Florian Markowetzflorian.markowetz@cancer.org.uk

Probabilistic refinement

of cellular pathway models

Cambridge Statistical Laboratory Networks seminar series

2009 Jan 21

What is a signaling pathway?

DNA

mRNA

Protein

Environmentalstimuli

Receptor incell membrane

Protein cascade

Transcription factorsregulating target genes

Pathway

Pathway reconstruction

Signaling pathways are important-

Deregulation causes many diseases incl. cancer

Signaling pathways are poorly understood-

Only parts-lists

-

missing are interactions

within and between pathways

Biological research-

So far mostly focused on individual genes

New genome-scale datasets-

Opportunity for data integration and novel methods

What data do we have?

DNA

mRNA

Protein mRNA:-

Expression under different stimuli-

binding to DNA

Sequence:- binding motifs- epigenetic marks

Proteins:- interactions between proteins- binding to DNA

Morphology

Bulk of data:Microarray

Pathways as graphs•

Nodes

are (mostly) known

•

Goal: infer edges from data•

Data are heterogeneous

• binding motifs at genes• Protein domains• Functional annotation

•

co-expression between genes •

interactions between

proteins •

binding of proteins to

DNA

• Cause-effect data: • changing environments• experimental perturbations

Edges

Nodes

Paths

Pathway reconstruction

“Classical”

statistical approaches:Treat the genes/proteins as random variables and

explore correlation structure

in the data:–

Correlation graphs

–

Gaussian graphical models (partial correlation)–

Bayesian networks

Review: Markowetz and Spang (2007)

Challenges/Problems/Opportunities1. Correlation may be un-informative2. Integrate heterogeneous and noisy and

complementary data sources

– Part 1 –

Nested Effects Models

Experimental perturbations

DNA

mRNA

Protein

RNAi

Knockout

DrugsSmallmolecules

Stress

Readout:Global gene expression measurements

Drosophila immune response

Columns: perturbed genesRows: effects on other genes

1.

Silencing tak1

reduces expression of all

LPS-

inducible transcripts2.

Silencing rel

(key) or

mkk4/hep

reduces expression of subsets

of

induced transcripts

(Boutros et al, Dev Cell 2002)

(!)

Two types of entities

Components of signaling pathway

which are

experimentally perturbed

Downstream

effect reporters

(!!)

Only indirect information

No direct observation

of perturbation effects on other pathway components!

Inference from observed perturbation effects on downstream reporters.

The information gap

B

A C

DPathway

-

Cell survival or death- Growth rate- downstream genes

BA C

DPathway

Direct information: effects are visible at other

pathway components

Indirect information: effects are only visible at

down-stream reporters

Correlation won’t do

Downstream regulated

genes

BA C

DPathway Correlation

Graphical models:- Bayes Nets- GGMsMutual Information

NestedEffects Models

“Classical” approach

Nested Effects Models

Inferred pathwayPhenotypic profiles

A B

C D E F

G H

ABC

F

D

H

E

G

Gen

e pe

rtur

batio

ns

Effects

1.

Set of candidate pathway genes2.

High-dimensional phenotypic profile, e.g. microarrayINPUT

OUTPUT Graph representation of information flow explaining the phenotypes

NEM: model formulation

M’xyz :X Y Z

E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5 E6

XYZ

Expected

E1 E2 E3 E4 E5 E6

XYZ

ObservedFN FN

FNFP

Pathway genes: X, Y, Z• core topology• to be reconstructed

= Model

M

Effect reporters: E1

, …, E6• states are observed

= Data D• positions in pathway unknown

= Parameters θ

Posterior:

P ( M | D ) = 1/Z .

P( D | M )

. P( M )Marginal likelihood

Likelihood P( D | M, θ

)

Error probabilitiese.g. false NEG rate 20%, false POS rate 5%

95.080.095.005.0)1Pr()0Pr()1Pr()1Pr( 2121

⋅⋅⋅==⋅=⋅=⋅== EEEELik

Prediction E1 =0 E2 =1Observation 1. E1 =1 E2 =1

2. E1 =0 E2 =1

Compare predictions with observations:

X

Y

Z

E1 E2

Marginal likelihood

∫ ΘΘΘ= dMPMDPMDP )|(),|()|(

∏∑∏= = =

==m

i

n

j

l

kiikm jMeP

n 1 1 1

),|(1 θ

Product over replicate observation

Average over possible positions in the pathway

Product over all effect reporters

Uniformprior overpositions

Distribution of single effect reporter with known position

NEM: inference

Model space: all transitively closed directed graphs

Exhaustive enumeration: score all models to find the one fitting the data best

Markowetz et al. Bioinformatics, 2005

MCMC, Simulated Annealing: take small probabilistic steps to explore model space

. . . with A Tresch; in preparation

Divide and conquer: break a big model into smaller, manageable pieces and then re-assemble

Markowetz et al. ISMB 2007

NEM: extensions

Drop transitivityrequirement

Likelihood based on log-ratios

of effects

Feature selection

to concentrate on informative effect reporters

Tresch

and Markowetz (2008)

NEMs on Drosophila data

Summary of part 1

1.

Gene perturbation screens

with gene- expression readouts

2.

Perturbation screens suffer from the information gap

between pathways and

reporters

3.

Nested Effects Models

reconstruct pathway features from subset relations between observed effects

– Part 2 –

Data integration

and probabilistic refinement

of

a signaling pathway hypothesis

Pathway refinement1.

Start from given pathway hypothesis

Even if our understanding of pathways is poor, that does not mean we have none at all!

2.

Evaluate evidence for hypothesis in data

3.

Identify weakly supported areas and likely extensions

Not reconstruction from scratch.

Step 1:

assemble pathway hypothesis (KEGG, literature, …) for pheromone response pathway

in Yeast

Edge data I

Support for hypothesis in protein-protein interaction

data

Edge data II

Support for hypothesis in co-expression

data

Edge data IIIWhy is it so hard to reconstruct nuclear regulatory network from correlations?

Edge data IVSupport for hypothesis in

TF-DNA binding

data

Paths: cause-effect dataExpression profiling of knock-out mutants

(Hughes et al., 2000)

Result:transcriptional response to perturbation only visible on down-stream genes (information gap!)

Conclusion from data analysis

•

Every data source is informative for a specific compartment of the pathway

•

No data source is informative in all compartments

•

We expect these observations also to hold for other MAPK and signaling pathways.

Need compartment-specific integrative model encompassing edge, node, and path data.

Integrative model

Pathway graph as hidden/latent variables

Conditional distributions for each data type

Different data types contribute to each compartment

Graphical model defines posterior P(G|data)-> inference by Gibbs sampler

ParametersPrior

Evaluation

1.

Fit model parameters

on pheromone response pathway (training)

2.

Use fitted model on other MAPK pathways (generalization to closely related examples)

3.

Use fitted model on all other Yeast signaling pathways

(generalization to everything else)

… work in progress …

Acknowledgements

Nested Effects Models

Rainer Spang

(Univ. Regensburg) .:.

Dennis Kostka

(UC SF) .:.

Achim

Tresch

(Gene Center

Munich) .:.

Holger

Fröhlich

(DKFZ Heidelberg) .:. Tim Beißbarth

(Univ. Göttingen) .:. Josh

Stuart,

Charlie Vaske

(UC SC) .:.

Data integration

Olga G. Troyanskaya

(Princeton) .:. Edoardo Airoldi

(Harvard) .:.

David Blei

(Princeton) .:.

Florian Markowetzflorian.markowetz@cancer.org.uk

Probabilistic refinement of cellular pathway models

Thank you !