Bayesian network models of Biological signaling pathways

Bayesian network models of Biological signaling pathways

[email protected]

K. Sachs2

From Phospho-molecular profiling to Signaling pathways

High throughput dataR

af

Erk

p38

PKA

PKC

Jnk

PIP2

PIP3

Plc

Akt

...

Cell1Cell2Cell3Cell4

Cell600

Signaling Pathways

Flow Measurments

Picture: John Albeck

K. Sachs

Outline What are signaling

pathways? What kind of data

is available study them?

How do we use Bayesian networks to learn their structure?

Two extensions: Markov

neighborhood algorithm

Bayesian network based cyclic networks (BBCs)

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4

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Cell death ProliferationSecrete cytokines

Cells respond to their environment

Inside each cell is a molecular network

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“Central Dogma”

Translation

ProteinDNA

Transcription

mRNA

Modification

Modified Protein

‘Blueprint’- instructions

for production

of all proteins

Delivers instruction

s for specific gene

Ribosome: Protein-

production factory

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Signaling & Genetic pathways

A

B

C

A

BTF

DNA

RNA

C

Cell response

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d[R]dt k1[LR]

k2[R][L] ...

Spectrum of Modeling Tools in Systems Biology

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Graph Node: Measured level/activity of protein Edge: Influence (dependency) between proteinsConditional probability distributions Each node has a conditional probability given its parents

Protein A

Protein B

Protein C Protein D

Protein E

Bayesian Networks

P(B|A=‘On’)0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-1 0 10 1 2

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How do we use Bayesian Networks to infer pathways?

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The Technical Details

BayesianScore (S) logP(S D)

logP(S) logP(D S) c

Score candidate models

Use a heuristic search to find high scoring models

... P(D,S)P( S)dn

1

... P(D, S)dn

1

P(DS)

(analytical solution!)

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Protein data Western blot

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Protein data Protein arrays

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Protein data Mass Spectrometry

All of these lysate approaches give 1

measurement per protein for 10^3-10^7 cells

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Flow Cytometry: Single Cell Analysis

Thousands of datapoints

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MEK3/6

MAPKKK

PLC

Erk1/2

Mek1/2

Raf

PKC

p38

Akt

MAPKKK

MEK4/7

JNK

LATLck

VAVSLP-76

RAS

PKA

1 2 3CD28CD3

PI3K

LFA-1

CytohesinZap70

PIP3

PIP2

JAB-1

Activators 1.-CD3

2.-CD28 3. ICAM-2

4. PMA 5. 2cAMP

Inhibitors 6. G06976 7. AKT inh 8. Psitect 9. U0126

10. LY294002

10

5

46

7

9

8

Stimulations and perturbations

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Datasets of cells• condition ‘a’• condition ‘b’•condition…‘n’

Raf

Mek

1/2

Erk

p38

PKA

PKC

Jnk

PIP2

PIP3

Plc

Akt

12 Color Flow Cytometryperturbation a

perturbation n

perturbation b

Conditions (multi-well format)

T-Lymphocyte Data

Primary human T-Cells 9 conditions

(6 Specific interventions)

9 phosphoproteins, 2 phospolipids

600 cells per condition 5400 data-pointsOmar Perez

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Statistical Dependencies

A

B

C D

E

Phos

pho

APhospho B

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Statistical Dependencies

Edges can be directed (primarily) due to the use of

interventions

A

B

C D

E

Phos

pho

APhospho B

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Overview

Influence

diagram of

measured

variables

Bayesian Network Analysis

Datasets of cells• condition ‘a’• condition ‘b’•condition…‘n’

Raf

Mek

1/2

Erk

p38

PKA

PKC

Jnk

PIP2

PIP3

Plc

Akt

Multiparameter Flow Cytometry

perturbation a

perturbation n

perturbation b

Conditions (multi well format)

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PKC

Raf

P44/42

Mek

Plc

PKA

Akt

Jnk P38

PIP2

PIP3

Phospho-Proteins Phospho-Lipids Perturbed in data

Inferred Network

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PKC

Raf

P44/42

Mek

Plc

PKA

Akt

Jnk P38

PIP2

PIP3


How well did we do?

Direct phosphorylation

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Features of Approach Direct phosphorylation:

Mek

Difficult to detect using other forms of high-throughput data:

-Protein-protein interaction data-Microarrays

Erk

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PKC

Raf

P44/42

Mek

Plc

PKA

Akt

Jnk P38

PIP2

PIP3


How well did we do?

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PKC

Raf

P44/42

Mek

Plc

PKA

Akt

Jnk P38

PIP2

PIP3


How well did we do?

