library(ggplot2)
library(GenomicRanges)
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library(HiCExperiment)
## Consider using the `HiContacts` package to perform advanced genomic operations
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## hubUrl5 Matrix-centric analysis
Pre-loading packages and objects π¦
Aims
This chapter focuses on the various analytical tools offered by HiContacts to compute matrix-related metrics from a HiCExperiment object.
In the first part of this book, we have seen how to query parts or all of the data contained in Hi-C contact matrices using the HiCExperiment object (Chapter 2), how to manipulate HiCExperiment objects (Chapter 3) and how to visualize Hi-C contact matrices as heatmaps (Chapter 4).
The HiContacts package directly operates on HiCExperiment objects and extends its usability by providing a comprehensive toolkit to analyze Hi-C data, focusing on four main topics:
- Contact matrix-centric analyses (this chapter)
- Interactions-centric analyses (Chapter 6)
- Structural feature annotations (Chapter 7)
- Hi-C visualization (see previous chapter)
Matrix-centric analyses consider a HiCExperiment object from the βmatrixβ perspective to perform a range of matrix-based operations. This encompasses:
- Computing observed/expected (O/E) map
- Computing auto-correlation map
- Smoothing out a contact map
- Merging multiple Hi-C maps together
- Comparing two Hi-C maps to each other
Note
- All the functions described in this chapter are endomorphisms: they take
HiCExperimentobjects as input and return modifiedHiCExperimentobjects. - Internally, most of the functions presented in this chapter make a call to
as.matrix(<HiCExperiment>)to coerce it into amatrix.
Generating the example
hic object π
To demonstrate HiContacts functionalities, we will create an HiCExperiment object from an example .cool file provided in the HiContactsData package.
library(HiCExperiment)
library(HiContactsData)
# ---- This downloads an example `.mcool` file and caches it locally
coolf <- HiContactsData('yeast_wt', 'mcool')
## see ?HiContactsData and browseVignettes('HiContactsData') for documentation
## loading from cache
# ---- This creates a connection to the disk-stored `.mcool` file
cf <- CoolFile(coolf)
cf
## CoolFile object
## .mcool file: /home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752
## resolution: 1000
## pairs file:
## metadata(0):
# ---- This imports contacts from the chromosome `II` at resolution `2000`
hic <- import(cf, focus = 'II', resolution = 2000)hic
## `HiCExperiment` object with 471,364 contacts over 407 regions
## -------
## fileName: "/home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752"
## focus: "II"
## resolutions(5): 1000 2000 4000 8000 16000
## active resolution: 2000
## interactions: 34063
## scores(2): count balanced
## topologicalFeatures: compartments(0) borders(0) loops(0) viewpoints(0)
## pairsFile: N/A
## metadata(0):5.1 Operations in an individual matrix
5.1.1 Balancing a raw interaction count map
Hi-C sequencing coverage is systematically affected by multiple confounding factors, e.g. density of restriction sites, GC%, genome mappability, etc.. Overall, it generally ends up not homogenous throughout the entire genome and this leads to artifacts in un-normalized count matrices.
To correct for sequencing coverage heterogeneity of raw count maps, Hi-C data can be normalized using matrix balancing approaches (Cournac et al. (2012), Imakaev et al. (2012)). This is generally done directly on the disk-stored matrices using out-of-memory strategies (e.g. with cooler balance <.cool>). However, if contact matrix files are imported into a HiCExperiment object but no balanced scores are available, in-memory balancing can be performed using the normalize function. This adds an extra ICE element in scores list (while the interactions themselves are unmodified).
normalized_hic <- normalize(hic)
normalized_hic
## `HiCExperiment` object with 471,364 contacts over 407 regions
## -------
## fileName: "/home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752"
## focus: "II"
## resolutions(5): 1000 2000 4000 8000 16000
## active resolution: 2000
## interactions: 34063
## scores(3): count balanced ICE
## topologicalFeatures: compartments(0) borders(0) loops(0) viewpoints(0)
## pairsFile: N/A
## metadata(0):It is possible to plot the different scores of the resulting object to visualize the newly computed scores. In this example, ICE scores should be nearly identical to balanced scores, which were originally imported from the disk-stored contact matrix.
cowplot::plot_grid(
plotMatrix(normalized_hic, use.scores = 'count', caption = FALSE),
plotMatrix(normalized_hic, use.scores = 'balanced', caption = FALSE),
plotMatrix(normalized_hic, use.scores = 'ICE', caption = FALSE),
nrow = 1
)
5.1.2 Computing observed/expected (O/E) map
The most prominent feature of a balanced Hi-C matrix is the strong main diagonal. This main diagonal is observed because interactions between immediate adjacent genomic loci are more prone to happen than interactions spanning longer genomic distances. This βexpectedβ behavior is due to the polymer nature of the chromosomes being studied, and can be locally estimated using the distance-dependent interaction frequency (a.k.a. the βdistance lawβ, or P(s)). It can be used to compute an expected matrix on interactions.
