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Implication Networks from Large Gene-expression Datasets

Debashis SahooPhD Candidate, Electrical Engineering, Stanford UniversityJoint work with David Dill, Andrew Gentles, Rob Tibshirani, Sylvia Plevritis

Integrative Cancer Biology Program, Stanford University

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Motivation

Current approachesClustering Co-expressionLinear regressionMutual information

BUB1B

CC

NB

2

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Hidden Relationships

Pearson’s correlation = -0.1GABRB1 and ACPP are not linearly related.There is a Boolean relationship

ACPP high GABRB1 lowGABRB1 high ACPP low

ACPP

GA

BR

B1

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Outline

MotivationBoolean analysisBoolean implication networkBiological insightsConserved Boolean networkConclusion

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Outline

MotivationBoolean analysisBoolean implication networkBiological insightsConserved Boolean networkConclusion

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Boolean Analysis Workflow

Get data

Normalize

Determine thresholds

Discover Boolean relationships

Biological interpretation

GEO

RMA

[Edgar et al. 02]

[Irizarry et al. 03]

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Determine threshold

A threshold is determined for each gene.The arrays are sorted by gene expressionStepMiner is used to determine the threshold

Sorted arrays

CD

H e

xpre

ssio

n

[Sahoo et al. 07]

Threshold

High

Low

Intermediate

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Discovering Boolean Relationships

Analyze pairs of genes.Analyze the four different quadrants.Identify sparse quadrants.Record the Boolean relationships.

ACPP high GABRB1 lowGABRB1 high ACPP low

1

2 4

3

ACPP

GA

BR

B1

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Boolean Relationships

There are six possible Boolean relationshipsA low B lowA low B highA high B lowA high B highEquivalentOpposite

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Four Asymmetric Boolean Relationships

A low B lowA low B highA high B lowA high B high

PTPRC low CD19 low XIST high RPS4Y1 low

COL3A1 high SPARC highFAM60A low NUAK1 highPTPRC XIST

FAM60A COL3A1

NU

AK

1

SP

AR

C

CD

19

RP

S4Y

1

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Two Symmetric Boolean Relationships

BUB1B

CC

NB

2

XTP7E

ED

Equivalent Opposite

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Outline

MotivationBoolean analysisBoolean implication networkBiological insightsConserved Boolean networkConclusion

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Boolean Implication Network

Boolean implications form a directed graphNodes:

For each gene AA highA low

Edges:A high to B low

A high B low

A high

B low

C high

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Size of The Boolean Networks

0

10

20

30

40

50

60

70

Pe

rce

nta

ge

lo=>hi hi=>lo lo=>lo hi=>hi Equivalent Opposite

Human (208 million) Mouse (336 million) Fly (17 million)

highlow lowlowlowhigh Equivalenthighhigh Opposite

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Boolean Networks Are Not Scale FreeHuman

#relationships #relationships #relationships

#pro

bese

ts

#pro

bese

ts

#pro

bese

ts

Total Symmetric Asymmetric

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Outline

MotivationBoolean analysisBoolean implication networkBiological insightsConserved Boolean networkConclusion

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Gender Specific

XIST X inactivation specific transcriptExpressed in female

RPS4Y1Y-linked geneExpressed in male only

Boolean relationshipXIST highRPS4Y1 low

XIST

RP

S4Y

1

[Day et al. 07]

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Tissue Specific

ACPPAcid phosphatase, prostateProstate specific gene

GABRB1GABA A receptor, beta 1Brain specific

Boolean relationshipACPP highGABRB1 low

ACPP

GA

BR

B1

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Development

HOXD3Homeobox D3Fruit fly antennapedia homolog

HOXA13Homeobox A13Fruit fly ultrabithorax homolog

Boolean relationshipHOXD3 high HOXA13 low

HOXD3

HO

XA

13

[Rinn et al. 07]

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Differentiation

PTPRC protein tyrosine phosphatase, receptor type, CB220Expressed in B cell precursors and mature B cell

CD19Expressed in mature B cell

Boolean relationshipPTPRC low CD19 lowPTPRC

CD

19

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Biological Insights

Gender Tissue

Development DifferentiationXIST ACPP

HOXD3 PTPRC

HO

XA

13

CD

19

RP

S4Y

1

GA

BR

B1

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Outline

MotivationBoolean analysisBoolean implication networkBiological insightsConserved Boolean networkConclusion

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Conserved Boolean Networks

Find orthologs between human, mouse and fly using EUGene database.Search for orthologous gene pairs that have the same Boolean relationship.

[Gilbert, 02]

Human

208M

Mouse

336M

Fly17M

4M

41K

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Conserved Boolean Relationships

Two largest connected components in the network of equivalent genes

178 genes: highly enriched for cell-cycle and DNA replication32 genes: highly enriched for synaptic functions

Bub1

Cyc

B

Ccn

b2

CC

NB

2

Bub1b BUB1B

Fly Mouse Human

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Conserved Asymmetric Boolean Relationships

GABRB1 expressing cells have low cell cycle (BUB1B) activity.

Bub1

Lcc

h3

Gab

rb1

GA

BR

B1

Bub1b BUB1B

Fly Mouse Human

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Outline

MotivationBoolean analysisBoolean implication networkBiological insightsConserved Boolean networkConclusion

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Conclusion

Boolean analysisBoolean relationships are directly visible on the scatter plot.Enables discovery of asymmetric relationship.Can reveal known biological processes.Has potential for new biological discovery.

Boolean networkIs largeIs not scale free

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Acknowledgements

The Felsher Lab:Natalie WuCathy ShachafDean Felsher

Funding: ICBP Program (NIH grant: 5U56CA112973-02)

Leonore A HerzenbergJames Brooks Joe LipsickGavin SherlockHoward ChangStuart Kim

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The END

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Example

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Determine threshold

Its hard to determine a threshold for this gene.StepMiner usually puts a threshold in the middle for this case.

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Statistical Tests

Compute the expected number of points under the independence model

Compute maximum likelihood estimate of the error rate

statistic =(expected – observed)

expected√

a00

(a00+ a01)

a00

(a00+ a10)+( )1

2error rate =

a00

a01 a11

a10