) (square
numerical matrix with the additional chromosome, start, end columns),
and 3-column sparse matrices (described below). There are no parameters
required for running the functions, though certain methods for
customizing the results are available. The idea is to give users the
freedom to control how they call TADs while giving them the option to
perform it in an unsupervised manner.
The package is based around the windowed spectral clustering algorithm, introduced by (Cresswell, Stansfield, and Dozmorov 2019) , which is designed to be robust to sparsity, noise, and sequencing depth of Hi-C data.
n × n contact matrices, are most commonly associated with data coming from the Bing Ren lab (http://chromosome.sdsc.edu/mouse/hi-c/download.html). These contact matrices are square and symmetric with entry ij corresponding to the number of contacts between region i and region j. Below is an example of a 5 × 5 region of an n × n contact matrix. Derived from (Rao et al. 2014), chromosome 20 data at 25kb resolution. Note the symmetry around the diagonal - the typical shape of chromatin interaction matrix.
## 50000 75000 100000 125000 150000
## 50000 2021 727 203 205 155
## 75000 727 3701 583 491 348
## 100000 203 583 2023 603 274
## 125000 205 491 603 3350 676
## 150000 155 348 274 676 2528n × (n + 3) matrices are commonly associated with the TopDom tad-caller (http://zhoulab.usc.edu/TopDom/). These matrices consist of a normal n × n matrix but with 3 additional leading columns containg the chromosome, the start of the region and the end of the region. Regions in this case are determined by the resolution of the data. The typical n × (n + 3) matrix is shown below.
##
## 1 chr19 50000 75000 2021 727 203 205 155 165 193
## 2 chr19 75000 100000 727 3701 583 491 348 335 350
## 3 chr19 100000 125000 203 583 2023 603 274 228 213
## 4 chr19 125000 150000 205 491 603 3350 676 447 390
## 5 chr19 150000 175000 155 348 274 676 2528 732 463
## 6 chr19 175000 200000 165 335 228 447 732 3497 998
## 7 chr19 200000 225000 193 350 213 390 463 998 4450
## 8 chr19 225000 250000 135 236 137 259 301 543 1061
## 9 chr19 250000 275000 158 259 183 299 317 554 731
## 10 chr19 275000 300000 96 166 115 171 179 319 416Sparse 3-column matrices, sometimes referred to as a coordinated
lists, are matrices where the first and second column refer to region
i and region j of the chromosome, and the third
column is the number of contacts between them. This style is becoming
increasingly popular and is associated with raw data from Rao (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE63525),
and is the data output produced by the Juicer tool (Durand et al. 2016). 3-column matrices are
handled internally in the package by converting them to n × n matrices using the
HiCcompare package’s sparse2full() function.
The first 5 rows of a typical sparse 3-column matrix is shown below.
## region1 region2 IF
## <num> <num> <num>
## 1: 50000 50000 2021
## 2: 50000 75000 727
## 3: 75000 75000 3701
## 4: 50000 100000 203
## 5: 75000 100000 583Users can also find TADs from data output by juicer (https://github.com/aidenlab/juicer, .hic format),
cooler (http://cooler.readthedocs.io/en/latest/index.html, .cool
format), and HiC-Pro (https://github.com/nservant/HiC-Pro, .matrix and .bed
formats) with minor pre-processing using the HiCcompare
package.
Sparse matrices can be extracted from .hic files using the
straw tool https://github.com/theaidenlab/straw.
See examples on how to use straw at https://github.com/theaidenlab/straw/wiki/CPP#running.
Briefly, straw requires several inputs for the extraction
of data from a .hic file:
<NONE/VC/VC_SQRT/KR> <hicFile(s)> <chr1>[:x1:x2] <chr2>[:y1:y2] <BP/FRAG> <binsize>
The first field indicates the type of normalization to be applied. The Vanilla Coverage (VC), the square root of Vanilla Coverage (VC_SQRT), and Knight-Ruiz (KR) normalization techniques are available to be applied to the contact maps. Alternatively, the raw contact maps can be extracted using the NONE option (recommended for SpectralTAD).
The second field is the file name of the .hic file to be
extracted. The following two fields are the chromosome numbers for the
contact map desired, i.e., for the intrachromosomal map of chr1 the user
would enter 1 1 in these fields. The next field determines if basepairs
or restriction fragment resolution files will be returned. Typically,
the user will want to use the BP option. The final field
specifies the resolution of the contact map.
