MSPC: Joint analysis of ChIP-seq replicates

POLITECNICO

DI MILANO

Department of Electronics,

Information and Bioengineering

July 20, 2015

Using combined evidence from replicates to evaluate ChIP-seq peaks

Vahid Jalili

Vahid Jalili (vahid.jalili@polimi.it)

Matteo Matteucci (matteo.matteucci@polimi.it)

Marco Masseroli (marco.masseroli@polimi.it)

Marco Morelli (marco.morelli@iit.it)

Website: https://mspc.codeplex.com

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MotivationTag c

ount

Genomic DNA

Signal Background

ChIP-seq sample

True Positive False Positive

False Negative True Negative

Stringent

Threshold

Permissive

Threshold

Stringent

Threshold

Permissive

Threshold

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Motivation

Benefit from ReplicatesUtilize replicates to discriminate between

sub-threshold binding from truly none-bounding regions

Tag c

ount

Genomic DNA

Signal Background

Replicate 1

Replicate 2

Tag c

ount

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Motivation

Benefit from Replicates

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Method

Notations

𝒯𝑠

𝒯𝑤

Strong threshold

Weak threshold

𝑝 − 𝑣𝑎𝑙𝑢𝑒 ≤ 𝒯𝑠

Strong Peak

Weak Peak

𝒯𝑠 < 𝑝 − 𝑣𝑎𝑙𝑢𝑒 ≤ 𝒯𝑤

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Method

Combining Evidences

𝑋2𝑘2 follows a 𝜒2 distribution with 2𝑘 degrees of freedom.

Alternatives for combining test statistics :

Liptak’s method (Liptak, 1958)

Mudholkar and George (Mudholkar & George, 1979)

Wilkinson’s method (Wilkinson, 1951)

Truncated product method (Zaykin D. , Zhivotovsky, Westfall, & Weir, 2002)

…

How to combine evidences ?

Fisher’s combined probability test

𝑋2𝑘2 = −2

𝑖=1

𝑘

ln 𝑝𝑖

𝐶𝑜𝑛𝑓𝑖𝑟𝑚, 𝑋2𝑘

2 ≥ 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

𝐷𝑖𝑠𝑐𝑎𝑟𝑑, 𝑋2𝑘2 < 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

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Method

Combining Evidences

Replicate 1

Replicate 2

Replicate 3

Which evidences to combine ?

Replicate 4

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Method

Combining Evidences

Replicate 1

Replicate 2

Replicate 3

Which evidences to combine ?

Replicate 4

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Method

Combining Evidences

Replicate 1

Replicate 2

Replicate 3

Which evidences to combine ?

Replicate 4

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Method

Combining Evidences

Replicate 1

Replicate 2

Replicate 3

Which evidences to combine ?

Replicate 4

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Method

Intersection DeterminationThe Challenge …

an optimal method for finding the intersections

Sorted Lists

Naïve method

Hashing Based

Interval Trees

𝑶 𝒎 𝒏

𝑶 𝒏𝒎

𝑶𝒏 𝒍𝒐𝒈𝟐𝒘

𝒘+𝒎𝒓

𝑶 𝒏 log𝟐 𝒏

S o m e Po s s i b l e M e t h o d s

• 𝑛 average peaks count on a sample

• 𝑚 sample count

M e t h o d ’ s C o m p l ex i t y

• 𝑤 number of bits in a machine-word

• 𝑟 intersection size

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Method

Intersection DeterminationInterval Trees

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

[ 16 , 21 ]

Data

[ 8 , 9 ]

Data

[ 25 , 30 ]

Data

[ 17 , 19 ]

Data

[ 26 , 27 ]

Data

[ 19 , 20 ]

Data

[ 15 , 23 ]

Data

[ 5 , 8 ]

Data

[ 6 , 10 ]

Data

[ 0 , 3 ]

Data

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Method

Algorithm

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Method

Algorithm

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Method

Algorithm

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3

R 1 (weak peak)

R 4 (strong region)

R 3 (weak peak)

Algorithm … an example

R 2 (weak peak)

R 1 (weak peak)

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

R 3 (weak peak)

Algorithm … an example

R 2 (weak peak)

Determine intersecting regions across all samples

R 1 (weak peak)

R 2 (weak peak) R 3 (weak peak)

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 1 (weak peak)

R 2 (weak peak) R 3 (weak peak)

If multiple regions determined intersecting on a

sample, choose the strongest one

R 3 (weak peak)

Determine intersecting regions across all samples

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 1 (weak peak)

R 2 (weak peak) R 3 (weak peak)

If multiple regions determined intersecting on a

sample, choose the strongest one

Determine intersecting regions across all samples

Combine test statistics using Fisher’s method

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 1 (weak peak)

R 2 (weak peak) R 3 (weak peak)

If multiple regions determined intersecting on a

sample, choose the strongest one

Determine intersecting regions across all samples

Combine test statistics using Fisher’s method

𝑋2 ≥ 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 ? NO !

