1. CSCI2950-C Lecture 12 Networks
Ben Raphael
November 18, 2008

2. Biological Interaction Networks
Many types:
Protein-DNA (regulatory)
Protein-metabolite (metabolic)
Protein-protein (signaling)
RNA-RNA (regulatory)
Genetic interactions (gene knockouts)

3. Outline Biology of cellular interaction networks Network Alignment
Network Motifs
Network Integration

4. Metabolic Networks Nodes = reactants Edges = reactions
labeled by enzyme (protein) that catalyzes reaction

5. Regulatory Networks

6. Regulatory Networks Protein-DNA interaction network Nodes = genes
Edges = regulatory interaction
A “activates” B A B
A “represses” C C
Protein-DNA interaction
network

7. Signaling Networks

8. Protein Interaction Networks
Proteins rarely function in isolation, protein interactions affect all processes in a cell.
Forms of protein-protein interactions:
Modification, complexation [Cardelli, 2005].
phosphorylation
A brief introduction for protein interactions.
Proteins in a cell interact with eachother in the forms of activation, binding and inhibition. And their interactions affect all processes in a cell.
With the emergence of high-throughput methods,
protein complex

9. Protein Interaction Networks
High-throughput methods are available to find all interactions, “PPI network”, of a species.
an undirected graph
nodes: protein, edges: interactions
Edges may have weights
Yeast DIP network: ~5K proteins, ~18K interactions
Fly DIP network: ~7K proteins, ~20K interactions
A brief introduction for protein interactions.
The interactions between proteins are important for many biological processes. They may activate/inhibit eachother by modification or they may bind to eachother to make a protein complex.
High throughput methods have been available to find all interactions in the cell. This resulting interactome is represented by a
Network. A protein protein interaction network is an undirected graph where the nodes are proteins and the edges are the interactions.
PPI network

10. How are protein-protein interaction networks derived?
Yeast two-hybrid screens

11. How are protein-protein interaction networks derived?
Protein purification and separation

12. Computational Problems
Classifying Network Topology
Finding paths, cliques, dense subnetworks, etc.
Comparing Networks Across Species
Using networks to explain data
Dependencies revealed by network topology
Modeling dynamics of networks

13. Alignment Sequences Networks
mouse
human
Sequences
Evolve via substitutions
Conservation implies function
EFTPPVQAAYQKVVAG
DFNPNVQAAFQKVVAG
Networks
Evolve via gain/loss of proteins or interactions (?)

14. Motivation
By similar intuition, subnetworks conserved across species are likely functional modules

15. Network Alignment
“Conserved” means two subgraphs contain proteins serving similar functions, having similar interaction profiles
Key word is similar, not identical
mismatch/substitution

16. Alignment Analogy
Sharan and Ideker. Modeling cellular machinery through biological network comparison. Nature Biotechnology 24, pp , 2006

17. Earlier approaches: interologs
Interactions conserved in orthologs
Orthology (descended from common ancestor) is a fuzzy notion
Sequence similarity not necessary for conservation of function

18. Complications Protein sequence similarity not 1-1 Interaction data:
Orthologs
Paralogs
Interaction data:
Noisy
Incomplete
Dynamic
Computational tractability

19. Network Alignment
Sharan and Ideker. Modeling cellular machinery through biological network comparison. Nature Biotechnology 24, pp , 2006

20. The Network Alignment Problem
Given: k different interaction networks belonging to different species,
Find: Conserved sub-networks within these networks
Conserved defined by protein sequence similarity (node similarity) and interaction similarity (network topology similarity)

21. PathBLAST Goal: identify conserved pathways (chains)
Idea: can be done efficiently by dynamic programming if networks are DAGs A A’
Score: match B
+ gap C X’
+ mismatch D D’
+ match
Kelley et al (2003)

22. Why paths?

23. PathBLAST (Kelley, et al. PNAS 2003)
Find conserved pathways in protein interaction maps of two species
Model & Scoring: See class notes.

24. PathBLAST Problem: Networks are neither acyclic nor directed
Solution: Randomize
Impose random ordering on nodes, perform DP; repeat many times
On average, highest scoring path preserved in 2/L! subgraphs
Finds conserved paths of length L within networks of size n in O(L!n) expected time
Drawbacks
Computationally expensive
Restricts search to specific topology 5 2 1 3 4 2 1 4 5 3 1 4 2 3 5
Kelley et al (2003)

25. PathBLAST

26. PathBLAST Scoring

27. PathBLAST: Computational Formulation
Given:
Undirected weighted graph G = (V, E, w)
Set of start vertices I, and end vertex v,
Find: a minimum-weight simple path starting in I and ending at v.
NP-hard in general (reduction from TSP)
Dynamic Programming formulation (see class notes)
Scott, et al. JCB 2006

28. Color-coding (Alon, Yuster, & Zwick)
Assign each vertex random color between 1 and k.
Search for path w/ distinct colors. (colorful path)
Resulting paths are simple.
High-scoring path not discovered when two vertices have same color.
Repeat for many random colorings.

29. Color-coding (Alon, Yuster, & Zwick)
Extends to many other cases of subgraph isomorphism problem:
Does a graph G have a subgraph isomorphic to graph H?
H = simple path of length k.
H = simple cycle of length k.
H = tree.
H = graph of fixed (bounded) tree-width

30. Additional Problems Efficient querying of a network (e.g. QNET)
Find conserved subgraphs
Heavy subgraphs in product graph
Multiple network alignment