For example, to extract the raw matrix corresponding to chromosome 22
at 500kb resolution from the GSE63525_K562_combined_30.hic
file, we would use the following command:
./straw NONE GSE63525_K562_combined_30.hic 22 22 BP 500000 > K562.chr22.500kb.txt
This will extract the data from the .hic file and save
it to the K562.chr22.500kb.txt text file, in the sparse
upper triangular matrix format. Typically, chromosome-specific matrices
are saved in separate files. #### Working with .cool files
The cooler software can be downloaded from http://cooler.readthedocs.io/en/latest/index.html. It essentially provides access to a catalog of popular HiC datasets. We can pre-process and use .cool files that are associated with cooler files using the following steps:
.cool file from (ftp://cooler.csail.mit.edu/coolers)cooler dump --join Rao2014-GM12878-DpnII-allreps-filtered.50kb.cool > Rao.GM12878.50kb.txt#Read in data
cool_mat = read.table("Rao.GM12878.50kb.txt")
#Convert to sparse 3-column matrix using cooler2sparse from HiCcompare
sparse_mats = HiCcompare::cooler2sparse(cool_mat)
#Remove empty matrices if necessary
#sparse_mats = sparse_mats$cis[sapply(sparse_mats, nrow) != 0]
#Run SpectralTAD
spec_tads = lapply(names(sparse_mats), function(x) {
SpectralTAD(sparse_mats[[x]], chr = x)
})HiC-Pro data comes with 2 files, the .matrix file and
the .bed file. The .matrix file is a 3-column
matrix where instead of coordinates as the 1st and 2nd column, there is
an ID. The .bed file maps these IDs to genomic coordinates.
The steps for analyzing these files is shown below:
#Read in both files
mat = read.table("amyg_100000.matrix")
bed = read.table("amyg_100000_abs.bed")
#Convert to modified bed format
sparse_mats = HiCcompare::hicpro2bedpe(mat,bed)
#Remove empty matrices if necessary
#sparse_mats$cis = sparse_mats$cis[sapply(sparse_mats, nrow) != 0]
#Go through all matrices
sparse_tads = lapply(sparse_mats$cis, function(x) {
#Pull out chromosome
chr = x[,1][1]
#Subset to make three column matrix
x = x[,c(2,5,7)]
#Run SpectralTAD
SpectralTAD(x, chr=chr)
})Once matrices are in an acceptable format, SpectralTAD can be run with as little as two parameters or as many as eight. Below we show how to run the algorithm with just TAD detection and no quality filtering.
## V1 V2 V3
## 1 50000 50000 2021
## 2 50000 75000 727
## 3 75000 75000 3701
## 4 50000 100000 203
## 5 75000 100000 583
## 6 100000 100000 2023#We see that this is a sparse 3-column contact matrix
#Running the algorithm with resolution specified
results = SpectralTAD(rao_chr20_25_rep, chr = "chr20", resolution = 25000, qual_filter = FALSE, z_clust = FALSE)
#Printing the top 5 TADs
head(results$Level_1, 5)## # A tibble: 5 × 4
## chr start end Level
## <chr> <dbl> <dbl> <dbl>
## 1 chr20 50000 325000 1
## 2 chr20 325000 525000 1
## 3 chr20 525000 725000 1
## 4 chr20 725000 1200000 1
## 5 chr20 1200000 1450000 1#Repeating without specifying resolution
no_res = SpectralTAD(rao_chr20_25_rep, chr = "chr20", qual_filter = FALSE, z_clust = FALSE)
#We can see below that resolution can be estimated automatically if necessary
identical(results, no_res)## [1] TRUEOne method for filtering TADs is using group-wise silhouette scores. This is done by getting the overall silhouette for each group and removing those with a score of less than .25. A low silhouette score for a given TAD indicates a poor level of connectivity within it.
#Running SpectralTAD with silhouette score filtering
qual_filt = SpectralTAD(rao_chr20_25_rep, chr = "chr20", qual_filter = TRUE, z_clust = FALSE, resolution = 25000)
#Showing quality filtered results
head(qual_filt$Level_1,5)## # A tibble: 5 × 5
## chr start end Sil_Score Level
## <chr> <dbl> <dbl> <dbl[1d]> <dbl>
## 1 chr20 50000 325000 0.475 1
## 2 chr20 325000 525000 0.699 1
## 3 chr20 525000 725000 0.640 1
## 4 chr20 725000 1200000 0.384 1
## 5 chr20 1200000 1450000 0.676 1## [1] 168 5## [1] 170 4The results when using the quality filtering option are altered to
include a new column called Sil_Score. This column includes
a group-wise silhouette score. In this example a single TAD was removed
due to having poor organization (Low silhouette score).
