Bio Hi C Analysis Compartment Analysis

Version Compatibility

Reference examples tested with: cooler 0.9+, cooltools 0.6+, matplotlib 3.8+, numpy 1.26+, pandas 2.2+, scipy 1.12+

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

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

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Compartment Analysis

"Identify A/B compartments from my Hi-C data" → Decompose the contact matrix via eigenvector analysis to classify chromatin into active (A) and inactive (B) compartments.

• Python: cooltools.eigs_cis(clr, gc_cov) for eigenvector decomposition

Detect A/B compartments from Hi-C contact matrices.

Required Imports

import cooler
import cooltools
import cooltools.lib.plotting
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import bioframe

Compute Compartment Eigenvectors

clr = cooler.Cooler('matrix.mcool::resolutions/100000')

# Get reference genome info
view_df = bioframe.make_viewframe(clr.chromsizes)

# Compute expected values first
expected = cooltools.expected_cis(clr, view_df=view_df, ignore_diags=2)

# Compute eigenvector decomposition (compartments)
eigenvector_track = cooltools.eigs_cis(
    clr,
    view_df=view_df,
    phasing_track=None,  # Or provide GC content track
    n_eigs=3,
)

# Results are returned as a tuple (eigenvalues, eigenvectors)
eigenvalues, eigenvectors = eigenvector_track
print(f'Eigenvalues shape: {eigenvalues.shape}')
print(eigenvectors.head())

Use GC Content for Phasing

# GC content helps orient A/B compartments correctly
# (A compartments typically have higher GC)

# Fetch GC content
gc_track = bioframe.frac_gc(
    bioframe.make_viewframe(clr.chromsizes),
    bioframe.load_fasta('genome.fa'),
)

# Compute eigenvectors with GC phasing
eigenvalues, eigenvectors = cooltools.eigs_cis(
    clr,
    view_df=view_df,
    phasing_track=gc_track,
    n_eigs=1,
)

Extract Compartment Calls

# E1 (first eigenvector) defines compartments
# Positive = A (active), Negative = B (inactive)

eigenvectors['compartment'] = np.where(eigenvectors['E1'] > 0, 'A', 'B')
print(eigenvectors[['chrom', 'start', 'end', 'E1', 'compartment']].head(20))

# Count compartments
print(eigenvectors['compartment'].value_counts())

Compartment Strength (Saddle Plot)

# Compute saddle plot to quantify compartmentalization strength
saddle_data = cooltools.saddle(
    clr,
    expected=expected,
    eigenvector_track=eigenvectors,
    view_df=view_df,
    n_bins=50,
    vrange=(-0.5, 0.5),
)

# saddle_data contains: (saddledata, binedges)
# saddledata is the saddle matrix
saddle_matrix = saddle_data[0]
print(f'Saddle matrix shape: {saddle_matrix.shape}')

Plot Saddle

fig, ax = plt.subplots(figsize=(6, 6))

# Get saddle matrix (aggregate over chromosomes)
saddle_agg = np.nanmean(saddle_data[0], axis=0)

im = ax.imshow(saddle_agg, cmap='coolwarm', vmin=-1, vmax=1)
ax.set_xlabel('E1 (compartment)')
ax.set_ylabel('E1 (compartment)')
ax.set_title('Saddle plot')
plt.colorbar(im, ax=ax, label='log2(O/E)')

# Mark A and B regions
n = saddle_agg.shape[0]
ax.axhline(n/2, color='k', linewidth=0.5)
ax.axvline(n/2, color='k', linewidth=0.5)
ax.text(n*0.25, n*0.25, 'B-B', ha='center', va='center', fontsize=12)
ax.text(n*0.75, n*0.75, 'A-A', ha='center', va='center', fontsize=12)
ax.text(n*0.25, n*0.75, 'B-A', ha='center', va='center', fontsize=12)
ax.text(n*0.75, n*0.25, 'A-B', ha='center', va='center', fontsize=12)

plt.savefig('saddle_plot.png', dpi=150)

Compartment Strength Score

Goal: Quantify the degree of compartmentalization by measuring the enrichment of A-A and B-B contacts relative to A-B contacts.