Indirect Signaling

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Indirect signaling

Dismissing edges

Raf Mek Erk

PKC Jnk PKC Mapkkk Jnk

Not measured

Mek4/7

Indirect connections can be found even when the intermediate molecule(s) are not

measured

Indirect signaling

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Indirect signaling - Complex example

Is this a mistake?

The real picture

Phoso-protein specific More than one pathway of influence

PKC Raf Mek

PKC Rafs259 Mek

Rafs497

Ras

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PKC

Raf

P44/42

Mek

Plc

PKA

Akt

Jnk P38

PIP2

PIP3

Expected Pathway

15/17 Classic


How well did we do?

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PKC

Raf

Erk

Mek

Plc

PKA

Akt

Jnk P38

PIP2

PIP3

Expected PathwayReported

Missed

15/17 Classic 17/17 Reported 3 Missed

Reversed


Signaling pathway reconstruction

[Sachs et al 2005]

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Caveats Inhibitor specificity

Binding site similar across proteins

Reagent availability and specificity

Data quality These are issues in

many biological apps!

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I think I’ll bind here

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Markov Neighborhood Algorithm

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Building larger networks 12 color capability Model 50-100

variables 4 color capability Model 12

variables

PKC

Raf

P44/42

MekPlc

PKA

Akt

Jnk P38

PIP2

PIP3~80 proteins involved in

MAPK signaling (11- at the

cutting edge- is NOT enough!)

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Measured subsets = Incomplete dataset (Missing data)

Insufficient information for standard approaches (will perform poorly)

Use a set of biologically motivated assumptions to constrain search..

And to reduce the number of experiments ( )11

4= 330

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Constraining the search

Plus potential perturbation parents

Identify candidate parents

Using ‘Markov neighborhoods’(for each variable)

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Bayesian Network Analysis

(Constrained search)

Raf

Mek

1/2

Erk

p38

PKA

PKC

Jnk

PIP2

PIP3

Plc

Akt

Molecules 1, 3, 7, 9



Approach overview

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Neighborhood reduction

CB

ED

A

F

4 color capabilityConditional

independencies in the substructure?

ABC

411

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Accurate Reproduction of Model ~15 experiments, 4-colors

Confidence value different from original

model

PKC

Raf

Erk

Mek

Plc

Akt

Jnk P38

PIP2

PIP3

PKA

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Raf

Mek

1/2

Erk

p38

PKA

PKC

Jnk

PIP2

PIP3

Plc

Akt

Active learning approach

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Learning cyclic structures with Bayesian networks

Biological networks contain many loops

Bayesian networks are constrained to be acyclic

So…

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Overcoming acyclicity Signaling pathways contain

many cycles Bayesian networks are

constrained to be acyclic How can we accurately

model pathways with cycles?

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GRB2/SOS

Raf

MEK

Erk

Ras

Develop a new, Bayesian network derived algorithm that models

cycles…

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Bayesian Network Based Cyclic Networks (BBNs)

I. Break loops with molecule inhibitors

II. Use BN to learn the structure (now not cyclic!)

III. Close loops

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GRB2/SOS

Raf

MEK

Erk

Ras

Mek inhibitorSolomon

Itani

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GRB2/SOS

Raf

MEK

Erk

Ras

I. Break loops with molecule inhibitors Detect loops P(A)A* ~= P(A)

II. Use BN to learn the structure (now not cyclic!)

III. Close loopsP(B|Pa(B)) A* ~= P(B|Pa(B)) AB

Bayesian Network Based Cyclic Networks (BBNs)

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Future work Larger network from overlapping sets

(Markov neighborhood) Dynamic models over time Differences in signaling (sub-

populations, treatment conditions, cell types, disease states)

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Acknowledgements

Shigeru Okumur

a

Funding

LLS post doctoral fellowship

Solomon Itani

Garry Nolan

Dana Pe’er

Doug Lauffenburge

r

Omar Perez

Dennis Mitchell

Mesrob Ohannessia

n

Extra slides

Mathematical IntuitionB C C is independent of A given

B.A

A B

CDC independent of A given B and

D

1) No need to introduce time!!!2) When loops are broken, the result is a

BN!!!

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Prediction: ErkAktErk1/2 unperturbed Erk Akt not well established

in literature

Predictions: Erk1/2 influences Akt While correlated, Erk1/2

does not influence PKA

PKC

Raf

Erk1/2

Mek

PKA

Akt

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Validation

control, stimulatedErk1 siRNA, stimulated

SiRNA on Erk1/Erk2 Select transfected cells Measure Akt and PKA

100 101 102 103 104

APC-A: p-akt-647 APC-A100 101 102 103 104

PE-A: p-pka-546 PE-AP-Akt P-PKA

P=9.4e-5 P=0.28

Bayesian network models of Biological signaling pathways

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