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Reverse engineering gene regulatory networks

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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

machine learning

statistical methods

extracted network

true network

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

- 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)

direct

interaction

common

regulator

indirect

interaction

co-regulation

- Relevance networks
- Graphical Gaussian models
- Bayesian networks

- Relevance networks
- Graphical Gaussian models
- Bayesian networks

- 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

Association scores

1

2

‘direct interaction’

X

1

2

1

2

X

X

‘common regulator’

1

1

2

2

‘indirect interaction’

strong correlation σ12

Pairwise associations without taking the context of the system into consideration

- Relevance networks
- Graphical Gaussian models
- Bayesian networks

1

2

direct interaction

1

2

strong partial correlation π12

Partial correlation, i.e. correlation

conditional on all other domain variables

Corr(X1,X2|X3,…,Xn)

Distinguish between direct and indirect interactions

direct

interaction

common

regulator

indirect

interaction

co-regulation

A and B have a low partial correlation

1

2

direct interaction

1

2

strong partial correlation π12

Partial correlation, i.e. correlation

conditional on all other domain variables

Corr(X1,X2|X3,…,Xn)

Problem: #observations < #variables

Shrinkage estimation and the lemma of Ledoit-Wolf

Shrinkage estimation and the lemma of Ledoit-Wolf

direct

interaction

common

regulator

indirect

interaction

P(A,B)=P(A)·P(B)

But: P(A,B|C)≠P(A|C)·P(B|C)

- 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.

- Relevance networks
- Graphical Gaussian models
- Bayesian networks

Bayesian networks

- 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

Bayesian networks versus causal networks

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

Node A unknown

A

A

True causal graph

B

C

B

C

Bayesian networks versus causal networks

Bayesian networks versus causal 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

A

C

B

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

Symmetry breaking

A

A

A

B

C

B

C

B

C

A

- Interventions
- Priorknowledge

B

C

Symmetry breaking

A

A

A

B

C

B

C

B

C

A

- Interventions
- Priorknowledge

B

C

A and B are correlated

A

B

inhibition of A

A

B

A

B

A

B

down-regulation of B

no effect on B

Learning Bayesian networks from data

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

M: Network structure. D: Data

Learning Bayesian networks from data

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

M: Network structure. D: Data

- On real experimental data, using the gold standard network from the literature
- On synthetic data simulated from the gold-standard network

- On real experimental data, using the gold standard network from the literature
- On synthetic data simulated from the gold-standard network

From Sachs et al., Science 2005

- Cellular signalling network of 11 phosphorylated proteins and phospholipids in human immune systems cell
- Deregulation carcinogenesis
- Extensively studied in the literature gold standard network

Raf regulatory network

From Sachs et al Science 2005

Flow cytometry data

- 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

Two types of experiments

- On real experimental data, using the gold standard network from the literature
- On synthetic data simulated from the gold-standard network

Comparison with simulated data 1

Raf pathway

Comparison with simulated data 2

Comparison with simulated data 2

Steady-state approximation

Real biological data: full 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.

How can we evaluate the reconstruction accuracy?

extracted network

true network

Evaluation of

learning

performance

biological knowledge

(gold standard network)

Performance evaluation:ROC curves

Performance evaluation:ROC curves

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

AUC=1

0.5<AUC<1

AUC=0.5

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

Alternative performance evaluation:

True positive (TP) scores

BN

GGM

RN

5 FP counts

Directed graph evaluation - DGE

true regulatory network

edge scores

data

high

low

Thresholding

concrete network

predictions

TP:1/2

FP:0/4

TP:2/2

FP:1/4

Undirected graph evaluation - UGE

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

Synthetic data, observations

Synthetic data, interventions

Cytometry data, interventions

How can we explain the difference between synthetic and real data ?

Simulated data are “simpler”.

No mismatch between models used for data generation and inference.

Can we trust our gold-standard network?

Raf regulatory network

From Sachs et al Science 2005

Disputed structure of the gold-standard network

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

Complications with real data

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

Stabilisation

through negative feedback loops

inhibition

- 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.

Performance on synthetic data better than on real data.

- Real data: more complex
- Real interventions are not ideal
- Errors in the gold-standard network

How do we model feedback loops?

Unfolding in time