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Interval Arithmetic

Core set operations on genomic intervals using bedtools (CLI) and pybedtools (Python).

Intersect - Find Overlapping Regions

CLI

bash
# Find overlapping intervals (report A entries that overlap B)
bedtools intersect -a peaks.bed -b genes.bed > overlapping.bed

# Report original A intervals (default behavior)
bedtools intersect -a peaks.bed -b genes.bed > peaks_in_genes.bed

# Report overlapping portion only
bedtools intersect -a peaks.bed -b genes.bed > overlap_regions.bed

# Report both A and B fields
bedtools intersect -a peaks.bed -b genes.bed -wa -wb > with_gene_info.bed

# Write original A entries that overlap B (-u for unique)
bedtools intersect -a peaks.bed -b genes.bed -u > peaks_overlapping_genes.bed

# Report A entries that do NOT overlap B
bedtools intersect -a peaks.bed -b genes.bed -v > peaks_not_in_genes.bed

# Require minimum overlap fraction (50% of A must overlap)
bedtools intersect -a peaks.bed -b genes.bed -f 0.5 > min_50pct.bed

# Reciprocal overlap (both A and B must have 50% overlap)
bedtools intersect -a peaks.bed -b genes.bed -f 0.5 -r > reciprocal_50pct.bed

# Count overlaps
bedtools intersect -a peaks.bed -b genes.bed -c > with_counts.bed

# Multiple B files
bedtools intersect -a peaks.bed -b genes.bed promoters.bed enhancers.bed -names genes promoters enhancers > multi.bed

Python

python
import pybedtools

a = pybedtools.BedTool('peaks.bed')
b = pybedtools.BedTool('genes.bed')

# Basic intersection
result = a.intersect(b)

# Keep original A entries that overlap
result = a.intersect(b, u=True)

# Report both A and B
result = a.intersect(b, wa=True, wb=True)

# Non-overlapping (inverse)
result = a.intersect(b, v=True)

# Minimum overlap fraction
result = a.intersect(b, f=0.5)

# Reciprocal overlap
result = a.intersect(b, f=0.5, r=True)

# Count overlaps
result = a.intersect(b, c=True)

# Save result
result.saveas('output.bed')

Subtract - Remove Overlapping Regions

CLI

bash
# Remove portions of A that overlap B
bedtools subtract -a regions.bed -b exclude.bed > remaining.bed

# Remove entire A interval if ANY overlap with B
bedtools subtract -a regions.bed -b exclude.bed -A > non_overlapping.bed

# Require minimum overlap before removal
bedtools subtract -a regions.bed -b exclude.bed -f 0.5 > subtract_50pct.bed

Python

python
import pybedtools

a = pybedtools.BedTool('regions.bed')
b = pybedtools.BedTool('exclude.bed')

# Basic subtraction (remove overlapping portions)
result = a.subtract(b)

# Remove entire interval if any overlap
result = a.subtract(b, A=True)

# Require minimum overlap
result = a.subtract(b, f=0.5)

result.saveas('remaining.bed')

Merge - Combine Overlapping/Adjacent Intervals

CLI

bash
# Merge overlapping intervals (input must be sorted)
bedtools sort -i peaks.bed | bedtools merge > merged.bed

# Merge intervals within N bp of each other
bedtools sort -i peaks.bed | bedtools merge -d 100 > merged_100bp.bed

# Report number of merged intervals
bedtools sort -i peaks.bed | bedtools merge -c 1 -o count > merged_counts.bed

# Aggregate columns (e.g., concatenate names, sum scores)
bedtools sort -i peaks.bed | bedtools merge -c 4,5 -o collapse,sum > merged_agg.bed

# Keep max score
bedtools sort -i peaks.bed | bedtools merge -c 5 -o max > merged_max.bed

# Strand-specific merge
bedtools sort -i peaks.bed | bedtools merge -s > merged_stranded.bed

Python

python
import pybedtools

bed = pybedtools.BedTool('peaks.bed')