When it is desirable to βmaskβ this polymer behavior to emphasize topological structures formed by chromosomes, one can divide a given balanced matrix by its expected matrix, i.e. calculate the observed/expected (O/E) map. This is sometimes called βdetrendingβ, as it effectively removes the average polymer behavior from the balanced matrix.
The detrend function performs this operation on a given HiCExperiment object. It adds two extra elements in scores list: expected and detrended metrics (while the interactions themselves are unmodified).
detrended_hic <- detrend(hic)
detrended_hic
## `HiCExperiment` object with 471,364 contacts over 407 regions
## -------
## fileName: "/home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752"
## focus: "II"
## resolutions(5): 1000 2000 4000 8000 16000
## active resolution: 2000
## interactions: 34063
## scores(4): count balanced expected detrended
## topologicalFeatures: compartments(0) borders(0) loops(0) viewpoints(0)
## pairsFile: N/A
## metadata(0):Topological features will be visually more prominent in the O/E detrended Hi-C map.
cowplot::plot_grid(
plotMatrix(detrended_hic, use.scores = 'balanced', scale = 'log10', limits = c(-3.5, -1.2), caption = FALSE),
plotMatrix(detrended_hic, use.scores = 'expected', scale = 'log10', limits = c(-3.5, -1.2), caption = FALSE),
plotMatrix(detrended_hic, use.scores = 'detrended', scale = 'linear', limits = c(-1, 1), cmap = bwrColors(), caption = FALSE),
nrow = 1
)
Scale for
detrended scores
-
expectedscores are inlinearscale and Β± in the same amplitude thanbalancedscores; -
detrendedscores are inlog2scale, in general approximately centered around 0. When plottingdetrendedscores,scale = linearshould be set to prevent the defaultlog10scaling.
5.1.3 Computing autocorrelated map
Correlation matrices are often calculated from balanced Hi-C matrices. For instance, in genomes composed of eu- and heterochromatin, a correlation matrix can be used to reveal a checkerboard pattern emphasizing the segregation of chromatin into two A/B compartments (Lieberman-Aiden et al. (2009)).
The autocorrelate function is used to compute a correlation matrix of a HiCExperiment object. For each pair of interacting loci, the autocorrelated score represents the correlation between their respective interaction profiles with the rest of the genome.
autocorr_hic <- autocorrelate(hic)
##
autocorr_hic
## `HiCExperiment` object with 471,364 contacts over 407 regions
## -------
## fileName: "/home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752"
## focus: "II"
## resolutions(5): 1000 2000 4000 8000 16000
## active resolution: 2000
## interactions: 34063
## scores(5): count balanced expected detrended autocorrelated
## topologicalFeatures: compartments(0) borders(0) loops(0) viewpoints(0)
## pairsFile: N/A
## metadata(0):Since these metrics represent correlation scores, they range between -1 and 1. Two loci with an autocorrelated score close to -1 have anti-correlated interaction profiles, while two loci with a autocorrelated score close to 1 are likely to interact with shared targets.
Correlated and anti-correlated loci will be visually represented in the autocorrelated Hi-C map in red and blue pixels, respectively.
Note
Here we have illustrated how to compute an autocorrelation matrix from a HiCExperiment object using the example yeast Hi-C experiment. Bear in mind that this is unusual and not very useful, as yeast chromatin is not segregated in two compartments but rather follows a Rabl conformation (Duan et al. (2010)). An example of autocorrelation map from a vertebrate Hi-C experiment (for which chromatin is segregated in A/B compartments) is shown in Chapter 10.
plotMatrix(
autocorr_hic,
use.scores = 'autocorrelated',
scale = 'linear',
limits = c(-0.4, 0.4),
cmap = bgrColors()
)
Scale for
autocorrelated scores
-
autocorrelatedscores are inlinearscale, in general approximately centered around 0. When plottingautocorrelatedscores,scale = linearshould be set to prevent the defaultlog10scaling. -
limitsshould be manually set toc(-x, x)(0 < x <= 1) to ensure that the color range is effectively centered on0.
5.1.4 Despeckling (smoothing out) a contact map
Shallow-sequenced Hi-C libraries or matrices binned with an overly small bin size sometimes produce βgrainyβ Hi-C maps with noisy backgrounds. A grainy map may also be obtained when dividing two matrices, e.g. when computing the O/E ratio with detrend. This is particularly true for sparser long-range interactions. To overcome such limitations, HiCExperiment objects can be βdespeckledβ to smooth out focal speckles.
hic2 <- detrend(hic['II:400000-700000'])
hic2 <- despeckle(hic2, use.scores = 'detrended', focal.size = 2)
hic2
## `HiCExperiment` object with 168,785 contacts over 150 regions
## -------
## fileName: "/home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752"
## focus: "II:400,000-700,000"
## resolutions(5): 1000 2000 4000 8000 16000
## active resolution: 2000
## interactions: 11325
## scores(5): count balanced expected detrended detrended.despeckled
## topologicalFeatures: compartments(0) borders(0) loops(0) viewpoints(0)
## pairsFile: N/A
## metadata(0):The added <use.scores>.despeckled scores correspond to scores averaged using a window, whose width is provided with the focal.size argument. This results in a smoother Hi-C heatmap, effectively removing the βspecklesβ observed at longer range.
