Gene Expression Analysis Using Bayesian Networks

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Gene Expression Analysis Using Bayesian Networks

• Éric Paquet
• LBIT
• Université de Montréal

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Biological basis
RNA Polymerase (Copy DNA in RNA)
DNA (Storage of Genetic Information)
Ribosome (Translate Genetic Information in
Proteins)
mRNA (Storage Transport of Genetic Information)
Proteins (Expression of Genetic Information)
-PDB file 1L3A, Transcriptional Regulator Pbf-2
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Biological basis

• How do proteins get regulated?
• E. coli operon lactose example
• In normal time, E. coli uses glucose to get
  energy, but how does it react if there is no more
  glucose but only lactose?

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Biological basis
E. coli environment
RNA Polymerase
...
...
Gene Lac I associated protein
Polymerase action is blocked because of a DNA lock
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Biological basis
E. coli environment
X
RNA Polymerase
...
...
Lactose
Lactose
unlocking the DNA that is then accessible to the
polymerase
Lactose recruits gene lacI associated protein
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Biological basis
Lactose decomposor (ß-galactosidase)
Lactose getter (permease)
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Biological basis
E.coli environment
X
RNA Polymerase
...
...
Lactose
In absence of glucose, a polymerase magnet binds
to the DNA to accelerate the products of
information that help lactose decomposition
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Biological basis
Lactose decomposor (ß-galactosidase)
Lactose getter (permease)
activate
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Why?

• Get insights about cellular processes
• Help understand diseases
• Find drug targets

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How?

• Using gene expression data and tools for learning
  Bayesian networks

Experiments


Tools for Learning Bayesian networks
mRNA
-Spellman et al.(1998) Mol Biol Cell 93273-97
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What is gene expression data?

• Data showing the concentration of a specific mRNA
  at a given time of the cell life.

Experiments

mRNA
A real value is coming from one spot and tells if
the concentration of a specific mRNA is higher()
or lower(-) than the normal value
Every columns are the result of one image
-Spellman et al.(1998) Mol Biol Cell 93273-97
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What is Bayesian networks?

• Graphic representation of a joint distribution
  over a set of random variables.

P(A,B,C,D,E) P(A)P(B)
P(CA)P(DA,B)
P(ED)
Nodes represent gene expression while edges
encode the interactions (cf. inhibition,
activation)
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Bayesian networks little problem

• A Bayesian network should be a DAG (Direct
  Acyclic Graph), but there are a lot of example of
  regulatory networks having directed cycles.

-Husmeier D.,Bioinformatics,Vol. 19 no. 17 2003,
pages 22712282
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How can we deal with that?

• Using DBN (Dynamic Bayesian Networks) and
  sequential gene expression data

t
t1
We unfold the network in time
DBN BN with constraints on parents and children
nodes
-Friedman, Murphy, Russell,Learning the
Structure of Dynamic Probabilitic Networks
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What are we searching for?

• A Bayesian network that is most probable given
  the data D (gene expression)
• We found this BN like that
• BN argmaxBNP(BND)

Where
Marginal likelihood
Prior on network structure
Data probability
Naïve approach to the problem try all possible
dags and keep the best one!
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It is impossible to try all possible DAGs because

• The number of dags increases super-exponentially
  with the number of nodes
• n 3 ? 25 dags
• n 4 ? 543 dags
• n 5 ? 29281 dags
• n 6 ? 3781503 dags
• n 7 ? 1138779265 dags
• n 8 ? 783702329343 dags

We are interested in problem having around 60
nodes .
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Learning Bayesian Networks from data?

• Choosing search space method and a conditional
  distribution representation

• Networks space search methods
• Greedy hill-climbing
• Beam-search
• Stochastic hill-climbing
• Simulated annealing
• MCMC simulation

• Conditional distribution representation
• Linear Gaussian
• Multinomial, binomial

A
P(a) ? P(b) ? P(ca,b) ?
C
Basically add, remove and reverse edges
B
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Learning Bayesian Networks from data?

