341: Introduction to Bioinformatics

1. 341: Introduction to Bioinformatics Dr. Nataša Pržulj Department of Computing Imperial College London natasha@imperial.ac.uk

2. Topics • Introduction to biology (cell, DNA, RNA, genes, proteins) • Sequencing and genomics (sequencing technology, sequence alignment algorithms) • Functional genomics and microarray analysis (array technology, statistics, clustering and classification) • Introduction to graph theory • Protein 3D structure • Introduction to biological networks • Network comparisons: network properties • Network/node centralities • Network motifs and graphlets • Network models • Network/node clustering • Network comparison/alignment • Software tools for network analysis • Interplay between topology and biology 2 2

3. Topics • Introduction to biology (cell, DNA, RNA, genes, proteins) • Sequencing and genomics (sequencing technology, sequence alignment algorithms) • Functional genomics and microarray analysis (array technology, statistics, clustering and classification) • Introduction to graph theory • Protein 3D structure • Introduction to biological networks • Network comparisons: network properties • Network/node centralities • Network motifs and graphlets • Network models • Network/node clustering • Network comparison/alignment • Software tools for network analysis • Interplay between topology and biology 3 3

4. Network properties: summary of last class Network Comparisons: • Large network comparison is computationally hard due to NP-completeness of the underlying subgraph isomorphism problem: • Given 2 graphs G and H as input, determine whether G contains a subgraph that is isomorphic to H. • Thus, network comparisons rely on easily computable heuristics (approximate solutions), called “network properties” • Network properties can roughly & historically be divided in two categories: • Global network properties: give an overall view of the network, but might not be detailed enough to capture complex topological characteristics of large networks. • Local network properties: more detailed network descriptors which usually encompass larger number of constraints, thus reducing “degrees of freedom” in which the networks being compared can vary. 4

5. Network properties: summary of last class 1. Global Network Properties • Readings: Chapter 3 of “Analysis of biological networks” by Junker and Schreiber. • Some Global Network Properties: • Degree distribution • Average clustering coefficient • Clustering spectrum • Average Diameter • Spectrum of shortest path lengths • Centralities

6. Network properties: summary of last class • 2. Local Network Properties • Readings: Chapter 5 of “Analysis of Biological Networks” by Junker and Schreiber. • Network motifs • Graphlets Two network comparison measures based on graphlets: • 2.1) Relative Graphlet Frequency Distance between two networks • 2.2) Graphlet Degree Distribution Agreement between two networks

7. 1) Network motifs (Uri Alon’s group, ’02-’04) http://www.weizmann.ac.il/mcb/UriAlon/ Also, see Pajek, MAVisto, and FANMOD

8. 2) Graphlets 2.1) Reltive graphlet frequency distance between two networks N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.

9. 2.1) Relative Graphlet Frequency (RGF) distance between networks G and H: N. Przulj, D. G. Corneil, and I. Jurisica, “Modeling Interactome: Scale Free or Geometric?,” Bioinformatics, vol. 20, num. 18, pg. 3508-3515, 2004.

10. 2) Graphlets 2.1) Graphlet degree distribution agreement between two networks N. Przulj, “Biological Network Comparison Using Graphlet Degree Distribution,” ECCB, Bioinformatics, vol. 23, pg. e177-e183, 2007.

11. 2) Graphlets 2.1) Graphlet degree distribution agreement between two networks Signature Similarity Measure between nodes u and v T. Milenkovic and N. Przulj, “Uncovering Biological Network Function via Graphlet Degree Signatures”, Cancer Informatics, vol. 4, pg. 257-273, 2008.

12. Use this and other techniques to link network structure • with biological function: • cluster nodes of a net. using their “signature similarity” • can use various clustering methods introduced in • previous lectures • obtained clusters are statistically significantly • enriched with: • a particular biological function, • membership in the same protein complexes, • The same sub-cellular localization, • tissue coexpression, • involvement in pathways, • Involvement in diseases... • predict function of uncharacterized prot’s in clusters

13. Software that implements many of these network properties and compares networks with respect to them: GraphCrunch http://bio-nets.doc.ic.ac.uk/graphcrunch/

14. Software that implements many of these network properties and compares networks with respect to them: GraphCrunch http://bio-nets.doc.ic.ac.uk/graphcrunch2/

15. Another Software: Cytoscape http://www.cytoscape.org/

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

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

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

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

20. Software that implements many of these network properties and compares networks with respect to them: GraphCrunch http://bio-nets.doc.ic.ac.uk/graphcrunch/

21. Software that implements many of these network properties and compares networks with respect to them: GraphCrunch http://bio-nets.doc.ic.ac.uk/graphcrunch2/

22. Topics • Introduction to biology (cell, DNA, RNA, genes, proteins) • Sequencing and genomics (sequencing technology, sequence alignment algorithms) • Functional genomics and microarray analysis (array technology, statistics, clustering and classification) • Introduction to graph theory • Protein 3D structure • Introduction to biological networks • Network comparisons: network properties • Network/node centralities • Network motifs and graphlets • Network models • Network/node clustering • Network comparison/alignment • Software tools for network analysis • Interplay between topology and biology 22 22

23. What is a network (graph) model?

24. Does the model network fit the data? • Use network properties: • Local • Global • Why? • “Hardness” of graph theoretic problems • E.g., NP-completeness of subgraph isomorphism • Cannot exactly compare/align networks • Use heuristics (approximate solutions) • Exact comparison inappropriate in biology • Due to biological variation • Noise revise models as data sets evolve

