1. Network applications Sushmita Roy BMI/CS 576 www.biostat.wisc.edu/bmi576 sroy@biostat.wisc.edu Dec 9 th, 2014

2. RECAP from last time We talked about modularity, degree distribution, and path-based measures to study properties of graphs Today we will touch briefly on the many different applications of networks.

3. Applications of Networks Differential subgraph identification – Given gene expression studies from disease and normal studies – Identify pathways that are most differentially altered between these conditions Module detection – Dense subgraph identification Interpretation of gene sets Identification of novel pathways – Set cover based methods Network information flow – Sparse subgraph identification Integration of different data sets Interpretation of gene sets Prioritization of genes Adapted from Network biology approaches to Complex Diseases.

4. Identifying differential networks Given – Gene expression data from two conditions: treatment and control Do – Find the subnetworks are significantly different between conditions

5. Motivating example Metastases is a major cause of death among breast cancer patients Gene expression levels of marker genes can be used to predict metastasis state, but are 60-70% accurate Because cancer is a complex disease, involving multiple genes, incorporating interactions among them might improve predictive power

6. Tasks for identifying differential networks Define a measure of activity for a subnetwork – Sum of activity of individual genes Define a measure of differential activity between two conditions – Chuang et al, used an information theoretic measure to information between the class variable and the discretized expression of a subgraph

7. Identifying differential subgraphs in cancer Chuang et al, 2007 Subnetworks were obtained using a greedy process

8. Improved predictive power using subnetworks as classification features AUC

9. Identification of modules dysregulated in diseases Cho D-Y, Kim Y-A, Przytycka TM (2012) Chapter 5: Network Biology Approach to Complex Diseases. PLoS Comput Biol 8(12): e1002820. doi:10.1371/journal.pcbi.1002820 http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002820

10. Problem definition of identifying dysregulated modules Given – A network of possibly weighted gene interactions and a set of genetic alterations Do – Find a subgraph that best connects these genetic alterations Best can mean – A dense subgraph with large number of connections among the vertices (genes) – A sparse subgraph with few intermediate nodes

11. Some approaches for finding dense subgraphs HOTNET: A set cover approach – Best: use fewest possible external nodes NETBAG: Network Based Analysis of Genetic Associations

12. Set cover approach A gene is said to be covered by a disease if it is dysregulated in the disease sample Main idea: Each disease has a set of dysregulated genes Different cases have different covered gene sets Identify the smallest set that covers as many disease samples as possible

13. HOTNET optimizes two criteria Genes in a perturbed pathway must be – close to each other – Must have a few alternate paths between them

14. HOTNET heuristic Mutations in a linear chain are more “interesting” than in a star graph

15. Steps in HOTNET Obtain an influence score of vertex i on vertex j Weight each edge by the influence score Remove all edges with weight less than a threshold δ Find the subgraph of size k that covers as many samples as possible

16. Computing the influence between vertex pairs Assume we have two vertices u and v Influence can be defined based on how fast a signal at u reaches v Diffusion of this signal is governed by the connectivity of the graph based on what is called the Graph Laplacian

17. HOTNET algorithm Exploration Keep adding a neighbor that has the maximal coverage with fewest additional vertices

18. HOTNET recovers pathways relevant to cancer

19. Summary Given an existing interaction network, many network applications are based on overlaying information on these networks We talked about two applications – Identifying differential networks – Identifying a subnetwork that best explains a set of mutations in patient samples