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Reverse engineering gene regulatory networks. Dirk Husmeier Adriano Werhli Marco Grzegorczyk. Systems biology Learning signalling pathways and regulatory networks from postgenomic data. unknown. unknown. high-throughput experiments. postgenomic data. unknown. data. data.

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Reverse engineering gene regulatory networks

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Reverse engineering gene regulatory networks

Reverse engineering gene regulatory networks

Dirk Husmeier

Adriano Werhli

Marco Grzegorczyk


Reverse engineering gene regulatory networks

Systems biology

Learning signalling pathways and regulatory networks from postgenomic data



Reverse engineering gene regulatory networks

unknown

high-throughput experiments

postgenomic data


Reverse engineering gene regulatory networks

unknown

data

data

machine learning

statistical methods


Reverse engineering gene regulatory networks

extracted network

true network

Does the extracted network provide a good prediction of the true interactions?


Reverse engineering of regulatory networks
Reverse Engineering of Regulatory Networks

  • Can we learn the network structure from postgenomic data themselves?

  • Statistical methods to distinguish between

    • Direct interactions

    • Indirect interactions

  • Challenge: Distinguish between

    • Correlations

    • Causal interactions

  • Breaking symmetries with active interventions:

    • Gene knockouts (VIGs, RNAi)


Reverse engineering gene regulatory networks

direct

interaction

common

regulator

indirect

interaction

co-regulation


Reverse engineering gene regulatory networks


Reverse engineering gene regulatory networks


Relevance networks butte and kohane 2000
Relevance networks(Butte and Kohane, 2000)

  • Choose a measure of association A(.,.)

  • Define a threshold value tA

  • For all pairs of domain variables (X,Y) compute their association A(X,Y)

    4. Connect those variables (X,Y) by an undirected edge whose association A(X,Y) exceeds the predefined threshold value tA



Reverse engineering gene regulatory networks

1

2

‘direct interaction’

X

1

2

1

2

X

X

‘common regulator’

1

1

2

2

‘indirect interaction’

strong correlation σ12



Reverse engineering gene regulatory networks


Graphical gaussian models

1 system into consideration

2

direct interaction

1

2

Graphical Gaussian Models

strong partial correlation π12

Partial correlation, i.e. correlation

conditional on all other domain variables

Corr(X1,X2|X3,…,Xn)


Reverse engineering gene regulatory networks

Distinguish between direct and indirect interactions system into consideration

direct

interaction

common

regulator

indirect

interaction

co-regulation

A and B have a low partial correlation


Graphical gaussian models1

1 system into consideration

2

direct interaction

1

2

Graphical Gaussian Models

strong partial correlation π12

Partial correlation, i.e. correlation

conditional on all other domain variables

Corr(X1,X2|X3,…,Xn)

Problem: #observations < #variables




Graphical gaussian models2
Graphical Gaussian Models system into consideration

direct

interaction

common

regulator

indirect

interaction

P(A,B)=P(A)·P(B)

But: P(A,B|C)≠P(A|C)·P(B|C)


Undirected versus directed edges
Undirected versus directed edges system into consideration

  • Relevance networks and Graphical Gaussian models can only extract undirected edges.

  • Bayesian networks can extract directed edges.

  • But can we trust in these edge directions?

    It may be better to learn undirected edges than learning directed edges with false orientations.


Reverse engineering gene regulatory networks


Reverse engineering gene regulatory networks

Bayesian networks system into consideration

  • Marriage between graph theory and probability theory.

  • Directed acyclic graph (DAG) representing conditional independence relations.

  • It is possible to score a network in light of the data: P(D|M), D:data, M: network structure.

  • We can infer how well a particular network explains the observed data.

NODES

A

B

C

EDGES

D

E

F


Reverse engineering gene regulatory networks

Bayesian networks versus system into considerationcausal networks

Bayesian networks represent conditional (in)dependence relations - not necessarily causal interactions.


Reverse engineering gene regulatory networks

Node A unknown system into consideration

A

A

True causal graph

B

C

B

C

Bayesian networks versus causal networks


Reverse engineering gene regulatory networks

Bayesian networks versus system into considerationcausal networks

A

A

A

B

C

B

C

B

C

  • Equivalence classes: networks with the same scores: P(D|M).

  • Equivalent networks cannot be distinguished in light of the data.

