1. Algorithms for Biological Networks Prof. Tijana Milenković Computer Science and Engineering University of Notre Dame tmilenko@nd.edu Fall 2010

2. Topics Introduction: biology Introduction: graph theory Network properties –Network/node centralities –Network motifs Network models Network/node clustering Network comparison/alignment Software tools for network analysis Interplay between topology and biology

5. Network Properties 1.Global Network Properties ( Chapter 3 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber) They give an overall view of a network: 1)Degree distribution 2)Clustering coefficient and spectrum 3)Average diameter

6. 1) Degree Distribution G

7. Research debates… Degree correlation: –Pearson corr. coefficient between degrees of adjacent vertices –Average neighbor degree; then average over all nodes of degree k Structural robustness and attack tolerance: –“Robust, yet fragile” Scale-free degree distribution: –Party vs. date hubs J.D. Han et al., Nature, 430:88-93, 2004 –Bias in the data construction (sampling)? M. Stumpf et al., PNAS, 102:4221-4224, 2005 J. Han et al., Nature Biotechnology, 23:839-844, 2005 High degree nodes: –Essential genes H. Jeong at al., Nature 411, 2001. –Disease/cancer genes Jonsson and Bates, Bioinformatics, 22(18), 2006 Goh et al., PNAS, 104(21), 2007

8. C v – Clustering coefficient of node v C A = 1/1 = 1 C B = 1/3 = 0.33 C C = 0 C D = 2/10 = 0.2 … C = Avg. clust. coefficient of the whole network = avg {C v over all nodes v of G} C(k) – Avg. clust. coefficient of all nodes of degree k E.g.: C(2) = (C A + C C )/2 = (1+0)/2 = 0.5 => Clustering spectrum E.g. (not for G ) 2) Clustering Coefficient and Spectrum G Need to evaluate whether the value of C (or any other property) is statistically significant.

9. 3) Average Diameter G u v E.g. (not for G) Distance between a pair of nodes u and v: D u, v = min {length of all paths between u and v} = min {3,4,3,2} = 2 = dist(u,v) Average diameter of the whole network: D = avg {D u,v for all pairs of nodes {u,v} in G} Spectrum of the shortest path lengths

10. Network Properties Global network properties might not be detailed enough to capture complex topological characteristics of large networks

11. Network Properties 2. Local Network Properties ( Chapter 5 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber) They encompass larger number of constraints, thus reducing degrees of freedom in which networks being compared can vary How do we show that two networks are different? How do we show that they are the same? How do we quantify the level of their similarity?

12. Network Properties 2. Local Network Properties ( Chapter 5 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber) 1)Network motifs 2)Graphlets: 2.1) Relative Graphlet Frequency Distance between 2 networks 2.2) Graphlet Degree Distribution Agreement between 2 networks

13. Small subgraphs that are overrepresented in a network when compared to randomized networks Network motifs: –Reflect the underlying evolutionary processes that generated the network –Carry functional information –Define superfamilies of networks  - Z i is statistical significance of subgraph i, SP i is a vector of numbers in 0-1 But: –Functionally important but not statistically significant patterns could be missed –The choice of the appropriate null model is crucial, especially across “families” 1) Network motifs (Uri Alon’s group, ’02-’04)

14. Small subgraphs that are overrepresented in a network when compared to randomized networks Network motifs: –Reflect the underlying evolutionary processes that generated the network –Carry functional information –Define superfamilies of networks  - Z i is statistical significance of subgraph i, SP i is a vector of numbers in 0-1 But: –Functionally important but not statistically significant patterns could be missed –The choice of the appropriate null model is crucial, especially across “families” –Random graphs with the same in- and out- degree distribution as data might not be the best network null model 1) Network motifs (Uri Alon’s group, ’02-’04)

15. http://www.weizmann.ac.il/mcb/UriAlon/ Also, see Pajek, MAVisto, and FANMOD

16. N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004. _____ Different from network motifs:  Induced subgraphs  Of any frequency 2) Graphlets (Przulj group, ’04-’10)

17. N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.

18. N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.

19. N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004. 2.1) Relative Graphlet Frequency (RGF) distance between networks G and H:

20. Generalize node degree 2.2) Graphlet Degree Distributions

21. N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” ECCB, Bioinformatics, vol. 23, pg. e177-e183, 2007.

23. T. Milenkovic and N. Przulj, “Uncovering Biological Network Function via Graphlet Degree Signatures”, Cancer Informatics, vol. 4, pg. 257-273, 2008. Network structure vs. biological function & disease Graphlet Degree (GD) vectors, or “node signatures”

24. Similarity measure between “node signature” vectors T. Milenkovic and N. Przulj, “Uncovering Biological Network Function via Graphlet Degree Signatures”, Cancer Informatics, vol. 4, pg. 257-273, 2008.

25. Signature Similarity Measure between nodes u and v

26. T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).

27. 40% SMD1 PMA1 YBR095C T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible).

29. 90%* SMD1 SMB1 RPO26 T. Milenković and N. Pržulj, “Uncovering Biological Network Function via Graphlet Degree Signatures,” Cancer Informatics, 2008:6 257-273, 2008 (Highly Visible). *Statistically significant threshold at ~85%

30. Later we will see how to use this and other techniques to link network structure with biological function

31. N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007. Generalize Degree Distribution of a network The degree distribution measures: the number of nodes “touching” k edges for each value of k

32. N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” Bioinformatics, vol. 23, pg. e177-e183, 2007.

34. / sqrt(2) (  to make it between 0 and 1) This is called Graphlet Degree Distribution (GDD) Agreement between networks G and H.

35. Software that implements many of these network properties and compares networks with respect to them: GraphCrunch http://www.ics.uci.edu/~bio-nets/graphcrunch/

36. Network properties 3. Network/node centralities ( Chapter 4 of the course textbook “Analysis of Biological Networks” by Junker and Schreiber) Rank nodes according to their “topological importance”

37. 3) Network/node centralities 123456 7 8 9 10 If nodes are housing communities, where to build a hospital?

38. 3) Network/node centralities 123456 If nodes are housing communities, where to build a hospital?

39. Network properties 3. Network/node centralities Different centrality measures exist Centrality values comparable inside a given network only Centrality values of two centrality measures incomparable even within the same network Some centrality measures can be applied to connected networks only

40. 3) Network/node centralities Degree centrality Closeness centrality Eccentricity centrality Betweenness centrality Other centrality measures exist, e.g.: –Eigenvector centrality –Subgraph centrality –… Software tools: Visone (social nets) and CentiBiN (biological nets)

41. 3) Network/node centralities Degree centrality: –Nodes with high degrees have high centrality C d (v)=deg(v) Closeness centrality: –Nodes with short paths to all other nodes have high centrality

42. 3) Network/node centralities Essentricity centrality: –Nodes with short paths to any other node have high centrality Betweenness centrality: –Nodes (or edges) that occur in many of the shortest paths have high centrality

43. Topics Introduction: biology Introduction: graph theory Network properties –Network/node centralities –Network motifs Network models Network/node clustering Network comparison/alignment Software tools for network analysis Interplay between topology and biology