1. 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
Hello and welcome. I will talk about my thesis work today, which is about comparative analysis of molecular interaction networks.

2. 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 other’s expression
Any step of gene expression can be modulated
Transcription, translation, post-transcriptional modification, RNA transport, mRNA degradation…
I will start with a brief overview of molecular interaction networks. I will talk about where the data comes from, how it is modeled, and present some biological observations that motivate comparative network analysis. Then, I will talk about how we address various algorithmic and analytical problems on interaction networks. Finally, I will briefly discuss problems I am currently working on and what I am planning explore in the near future.
Ligand independent transcriptional
regulation at chromatin level

3. 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)
Gene
Up-regulation
Down-regulation
Flowering time in Arabidopsis

4. 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 gene’s product localized?
Gene Ontology provides a library of molecular annotation
We refer to each annotation class as a functional attribute

5. 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)

6. INDIRECT REGULATION
Assessment of pairwise interactions is simple, but not adequate g1 g3 g5 g1 g3 g5 g2 g4 g4 g2 g4 g4

7. 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 g1 g2 g3 g4 g5 g6
Gene network
Functional attribute network

8. 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

9. 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

10. STATISTICAL INTERPRETABILITY
Additional positive observation => increased significance
Additional negative observation => decreased significance B B’ A A
P(B) < P(A)
P(B’) > P(A)
Frequency is not statistically interpretable!

11. 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

12. GO HIERARCHY P( ) < P( ) < P( )
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( ) < g1 g5 g3
P( ) < g2 g4
P( )

13. PATHWAY LENGTH P( ) > P( ) P( ) < 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?

14. STATISTICAL MODEL π123: 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 π123:
p123 = P (N123 ≥ n123|N12=n12, N23=n23, N1=n1, N2=n2, N3=n3)
π123: N1 N2 N3
N12
N23
N123

15. SIGNIFICANCE OF A PATHWAY
Assume that regulatory interactions are independent
There are n12 n23 occurrences of π 12 and π 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

16. 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

17. 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

18. NARADA http://www.cs.purdue.edu/homes/jpandey/narada/
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

19. 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
208
183
142
Common terms shortcut
184
119 1

20. MOLYBDATE ION TRANSPORT
Significant regulatory pathways
that originate at
molybdate ion transport
Their occurrences
in the gene network

21. 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!

22. 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?