Detecting robust time-delayed regulation in Mycobacterium tuberculosis

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Detecting robust time-delayed regulation in
Mycobacterium tuberculosis
Iti Chaturvedi and Jagath C Rajapakse
INCOB 2009
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Gene Regulatory Networks (GRN)

• GRN represents the regulatory effects (causal
  effects) among genes involved in a particular
  pathway.
• Signal transduction may is transient dynamic
  delayed regulations seem to exist.
• Distributed nature causes intense cross-talk
• M. tuberculosis is a bacteria causing TB in man
  and has a very slow growth rate in vitro .
• The DNA repair pathway is activated when a damage
  to DNA occurs.
• System consists of LexA and RecA and upto 40
  other genes that are regulated by these two
  proteins.

Rv2719c
linB
dnaB
lexA
ruvC
recA
fadd21
dnaE2
fadd23
agenda
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Methods of Building GRN

• Bayesian networks (BN) graphical models with
  regulations denoted by conditional probabilities
  (Heckerman et al 1995)
• Dynamic BN (DBN) Transition network over time
  can model cyclic events (Friedman, N. et al 1998)
• Higher-order (HDBN) Extended transition network
  for longer delays
• (Zheng et al 2006)
• Skip-chain BN Can model very long delays of
  arbitary length using feature functions. (Galley,
  M. 2006)

ai are the parents of gene i
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Optimization Using GA
Each individual is an o-nary interaction matrix
where for no interaction
and for o-order interaction
Crossover involves swapping several rows between
two parents.
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GA Algorithm
Initialize N individuals with 0.7 similarity
using Mutual Information
Initialize
Rank all individuals using fitness function.
Selection
Elite individual E is sent to next generation.
Select two parents using roulette strategy for
mating.
Mating
E is optimal network
Swap last few rows of the selected parents to
generate two new children. Try another crossover
point if population similarity is lt 0.7
Crossover
Yes
Terminate
Invert a random cell to cause mutation
No
If dga lt 1 for 20 generations or number of
generations greater than Q
Mutate
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Skip-chain Model

• The likelihood of a gene expression xi is given
  by a weighted sum of linear and skip edge scores
  
• Linear-chain feature functions
  represent local dependencies of o-order.
• The skip-chain features
  represent long range
• dependencies in a GRN using a HMM

agenda
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Viterbi Forward Path

• The skip-edge score is given as a the normalized
  MAP interaction
• We can use maximum likelihood to estimate state
  transition and emission probabilities
• where denotes number of occurrences
  for
• The most probable path is given by MAP estimate
  using dynamic programming

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Priors for Networks

• Most higher-order Markov models are sensitive to
  change in pathways and associated data.
• Gibbs prior is used to model target network
  prior.
• Interaction potentials, denotes an
  interaction in target network and no
  interaction
• Here a small and large will reflect prior
  more and vice versa.
• We use adaption to reduce over-fitting due to
  sparse feature
• specific data.
• Adaption model can combine the reliable DBN with
  a volatile feature specific HMM for long delays.

where
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Dirichlet Prior over Parameters

• We extend the MLE to a Bayesian learning.
  Dirichlet is a conjugate prior for multinomial
  distribution.
• We can maximize probability as (MAP)
• Using the linear feature as a Dirichlet conjugate
  prior for the skip feature of a gene we get
• Lastly, the interpolated probability of gene
  based on linear and skip-edges is

where
where
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Experiments M. tuberculosis

• Here we looked at the response of bacteria to
  drug-induced stress. Treatment with Mitocyin C
  caused DNA damage and hence led to the
  upregulation of associated repair genes.
• Eight time points are available at NCBI Gene
  Expression Omnibus (GSE1642-GPL1396 series)
  0.33hr, 0.75hr,1.5hr, 2hr, 4hr, 6hr, 8hr and 12hr
  after DNA damage.
• Data was discretized into 0 for down and 1 for up
  regulation.
• The corresponding skip probabilities were
  calculated as described in methods . Upto seven
  time points of delays were allowed.
• Firstly, we used 9 genes previously specified. In
  order to get an expanded dataset, the original
  dataset was subjected to ICA and the components
  closest to 9 genes were identified. This gave us
  a second dataset of 32 genes.