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Method

Algorithm

██ Confirmed Peaks Set

██ Discarded Peaks Set

Algorithm … an example

R 1

I n t e r m e d i a t e S e t s

R e p l i c a t e 1 R e p l i c a t e 2 R e p l i c a t e 3

R 2

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 1 (weak peak)

R 2 (weak peak) R 3 (weak peak)

Determine intersecting regions across all samples

R 2 (weak peak)

Since R2 intersects only with R1, and R1-R2 test is

already performed, no further process will be taken

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 1 (weak peak)

R 3 (weak peak)

Determine intersecting regions across all samples

R 2 (weak peak) R 3 (weak peak)

R 4 (strong region)

R 1 (weak peak)

Combine test statistics using Fisher’s method

𝑋2 ≥ 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 ? YES !

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Method

AlgorithmAlgorithm … an example

██ Confirmed Peaks Set

██ Discarded Peaks Set

R 1

I n t e r m e d i a t e S e t s

R e p l i c a t e 1 R e p l i c a t e 2 R e p l i c a t e 3

R 2

R 3 R 4

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 3 (weak peak)R 2 (weak peak)

R 1 (weak peak)

R 4 (strong region)

Determine intersecting regions across all samples

Combine test statistics using Fisher’s method

𝑋2 ≥ 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 ? YES !

R 3 (weak peak)

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Method

AlgorithmAlgorithm … an example

██ Confirmed Peaks Set

██ Discarded Peaks Set

I n t e r m e d i a t e S e t s

R e p l i c a t e 1 R e p l i c a t e 2 R e p l i c a t e 3

R 2

R 3 R 4

R 1

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Method

AlgorithmAlgorithm … an example

I n t e r m e d i a t e S e t s

R e p l i c a t e 1 R e p l i c a t e 2 R e p l i c a t e 3

R 2

R 3 R 4

R 1

R 1

██ Confirmed Peaks Set

██ Discarded Peaks Set

██ Output Set

O u t p u t S e t s

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Method

Algorithm

Replicate 1

Replicate 2

Replicate 3 R 4 (strong region)

Algorithm … an example

R 3 (weak peak)R 2 (weak peak)

R 1 (weak peak)

R 2 (weak peak)

R 1 (weak peak)

R 3 (weak peak)

R 4 (strong region)

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Results

Myc2_1

0e

+0

02

e+

04

4e

+0

46

e+

04

8e

+04

1e+

05

Myc2_2Myc3_1

05

00

010

00

015

00

02

000

02

50

00

30

00

0

Myc3_2

Myc2_1

0e+

00

2e+

04

4e+

04

6e+

04

8e+

04

1e

+0

5

Myc2_2 Myc3_1 Myc3_2

Abbreviation File name

Myc2_1 wgEncodeSydhTfbsK562CmycIggrabAlnRep1

Myc2_2 wgEncodeSydhTfbsK562CmycIggrabAlnRep2

Myc3_1 wgEncodeSydhTfbsK562CmycStdAlnRep1

Myc3_2 wgEncodeSydhTfbsK562CmycStdAlnRep2

Category Abbreviation Color Implication

Input (source BED file) In██ Strong

██ Weak

Analysis Results Re

██ Strong Confirmed

██ Weak Confirmed

██ Weak Discarded

S e t 1 S e t 2 S e t 3

In Re In Re In Re In Re In Re In Re In Re In Re

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Results

Motif was enriched in the sequence defined by peaks

Motif was NOT enriched in the sequence defined by peaks

Presence of Ebox

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Implementation

Performance

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45

Tim

e (

seco

nds)

Peaks Count

x 10000

Running Time

2-Replicates 4-Replicates 6-Replicates

Demo

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Questions

Q u e s t i o n sare welcome at: https://mspc.codeplex.com/discussions