CSCI2950-C Lecture 12 Networks Ben Raphael November 18, 2008 http://cs.brown.edu/courses/csci2950-c/

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

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

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

Regulatory Networks

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

Signaling Networks

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

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

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

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

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

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

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

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

Alignment Analogy Sharan and Ideker. Modeling cellular machinery through biological network comparison. Nature Biotechnology 24, pp. 427-433, 2006

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

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

Network Alignment Sharan and Ideker. Modeling cellular machinery through biological network comparison. Nature Biotechnology 24, pp. 427-433, 2006

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)

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)

Why paths?

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

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)

PathBLAST

PathBLAST Scoring

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

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.

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

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