A

B

C


Equivalence classes of bns

A system into consideration

C

B

Equivalence classes of BNs

A

C

B

A

C

A

B

P(A,B)≠P(A)·P(B)

P(A,B|C)=P(A|C)·P(B|C)

C

B

A

C

completed partially directed graphs (CPDAGs)

B

v-structure

A

P(A,B)=P(A)·P(B)

P(A,B|C)≠P(A|C)·P(B|C)

C

B


Reverse engineering gene regulatory networks

Symmetry breaking system into consideration

A

A

A

B

C

B

C

B

C

A

  • Interventions

  • Priorknowledge

B

C


Reverse engineering gene regulatory networks

Symmetry breaking system into consideration

A

A

A

B

C

B

C

B

C

A

  • Interventions

  • Priorknowledge

B

C


Interventional data
Interventional data system into consideration

A and B are correlated

A

B

inhibition of A

A

B

A

B

A

B

down-regulation of B

no effect on B


Reverse engineering gene regulatory networks

Learning Bayesian networks from data system into consideration

P(M|D) = P(D|M) P(M) / Z

M: Network structure. D: Data


Reverse engineering gene regulatory networks

Learning Bayesian networks from data system into consideration

P(M|D) = P(D|M) P(M) / Z

M: Network structure. D: Data


Evaluation
Evaluation system into consideration

  • On real experimental data, using the gold standard network from the literature

  • On synthetic data simulated from the gold-standard network


Evaluation1
Evaluation system into consideration

  • On real experimental data, using the gold standard network from the literature

  • On synthetic data simulated from the gold-standard network


Reverse engineering gene regulatory networks

From Sachs et al., Science 2005 system into consideration


Evaluation raf signalling pathway
Evaluation: system into considerationRaf signalling pathway

  • Cellular signalling network of 11 phosphorylated proteins and phospholipids in human immune systems cell

  • Deregulation  carcinogenesis

  • Extensively studied in the literature  gold standard network


Reverse engineering gene regulatory networks

Raf regulatory network system into consideration

From Sachs et al Science 2005


Reverse engineering gene regulatory networks

Flow cytometry data system into consideration

  • Intracellular multicolour flow cytometry experiments: concentrations of 11 proteins

  • 5400 cells have been measured under 9 different cellular conditions (cues)

  • Downsampling to 100 instances (5 separate subsets): indicative of microarray experiments


Reverse engineering gene regulatory networks

Two types of experiments system into consideration


Evaluation2
Evaluation system into consideration

  • On real experimental data, using the gold standard network from the literature

  • On synthetic data simulated from the gold-standard network


Reverse engineering gene regulatory networks

Comparison with simulated data 1 system into consideration


Reverse engineering gene regulatory networks

Raf pathway system into consideration


Reverse engineering gene regulatory networks

Comparison with simulated data 2 system into consideration


Reverse engineering gene regulatory networks

Comparison with simulated data 2 system into consideration

Steady-state approximation


Real versus simulated data

Real biological data: system into considerationfull complexity of biological systems.

The “gold-standard” only represents our current state of knowledge; it is not guaranteed to represent the true network.

Simulated data: Simplifications that might be biologically unrealistic.

We know the true network.

Real versus simulated data



Reverse engineering gene regulatory networks

extracted network system into consideration

true network

Evaluation of

learning

performance

biological knowledge

(gold standard network)


Reverse engineering gene regulatory networks

Performance evaluation: system into considerationROC curves


Reverse engineering gene regulatory networks

Performance evaluation: system into considerationROC curves

  • We use the Area Under the Receiver Operating Characteristic Curve(AUC).

AUC=1

0.5<AUC<1

AUC=0.5


Alternative performance evaluation true positive tp scores
Alternative performance evaluation: True positive (TP) scores

We set the threshold such that we obtain 5 spurious edges (5 FPs) and count the corresponding number of true edges (TP count).


Reverse engineering gene regulatory networks

Alternative performance evaluation: scores

True positive (TP) scores

BN

GGM

RN

5 FP counts


Reverse engineering gene regulatory networks

Directed graph evaluation - scoresDGE

true regulatory network

edge scores

data

high

low

Thresholding

concrete network

predictions

TP:1/2

FP:0/4

TP:2/2

FP:1/4


Reverse engineering gene regulatory networks

Undirected graph evaluation - scoresUGE

skeleton of the

true regulatory network

undirected edge scores

data

high

low

Thresholding

concrete network

(skeleton) predictions

TP:1/2

FP:0/1

TP:2/2

FP:1/1






Reverse engineering gene regulatory networks

Simulated data are “simpler”. scores

No mismatch between models used for data generation and inference.


Complications with real data
Complications with real data scores

Can we trust our gold-standard network?


Reverse engineering gene regulatory networks

Raf regulatory network scores

From Sachs et al Science 2005


Reverse engineering gene regulatory networks

Disputed structure of the gold-standard network scores

Regulation of Raf-1 by Direct Feedback Phosphorylation. Molecular Cell, Vol. 17, 2005 Dougherty et al


Reverse engineering gene regulatory networks

Complications with real data scores

Interventions might not be “ideal” owing to negative feedback loops.

Stabilisation

through negative feedback loops

inhibition


Conclusions 1
Conclusions 1 scores

  • BNs and GGMs outperform RNs, most notably on Gaussian data.

  • No significant difference between BNs and GGMs on observational data.

  • For interventional data, BNs clearly outperform GGMs and RNs, especially when taking the edge direction (DGE score) rather than just the skeleton (UGE score) into account.


Conclusions 2
Conclusions 2 scores

Performance on synthetic data better than on real data.

  • Real data: more complex

  • Real interventions are not ideal

  • Errors in the gold-standard network




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