Reverse Engineering of Genetic Networks (Final presentation)

Reverse Engineering of Genetic Networks (Final presentation)

Ji Won Yoon (s0344084) supervised by Dr. Dirk Husmeier.

MSc in Informatics at Edinburgh University,[email protected]

Reverse Engineering

What is reverse engineering of gene network?

- Relevance Network- My own method - MCMC for Bayesian network

Missing gene

+ “up” and “down” data from micro array

Past works Comparison of existing approaches to the

reverse engineering of genetic networks, Mutual information relevance networks My own method Bayesian networks using Markov Chain Monte Carlo

method

Applying all methods to synthetic data generated from a gene network simulator.

Applying to Biological data Diffuse large B cell Lymphoma gene expression data Arabidopsis gene expression data

Relevance Network (Butte, 2000)

Using mutual informationMI(A, B) = H(A) – H(A|B)

= H(B) – H(B|A) = MI(B, A) -> SymmetricMI(A, B) = H(A) + H(B) – H(A, B)

Mutual information is zero if two genes are independent.

Pair wise relation

Relevance Network (cont.)

Relevance Network (Butte, 2000) Useful only to local relation due to pair wise relation. Important to select proper threshold to get good relations.

Bootstrapping (Comparison of results in real data and in randomly permuted data)

Difficulty to identify the relation with two parents due to the locality. MI(A, [B, C, D])> MI(A, B)< MI(A, C)< MI(A, D)< Cannot detect XOR operation

MI(A, C) = MI(B, C) = 0

No direction of edges due to symmetric property Fast and light computation.

Useful for a number of genes

C D

A

B D

A

B C

A B C

0 0 0

0 1 1

1 0 1

1 1 0

My method (using mutual information)

Based on Scale free network Crucial genes will have more connections than other genes.

A

B C D

A

B C D E

On insert new gene F, A will have more chance to have it than other genes.

G = (N, E)

'G= (N, E, L)(L is level information}

My method (Insertion step)

Finding better parents and merging Clusters

a

MI(1, a) = 0.34

MI(5, a) = 0.35MI(6, a) = 0.31MI(7, a) = 0.4

MI(4, a) = 0.28

Threshold = 0.3

1

4

5

6

7

( )

1

4

5

3 8

2

6

a

10

12

7

9

S1

S2

S3

S4

11

My method (Deletion step)

AssumptionThe network generated from insertion step of my method is in stationary state in marginal log likelihood except one edge, which is investigated to check the connection

Three case in an edge e X->Y, X<-Y, and X Y

P (D | M) = U * P (X | pa (X)) * P (Y | pa (Y))

YXYpaYPXpaXPU

YXYpaYPXpaXPU

YXYpaYPXpaXPU

))(|(*))(|(*

))(|(*))(|(*

))(|(*))(|(*

333

222

111

))(|(*))(|( YpaYPXpaXP ii

My method (Deletion step)

X

Y

Graph G

e

A

C

D

H

I

B

E

F

YXHEYpaBAXpa

YXHEYpaYBAXpa

YXHEXYpaBAXpa

},{)(},,{)(

},{)(},,,{)(

},,{)(},,{)(

33

22

11

My method

Mainly two stepsInsertion and deletion steps

e f g h

c

d

a

be f g hc

d

ab

= 0.5

efg

hc

da

be

f

g hd

= 0.4c

ab

ef

ghdc

a

be

fg

hdc

a

b

= 0.3

Continue up to t = 0.…

5T

6T

7T

10 T

… …

Insertion step Deletion step

My method

AdvantageBased on Biological facts (Scale Free Network)

No need of thresholdsOnline approachScalabilityEasy to explore sub-networksFast computation

My method Disadvantage

Input order dependency

Risky in exploring parents in data with big noise values. (It can be over-fitted to training data)

61 % edges are less order dependent(in part B)

Bayesian network with MCMC Bayesian network

Problem 1 Problem 2

A

B C

D E

i

ii XpaXPEDCBAP ))(|(),,,,(

)|()|()|()|()( BEPBDPACPABPAP

)(

)()|()|(

DP

MPMDPDMP

M

MPMDP

MPMDP

)()|(

)()|(

Left: in large data set. Right: in small data set.

Bayesian network with MCMCMCMC (Markov Chain Monte Carlo)

Inference rule for Bayesian Network

Sample from the posterior distribution

Proposal Move : Given M_old, propose a new network M_new with probability

Acceptance and Rejection :)|( oldnew MMQ

)|(

)|(

)()|(

)()|(,1min

oldnew

newold

oldold

newnewaccept MMQ

MMQ

MPMDP

MPMDPP

Bayesian network with MCMC

MCMC in Bayes Net toolbox

Hasting factorThe proposal probability is calculated from the number of neighbours of the model.

Improvement of MCMCs

Fan-in The sparse data leads the prior probability to have a non-negligible influence on the posterior P(M|D). Limit the maximum number of edges converging on a node, fan-in. If FI(M) > a, P(M)=0. Otherwise, P(M)=1. The time complexity reduced largely

Acceptable configuration of child and parents in fan-in 3

AA A A

B B B CC D

A

B C D E

Improvement of MCMCsDAG to CPDAG (DAG : Directed Acyclic Graph, CPDAG : Completed Partially Directed Acyclic Graph)

X Y X Y

P(X, Y) = P(X)P(X|Y) = P(Y|P(Y|X)

Set of all equivalent DAGs

DAG to CPDAG

DE is reversible others are compelled.