library(InteractionSet)
loops <- system.file('extdata', 'S288C-loops.bedpe', package = 'HiCExperiment') |>
import() |>
makeGInteractionsFromGRangesPairs()
borders <- system.file('extdata', 'S288C-borders.bed', package = 'HiCExperiment') |>
import()
cowplot::plot_grid(
plotMatrix(hic2, caption = FALSE),
plotMatrix(hic2, use.scores = 'detrended', scale = 'linear', limits = c(-1, 1), caption = FALSE),
plotMatrix(
hic2,
use.scores = 'detrended.despeckled',
scale = 'linear',
limits = c(-1, 1),
caption = FALSE,
loops = loops,
borders = borders
),
nrow = 1
)
Scale for
despeckled scores
despeckled scores are in the same scale than the scores they were computed from.
5.2 Operations between multiple matrices
5.2.1 Merging maps
Hi-C libraries are often sequenced in multiple rounds, for example when high genome coverage is required. This results in multiple contact matrix files being generated. The merge function can be used to bind several HiCExperiment objects into a single one.
The different HiCExperiment objects do not need to all have identical regions, as shown in the following example.
hic_sub1 <- subsetByOverlaps(hic, GRanges("II:100001-200000"))
hic_sub2 <- subsetByOverlaps(hic, GRanges("II:300001-400000"))
bound_hic <- merge(hic_sub1, hic_sub2)
plotMatrix(bound_hic)
5.2.2 Computing ratio between two maps
Comparing two Hi-C maps can be useful to infer which genomic loci are differentially interacting between experimental conditions. Comparing two HiCExperiment objects can be done in R using the divide function.
For example, we can divide the eco1 mutant Hi-C data by wild-type Hi-C dataset using the divide function.
hic_eco1 <- import(
CoolFile(HiContactsData('yeast_eco1', 'mcool')),
focus = 'II',
resolution = 2000
)
## see ?HiContactsData and browseVignettes('HiContactsData') for documentation
## loading from cachediv_contacts <- divide(hic_eco1, by = hic)
div_contacts
## `HiCExperiment` object with 996,154 contacts over 407 regions
## -------
## fileName: N/A
## focus: "II"
## resolutions(1): 2000
## active resolution: 2000
## interactions: 60894
## scores(6): count.x balanced.x count.by balanced.by balanced.fc balanced.l2fc
## topologicalFeatures: ()
## pairsFile: N/A
## metadata(2): hce_list operationWe can visually compare wild-type and eco1 maps side by side (left) and their ratio map (right). This highlights the depletion of short-range and increase of long-range interactions in the eco1 dataset.
cowplot::plot_grid(
plotMatrix(hic_eco1, compare.to = hic, limits = c(-4, -1)),
plotMatrix(
div_contacts,
use.scores = 'balanced.fc',
scale = 'log2',
limits = c(-1, 1),
cmap = bwrColors()
)
)
## [1] "/home/biocbuild/.cache/R/ExperimentHub/1896576048dd6b_7754 | /home/biocbuild/.cache/R/ExperimentHub/1895c561583f2e_7752"
Session info
Click to expand π
sessioninfo::session_info(include_base = TRUE)
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## setting value
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## language (EN)
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## ctype en_US.UTF-8
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##
## [1] /home/biocbuild/bbs-3.20-books/tmpdir/RtmphzOvfD/Rinst2020235c565b68
## [2] /home/biocbuild/bbs-3.20-bioc/R/site-library
## [3] /home/biocbuild/bbs-3.20-bioc/R/library
##
## βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββReferences
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Duan, Z., Andronescu, M., Schutz, K., McIlwain, S., Kim, Y. J., Lee, C., Shendure, J., Fields, S., Blau, C. A., & Noble, W. S. (2010). A three-dimensional model of the yeast genome. Nature, 465(7296), 363β367. https://doi.org/10.1038/nature08973
Imakaev, M., Fudenberg, G., McCord, R. P., Naumova, N., Goloborodko, A., Lajoie, B. R., Dekker, J., & Mirny, L. A. (2012). Iterative correction of hi-c data reveals hallmarks of chromosome organization. Nature Methods, 9(10), 999β1003. https://doi.org/10.1038/nmeth.2148
Lieberman-Aiden, E., Berkum, N. L. van, Williams, L., Imakaev, M., Ragoczy, T., Telling, A., Amit, I., Lajoie, B. R., Sabo, P. J., Dorschner, M. O., Sandstrom, R., Bernstein, B., Bender, M. A., Groudine, M., Gnirke, A., Stamatoyannopoulos, J., Mirny, L. A., Lander, E. S., & Dekker, J. (2009). Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science, 326(5950), 289β293. https://doi.org/10.1126/science.1181369