Author: Cyril Kurylo & Matthias Zytnicki & Sylvain Foissac & Elise Maigné

# HiCDOC

# Introduction

The aim of HiCDOC is to detect significant A/B compartment changes, using Hi-C data with replicates.

HiCDOC normalizes intrachromosomal Hi-C matrices, uses unsupervised learning to predict A/B compartments from multiple replicates, and detects significant compartment changes between experiment conditions.

It provides a collection of functions assembled into a pipeline:

1. Filter:
   1. Remove chromosomes which are too small to be useful.
   2. Filter sparse replicates to remove uninformative replicates with few interactions.
   3. Filter positions (bins) which have too few interactions.
2. Normalize:
   1. Normalize technical biases (inter-matrix normalization) using cyclic loess normalization (Stansfield et al. 2019), so that matrices are comparable.
   2. Normalize biological biases (intra-matrix normalization) using Knight-Ruiz matrix balancing (Knight and Ruiz 2012), so that all the bins are comparable.
   3. Normalize the distance effect, which results from higher interaction proportions between closer regions, with a MD loess.
3. Predict:
   1. Predict compartments using constrained K-means (Wagstaff et al. 2001).
   2. Detect significant differences between experiment conditions.
4. Visualize:
   1. Plot the interaction matrices of each replicate.
   2. Plot the overall distance effect on the proportion of interactions.
   3. Plot the compartments in each chromosome, along with their concordance (confidence measure) in each replicate, and significant changes between experiment conditions.
   4. Plot the overall distribution of concordance differences.
   5. Plot the result of the PCA on the compartments’ centroids.
   6. Plot the boxplots of self interaction ratios (differences between self interactions and the medians of other interactions) of each compartment, which is used for the A/B classification.

# Installation

HiCDOC can be installed from Bioconductor:

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

The package can then be loaded:

    library(HiCDOC)
    #> Loading required package: InteractionSet
    #> Loading required package: GenomicRanges
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# Importing Hi-C data

HiCDOC can import Hi-C data sets in various different formats: - Tabular `.tsv` files. - Cooler `.cool` or `.mcool` files. - Juicer `.hic` files. - HiC-Pro `.matrix` and `.bed` files.

## Tabular files

A tabular file is a tab-separated multi-replicate sparse matrix with a header:

chromosome position 1 position 2 C1.R1 C1.R2 C2.R1 … Y 1500000 7500000 145 184 72 … …

The number of interactions between `position 1` and `position 2` of `chromosome` are reported in each `condition.replicate` column. There is no limit to the number of conditions and replicates.

To load Hi-C data in this format:

    hic.experiment <- HiCDOCDataSetFromTabular('path/to/data.tsv')

## Cooler files

To load `.cool` or `.mcool` files generated by Cooler (Abdennur and Mirny 2019):

    # Path to each file
    paths = c(
        'path/to/condition-1.replicate-1.cool',
        'path/to/condition-1.replicate-2.cool',
        'path/to/condition-2.replicate-1.cool',
        'path/to/condition-2.replicate-2.cool',
        'path/to/condition-3.replicate-1.cool'
    )

    # Replicate and condition of each file. Can be names instead of numbers.
    replicates <- c(1, 2, 1, 2, 1)
    conditions <- c(1, 1, 2, 2, 3)

    # Resolution to select in .mcool files
    binSize = 500000

    # Instantiation of data set
    hic.experiment <- HiCDOCDataSetFromCool(
        paths,
        replicates = replicates,
        conditions = conditions,
        binSize = binSize # Specified for .mcool files.
    )

## Juicer files

To load `.hic` files generated by Juicer (Durand 2016):

    # Path to each file
    paths = c(
        'path/to/condition-1.replicate-1.hic',
        'path/to/condition-1.replicate-2.hic',
        'path/to/condition-2.replicate-1.hic',
        'path/to/condition-2.replicate-2.hic',
        'path/to/condition-3.replicate-1.hic'
    )

    # Replicate and condition of each file. Can be names instead of numbers.
    replicates <- c(1, 2, 1, 2, 1)
    conditions <- c(1, 1, 2, 2, 3)

    # Resolution to select
    binSize <- 500000

    # Instantiation of data set
    hic.experiment <- HiCDOCDataSetFromHiC(
        paths,
        replicates = replicates,
        conditions = conditions,
        binSize = binSize
    )

## HiC-Pro files

To load `.matrix` and `.bed` files generated by HiC-Pro (Servant 2015):

