“Hotspot” algorithm

chr5:131,975,056-132,012,092

Idea: gauge enrichment of tags relative to a local background model basedon the number of tags in a 50kb surrounding window.

Hotspots (height = score)

“Hotspot” algorithm

Enrichment is measured as a z-score based on the binomial distributionnull model.

250 bp50kb

Each tag in the large window is considered an “experiment,” with probability of success (landing in the smaller window)

n tags

N tags

(adjusted for uniquely mapping bases)

Given N tags in the large window, expected number of tags in smaller window is Np

50000

250p

“Hotspot” algorithm

250 bp50kb

n tags

N tags

Given N tags in the large window, expected number of tags in smaller window is Np

The standard deviation for the expected number of tags in the smaller window is )1( pNp

And the z-score for the observed number of tags in the smaller window is

n

z

“Hotspot” algorithm

•Each tag gets a z-score for the 250bp and 50kb windows centered on it.•A hotspot is a succession of tags within a 250bp window, each of whose z-score is greater than 2. •The hotspot is scored with the z-score for the 250bp window centered on those tags.

hotspot

Examples of different kinds of hotspots

1. Monsters2. Noisy regions

Shadowed hotspots

Problem: regions of very high enrichment can inflate the background for neighboring regions, deflating z-scores

chr1:604,351-609,350

Same as above, rescaled

These would be highly significant in isolation, but are missed due to shadowing by the monster.

Shadowed hotspots

Solution: implement a two-pass hotspot detection scheme.1. Run first pass of hotspot detection2. Delete all tags falling in the first-pass hotspots3. Compute new hotspots with deleted background4. Combine hotspots from first and second passes,

and re-score all using the deleted background: all 50kb windows will only include tags from deleted background.Pass 1

Deletedbackground

Pass 2

Hotspots are robust to regions of duplication

chr8:129,897,976-130,347,975

chr8:130,151,726-130,201,725

chr8:129,904,851-129,979,850

Called peaks(height = z-score)

Disparate peak heights, but comparable z-scores

Random Tags

As a null model for doing FDR calculations, we generate tags uniformly over the uniquely mappable (for 27-mers) bases of the genome. We use the same number of tags for observed and random data.

Observed tags

Random tags

The random data still coalesce into hotspots.

Observed hotspots

Random hotspots

Properties of Random Tags

Still lots of hotspots! • 146,752 in random data with same

number of tags as observed• 395,433 in observed (GM)

Properties of Random Tags

Enriched in promoters?!

(Yes, slightly, since uniquely mappable 27-mers are enriched in promoters.)

Distance to Tx start sites

Ave

rage

tag

dens

ity

FDR Calculations Using Random Tags

FDR(z-score = T) = # of random peaks with z >=T# of observed peaks with z >=T

This is probably conservative, since numerator is likely an overestimate of the number of false positives in the observed data.

Observed

Random

Extending to multiple cell types

•Call a location multi-cell verified (MCV) if hotspot peaks from different cell types overlap there (after fattening peaks to 300bp).•Score these MCV zones with the maximum z-score over the cell type peaks.•MCV peaks are then identified by looking at the summed density in the zones.•Repeat with multiple random datasets to get random MCV peaks for FDR calc’s.

MCV zones

Summed density

MCV peaks

chr5:131,585,550-131,597,894 (GM and BJ)