25. Why model networks? • Understand laws  reproduction/predictions • Network models have already been used in biological applications: • Network motifs (Shen-Orr et al., Nature Genetics 2002, Milo et al., Science 2002) • De-noising of PPI network data (Kuchaiev et al., PLoS Comp. Biology, 2009) • Guiding biological experiments (Lappe and Holm, Nature Biotechnology, 2004) • Development of computationally easy algorithms for PPI nets that are computationally intensive on graphs in general(Przulj et al., Bioinformatics, 2006)

26. Network models We will cover the following network models: • Erdos–Renyi random graphs • Generalized random graphs (with the same degree distribution as the data networks) • Small-world networks • Scale-free networks • Hierarchical model • Geometric random graphs • Stickiness index-based network model

27. Erdos–Renyi random graphs (ER) • Model a data network G(V,E) with |V|=n and |E|=m • An ER graph that models G is constructed as follows: • It has n nodes • Edges are added between pairs of nodes uniformly at random with the same probability p • Two (equivalent) methods for constructing ER graphs: • Gn,p: pick p so that the resulting model network has m edges • Gn,m: pick randomly m pairs of nodes and add edges between them with probability 1

29. Erdos–Renyi random graphs (ER) • Number of edges, |E|=m, in Gn,pis: • Average degree is:

30. Erdos–Renyi random graphs (ER) • Many properties of ER can be proven theoretically (See: Bollobas, "Random Graphs," 2002) • Example: • When m=n/2,suddenly the giant component emerges, i.e.: • One connected component of the network has O(n) nodes • The next largest connected component has O(log(n)) nodes

31. Erdos–Renyi random graphs (ER) • The degree distribution is binomial: • For large n, this can be approximated with Poisson distribution: where z is the average degree (compute it!) • However, currently available biological networkshave power-law degree distribution

32. Erdos–Renyi random graphs (ER) • Clustering coefficient, C, of ER is low (for low p) • C=p, since probability p of connecting any two nodes in an ER graph is the same, regardless of whether the nodes are neighbors • However, biological networkshave high clustering coefficients

33. Erdos–Renyi random graphs (ER) • Average diameter of ER graphs is small • It is equal to • Biological networks alsohave small average diameters • Summary

34. Generalized random graphs (ER-DD) • Preserve the degree distribution of data (“ER-DD”) • Constructed as follows: • An ER-DD network has n nodes (so does the data) • Edges are added between pairs of nodes using the “stubs method”

35. Generalized random graphs (ER-DD) • The “stubs method” for constructing ER-DD graphs: • The number of “stubs” (to be filled by edges) is assigned to each node in the model network according to the degree distribution of the real network to be modeled • Edges are created between pairs of nodes with “available” stubs picked at random • After an edge is created, the number of stubs left available at the corresponding “end nodes” of the edges is decreased by one • Multiple edges between the same pair of nodes are not allowed

36. Generalized random graphs (ER-DD) • Summary • 2 global network properties are matched by ER-DD • How about local network properties (graphlet frequencies)? • Low-density (sparse) graphlets are frequent in ER and ER-DD • However, data networks have lots of dense graphlets, since data networks have high clustering coefficients

37. Small-world networks (SW) • Watts and Strogatz, 1998 • Created from regular ring lattices by random rewiring of a small percentage of their edges • E.g.

38. Small-world networks (SW) • SW networks have: • High clustering coefficients – introduced by “ring regularity” • Large average diameters of regular lattices – made small by randomly re-wiring a small percentage of edges • Summary

39. Scale-free networks (SF) • Power-law degree distributions: P(k) = k−γ • γ > 0; 2 < γ < 3

40. Scale-free networks (SF) • Power-law degree distributions: P(k) = k−γ • γ > 0; 2 < γ < 3

41. Scale-free networks (SF) • Different models exist, e.g.: • Preferential Attachment Model (SF-BA) (Barabasi-Albert, 1999) • Gene Duplication and Mutation Model (SF-GD) (Vazquez et al., 2003)

42. Scale-free networks (SF) • Preferential Attachment Model (SF-BA) • “Growth” model: nodes are added to an existing network • New nodes preferentially attach to existing nodes with probability proportional to the degrees of the existing nodes; e.g.: • This is repeated until the size of SF network matches the size of the data • “Rich getting richer” • The starting network strongly influences the properties of the resulting network (F. Hormozdiari, et al., PLoS Computational Biology, 3(7):e118, July 2007. ) • SF-BA: particularly effective at describing Internet

43. Scale-free networks (SF) • Gene Duplication and Mutation Model (SF-GD) • Biologically motivated • Attempts to mimic gene duplication and mutation processes

44. Scale-free networks (SF) • Gene Duplication and Mutation Model (SF-GD) • At each time step, a node is added to the network as follows:

45. Scale-free networks (SF) • Summary

46. Hierarchical model • Preserves network “modularity” via a fractal-like generation of the network

47. Hierarchical model • These graphs do not match any biological data and are highly unlikely to be found in data sets

48. Geometric random graphs • “Uniform” geometric random graphs (GEO) N. Przulj lab, 2004-2010 • Geometric gene duplication and mutation model (GEO-GD) N. Przulj et al., PSB 2010

49. Geometric random graphs • “Uniform” geometric random graphs (GEO) • Take any metric space and, using a uniform random distribution, place nodes within the space • If any nodes are within radius r (calculated via any chosen distance norm for the space), they will be connected • Choose r so that the size of the GEO network matches that of the data • There are many possible metric spaces (e.g., Euclidean space) • There are many possible distance norms (e.g. the Euclidean distance, the Chessboard distance, and the Manhattan/Taxi Driver distance)