agenda
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Time delays
Table 1. Predicted by DBN, HDBN, and skip-chain
without priors
Higher-order edges(hrs) Higher-order edges(hrs) Higher-order edges(hrs) Higher-order edges(hrs) Higher-order edges(hrs)
Genes Modelo ML 1(0.75) 2(1.5) 3(2) 4(4) 5(6)
9 DBN1 -14.7 9
9 HDBN3 -8.69 8 2 7
9 SKIP-CHAIN1/5 -6.05 13 (3)
32 DBN1 -48.9 36
32 HDBN4 -39.4 20 6 14 20
32 SKIP-CHAIN2/5 -37.2 54 18 (41) (4)
It can be seen that the ML of the underlying
skip-chain prediction is much higher than the DBN
or HDBN, confirming that the network fits data
well.
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Time delays Priors
Table 2. Predicted by skip-chain models with
priors Gibbs prior for structures and
Dirichlet prior for parameters
      Higher-order edges(hrs) Higher-order edges(hrs) Higher-order edges(hrs) Higher-order edges(hrs) Higher-order edges(hrs)
Genes Modelo ML 1(0.75) 2(1.5) 3(2) 4(4) 5(6)
9 SKIP-CHAIN1 -6.05 13   (3)    
9 SKIP-CHAIN(Gibbs)1 -5.8 11   (2)    
9 SKIP-CHAIN(Dirichlet)2 -5.2 7 13 (11) (1)  
9 SKIP-CHAIN(Gibbs and Dirichlet)3 -3.27 2 7 (4) (5)  
32 SKIP-CHAIN2 -37.2 54 18 (41) (4)  
32 SKIP-CHAIN(Gibbs)3 -35.2 37 16 24 (40) (3)
32 SKIP-CHAIN(Dirichlet)2 -35.05 54 16 (37) (4)  
32 SKIP-CHAIN(Gibbs and Dirichlet)2 -34.54 50 15 (41) (4)  
Using priors further increased likelihood and
gave many new time-delayed interactions. The
combined use of both Dirichlet and Gibbs priors
is optimal.
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Networks 9 genes
Fig 3 Time-delayed interactions in predicted
network of 9 genes (a) DBN network, (b) HDBN
network, (c) Skip-chain network, (d) Skip-chain
network with Gibbs prior, (e) Skip-chain network
with Dirichlet prior, (f) Skip-chain network with
Gibbs and Dirichlet prior
A small number of transcription factors (TF)
regulate the rest of the repair system. At the
same time the in-degree is low, as each gene is
regulated by just one TF.
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Networks 32 genes
Fig 4 Time-delayed interactions in predicted
network of 32 genes (a) DBN network, (b) HDBN
network, (c) Skip-chain network, (d) Skip-chain
network with Gibbs prior, (e) Skip-chain network
with Dirichlet prior, (f) Skip-chain network with
Gibbs and Dirichlet prior
The second dataset of 32 genes indicated that our
method is good for identifying core genes. Use of
priors gave better networks with fewer hubs.
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Conclusion

• An organism responds to changes in its
  environment by altering the level of expression
  of critical genes.
• Skip-chain models address the difficulties of a
  HDBN by easily incorporating long time-delayed
  regulations.
• Numerous time-delays are identified between the
  same pair of genes. The forward Viterbi path
  determines the best long-distant time delay
  between two genes.
• Using priors gave us higher likelihood and
  improved the over-fitting in building the
  regulatory networks.
• The work can be extended to skip-chain
  conditional random fields and fusion with protein
  interaction networks.

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Thank You
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