# Basic merge (auto-sorts)
merged = bed.sort().merge()

# Merge within distance
merged = bed.sort().merge(d=100)

# Count merged intervals
merged = bed.sort().merge(c=1, o='count')

# Aggregate columns (collapse names, sum scores)
merged = bed.sort().merge(c='4,5', o='collapse,sum')

# Strand-specific
merged = bed.sort().merge(s=True)

merged.saveas('merged.bed')

Complement - Get Uncovered Regions

CLI

bash
# Get regions NOT covered by intervals (requires genome file)
bedtools complement -i covered.bed -g genome.txt > uncovered.bed

# genome.txt format: chr<TAB>size
# chr1	248956422
# chr2	242193529
# ...

Python

python
import pybedtools

bed = pybedtools.BedTool('covered.bed')
genome = 'genome.txt'  # or dict: {'chr1': (0, 248956422), ...}

# Get complement
uncovered = bed.complement(g=genome)
uncovered.saveas('uncovered.bed')

# Using genome dict
genome_dict = pybedtools.chromsizes('hg38')  # Built-in genome sizes
uncovered = bed.complement(genome=genome_dict)

Cluster - Group Overlapping Intervals

CLI

bash
# Assign cluster IDs to overlapping intervals
bedtools sort -i peaks.bed | bedtools cluster > clustered.bed

# Cluster within distance
bedtools sort -i peaks.bed | bedtools cluster -d 100 > clustered_100bp.bed

Python

python
import pybedtools

bed = pybedtools.BedTool('peaks.bed')
clustered = bed.sort().cluster()
clustered.saveas('clustered.bed')

Multiinter - Find Multi-way Overlaps

CLI

bash
# Find regions covered by multiple files
bedtools multiinter -i sample1.bed sample2.bed sample3.bed > multi_overlap.bed

# With sample names
bedtools multiinter -i sample1.bed sample2.bed sample3.bed \
    -names s1 s2 s3 > multi_overlap.bed

# Header output
bedtools multiinter -i sample1.bed sample2.bed sample3.bed -header > multi_overlap.bed

Python

python
import pybedtools

beds = [pybedtools.BedTool(f) for f in ['s1.bed', 's2.bed', 's3.bed']]
# Note: multiinter requires CLI workaround
result = pybedtools.BedTool().multi_intersect(i=[b.fn for b in beds])

Jaccard - Similarity Metric

CLI

bash
# Calculate Jaccard similarity between two BED files
bedtools jaccard -a sample1.bed -b sample2.bed

# Output: intersection, union, jaccard, n_intersections

Python

python
import pybedtools

a = pybedtools.BedTool('sample1.bed')
b = pybedtools.BedTool('sample2.bed')

result = a.jaccard(b)
print(f"Jaccard index: {result['jaccard']}")
print(f"Intersection: {result['intersection']} bp")
print(f"Union: {result['union']} bp")

Fisher's Exact Test

CLI

bash
# Statistical test for overlap significance
bedtools fisher -a peaks.bed -b genes.bed -g genome.txt

Python

python
import pybedtools

a = pybedtools.BedTool('peaks.bed')
b = pybedtools.BedTool('genes.bed')

result = a.fisher(b, genome='genome.txt')
print(result)  # Contains p-values and odds ratio

Shuffle - Random Permutation

CLI

bash
# Randomly shuffle intervals (for null hypothesis testing)
bedtools shuffle -i peaks.bed -g genome.txt > shuffled.bed

# Exclude certain regions
bedtools shuffle -i peaks.bed -g genome.txt -excl blacklist.bed > shuffled.bed

# Maintain chromosome distribution
bedtools shuffle -i peaks.bed -g genome.txt -chrom > shuffled.bed

Python

python
import pybedtools

bed = pybedtools.BedTool('peaks.bed')
shuffled = bed.shuffle(g='genome.txt')
shuffled.saveas('shuffled.bed')

Map - Transfer Values Between Files

Map overlapping B values onto A intervals with aggregation.

