.

Inferring Subnetworks from Perturbed Expression

Profiles

D. Pe’er

A. Regev G. Elidan N. Friedman

Expression Profiling An Expression Profile is

a simultaneous measurement of the level of all mRNAs in a cell population

Experimental design: Measure profiles of mutated or treated cultures

Goal: infer regulatory and molecular interactions

Wild-Type Mutant

Profile

Compare

Common Approaches

Comparative Analysis (Holstage et al. 1998) Clustering (Hughes et al. 2000) Limitations:

Cannot distinguish between direct and indirect interactions

Limited to pair-wise relations Can not infer a finer context

Bayesian Network FrameworkFriedman, Linial, Nachman ,Pe’er (JCB 2000)

Probabilistic: Characterize statistical relationships between expression patterns of different genes

Multi-variable interactions (beyond pair-wise): Identify intermediate interactions Handle combinatorial regulation by several

gene-products Statistical confidence: Asses the statistical

significance of interactions found

Our Contributions

Modeling of mutations and treatments into the Bayesian network framework

Novel data discretization based on guided k-means clustering

New features: Mediator and Regulator

Automatic reconstruction of statistically significant sub-networks.

- 0 +

+

Modeling Gene Expression

Gene 1

Expression level of each gene = Random variable

Gene 3Gene 4

Gene 5

Gene 2

Gene interaction =Probabilistic dependency

Directed Acyclic graphModels dependency structure of distribution

0.9 0.1

1

2

1

0.2 0.8

0.6 0.4

0.9 0.1

21

2

2

1

21 P(3 | 1,2)

Each node has a probabilistic functionConditioned on its parents in the graph

Activator Inhibitor

Graph structure + local probabilityDefine a unique multivariate distribution

Mutational AssayWild-Type

Measurements

0.9 0.1

pgk10.1 0.9

pgk1

P(rap1|pgk1)

Equivalence: Two models explain

correlation between RAP1 & PGK1

RAP1 PGK1

RAP1 PGK1

Mutated pgk1Measurements

0.5 0.5

pgk10.5 0.5

pgk1

P(rap1|pgk1)

Note causalityinto mutated variable

Compendium Dataset (Hughes et al., 2000)

300 samples of yeast deletion mutants and other treatments Deleted genes are from various functional families

A rich variety of profiles, but… There is only one sample from each mutation

cell growth, division, DNA

synthesis

cell rescue, cell defense, aging

cellular biogenesis

cellular organization

unclear classification

energy

intracellular transport

ionic homeostasis

metabolism

protein destination

protein synthesis

signal transduction

transcription

transport facilitation

unclassified proteins

Guided K-meansDiscretization

Guided K-meansDiscretization

Expressiondata

MarkovMarkov SeparatorSeparatorEdgeEdge RegulatorRegulator

Bayesian Network Learning Algorithm

+ Bootstrap

Bayesian Network Learning Algorithm

+ Bootstrap

Reconstruct SubNetworksReconstruct SubNetworks

Visualize UsingPathway ExplorerVisualize Using

Pathway Explorer

Preprocess

Learn model

Featureextraction

Featureassembly

Visualization

E

R

B

A

CS

Resulting PDAG

Confidence Estimates: Bootstrap

D resample

resample

resample

D1

D2

Dm

...

Learn

Learn

Learn

E

R

B

A

C

E

R

B

A

C

E

R

B

A

C

m

iiGf

mfC

1

11

)(Estimate:

Bootstrap approach[FGW, UAI99]

Estimating Confidence

Common Practice: Pick a single top scoring modelProblem: Insufficient information!!In gene expression data: only few hundred experiments => many high scoring models

Answer based on one model uselessSolution: Search for features common to

many likely models!Sample models from posterior distribution

P(Model|Data)Confidence of feature:

G

DGPGfDfP )|()()|(Feature of G,e.g., XY

Guided K-meansDiscretization

Guided K-meansDiscretization

Expressiondata

MarkovMarkov SeparatorSeparatorEdgeEdge RegulatorRegulator

Bayesian Network Learning Algorithm

+ Bootstrap

Bayesian Network Learning Algorithm

+ Bootstrap

Reconstruct SubNetworksReconstruct SubNetworks

Visualize UsingPathway ExplorerVisualize Using

Pathway Explorer

Preprocess

Learn model

Featureextraction

Featureassembly

Visualization

Markov Relations

Question: Do X and Y directly interact? Parent-child (one gene regulating the other)

Hidden Parent (two genes co-regulated by a hidden factor)

(0.91,0.67) SST2 STE6 SST2 STE6

Mating pathway regulator

Exporter of mating factor

ARG5 ARG3(0.84,0.79)

ARG3 ARG5

GCN4

Arginine Biosynthesis

Transcription factor

Low Correlation Relations

Previously unknown link strongly supported by evidence in the literature

High confidence, Low correlation Processes occur under specific conditions Captured by our context specific score

ESC4 KU70(0.91, 0.16)

DNA ds break repair

Chromatin silencing

Separators

Question: Given that X andY are indirectly dependant, who mediates this dependence?

Separator relation: X affects Z who in turn affects Z Z regulates both X and Y

AGA1 FUS1

KAR4

Mating transcriptional

regulator of nuclear fusion

Cell fusion Cell fusion

Separators: Intra-cluster Context

CRH1 YPS3

SLT2

Cell wall protein

MAPK of cell wall

integrity pathway

Cell wall protein

YPS1Cell wall protein

SLR3Protein of unknown function

++

All gene pairs have high correlation, clustering groups them together

assigned putative function to SLR3 - cell wall protein We can assign regulatory role to SLT2 Many other signaling and regulatory proteins were identified

as direct and indirect separators

Guided K-meansDiscretization

Guided K-meansDiscretization

Expressiondata

MarkovMarkov SeparatorSeparatorEdgeEdge RegulatorRegulator

Bayesian Network Learning Algorithm

+ Bootstrap

Bayesian Network Learning Algorithm

+ Bootstrap

Reconstruct SubNetworksReconstruct SubNetworks

Visualize UsingPathway ExplorerVisualize Using

Pathway Explorer

Preprocess

Learn model

Featureextraction

Featureassembly

Visualization

Sub-Networks

Reconstruct a Conserved sub-network Provides a more global picture Allows to include features with lower-confidence Preserved in most networks with high posterior Probably reflects a real biological process

Automatic algorithm Score: high concentration of pairwise features Greedy search for high scoring subgraphs

Increased Confidence(simulated data)

Percent of

False positives

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Confidence

Entire network

Subnetwork

Guided K-meansDiscretization

Guided K-meansDiscretization

Expressiondata

MarkovMarkov SeparatorSeparatorEdgeEdge RegulatorRegulator

Bayesian Network Learning Algorithm

+ Bootstrap

Bayesian Network Learning Algorithm

+ Bootstrap

Reconstruct SubNetworksReconstruct SubNetworks

Visualize UsingPathway ExplorerVisualize Using

Pathway Explorer

Preprocess

Learn model

Featureextraction

Featureassembly

Visualization

Rosetta networks in Pathway Explorer

http://www.cs.huji.ac.il/labs/compbio/ismb01

Summary

Primary contribution: automated methodology for finding patterns of interactions among genes

Clear semantics Principled handing of mutations and interventions

Built in handling of statistical significance Feature confidence Extracts significant sub-networks

Differs from clustering Inter-cluster relations Finer intra-cluster structure

Provides biologist with promising hypothesis