• Choosing search space method and a conditional
  distribution representation

• Networks space search methods
• Greedy hill-climbing
• Beam-search
• Stochastic hill-climbing
• Simulated annealing
• MCMC simulation

• Conditional distribution representation
• Linear Gaussian
• Multinomial, binomial

A
P(a) ? P(b) ? P(ca,b) ?
C
Basically add, remove and reverse edges
B
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We use three types of gene expression level?
Sort
-1.06 -0.12 0.18 0.21 1.16
1.19
Split data in 3 equal buckets
Discretized data
0 0 2 2 1 1
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Return on
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Insight on each terms

• P(BN) ? prior on network
• In our research, we always use a prior equals to
  1
• We could incorporate knowledge using it
• Eg. we know the presence of an edge. If the
  edge is in the BN, P(BN) 1 else P(BN) 0
• Efforts are made to reduce the search space by
  using knowledge eg. limit the number of parents
  or children

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Insight on each terms

• P(DBN) ? marginal likelihood
• Easy to calculate using Multinomial distribution
  with Dirichlet prior

-Heckerman,A Tutorial on Learning With Bayesian
Networks and Neapolitan,Learning Bayesian Networks
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MCMC (Markov Chain Monte Carlo) simulation

• Markov Chain part
• Zoom on a node of the chain

A
A
P(BNnew)
B
C
B
C
1/5
1/5
A
1/5
0
A
B
C
B
1/5
C
1/5
A
A
B
C
B
C
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MCMC (Markov Chain Monte Carlo) simulation

• Monte Carlo part
• Choose next BN with probability P(BNnew)
• Accept the new BN with the following
  MetropolisHastings acceptance criterion

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Monte Carlo part example

1. Choose a random path. Each path having a P(BNnew)
   of 1/5

1. Choose a random path. Each path having a P(BNnew)
   of 1/5
2. Choose another random number. If it is smaller
   than the Metropolis-Hasting criterion, accept
   BNnew else return to BNold

A
A
P(BNnew)
B
C
B
C
1/5
1/5
A
1/5
0
A
B
C
B
1/5
C
1/5
A
A
B
C
B
C
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MCMC (Markov Chain Monte Carlo) simulation recap

• Choose a starting BN at random
• Burning phase (generate 5N BN from MCMC without
  storing them)
• Storing phase (get 100N BN structure from MCMC)

Burning phase
Storing phase
log(P(D BN)P(BN))
Iteration
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Why 100N BN and not only 1

• Cause we dont have enough data and there are a
  lot of high scoring networks
• Instead, we associate confidence to edge. Eg.
  how many time in the sample can we find edge
  going from A to B?
• We could fix a threshold on confidence and
  retrieve a global network construct with edges
  having confidence over the threshold

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What we are working on

• Mixing both sequential and non-sequential data to
  retrieve interesting relation between genes
• How?
• Using DBN and MCMC for sequential data BN and
  MCMC for non-sequential

100N networks from BN
100N networks from DBN
Information tuner
Learn network
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How to test the approach

• Problem There is no way to test it on real data
  cause there is no completely known network
• Solution Work on realistic simulation where we
  know the network structure
• Example

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Simulate
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-Hartemink A. Using Bayesian Network Inference
Algorithms to Recover Molecular Genetic
Regulatory Networks
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How to test the approach
BN MCMC
Info tuner
DBN MCMC
Sequential data
Non-Sequential data
Compare using ROC curves

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1
12
2
4
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Simulate
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-Hartemink A. Using Bayesian Network Inference
Algorithms to Recover Molecular Genetic
Regulatory Networks
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Test description

• Generate 60 sequential data
• Generate 120 non-sequential data (reality
  proportion)
• Run DBN MCMC on sequential data keep 100N sample
  net
• Run BN MCMC on non-sequential data keep 100N
  sample net
• Test performance using weight on sample
• 0 BN 1 DBN
• .05 BN 0.95 DBN
• 0.95 BN .05 DBN
• 1 BN 0 DBN
• The metric used is the area under ROC curve.
  Perfect learner gets 1.0 , random gets 0.5 and
  the worst one gets 0.

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Results
Area under ROC curve
1
0 BN
0
1 DBN
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Perspective

• Working on more sophisticated ways to mix
  sequential and non-sequential data
• Working on real cases
• Yeast cell-cycle
• Arabidopsis Thaliana circadian rhythm
• Real data also means missing values
• Evaluate missing values solution (EM, KNNImpute)

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Acknowledgements
François Major
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Why are there missing datas?
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ROC Curve

• Receiver Operating Characteristic curve

-http//gim.unmc.edu/dxtests/roc2.htm
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MCMC simulation and number of sampled networks