hi-c-analysis-compartment-analysis

name	hi-c-analysis-compartment-analysis
description	Detects A/B chromatin compartments from balanced Hi-C contact matrices via eigenvector decomposition of the distance-normalized, Pearson-correlated cis matrix with cooltools (eigs_cis), then orients (phases) the compartment eigenvector against a GC or gene-density track so the active (A) sign is not arbitrary. Covers the eigenvector-is-a-choice problem (per-arm view_df to remove the centromere gradient; picking the eigenvector by max correlation with activity, not by eigenvalue), GC phasing with bioframe.frac_gc, resolution choice (100kb-1Mb), saddle plots and saddle_strength for compartmentalization strength, the cohesin-loss-strengthens-compartments result, subcompartments (SNIPER/Calder/dcHiC), and cross-condition compartment switching. Use when calling A/B compartments, computing E1/eigenvectors, phasing the eigenvector, building saddle plots, choosing a compartment resolution, quantifying compartment strength, or comparing compartmentalization across conditions.
tool_type	python
primary_tool	cooltools

Version Compatibility

Reference examples tested with: cooler 0.10+, cooltools 0.7+, bioframe 0.7+

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures

cooltools had a major API shift around 0.5 -> 0.7+ (functions standardized on view_df/viewframe arguments; eigs_cis, expected_cis, saddle signatures changed). The cooler MUST be balanced before any compartment analysis: clr.matrix(balance=True) requires a stored weight column. A .mcool is multi-resolution -- pass a single-resolution URI (file.mcool::/resolutions/100000), not the bare .mcool. The phasing_track MUST share the cooler's exact binning or phasing silently no-ops. If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

A/B Compartment Analysis

"Which regions of my genome are in the active vs inactive compartment?" -> Distance-normalize the cis matrix, take an eigenvector of its Pearson correlation matrix, then orient it by GC/gene density so positive = A (active) -- but verify the kept eigenvector is the compartment one, not an arm gradient.

• Python: cooltools.eigs_cis(clr, gc_track, view_df=arms, n_eigs=3, sort_metric='pearsonr')

The Single Most Important Modern Insight -- E1 Is a Choice, Not an Output, and Its Sign Is Arbitrary Until Phased

The two most damaging beginner assumptions are "E1 = compartments" and "positive E1 = active." Both are false out of the box, and both fail silently -- the pipeline runs, returns a track, and is wrong.

1. E1 is not guaranteed to be the compartment track. On a whole-chromosome O/E correlation matrix the largest eigenvalue very often belongs to a smooth p-arm-vs-q-arm or centromere-to-telomere GRADIENT, not the plaid A/B checkerboard -- the real compartment signal then lands in E2 or E3. cooltools' own docs concede the first eigenvector "occasionally describes chromosomal arms or translocation blowouts." The compartment eigenvector is the one with the largest |correlation| to an activity track (GC, gene density, H3K27ac), not the one with the largest eigenvalue. The structural fix removes the gradient at the source: run eigs_cis per chromosome ARM (a view_df split at centromeres, from bioframe.make_chromarms), so the arm gradient is never in the within-arm matrix. Set sort_metric='pearsonr' so the returned eigenvectors are ordered by GC correlation, not eigenvalue -- otherwise the arm gradient is reported as "E1." A monotonic "compartment track" with no sign flips across a chromosome is the failure signature of a captured arm gradient.

2. The sign is arbitrary until phased. Eigenvectors are defined up to sign; the positive lobe is meaningless and can differ per chromosome AND per sample. The eigenvector MUST be oriented with an external active-chromatin track via the phasing_track argument so A = positive. GC content is the field default (it needs no extra assay and tracks compartment A; Lieberman-Aiden 2009 Science 326:289) -- compute it with bioframe.frac_gc at the compartment resolution, exactly matching the cooler's binning. Wrong/weak phasing flips A<->B silently, and every downstream saddle, switch call, and differential result inverts with no error. This is a classic source of irreproducible compartment papers.