CLI

bash
# Map mean scores from B to A
bedtools map -a genes.bed -b scores.bedGraph -c 4 -o mean > genes_with_scores.bed

# Multiple operations at once
bedtools map -a regions.bed -b data.bed -c 5,5,5 -o mean,min,max > multi_stats.bed

# Count overlapping features
bedtools map -a genes.bed -b peaks.bed -c 1 -o count > genes_with_peak_counts.bed

# Collapse names of overlapping features
bedtools map -a genes.bed -b peaks.bed -c 4 -o collapse > genes_with_peak_names.bed

# Distinct values only
bedtools map -a genes.bed -b annotations.bed -c 4 -o distinct > unique_annotations.bed

Python

python
import pybedtools

a = pybedtools.BedTool('genes.bed')
b = pybedtools.BedTool('scores.bedGraph')

# Map mean scores
result = a.map(b, c=4, o='mean')

# Multiple operations
result = a.map(b, c='5,5,5', o='mean,min,max')

result.saveas('mapped.bed')

Map Operations

| Operation | Description | |-----------|-------------| | sum | Sum of values | | count | Number of overlapping features | | count_distinct | Number of distinct values | | min, max | Minimum/maximum value | | mean, median | Average values | | collapse | Comma-separated list | | distinct | Unique values only | | first, last | First/last overlapping value |

Groupby - Aggregate by Columns

Group intervals and compute summary statistics.

CLI

bash
# Sum scores by gene (column 4)
bedtools groupby -i sorted.bed -g 4 -c 5 -o sum > gene_totals.bed

# Group by chromosome and compute stats
bedtools groupby -i sorted.bed -g 1 -c 2,3 -o min,max > chr_ranges.bed

# Multiple grouping columns
bedtools groupby -i sorted.bed -g 1,4 -c 5 -o mean > by_chr_gene.bed

# Collapse names within groups
bedtools groupby -i sorted.bed -g 1,2,3 -c 4 -o collapse > merged_names.bed

# Count features per group
bedtools groupby -i sorted.bed -g 1 -c 1 -o count > features_per_chr.bed

# Use column ranges
bedtools groupby -i sorted.bed -g 1-3 -c 5 -o sum > grouped.bed

Python

python
import pybedtools

bed = pybedtools.BedTool('sorted.bed')

# Group by column 4, sum column 5
result = bed.groupby(g=4, c=5, o='sum')

# Multiple operations
result = bed.groupby(g=[1, 4], c=[5, 5], o=['mean', 'count'])

result.saveas('grouped.bed')

Note: Input must be sorted by grouping columns.

Common Patterns

Find Peaks in Promoters

python
import pybedtools

peaks = pybedtools.BedTool('peaks.bed')
promoters = pybedtools.BedTool('promoters.bed')

# Peaks overlapping promoters
peaks_in_promoters = peaks.intersect(promoters, u=True)
print(f'{peaks_in_promoters.count()} peaks in promoters')

Find Unique Regions in Sample

python
import pybedtools

sample_a = pybedtools.BedTool('sample_a.bed')
sample_b = pybedtools.BedTool('sample_b.bed')

# Regions unique to sample A
unique_a = sample_a.intersect(sample_b, v=True)
unique_a.saveas('unique_to_a.bed')

Merge Replicates

bash
# Concatenate and merge peaks from replicates
cat rep1.bed rep2.bed rep3.bed | bedtools sort | bedtools merge -d 100 > consensus.bed

Key Parameters

| Operation | Key Flags | Description | |-----------|-----------|-------------| | intersect -u | Unique | Report A once if overlap | | intersect -v | Inverse | A that don't overlap B | | intersect -f | Fraction | Minimum overlap fraction | | intersect -r | Reciprocal | Both must meet -f threshold | | intersect -c | Count | Count overlapping B features | | subtract -A | All | Remove entire A if any overlap | | merge -d | Distance | Merge within N bp | | merge -c -o | Columns/Ops | Aggregate columns |

Related Skills

• bed-file-basics - BED format and creation
• proximity-operations - closest, window, flank, slop
• coverage-analysis - coverage calculations
• chip-seq/peak-calling - peak file operations

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