    # Path to each matrix file
    matrixPaths = c(
        'path/to/condition-1.replicate-1.matrix',
        'path/to/condition-1.replicate-2.matrix',
        'path/to/condition-2.replicate-1.matrix',
        'path/to/condition-2.replicate-2.matrix',
        'path/to/condition-3.replicate-1.matrix'
    )

    # Path to each bed file
    bedPaths = c(
        'path/to/condition-1.replicate-1.bed',
        'path/to/condition-1.replicate-2.bed',
        'path/to/condition-2.replicate-1.bed',
        'path/to/condition-2.replicate-2.bed',
        'path/to/condition-3.replicate-1.bed'
    )

    # Replicate and condition of each file. Can be names instead of numbers.
    replicates <- c(1, 2, 1, 2, 1)
    conditions <- c(1, 1, 2, 2, 3)

    # Instantiation of data set
    hic.experiment <- HiCDOCDataSetFromHiCPro(
        matrixPaths = matrixPaths,
        bedPaths = bedPaths,
        replicates = replicates,
        conditions = conditions
    )

# Running the HiCDOC pipeline

An example dataset can be loaded from the HiCDOC package:

    data(exampleHiCDOCDataSet)

Once your data is loaded, you can run all the filtering, normalization, and prediction steps with the command : `HiCDOC(exampleHiCDOCDataSet)`. This one-liner runs all the steps detailed below.

Note that before running `HiCDOC()` you can set the specific parameters (or only a subset of them) for your object :

    parameters(exampleHiCDOCDataSet) <- list(
      smallChromosomeThreshold = 100,
      sparseReplicateThreshold = 0.3,
      weakPositionThreshold = 1,
      cyclicLoessSpan = NA_real_,
      loessSampleSize = 20000,
      kMeansDelta = 0.0001,
      kMeansIterations = 50,
      kMeansRestarts = 20,
      PC1CheckThreshold = 0.75
    )

In the examples below, all that parameters are pass directly to the functions.

## Filtering data

Remove small chromosomes of length smaller than 100 positions (100 is the default value):

    hic.experiment <- filterSmallChromosomes(exampleHiCDOCDataSet, threshold = 100)
    #> Keeping chromosomes with at least 100 positions.
    #> Kept 3 chromosomes: X, Y, Z
    #> Removed 1 chromosome: W

Remove sparse replicates filled with less than 30% non-zero interactions (30% is the default value):

    hic.experiment <- filterSparseReplicates(hic.experiment, threshold = 0.3)
    #> Keeping replicates filled with at least 30% non-zero interactions.
    #>
    #> Removed interactions matrix of chromosome X, condition 1, replicate R2 filled at 2.347%.
    #> Removed 1 replicate in total.

Remove weak positions with less than 1 interaction in average (1 is the default value):

    hic.experiment <- filterWeakPositions(hic.experiment, threshold = 1)
    #> Keeping positions with interactions average greater or equal to 1.
    #> Chromosome X: 2 positions removed, 118 positions remaining.
    #> Chromosome Y: 3 positions removed, 157 positions remaining.
    #> Chromosome Z: 0 positions removed, 200 positions remaining.
    #> Removed 5 positions in total.

## Normalizing biases

### Technical biases

Normalize technical biases such as sequencing depth (inter-matrix normalization) so that matrices are comparable :

    suppressWarnings(hic.experiment <- normalizeTechnicalBiases(hic.experiment))
    #> Normalizing technical biases.

This normalization uses uses cyclic loess normalization from [multiHiCcompare package] (Stansfield et al. 2019). Note : For large dataset, it is highly recommended to set a value for `cycleLoessSpan` parameter to reduce computing time and necessary memory. See `?HiCDOC::normalizeTechnicalBiases`

### Biological biases

Normalize biological biases, such as GC content, number of restriction sites, etc. (intra-matrix normalization):

    hic.experiment <- normalizeBiologicalBiases(hic.experiment)
    #> Chromosome X: normalizing biological biases.
    #> Chromosome Y: normalizing biological biases.
    #> Chromosome Z: normalizing biological biases.

### Distance effect

Normalize the linear distance effect resulting from more interactions between closer genomic regions (20000 is the default value for `loessSampleSize`):

    hic.experiment <-
        normalizeDistanceEffect(hic.experiment, loessSampleSize = 20000)
    #> Chromosome X: normalizing distance effect.
    #> Chromosome Y: normalizing distance effect.
    #> Chromosome Z: normalizing distance effect.

## Predicting compartments and differences

Predict A and B compartments and detect significant differences, here using the default values as parameters:

    hic.experiment <- detectCompartments(hic.experiment)
    #> Clustering genomic positions.
    #> Predicting A/B compartments.
    #> Detecting significant differences.