3. Compartments are an equilibrium phenomenon decoupled from TADs/loops. Compartments = microphase separation of A/B chromatin states (cohesin-independent; survive cohesin loss, Schwarzer 2017 Nature 551:51, and CTCF loss, Nora 2017 Cell 169:930). TADs/loops = ATP-driven loop extrusion stalled at CTCF. Removing cohesin reinforces compartments while erasing TADs (Schwarzer 2017 reports reinforced compartmentalization on Nipbl loss; Rao 2017 Cell 171:305 eliminates all loop domains with compartments retained) -- loop extrusion actively mixes chromatin across compartment boundaries, so removing the extruder lets microphase separation run to completion (Nuebler 2018 PNAS 115:E6697). A preserved-or-stronger saddle after a cohesin/Nipbl/RAD21 perturbation is the EXPECTED result, not a bug; compartment-strength and TAD-strength are antagonistic. If a CTCF/cohesin perturbation makes compartments vanish, suspect a phasing artifact, not biology.

Method / Output Taxonomy

Output	Tool / call	What it is	When
A/B eigenvector (E1)	cooltools.eigs_cis (cis, per-arm)	leading GC-phased eigenvector of the cis O/E correlation matrix; sign = A/B	standard A/B call, single map, per chromosome arm
Genome-wide A/B	cooltools.eigs_trans	eigenvector of inter-chromosomal blocks; immune to the cis arm-gradient	whole-genome A/B consensus with deep trans coverage
Compartment strength	cooltools.saddle + saddle_strength	(AA+BB)/(AB+BA) corner ratio of the saddle	comparing compartmentalization across conditions
5-6 subcompartments	SNIPER (Xiong & Ma 2019 Nat Commun 10:5069)	autoencoder imputes inter-chr contacts -> MLP classifies A1/A2/B1/B2/B3 at 100kb	deep inter-chr data; Rao-style subcompartments
Continuous compartment rank	Calder (Liu 2021 Nat Commun 12:2439)	intra-chr divisive hierarchical clustering -> 0-1 multi-scale rank	cross-cell-line repositioning; modest coverage
Differential compartments	dcHiC (Chakraborty 2022 Nat Commun 13:6827)	quantile-normalized scores + multivariate Mahalanobis distance + significance; solves cross-sample sign flips	>=2 samples, "which bins switch A<->B"
Single-cell compartment	scA/B (Tan 2018 Dip-C Science)	CpG/activity proxy per locus; do NOT eigendecompose one sparse cell	scHi-C, ~20-50k contacts/cell

Decision Tree by Scenario

Scenario	Recommended	Why
Matrix not yet balanced	cooler balance first (-> matrix-operations)	unbalanced -> O/E is all-NaN; meaningless eigenvector
Standard A/B call, one map	eigs_cis per arm at 100kb-1Mb, phase by GC	compartments are chromosome-scale; arms remove the centromere gradient
E1 looks monotonic / no sign flips	inspect E2/E3, pick by max	corr
Sign of A/B seems inverted	confirm phasing_track is at the cooler's binning	weak/mismatched phasing flips A<->B silently
Want compartment STRENGTH	saddle + saddle_strength, fixed extent across samples	a single eigenvector does not quantify strength
Want 5-6 subcompartments	SNIPER or Calder, NOT more eigenvectors	subcompartments need inter-chr ML or hierarchical clustering, not n_eigs
Two+ conditions, compartment shift	-> hic-differential (dcHiC)	replicate-aware, sign-coherent across the cohort; hand-diffing eigenvectors flips signs
Single-cell Hi-C	scA/B (Dip-C), not a per-cell eigenvector	one sparse cell is too noisy to eigendecompose
Annotate switched bins with marks	-> chip-seq/chromatin-state-segmentation, chip-seq/peak-annotation	overlay ChromHMM/histone state on compartment calls
Render the eigenvector/saddle	-> hic-visualization; export bigWig -> genome-intervals/bigwig-tracks	track/heatmap conventions live there

Per-Arm Eigenvector with GC Phasing

Goal: Assign each genomic bin to the active (A) or inactive (B) compartment with a non-arbitrary sign, avoiding the centromere arm-gradient artifact.