Approach: Partition the saddle matrix into four quadrants (AA, BB, AB, BA) and compute the difference between same-compartment and cross-compartment average contact enrichment.

# Compute compartment strength from saddle
def compartment_strength(saddle_matrix):
    n = saddle_matrix.shape[0]
    half = n // 2

    # AA and BB corners
    AA = np.nanmean(saddle_matrix[half:, half:])
    BB = np.nanmean(saddle_matrix[:half, :half])
    AB = np.nanmean(saddle_matrix[:half, half:])
    BA = np.nanmean(saddle_matrix[half:, :half])

    # Compartment strength = (AA + BB) / (AB + BA)
    strength = (AA + BB) / 2 - (AB + BA) / 2
    return strength

strength = compartment_strength(saddle_agg)
print(f'Compartment strength: {strength:.3f}')

Plot Eigenvector Track

fig, ax = plt.subplots(figsize=(15, 3))

# Plot for one chromosome
chr_data = eigenvectors[eigenvectors['chrom'] == 'chr1']

# Color by compartment
colors = ['red' if e > 0 else 'blue' for e in chr_data['E1']]
ax.bar(chr_data['start'] / 1e6, chr_data['E1'], width=0.1, color=colors)

ax.axhline(0, color='k', linewidth=0.5)
ax.set_xlabel('Position (Mb)')
ax.set_ylabel('E1 (compartment)')
ax.set_title('chr1 compartments (red=A, blue=B)')

plt.tight_layout()
plt.savefig('compartment_track.png', dpi=150)

Export Compartment Calls

# Save as BED file
compartment_bed = eigenvectors[['chrom', 'start', 'end', 'E1', 'compartment']].copy()
compartment_bed.to_csv('compartments.bed', sep='\t', index=False, header=False)

# Save as bedGraph
eigenvectors[['chrom', 'start', 'end', 'E1']].to_csv(
    'compartment_eigenvector.bedgraph',
    sep='\t',
    index=False,
    header=False
)

Compare Compartments Between Samples

Goal: Identify genomic regions that switch between A and B compartments across two experimental conditions.

Approach: Compute eigenvectors for both samples, correlate E1 values genome-wide, and flag bins where the sign of E1 flips between conditions.

# Load two samples
clr1 = cooler.Cooler('sample1.mcool::resolutions/100000')
clr2 = cooler.Cooler('sample2.mcool::resolutions/100000')

# Compute eigenvectors for both
_, eig1 = cooltools.eigs_cis(clr1, view_df=view_df, n_eigs=1)
_, eig2 = cooltools.eigs_cis(clr2, view_df=view_df, n_eigs=1)

# Merge and compare
merged = eig1.merge(eig2, on=['chrom', 'start', 'end'], suffixes=('_1', '_2'))

# Correlation
from scipy.stats import pearsonr
r, p = pearsonr(merged['E1_1'].dropna(), merged['E1_2'].dropna())
print(f'E1 correlation: r={r:.3f}, p={p:.2e}')

# Compartment switches
merged['switch'] = (merged['E1_1'] > 0) != (merged['E1_2'] > 0)
print(f'Compartment switches: {merged["switch"].sum()} bins')

Correlate with Gene Expression

# Load gene expression data
# Assume: gene_expr with columns ['chrom', 'start', 'end', 'expression']

# Bin genes into compartment bins
compartment_expr = eigenvectors.merge(
    gene_expr,
    on=['chrom'],
    how='left'
)
compartment_expr = compartment_expr[
    (compartment_expr['start_y'] >= compartment_expr['start_x']) &
    (compartment_expr['start_y'] < compartment_expr['end_x'])
]

# Compare expression in A vs B
a_expr = compartment_expr[compartment_expr['compartment'] == 'A']['expression']
b_expr = compartment_expr[compartment_expr['compartment'] == 'B']['expression']

print(f'A compartment expression: {a_expr.mean():.2f}')
print(f'B compartment expression: {b_expr.mean():.2f}')

Related Skills

• matrix-operations - Prepare matrices for compartment analysis
• hic-visualization - Visualize compartments
• chip-seq - Correlate with histone marks