Using Bayesian Networks to Analyze Expression Data

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Using Bayesian Networks to Analyze Expression Data

• N. Friedman M. Linial I. Nachman D. Peer
• Hebrew University, Jerusalem

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Central Dogma
Translation
Protein
Cells express different subset of the genes In
different tissues and under different conditions
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Gene Regulation

• Regulation of expression of genes is crucial
• Regulation occurs at many stages
• pre-transcriptional (chromatin structure)
• transcription initiation
• RNA editing (splicing) and transport
• Translation initiation
• Post-translation modification
• RNA Protein degradation
• Understanding regulatory processes is a central
  problem of biological research

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Microarrays (aka DNA chips)

• New technological breakthrough
• Measure RNA expression levels of thousands of
  genes in one experiment
• Measure expression on a genomic scale
• Opens up new experimental designs
• Many major labs are using,or will use this
  technology in the near future

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The Problem
Genes
j
Experiments
i

• Goal
• Learn regulatory/metabolic networks
• Identify causal sources of the biological
  phenomena of interest

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Analysis Approaches

• Clustering of expression data
• Groups together genes with similar expression
  patterns
• Does not reveal structural relations
  between genes
• Boolean networks
• Deterministic models of the logical interactions
  between genes
• Deterministic, impractical for real data

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Example Cell-Cycle Data Spellman et al
Cell cycle stages
clusters
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Our Approach

• Characterize statistical relationships between
  expression patterns of different genes
• Beyond pair-wise interactions
• Many interactions are explained by intermediate
  factors
• Regulation involves combined effects of several
  gene-products

• We build on the language of Bayesian networks

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Network Example

• Noisy stochastic process
• Example Pedigree
• A node represents an individualsgenotype

• Modeling assumptions
• Ancestors can effect descendants' genotype only
  by passing genetic materials through intermediate
  generations

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Network Structure
Ancestor

• Generalizing to DAGs
• A child is conditionally independent from its
  non-descendents, given the value of its parents
• Often a natural assumption for causal processes
• if we believe that we capture the relevant state
  of each intermediate stage.

Parent
Non-descendent
Non-descendent
Descendent
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Local Probabilities

• Associated with each variable Xi is a conditional
  probability distribution P(XiPai?)
• Discrete variables Multinomial distribution
• Continuous variables Choice for example
  linear Gaussian

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Bayesian Network Semantics
Qualitative part DAG specifies
conditional independence statements
Quantitative part local probability models
Unique joint distribution over domain

• Compact efficient representation
• ? k parents ?? O(2kn) vs. O(2n) params
• parameters pertain to local interactions

P(C,A,R,E,B) P(B)P(EB)P(RE,B)P(AR,B,E)P(C
A,R,B,E)
versus P(C,A,R,E,B) P(B)P(E)
P(RE) P(AB,E) P(CA)
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Why Bayesian Networks?

• Bayesian Networks
• Flexible representation of dependency structure
  of multivariate distributions
• Natural for modeling processes with local
  interactions
• Learning of Bayesian Networks
• Can learn dependencies from observations
• Handles stochastic processes
• true stochastic behavior
• noise in measurements

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Modeling Biological Regulation

• Variables of interest
• Expression levels of genes
• Concentration levels of proteins
• Exogenous variables Nutrient levels, Metabolite
  Levels, Temperature,
• Phenotype information
• Bayesian Network Structure
• Capture dependencies among these variables

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Examples

• Interactions are represented by a graph
• Each gene is represented by a node in the graph
• Edges between the nodes represent direct
  dependency

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More Complex Examples

• Dependencies can be mediated through other nodes
• Common effects can imply conditional dependence

B
A
C
B
A
C
Common cause
Intermediate gene
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Outline of Our Approach
Bayesian Network Learning Algorithm
Expression data
Use learned network to make predictions about
structure of the interactions between genes
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Learning With Many Variables
Sparse Candidate algorithm - efficient heuristic
search that relies on sparseness

• Choose candidate set for direct influence for
  each gene
• Find optimal BN constrained on candidates
• Iteratively improve candidate set

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Experiment

• Data from Spellman et al. (Mol.Bio. of the Cell
  1998).
• Contains 76 samples of all the yeast genome
• Different methods for synchronizing cell-cycle in
  yeast.
• Time series at few minutes (5-20min) intervals.
• Spellman et al. identified 800 cell-cycle
  regulated genes.

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Methods

• Experiment 1 discretized data into 3 levels
• Learn multinomial probabilities
• Experiment 2
• Learn linear interactions (w/ Gaussian noise)
• No prior biological knowledge was used

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Network Learned
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Challenge Statistical Significance

• Sparse Data
• Small number of samples
• Flat posterior -- many networks fit the data
• Solution
• estimate confidence in network features
• Two types of features
• Markov neighbors X directly interacts with Y
• Order relations X is an ancestor of Y

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Confidence Estimates
D1
Bootstrap approachFGW, UAI99
Learn
resample
D2
E
B
D
Learn
resample
R
A
C
...
resample
E
B
Dm
Learn
R
A
C
Estimate
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Testing for Significance

• We run our procedure on randomized data where we
  reshuffled the order of values for each gene
• Histograms of number of Markov features at each
  confidence level

Randomized Data
Original Data
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Testing for Significance

• We run our procedure on randomized data where we
  reshuffled the order of values for each gene

Markov w/ Gaussian Models
4000
3500
3000
2500
2000
Features with Confidence above t
1500
1000
500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t
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Testing for Significance
Markov w/ Multinomial Models
1400
1200
1000
800
Features with Confidence above t
600
400
200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t
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Local Map
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Finding Key Genes

• Key gene a gene that preceeds many other genes
• YLR183C
• MCD1 Mitotic Chromosome Determinant
• RAD27 DNA repair protein
• CLN2 role in cell cycle START
• SRO4 involved in cellular polarization during
  budding
• YOX1 Homeodomain protein that binds leu-tRNA gene
• POL30 required for DNA replication and repair
• YLR467W
• CDC5
• MSH6 Homolog of the human GTBP protein
• YML119W
• CLN1 role in cell cycle START

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Strong Markov Relations
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Future Work

• Finding suitable local distribution models
• Temporal aspect - DBN
• Correct handling of hidden variables
• Can we recognize hidden causes of coordinated
  regulation events?
• Incorporating prior knowledge
• Incorporate large mass of biological knowledge,
  and insight from sequence/structure databases
• Abstraction
• Combine with cluster analysis

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Future Work -- Causality

• Greatest promise -- dealing with causality
• Biological techniques allow to experiment with
  interventions
• These clearly provide better handle on causal
  interactions
• Goal Learning from observations interventions
• How to learn causality from knockout experiments?
  
• How to plan such experiments?

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Sensitivity Analysis Genes in Analysis

• To find sensitivity to removal of genes, we run
  our procedure on a subset of 250 genes

Markov
Order
800 Gene dataset
250 Gene dataset