Approach: Build a per-arm view_df (split at centromeres) so the arm gradient never enters the matrix; compute a GC-content phasing track at the cooler's exact binning; run eigs_cis with the GC track and sort_metric='pearsonr' so eigenvectors are ordered by GC correlation; then take the GC-correlated eigenvector as the compartment track.

import cooler
import cooltools
import bioframe

clr = cooler.Cooler('matrix.mcool::/resolutions/100000')   # 100kb: compartments are coarse-scale
chromsizes = clr.chromsizes
cens = bioframe.fetch_centromeres('hg38')
arms = bioframe.make_chromarms(chromsizes, cens)            # per-arm view removes the centromere gradient
arms = arms[arms.chrom.isin(clr.chromnames)].reset_index(drop=True)

genome = bioframe.load_fasta('hg38.fa')                     # FASTA index (.fai) must exist
bins = clr.bins()[:][['chrom', 'start', 'end']]
gc = bioframe.frac_gc(bins, genome)                         # phasing track at the cooler's exact binning

eigvals, eigvecs = cooltools.eigs_cis(clr, gc, view_df=arms, n_eigs=3, sort_metric='pearsonr')
eigvecs['compartment'] = ['A' if e > 0 else 'B' for e in eigvecs['E1']]   # GC-phased: positive E1 = A

After phasing, sanity-check that E1 correlates with gc['GC'] (sign and magnitude). If the strongest correlation is in E2/E3, that component -- not E1 -- is the compartment track; re-derive the call from it.

Compartment Strength via Saddle Plot

Goal: Quantify how strongly the genome demixes into A and B with a single comparable number across conditions.

Approach: Compute the distance-decay expected; pass the cooler, the expected, and the phased E1 eigenvector to saddle, which digitizes E1 into quantile groups internally (via qrange) and aggregates O/E into a 2D table of same-vs-cross-compartment interactions; then read saddle_strength (the (AA+BB)/(AB+BA) corner ratio) at one fixed extent, applied identically to every sample compared.

N_GROUPS = 38            # quantile groups for digitizing E1; ~30-50 is conventional (cooltools tutorial)
Q_LO, Q_HI = 0.025, 0.975   # trim the extreme 2.5% tails before digitizing to resist outlier bins

expected = cooltools.expected_cis(clr, view_df=arms)        # has the 'balanced.avg' column saddle needs
track = eigvecs[['chrom', 'start', 'end', 'E1']]           # the SAME phased E1 used for the A/B call
interaction_sum, interaction_count = cooltools.saddle(
    clr, expected, track, 'cis', n_bins=N_GROUPS, qrange=(Q_LO, Q_HI), view_df=arms
)
strength = cooltools.api.saddle.saddle_strength(interaction_sum, interaction_count)   # 1D array; lives in cooltools.api.saddle, not top level
EXTENT = N_GROUPS // 5   # read strength at the top/bottom ~20% of bins; pick one extent, use it everywhere
score = strength[EXTENT]

saddle_strength returns an ARRAY (cumulative corner ratio over increasing extent), not a scalar -- there is no canonical single number, so choose an extent and apply it identically across compared samples. Mismatched n_bins, resolution, qrange, or extent make strengths incomparable. Remember: a preserved-or-higher strength after cohesin/Nipbl/RAD21 loss is the expected result.

Compare Compartments Across Conditions

Goal: Find bins that switch A<->B between two conditions without being fooled by per-sample sign flips.

Approach: Do NOT independently phase two eigenvectors and diff them bin-by-bin -- a weak per-chromosome GC correlation can flip the sign in one sample only, manufacturing fake "switches." Use dcHiC, which computes eigenvectors on quantile-normalized scores in a shared framework (sign-coherent across the cohort) and reports a multivariate significance per bin. Route this to hic-differential.