Improvement of MCMCsThis CPDAG concept bring several advantages:

The space of equivalent classes is more reduced. It is easy to trap in local optimum in moving DAG spaces.

Incorporating CPDAG to MCMC

MCMCMCTrapping

A B A : global optimaB : local optima

Easy to be trapped in local optima B. Multi chains with different temperatures will be useful to escape from it.

MCMCMCTrapping

MCMCMCA super chain, S

Acceptance ratios of a super chain

j

Tij

iji jMPMDPDSP

1)()( )()|()|()|()|( 11 iiii SSQSSQ

lk

kl

TllTkk

TllTkkiaccept

MPMDPMPMDP

MPMDPMPMDPP 11

11

)()|()()|(

)()|()()|(,1min

Importance Sampling.

Partition function

Proposal distribution

Acceptance probability

We only case the prior distribution for acceptance.Importance Sampling is also combined with MCMCMC.

MCMCMC with Importance Sampling

: Likelihood for configuration of a node n and its parents

Order MCMC It sample over total orders not over structures.

A

B C

A B CA C B

B C AB A CC A BC B A

Order MCMC It sample over total orders not over structures.

Proposal move flipping two nodes of the previous order

Computational limitations Using candidate sets

Sets of parents with the highest scores in likelihood for each node Reduces the computation time.

Order MCMC

Order MCMC Selection features

We can extract the edges by approximating and averaging under the stationary distribution,

where

Synthetical data

41th to 50th genes are not connected.

Synthetic data

- MCMCMC with Importance Sampling has the best performance.- Order MCMC is the second.- Order MCMC is much faster than MCMCMC with Importance Sampling.

Synthetic data

I changed one parameters for MCMC simulation.

1) Standard application(using standard parameters)

2) Change a noise value(Decrease noise value to 0.1)

3) Change a training data size(Decrease the size to 50)

4) Change the number of iterations(Increase the number to 50000)

Standard parameters ( MCMC in Bayes Net Toolbox )training data size:200, noise value:0.3, the number of iterations: 5000 (5000 samples and 5000 burn-ins)

Synthetic data

Synthetic data

Convergence

1) MCMC in BNT

2) MCMCMC Importance Sampling (IM)

3) MCMCMC ImportanceSampling (ID)

4) Order MCMC

1 2

3 4

training set size : 200noise : 0.3

5000 iterations.

Synthetic data MCMCMC

(Burn-in# + Sample #)

Left: 5000 + 5000

Right: 100000 + 100000

Acceptance ratiosLeft: MCMC in BNT, Right : Order MCMC

Middle: MCMCMC with Importance Sampling

Diffuse large B cell lymphoma Data

Data discretisation I used K-means algorithms to discretise gene expression levels for each genes since the stationary level for each gene can be different from others. (up, down and normal)

Problem of this discretisationIf there are too many noises,

the noises can make fluctuations

Finally, this method can not work well for gene3.


Comparison of convergence

MCMC in BNT MCMCMC withImportance Sampling(ID)

Order MCMC

# of genes : 27Training data size : 105Iterations : 20000


Comparison of Acceptance Ratios

The number of genes : 27, Training data size : 105, Iterations : 20000

Gene expression inoculated by viruses

in susceptible Arabidopsis thaliana plants Viruses

• Cucumber mosaic cucumovirus• Oil seed rape tobamovirus• Turnip vein clearing tobamovirus• Potato virus X potexvirus• Turnip mosaic potyvirus

1)

2)

3)

4)

5)

1DAI 2DAI 3DAI 4DAI 5DAI 7DAI

Symptomoccurs.

DAI = Day after inoculationInoculation

Gene a

Training data : 127 genes with 20 data size ( 4 DAIs * 5 viruses )


in susceptible Arabidopsis thaliana plants only for 20 genes (1DAI and 2DAI)

1000 samples from my method 10000 samples from MCMCMC with Importance Sampling(ID)


in susceptible Arabidopsis thaliana plants127 genes

Genes with Higher

connectivity

Average global connectivity

= 1.5847


in susceptible Arabidopsis thaliana plants127 genes

p-value check for transcription function

- f is the number of genes with j th function in 127 genes.

- m is the number of genes with j th function in 14 genes.


in susceptible Arabidopsis thaliana plantsfor 127 genes from my method (100

samples)

Conclusion

We need to select methodologies depending on the characteristics of training data.

To obtain the closest result to real networks, MCMCMC with Importance and Order MCMC are suitable.

MCMCMC with Importance Sampling has the best performance but it is slower than other MCMCs. Order MCMC has the second performance but it is four times faster than MCMCMC with Importance Sampling.

If we want to process large scale data and we do not have enough time to run MCMCs,

Relevance Network and My method are proper.

Also, several methods generate different networks so that combining them will give better results.

Conclusion

Biological meaningTranscription genes have higher connectivities more than other genes (from my method). That is, genes with transcription function may act as hubs in a network for response against viruses in Arabidopsis thaliana plant.

Documents

Reverse Engineering of Genetic Networks (Final presentation)