# Visualizing data and results

Plot the interaction matrix of each replicate:

    p <- plotInteractions(hic.experiment, chromosome = "Y")
    p

Plot the overall distance effect on the proportion of interactions:

    p <- plotDistanceEffect(hic.experiment)
    #> `stat_bin2d()` using `bins = 30`. Pick better value `binwidth`.
    #> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
    #> `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
    #> `stat_bin2d()` using `bins = 30`. Pick better value `binwidth`.
    #> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
    p

List and plot compartments with their concordance (confidence measure) in each replicate, and significant changes between experiment conditions:

    compartments(hic.experiment)
    #> GRanges object with 1025 ranges and 6 metadata columns:
    #>          seqnames      ranges strand |     index condition compartment
    #>             <Rle>   <IRanges>  <Rle> | <numeric>  <factor>    <factor>
    #>      [1]        X       1-137      * |        81         1           A
    #>      [2]        X       1-137      * |        81         2           A
    #>      [3]        X       1-137      * |        81         3           A
    #>      [4]        X     138-274      * |        82         1           A
    #>      [5]        X     138-274      * |        82         2           A
    #>      ...      ...         ...    ... .       ...       ...         ...
    #>   [1021]        Z 26716-26852      * |       556         1           A
    #>   [1022]        Z 26853-26989      * |       557         1           A
    #>   [1023]        Z 26990-27126      * |       558         1           A
    #>   [1024]        Z 27127-27263      * |       559         1           A
    #>   [1025]        Z 27264-27400      * |       560         1           A
    #>          centroid.check PC1.check assignment.check
    #>               <logical> <logical>        <logical>
    #>      [1]           TRUE      TRUE             TRUE
    #>      [2]           TRUE      TRUE             TRUE
    #>      [3]           TRUE      TRUE             TRUE
    #>      [4]           TRUE      TRUE             TRUE
    #>      [5]           TRUE      TRUE             TRUE
    #>      ...            ...       ...              ...
    #>   [1021]           TRUE      TRUE             TRUE
    #>   [1022]           TRUE      TRUE             TRUE
    #>   [1023]           TRUE      TRUE             TRUE
    #>   [1024]           TRUE      TRUE             TRUE
    #>   [1025]           TRUE      TRUE             TRUE
    #>   -------
    #>   seqinfo: 3 sequences from an unspecified genome; no seqlengths

    concordances(hic.experiment)
    #> GRanges object with 2089 ranges and 5 metadata columns:
    #>          seqnames      ranges strand |     index condition replicate
    #>             <Rle>   <IRanges>  <Rle> | <numeric>  <factor>  <factor>
    #>      [1]        X       1-137      * |        81         1        R1
    #>      [2]        X       1-137      * |        81         1        R3
    #>      [3]        X       1-137      * |        81         2        R2
    #>      [4]        X       1-137      * |        81         3        R1
    #>      [5]        X       1-137      * |        81         3        R2
    #>      ...      ...         ...    ... .       ...       ...       ...
    #>   [2085]        Z 26990-27126      * |       558         1        R3
    #>   [2086]        Z 27127-27263      * |       559         1        R2
    #>   [2087]        Z 27127-27263      * |       559         1        R3
    #>   [2088]        Z 27264-27400      * |       560         1        R2
    #>   [2089]        Z 27264-27400      * |       560         1        R3
    #>          compartment concordance
    #>             <factor>   <numeric>
    #>      [1]           A  -0.0142842
    #>      [2]           A  -0.0137088
    #>      [3]           A  -0.0203050
    #>      [4]           A  -0.0165560
    #>      [5]           A  -0.0163555
    #>      ...         ...         ...
    #>   [2085]           A  -0.0207507
    #>   [2086]           A  -0.0196494
    #>   [2087]           A  -0.0246955
    #>   [2088]           A  -0.0204581
    #>   [2089]           A  -0.0207913
    #>   -------
    #>   seqinfo: 3 sequences from an unspecified genome; no seqlengths