# Hand-diffing is only safe when you have CONFIRMED both eigenvectors are sign-coherent (same arms phased
# to the same GC track with strong correlation). Otherwise use dcHiC -- see hic-differential.
import pandas as pd
merged = eig1.merge(eig2, on=['chrom', 'start', 'end'], suffixes=('_1', '_2'))
merged['switch'] = (merged['E1_1'] > 0) != (merged['E1_2'] > 0)   # only meaningful if both are phased coherently

Per-Method Failure Modes

Eigenvector captured the arm gradient

Trigger: eigs_cis run per whole chromosome (no per-arm view_df) and/or sort_metric=None. Mechanism: the largest eigenvalue belongs to the smooth p-vs-q arm / centromere gradient, not the A/B checkerboard. Symptom: a monotonic "compartment track" across a chromosome with no sign flips; weak correlation of E1 with GC. Fix: run per chromosome arm (bioframe.make_chromarms); set sort_metric='pearsonr'; pick the eigenvector with the largest |corr| to GC.

Eigenvector sign not phased

Trigger: eigs_cis called with phasing_track=None. Mechanism: the sign of an eigenvector is mathematically arbitrary. Symptom: active euchromatin lands in "B"; A/B inverted relative to GC; per-chromosome sign inconsistency. Fix: pass a GC (or gene-density / H3K27ac) phasing_track so positive E1 = A.

Phasing track at the wrong binning

Trigger: GC/activity track computed at a different resolution than the cooler. Mechanism: cooltools aligns the track to the cooler bins; a mismatch yields garbage correlations or a silent no-op. Symptom: phasing has no effect, or signs are random. Fix: compute the track on clr.bins() at the exact compartment resolution.

Calling compartments at TAD/loop resolution

Trigger: eigs_cis at 5-25kb. Mechanism: compartments are a 100kb-1Mb feature; fine bins are sparse and dominated by TAD/loop structure and noise. Symptom: a noisy, jagged E1 that does not correlate with GC. Fix: call at 100kb-1Mb (250kb common; up to 1Mb for shallow data).

Expecting subcompartments from more eigenvectors

Trigger: raising n_eigs to "get A1/A2/B1/B2/B3". Mechanism: Rao's 6 subcompartments came from clustering inter-chromosomal patterns in a 4.9-billion-contact map, not from extra eigenvectors. Symptom: higher eigenvectors are noise, not finer biology. Fix: use SNIPER (inter-chr ML) or Calder (hierarchical); for differential use dcHiC.

Hand-diffing independently phased eigenvectors

Trigger: subtracting/comparing two per-sample eigenvectors bin-by-bin. Mechanism: a weak GC correlation can flip the sign in one sample only. Symptom: spurious "compartment switches" concentrated on whole chromosomes/arms. Fix: use dcHiC (sign-coherent quantile-normalized framework) -- see hic-differential.

Saddle strengths not comparable across samples

Trigger: different n_bins, qrange, resolution, or extent between compared saddles. Mechanism: saddle_strength is an extent-dependent array, not an absolute scalar. Symptom: strength differences that track the settings, not the biology. Fix: fix n_bins, qrange, resolution, and the corner extent; apply identically to all samples.

Quantitative Thresholds

Threshold	Source	Rationale
Compartment resolution 100kb-1Mb (250kb typical)	compartment scale (Lieberman-Aiden 2009)	finer bins mix in TAD/loop structure and sparsity noise; A/B is chromosome-scale
Run per chromosome ARM	eigenvector-selection (cooltools docs; Mirny lab)	removes the centromere/arm gradient that otherwise hijacks E1
sort_metric='pearsonr'	cooltools default-mismatch	default sorts by eigenvalue, so the arm gradient is reported as E1; pearsonr sorts by GC correlation
n_eigs>=3 and inspect eigenvalues	eigenvector-selection	n_eigs=1 hides the arm-vs-compartment problem; which component is biology is then undeterminable
clip_percentile=99.9 (cooler eigs_cis default)	outlier suppression	dense cis_eig defaults clip_percentile=0; the entry points differ -- do not assume
Saddle quantile groups ~30-50; trim 2.5% tails	cooltools tutorial	enough groups to resolve the saddle; tail trim resists outlier bins
Saddle strength at a fixed extent (e.g. top/bottom ~20%)	saddle_strength is an array	no canonical scalar; one extent, applied identically across samples
Subcompartments require deep inter-chr data	Rao 2014 (4.9B contacts)	shallow maps + extra eigenvectors give noise, not subcompartments

