FUNCTIONAL ANNOTATION OF REGULATORY PATHWAYS

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FUNCTIONAL ANNOTATION OF REGULATORY PATHWAYS

• Jayesh Pandey, Mehmet Koyuturk, Wojciech
  Szpankowski, and Ananth Grama.
• PURDUE UNIVERSITY
• DEPARTMENT OF COMPUTER SCIENCE
• Supported by the National Institutes of Health

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GENE REGULATION

• Gene expression is the process of synthesizing a
  functional protein coded by the corresponding
  gene
• Genes (and their products) regulate the extent of
  each others expression
• Any step of gene expression can be modulated
• Transcription, translation, post-transcriptional
  modification, RNA transport, mRNA degradation

Ligand independent transcriptional regulation at
chromatin level
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GENE REGULATORY NETWORKS

• Model the organization of regulatory interactions
  in the cell
• Genes are nodes, regulatory interactions are
  directed edges
• Boolean network model Edges are signed,
  indicating up- (promotion) and down-regulation
  (supression)

Flowering time in Arabidopsis
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MOLECULAR ANNOTATION

• Similar systems involving different molecules
  (genes, proteins) in different species
• Functional annotation of genes provides an
  unified understanding of the underlying
  principles
• Molecular function What is the role of a gene?
• Biological process In which processes is a gene
  involved?
• Cellular component Where is a genes product
  localized?
• Gene Ontology provides a library of molecular
  annotation
• We refer to each annotation class as a functional
  attribute

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FROM MOLECULES TO SYSTEMS

• Networks are species-specific
• Annotation is at the molecular level
• Map networks from gene space to function space
• Can generate a library of annotated modular
  (sub-) networks

Network of Gene Ontology terms based on
significance of pairwise interactions in yeast
synthetic gene array (SGA) network (Tong et al.,
Science, 2004)
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INDIRECT REGULATION

• Assessment of pairwise interactions is simple,
  but not adequate

g1
g3
g5
g1
g3
g5
g2
g4
g4
g2
g4
g4
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FUNCTIONAL ATTRIBUTE NETWORKS

• Multigraph model
• A gene is associated with multiple functional
  attributes
• A functional attribute is associated with
  multiple genes
• Functional attributes are represented by nodes
• Genes are represented by ports, reflecting
  context

Functional attribute network
Gene network
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FREQUENCY OF A MULTIPATH

• A pathway of functional attributes occurs in
  various contexts in the gene network
• Multipath in the functional attribute network

Frequency of multipath is 4 on the left, it is 0
on the right
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SIGNIFICANCE OF A PATHWAY

• We want to identify multipaths with unusual
  frequency
• These might correspond to modular pathways
• Frequency alone is not a good measure of
  statistical significance
• The distribution of functional attributes among
  genes is highly skewed
• The degree distribution in the gene network is
  highly skewed
• Pathways that contain common functional
  attributes have high frequency, but they are not
  necessarily interesting

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STATISTICAL INTERPRETABILITY

• Additional positive observation gt increased
  significance
• Additional negative observation gt decreased
  significance

B
B
A
A
P(B) lt P(A)
P(B) gt P(A)
Frequency is not statistically interpretable!
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MONOTONICITY

• Frequency is a monotonic measure
• If a pathway is frequent, then all of its
  sub-paths are frequent
• Algorithmic advantage enumerate all frequent
  patterns in a bottom-up fashion
• Commonly exploited in traditional data mining
  applications
• Statistically interpretable measures are not
  monotonic!
• Statistical significance fluctuates in the search
  space
• Existing data mining algorithms do not apply
• Significance of pathways are non-monotonic in two
  dimensions

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GO HIERARCHY

• Functional attributes are organized in a
  hierarchical manner
• regulation of steroid biosynthetic process is a
  regulation of steroid metabolic process and is
  part of steroid biosynthetic process
• Interpretable statistical measures are not
  monotonic with respect to GO hierarchy

P( ) lt
g1
g5
g3
P( ) lt
g2
g4
P( )
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PATHWAY LENGTH
P( ) gt P( )
P( ) lt P( )

• Open problems
• How can we effectively search in the pathway
  space, where significance fluctuates?
• How can we find optimal resolution in functional
  attribute space?