    differences(hic.experiment)
    #> GRanges object with 54 ranges and 10 metadata columns:
    #>        seqnames      ranges strand |     index condition.1 condition.2
    #>           <Rle>   <IRanges>  <Rle> | <numeric>    <factor>    <factor>
    #>    [1]        X   1645-1781      * |        93           1           2
    #>    [2]        X   1645-1781      * |        93           2           3
    #>    [3]        X   1782-1918      * |        94           1           2
    #>    [4]        X   1782-1918      * |        94           2           3
    #>    [5]        X   1919-2055      * |        95           1           2
    #>    ...      ...         ...    ... .       ...         ...         ...
    #>   [50]        Y 14660-14796      * |       308           2           3
    #>   [51]        Y 14797-14933      * |       309           1           3
    #>   [52]        Y 14797-14933      * |       309           2           3
    #>   [53]        Y 14934-15070      * |       310           1           3
    #>   [54]        Y 14934-15070      * |       310           2           3
    #>           pvalue pvalue.adjusted direction significance centroid.check
    #>        <numeric>       <numeric>  <factor>  <character>      <logical>
    #>    [1]         0               0      A->B         ****           TRUE
    #>    [2]         0               0      B->A         ****           TRUE
    #>    [3]         0               0      A->B         ****           TRUE
    #>    [4]         0               0      B->A         ****           TRUE
    #>    [5]         0               0      A->B         ****           TRUE
    #>    ...       ...             ...       ...          ...            ...
    #>   [50]         0               0      B->A         ****           TRUE
    #>   [51]         0               0      B->A         ****           TRUE
    #>   [52]         0               0      B->A         ****           TRUE
    #>   [53]         0               0      B->A         ****           TRUE
    #>   [54]         0               0      B->A         ****           TRUE
    #>        PC1.check assignment.check
    #>        <logical>        <logical>
    #>    [1]      TRUE             TRUE
    #>    [2]      TRUE             TRUE
    #>    [3]      TRUE             TRUE
    #>    [4]      TRUE             TRUE
    #>    [5]      TRUE             TRUE
    #>    ...       ...              ...
    #>   [50]      TRUE             TRUE
    #>   [51]      TRUE             TRUE
    #>   [52]      TRUE             TRUE
    #>   [53]      TRUE             TRUE
    #>   [54]      TRUE             TRUE
    #>   -------
    #>   seqinfo: 3 sequences from an unspecified genome; no seqlengths

    p <- plotCompartmentChanges(hic.experiment, chromosome = "Y")
    p

Plot the overall distribution of concordance differences:

    p <- plotConcordanceDifferences(hic.experiment)
    p
    #> `stat_bin()` using `bins = 30`. Pick better value `binwidth`.

Plot the result of the PCA on the compartments’ centroids:

    p <- plotCentroids(hic.experiment, chromosome = "Y")
    p

Plot the boxplots of self interaction ratios (differences between self interactions and the median of other interactions) of each compartment:

    p <- plotSelfInteractionRatios(hic.experiment, chromosome = "Y")
    p

## Sanity checks

Sometimes, basic assumptions on the data are not met. We try to detect inconsistencies, and warn the user.

### PCA checks

We perform a principal component analysis on the centroids. Each centroid represent an ideal bin, located either on compartment A or B, in each sample, and each chromosome. Given a chromosome, if all the centroids of the A compartment do not have the same sign on the first principal component, we issue a warning for this chromosome. Likewise for the B compartment.

We also check that the inertia on the first principal component is at least 75%.

These checks make sure that centroids of the same compartments do cluster together. If the conditions are too different from each other, they may cluster together. This case is detected by this check.

### Compartment assignemnt

We use “self-interaction” in order to classify centroids to A and B compartments. The self-interaction of a bin is the ratio of the number of pairs that link this bin with other bins of the same compartment, divided by the number of pairs The self-interactions should be different from compartments A and B. We perform a Wilcoxon t-test. If it is not significant, then a warning is issued.

### Warnings

If at least of the PCA checks fail, the warnings are printed on the PCA plot. If the compartment assignment check fail, the warning is printed on the corresponding plot.

When accessing the compartments and the concordances, chromosomes which fail to pass the checks are removed (unless the appropriate parameter is set).