Z-score filtering is based on observations about the log-normality of the distance between eigenvector gaps from (Cresswell, Stansfield, and Dozmorov 2019). Z-score filtering bypasses the uses of silhouette score and defines a TAD boundary as the area between consecutive regions where the z-score of the eigenvector gap is greater than 2.
z_filt = SpectralTAD(rao_chr20_25_rep, chr = "chr20", qual_filter = FALSE, z_clust = TRUE, resolution = 25000)
head(z_filt$Level_1, 5)## # A tibble: 5 × 4
## chr start end Level
## <chr> <dbl> <dbl> <dbl>
## 1 chr20 50000 350000 1
## 2 chr20 350000 550000 1
## 3 chr20 550000 675000 1
## 4 chr20 675000 1125000 1
## 5 chr20 1125000 1475000 1## [1] 151 4We can see that TADs found using this method are generally more fine than those found using the silhouette score based filtering. Z-score filtering is more suited for people not interested in TAD hierarchies because the initial TADs detected are less broad than those by quality filtering.
Our method is specifically designed to find hierarchical TADs. To do
so, users must specify how many levels they are interested in using the
levels parameter. There is no limit to the number of levels
but after a certain point no new TADs will be found due to limitations
in TAD size or TAD quality. Hierarchies are found by running the
algorithm initially and then iteratively running it on sub-TADs until
none can be found. At the levels below the initial level we use z-score
filtering by default.
#Running SpectralTAD with 3 levels and no quality filtering
spec_hier = SpectralTAD(rao_chr20_25_rep, chr = "chr20", resolution = 25000, qual_filter = FALSE, levels = 3)
#Level 1 remains unchanged
head(spec_hier$Level_1,5)## # A tibble: 5 × 4
## chr start end Level
## <chr> <dbl> <dbl> <dbl>
## 1 chr20 50000 325000 1
## 2 chr20 325000 525000 1
## 3 chr20 525000 725000 1
## 4 chr20 725000 1200000 1
## 5 chr20 1200000 1450000 1## # A tibble: 5 × 4
## chr start end Level
## <chr> <dbl> <dbl> <dbl>
## 1 chr20 325000 525000 2
## 2 chr20 525000 725000 2
## 3 chr20 1200000 1450000 2
## 4 chr20 1450000 1750000 2
## 5 chr20 1775000 1975000 2## # A tibble: 5 × 4
## chr start end Level
## <chr> <dbl> <dbl> <dbl>
## 1 chr20 325000 525000 3
## 2 chr20 525000 725000 3
## 3 chr20 1200000 1450000 3
## 4 chr20 1775000 1975000 3
## 5 chr20 1975000 2175000 3Note that as we move down levels, more gaps form indicating regions where sub-TADs are not present.
Though, it has been shown that windowed spectral clustering is more
robust to sparsity than other common methods(Cresswell, Stansfield, and Dozmorov 2019),
there is still some instability caused by consecutive regions of gaps.
To counter this, we use a gap_threshold parameter to allow
users to exclude regions based on how many zeros are included. By
default this value is set to 1 which means only columns/rows with 100%
of values being zero are removed before analysis. Accordingly, setting
this value to .7 would mean rows/columns with 70% zeros would be
removed. Since we are not interested in long-range contacts for TAD
identification, this percentage only applies to the number of zeros
within a specific distance of the diagonal (Defined by the maximum TAD
size). Users must be careful not to filter too much as this can remove
informative regions of the matrix.
It is sometimes the case that people want to run SpectralTAD on
multiple chromosomes at once in parallel. This can be done using the
SpectralTAD_Par function. SpectralTAD_Par is identical to
SpectralTAD but takes a list of contact matrices as an input. These
matrices can be of any of the allowable types and mixing of types is
allowed. Users are required to provide a vector of chromosomes,
chr_over, where it is ordered such that each entry matches
up with its corresponding contact matrix in the list of matrices. Users
can also input list names using the labels parameter. In
terms of parallelization, users can either input the number of cores
they would like to use or the function will automatically use 1 less
than the total number of cores on the computer on which it is ran. The
function works on Linux/Mac and Windows with automatic OS detection
built in. We show the steps below.
#Creating replicates of our HiC data for demonstration
cont_list = replicate(3,rao_chr20_25_rep, simplify = FALSE)
#Creating a vector of chromosomes
chr_over = c("chr20", "chr20", "chr20")
#Creating a list of labels
labels = c("Replicate 1", "Replicate 2", "Replicate 3")
SpectralTAD_Par(cont_list = cont_list, chr_over = chr_over, labels = labels, cores = 3)The type of matrix input into the algorithm can affect runtimes for the algorithm. n × n matrices require no conversion and are the fastest. Meanwhile, n × (n + 3) matrices take slightly longer to run due to the need to remove the first 3 columns. Sparse 3-column matrices have the highest runtimes due to the complexity of converting them to an n × n matrix. The times are summarized below, holding all other parameters constant.