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STATISTICAL MODEL

• Emphasize modularity of pathways
• Condition on frequency of building blocks!
• We denote each frequency random variable by N,
  their realization by n
• Significance of pathway p123
• p123 P (N123 n123N12n12, N23n23, N1n1,
  N2n2, N3n3)

p123
N1
N2
N3
N12
N23
N123
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SIGNIFICANCE OF A PATHWAY

• Assume that regulatory interactions are
  independent
• There are n12 n23 occurrences of p 12 and p 23
• The probability that these go through the same
  gene is 1/n2
• The probability that at least n123 of the n12n23
  pairs of edges go through the same gene can be
  bounded by
• p123 exp(n12n23Hq(t)) where q 1/n2 and t
  n123 / n12n23
• Hq(t) t log(q/t) (1-t) log((1-q)/(1-t)) is the
  weighted entropy of t with respect to q
• Can be generalized to pathways of arbitrary length

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SIGNIFICANCE OF AN EDGE

• A single regulatory interaction is the shortest
  pathway
• Statistical significance is evaluated with
  respect to baseline model
• The number of edges leaving and entering each
  functional attribute is specified
• Edges are assumed to be independent
• The frequency of a regulatory interaction is a
  hypergeometric random variable
• Can derive a similar bound for the p-value of a
  single regulatory interaction

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ALGORITHMIC ISSUES

• Significance is not monotonic
• Need to enumerate all pathways?
• Strongly significant pathways
• A pathway is strongly significant if all its
  building blocks are significant (defined
  recursively)
• Allows pruning out the search space effectively
• Shortcutting common functional attributes
• Transcription factors, DNA binding genes, etc.
  are responsible for mediating regulation
• Shortcut these terms, consider regulatory effect
  of different processes on each other directly

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NARADAhttp//www.cs.purdue.edu/homes/jpandey/nara
da/

• A software for identification of significant
  pathways
• Queries
• Given functional attribute T, find all
  significant pathways that originate at T
• Given functional attribute T, find all
  significant pathways that terminate at T
• Given a sequence of functional attributes T1, T2,
  , Tk, find all occurrences of the corresponding
  pathway
• Identified pathways are displayed as a tree
• User can explore back and forth between the gene
  network and the functional attribute network

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RESULTS

• E. coli transcription network obtained from
  RegulonDB
• 3159 regulatory interactions between 1364 genes
• Using Gene Ontology, 881 of these genes are
  mapped to 318 processes

Pathway length 2 3 4 5
All 427 580 1401 942
Strongly significant 427 208 183 142
Common terms shortcut 184 119 3 1
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MOLYBDATE ION TRANSPORT
Significant regulatory pathways that originate at
molybdate ion transport
Their occurrences in the gene network
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WHAT IS SIGNIFICANT?

• Molybdate ion transport regulates various
  processes directly
• Mo-molybdopterin cofactor biosynthesis,
  oligopeptide transport, cytochrome complex
  assembly
• It regulates various other processes indirectly
• Through DNA-dependent regulation of
  transcription, two-component signal transduction
  system, nitrate assimilation
• Direct regulation of these mediator processes is
  not significant
• NARADA captures modularity of indirect
  regulation!

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CONCLUSION

• Mapping gene regulatory networks to functional
  attribute space demonstrates great potential
• Abstract, unified understanding of regulatory
  systems
• Algorithmically, a wide range of new challenges
• How can we bound interpretable statistical
  measures?
• How can we handle hierarchy in functional
  attribute space?
• Discovering new information
• How can we project identified canonical
  patterns on other species to discover new
  regulatory relationships?