# Session info

    sessionInfo()
    #> R version 4.6.0 (2026-04-24)
    #> Platform: x86_64-pc-linux-gnu
    #> Running under: Ubuntu 24.04.4 LTS
    #>
    #> Matrix products: default
    #> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
    #> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
    #>
    #> locale:
    #>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
    #>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
    #>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
    #>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
    #>  [9] LC_ADDRESS=C               LC_TELEPHONE=C
    #> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
    #>
    #> time zone: Etc/UTC
    #> tzcode source: system (glibc)
    #>
    #> attached base packages:
    #> [1] stats4    stats     graphics  grDevices utils     datasets  methods
    #> [8] base
    #>
    #> other attached packages:
    #>  [1] HiCDOC_1.15.2               InteractionSet_1.41.0
    #>  [3] SummarizedExperiment_1.43.0 Biobase_2.73.1
    #>  [5] MatrixGenerics_1.25.0       matrixStats_1.5.0
    #>  [7] GenomicRanges_1.65.0        Seqinfo_1.3.0
    #>  [9] IRanges_2.47.2              S4Vectors_0.51.3
    #> [11] BiocGenerics_0.59.7         generics_0.1.4
    #> [13] BiocStyle_2.41.0
    #>
    #> loaded via a namespace (and not attached):
    #>  [1] tidyselect_1.2.1        dplyr_1.2.1             farver_2.1.2
    #>  [4] S7_0.2.2                fastmap_1.2.0           digest_0.6.39
    #>  [7] lifecycle_1.0.5         statmod_1.5.2           HiCcompare_1.35.0
    #> [10] magrittr_2.0.5          compiler_4.6.0          rlang_1.2.0
    #> [13] sass_0.4.10             tools_4.6.0             yaml_2.3.12
    #> [16] calibrate_1.7.7         data.table_1.18.4       knitr_1.51
    #> [19] labeling_0.4.3          S4Arrays_1.13.0         DelayedArray_0.39.3
    #> [22] RColorBrewer_1.1-3      abind_1.4-8             BiocParallel_1.47.0
    #> [25] KernSmooth_2.23-26      withr_3.0.2             sys_3.4.3
    #> [28] grid_4.6.0              Rhdf5lib_2.1.0          edgeR_4.11.1
    #> [31] ggplot2_4.0.3           MASS_7.3-65             scales_1.4.0
    #> [34] gtools_3.9.5            cli_3.6.6               rmarkdown_2.31
    #> [37] otel_0.2.0              httr_1.4.8              pbapply_1.7-4
    #> [40] cachem_1.1.0            rhdf5_2.57.1            splines_4.6.0
    #> [43] parallel_4.6.0          BiocManager_1.30.27     XVector_0.53.0
    #> [46] aggregation_1.0.2       vctrs_0.7.3             Matrix_1.7-5
    #> [49] jsonlite_2.0.0          multiHiCcompare_1.31.0  qqman_0.1.9
    #> [52] maketools_1.3.2         locfit_1.5-9.12         limma_3.69.2
    #> [55] jquerylib_0.1.4         glue_1.8.1              codetools_0.2-20
    #> [58] cowplot_1.2.0           gtable_0.3.6            GenomeInfoDb_1.49.1
    #> [61] UCSC.utils_1.9.0        tibble_3.3.1            pillar_1.11.1
    #> [64] rhdf5filters_1.25.0     htmltools_0.5.9         GenomeInfoDbData_1.2.15
    #> [67] R6_2.6.1                evaluate_1.0.5          lattice_0.22-9
    #> [70] pheatmap_1.0.13         bslib_0.11.0            Rcpp_1.1.1-1.1
    #> [73] gridExtra_2.3           SparseArray_1.13.2      nlme_3.1-169
    #> [76] mgcv_1.9-4              HiCParser_1.5.0         xfun_0.58
    #> [79] buildtools_1.0.0        pkgconfig_2.0.3

# References

Abdennur, Nezar, and Leonid A Mirny. 2019. “Cooler: scalable storage for Hi-C data and other genomically labeled arrays.” Bioinformatics 36: 311–16. https://doi.org/10.1093/bioinformatics/btz540.
Durand, Muhammad S. AND Machol, Neva C. AND Shamim. 2016. “Juicer Provides a One-Click System for Analyzing Loop-Resolution Hi-C Experiments.” Cell Systems 3: 95–98. https://doi.org/10.1016/j.cels.2016.07.002.
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Servant, Nelle AND Lajoie, Nicolas AND Varoquaux. 2015. “HiC-Pro: an optimized and flexible pipeline for Hi-C data processing.” Genome Biology 16: 259. https://doi.org/10.1186/s13059-015-0831-x.
Stansfield, John C, Kellen G Cresswell, and Mikhail G Dozmorov. 2019. “multiHiCcompare: joint normalization and comparative analysis of complex Hi-C experiments.” Bioinformatics 35: 2916–23. https://doi.org/10.1093/bioinformatics/btz048.
Wagstaff, Kiri, Claire Cardie, Seth Rogers, and Stefan Schrödl. 2001. “Constrained k-Means Clustering with Background Knowledge.” Proceedings of the Eighteenth International Conference on Machine Learning, ICML ’01, 577–84. https://pdfs.semanticscholar.org/0bac/ca0993a3f51649a6bb8dbb093fc8d8481ad4.pdf.