library(microbenchmark)
#Converting to nxn
n_n = HiCcompare::sparse2full(rao_chr20_25_rep)
#Converting to nxn+3
n_n_3 = cbind.data.frame("chr20", as.numeric(colnames(n_n)), as.numeric(colnames(n_n))+25000, n_n)
#Defining each function
sparse = SpectralTAD(cont_mat = rao_chr20_25_rep, chr = "chr20", qual_filter = FALSE)
n_by_n = SpectralTAD(cont_mat = n_n, chr = "chr20", qual_filter = FALSE)
n_by_n_3 =SpectralTAD(cont_mat = n_n_3, chr = "chr20", qual_filter = FALSE)
#Benchmarking different parameters
microbenchmark(sparse = SpectralTAD(cont_mat = rao_chr20_25_rep, chr = "chr20", qual_filter = FALSE),
n_by_n = SpectralTAD(cont_mat = n_n, chr = "chr20", qual_filter = FALSE),
n_by_n_3 =SpectralTAD(cont_mat = n_n_3, chr = "chr20", qual_filter = FALSE), unit = "s", times = 3)## Unit: seconds
## expr min lq mean median uq max neval
## sparse 1.519551 1.530921 1.678542 1.542291 1.758038 1.973784 3
## n_by_n 1.300107 1.301922 1.312289 1.303737 1.318380 1.333023 3
## n_by_n_3 1.286734 1.299231 1.440413 1.311729 1.517252 1.722775 3Just as the type of data affects runtime, the parameters used to detect TADs do as well. The main bottleneck is the quality filter function which requires the inversion of a matrix and the calculation of silhouette score.
microbenchmark(quality_filter = SpectralTAD(cont_mat = n_n, chr = "chr20", qual_filter = TRUE, z_clust = FALSE), no_filter = SpectralTAD(cont_mat = n_n, chr = "chr20", qual_filter = FALSE, z_clust = FALSE), z_clust = SpectralTAD(cont_mat = n_n, chr = "chr20", qual_filter = FALSE, z_clust = TRUE), times = 3, unit = "s")## Unit: seconds
## expr min lq mean median uq max neval
## quality_filter 1.357013 1.3692439 1.377669 1.3814750 1.3879971 1.3945192 3
## no_filter 1.260052 1.2696051 1.281443 1.2791579 1.2921379 1.3051179 3
## z_clust 0.822790 0.8325662 0.842491 0.8423425 0.8523416 0.8623407 3As can be seen using the z-score method is the fastest.
SpectralTAD is designed to work in tandem with Juicebox (http://www.aidenlab.org/juicebox/) and HiCExplorer (https://hicexplorer.usegalaxy.eu/), two popular TAD visualization tools. Users may output files, corresponding to either tools.
HiCExplorer takes simple bed files. To use SpectralTAD with HiCExplorer, do the following:
#Get contact matrix
data("rao_chr20_25_rep")
head(rao_chr20_25_rep)
#Run spectral TAD with output format "hicexplorer" or "bed" and specify the path
spec_hier = SpectralTAD(rao_chr20_25_rep, chr = "chr20", resolution = 25000, qual_filter = FALSE, levels = 3, out_format = "hicexplorer", out_path = "chr20.bed")This code will output a three-column bed file with TAD coordinates for all three levels. hicPlotTADs from HiCExplorer takes a .ini configuration file. To use SpectralTAD results you simply just have to set the output file as the directory under the [tads] subheading. For a full walk-through see (https://hicexplorer.readthedocs.io/en/latest/content/tools/hicPlotTADs.html#id4) under the heading “Configuration file template.”
Juicebox takes bedpe files as its primary file type. To use SpectralTAD with Juicebox, do the following:
#Get contact matrix
data("rao_chr20_25_rep")
head(rao_chr20_25_rep)
#Run spectral TAD with output format "hicexplorer" or "bed" and specify the path
spec_hier = SpectralTAD(rao_chr20_25_rep, chr = "chr20", resolution = 25000, qual_filter = FALSE, levels = 3, out_format = "juicebox", out_path = "chr20.bedpe")The output for this code is an 11-column bedpe file, which is
formatted to work for Juicebox. To use the file, you must first select a
HiC matrix in the Juicebox interface (https://www.aidenlab.org/juicebox/). This is done by
choosing
Load Map -> Select File -> Select Contact Map. This
data corresponds to
Rao and Huntley et al. | Cell 2014 GM12878 (human) in situ ENCODE Batch 1 HIC048
so we select this. Alternatively, you can upload your own hic matrix in
.hic or .cool format. To select the TADs called by
SpectralTAD simply choose
Load Tracks -> Local Track File -> Choose File -> chr20.bedpe.
To view chromosome 20 specifically, select
≡ -> Chromosomes -> chr20.