Common Errors

Error / symptom	Cause	Solution
clr.matrix(balance=True) / O/E all NaN	cooler not balanced	run cooler balance / cooler.balance_cooler first (-> matrix-operations)
Empty / wrong-resolution result on .mcool	bare .mcool passed	use file.mcool::/resolutions/<bp> URI
A/B compartments inverted	eigenvector sign unphased or weak phasing	pass a GC/gene-density phasing_track at the cooler's binning
E1 monotonic, no sign flips	whole-chromosome run captured the arm gradient	run per arm (make_chromarms); pick by max
frac_gc / empty eigenvector on some chroms	chrom naming mismatch (chr1 vs 1) across cooler/FASTA/centromeres	harmonize names; subset the view to clr.chromnames
saddle KeyError on balanced.avg	wrong/absent expected table	pass cooltools.expected_cis(clr, view_df=...) output and contact_type='cis'
AttributeError on a cooltools function	pre-0.7 vs 0.7+ API change	help(cooltools.eigs_cis); update to the viewframe signature

References

• Lieberman-Aiden E, van Berkum NL, et al. 2009. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science 326:289-293.
• Rao SSP, Huntley MH, et al. 2014. A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping. Cell 159:1665-1680.
• Nora EP, Goloborodko A, et al. 2017. Targeted degradation of CTCF decouples local insulation of chromosome domains from genomic compartmentalization. Cell 169:930-944.
• Schwarzer W, Abdennur N, et al. 2017. Two independent modes of chromatin organization revealed by cohesin removal. Nature 551:51-56.
• Rao SSP, Huang S-C, et al. 2017. Cohesin loss eliminates all loop domains. Cell 171:305-320.
• Nuebler J, Fudenberg G, Imakaev M, Abdennur N, Mirny LA. 2018. Chromatin organization by an interplay of loop extrusion and compartmental segregation. PNAS 115:E6697-E6706.
• Xiong K, Ma J. 2019. Revealing Hi-C subcompartments by imputing inter-chromosomal chromatin interactions. Nat Commun 10:5069.
• Tan L, Xing D, Chang C-H, Li H, Xie XS. 2018. Three-dimensional genome structures of single diploid human cells. Science 361(6405):924-928.
• Liu Y, Nanni L, et al. 2021. Systematic inference and comparison of multi-scale chromatin sub-compartments connects spatial organization to cell phenotypes. Nat Commun 12:2439.
• Chakraborty A, Wang JG, Ay F. 2022. dcHiC detects differential compartments across multiple Hi-C datasets. Nat Commun 13:6827.
• Chen Y, Zhang Y, et al. 2018. Mapping 3D genome organization relative to nuclear compartments using TSA-Seq as a cytological ruler. J Cell Biol 217:4025-4048.
• Abdennur N, et al. (Open2C). 2024. Cooltools: enabling high-resolution Hi-C analysis in Python. PLoS Comput Biol 20:e1012067.
• Abdennur N, Mirny LA. 2020. Cooler: scalable storage for Hi-C data and other genomically labeled arrays. Bioinformatics 36:311-316.

Related Skills

• matrix-operations - Balancing and distance-normalized expected that compartment calling depends on
• hic-data-io - Load and access the cooler files this skill operates on
• hic-differential - dcHiC differential compartments and cross-condition switching
• tad-detection - The loop-extrusion partner of the two-mechanism framework; antagonistic strength
• hic-visualization - Render the eigenvector track and saddle plot
• chip-seq/chromatin-state-segmentation - Overlay ChromHMM/histone states on A/B compartments
• chip-seq/peak-annotation - Annotate switched bins with TF/histone peaks
• genome-intervals/bigwig-tracks - Export the eigenvector as a bigWig track
• single-cell/scatac-analysis - Single-cell chromatin context for scHi-C compartment work