Bioinformatics I Overview CPBS 7711 October 29, 2014 Protein interaction networks Debra Goldberg debra@colorado.edu Networks, protein interaction networks (PINs) Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words Overview Networks, protein interaction networks (PINs) Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words Introduction to Networks What is a network? Social networks A collection of objects (nodes, vertices) Binary relationships (edges) May be directed Also called a graph Networks are everywhere! People Friendship from www.liberality.org 1
Sexual networks Transportation networks People Romantic and sexual relations Locations Roads Power grids Airline routes Power station High voltage transmission line Airports Flights Internet World-Wide-Web MBone Routers Physical connection Web documents Hyperlinks 2
Quick activity What kinds of biological networks are there or might there be? Molecular biology Gene and protein networks Metabolic networks Signaling networks Metabolites Biochemical reaction (enzyme) Molecules (e.g., Proteins or Neurotransmitters) Activation or Deactivation from web.indstate.edu from www.life.uiuc.edu Gene regulatory networks Disease Networks Genes or gene products Regulation of expression Inferred from error-prone gene expression data from Wyrick et al. 2002 Diseases Common genes Obesity from Goh et al., PNAS 2007 Rheumatoid arthritis HIV SARS, progresssion_of Hypertension Myocardial infarction Alzheimer disease 3
10/29/14 Disease Gene Networks Protein interaction networks Proteins Observed interaction Genes Common diseases from Goh et al., PNAS 2007 Synthetic sick or lethal networks (SSL) Y Cells live (wild type) Y Cells live Y Cells live X X X X Y Other gene networks Homology edges Coexpression transcribed at same times, conditions Cells die or grow slowly Nonessential genes Genes co-lethal from www.embl.de Sometimes used to connect other network types across species Gene knockout / knockdown similar phenotype (defects) when suppressed from Tong et al. 2001 Gene function predicted Gene function, drug targets predicted What they really look like Overview Networks, protein interaction networks (PINs) We need models! Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words 4
Traditional graph modeling from GD2002 Random Regular Erdos-Renyi (1960) Lattice Network Research Renaissance Change in direction of network research: 1998 Four factors Theoretical analysis coupled with empirical evidence Networks are not static, they evolve over time Dynamical systems modeling real-world behaviors Computing power! Enables large system analysis Introduce small-world networks Small-World Networks Small-world Networks Six degrees of separation 100 1000 friends each Six steps: 10 12-10 18 But We live in communities Small-world measures Typical separation between two vertices Measured by characteristic path length (average distance) Watts-Strogatz small-world model Cliquishness of a typical neighborhood Measured by clustering coefficient v C v = 1.00 v C v = 0.33 5
10/29/14 Measures of the W-S model Small-world measures of various graph types Path length drops faster than cliquishness Wide range of p has both small-world properties Another network property: Degree distribution P (k) Cliquishness Characteristic Path Length Regular graph High Long Random graph Low Short Small-world graph High Short Degree distribution of E-R random networks The degree (notation: k) of a node is the number of its neighbors Erdös-Rényi random graphs The degree distribution is a histogram showing the frequency of nodes having each degree P(k) Binomial degree distribution, well-approximated by a Poisson Network figures from Strogatz, Nature 2001 Degree distribution of many realworld networks Other degree distributions Degree = k Scale-free networks Degree distribution follows a power law P (k = x) = α x -β Amaral, Scala, et al., PNAS (2000)" 6
Hierarchical Networks Properties of hierarchical networks Ravasz, et al., Science 2002 1. Scale-free 2. Clustering coefficient independent of N 3. Scaling clustering coefficient (DGM) 37 38 C of 43 metabolic networks Independent of N Clustering coefficient scaling C(k) Metabolic networks Ravasz, et al., Science 2002 Ravasz, et al., Science 2002 39 40 Summary of network models Many real-world networks are small-world, scale-free Random Small world Scale-free Hierarchical Poisson degree distribution high CC, short pathlengths power law degree distribution high CC, modular, power law degree distribution World-wide-web Collaboration of film actors (Kevin Bacon) Mathematical collaborations (Erdös number) Power grid of US Syntactic networks of English Neuronal network of C. elegans Metabolic networks Protein-protein interaction networks 7
Overview So What? Networks, protein interaction networks (PINs) Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words There is information in a gene s position in the network We can use this to predict Relationships Interactions Regulatory relationships Protein function Process Complex / molecular machine Implications from topology Edges indicate function Proteins that are connected by an edge in many types of biological networks are more likely to have a common function Adjacent edges indicate 3 rd In some biological networks, if gene A is connected both to genes B and C, then gene B is more likely to be connected to gene C 8
False positives, false negatives Can use topology to assess confidence if true edges and false edges have different network properties Assess how well each edge fits topology of true network Can also predict unknown relations SSL hubs might be good cancer drug targets Normal cell Cancer cells w/ random mutations Alive Dead Dead (Tong et al, Science, 2004) 2-hop predictors for SSL SSL SSL (S-S) Homology SSL (H-S) Co-expressed SSL (X-S) Physical interaction SSL (P-S) 2 physical interactions (P-P) S: Synthetic sickness or lethality (SSL) H: Sequence homology X: Correlated expression P: Stable physical interaction Wong, et al., PNAS 2004 v w Multi-color motifs S: Synthetic sickness or lethality H: Sequence homology X: Correlated expression P: Stable physical interaction R: Transcriptional regulation Zhang, et al., Journal of Biology 2005 Protein complexes Tightly connected proteins may indicate a protein complex Beware of bias from Girvan and Newman, PNAS 2002 9
Lethality Hubs are more likely to be essential Jeong, et al., Nature 2001 Protein abundance Abundant proteins are more likely to be represented in some types of experiments More likely to be essential Correlation between degree (hubs) and essentiality disappears or is reduced when corrected for protein abundance Bloom and Adami, BMC Evolutionary Biology 2003 Degree anti-correlation Degree correlation Few edges directly between hubs Edges between hubs and low-degree genes are favored Regulatory NW PPI Anti-correlation of degrees of interacting proteins disappears in un-biased data average degree K1 25 20 15 10 5 0 essential non-essential 0 10 20 30 40 50 60 70 degree k Maslov and Sneppen, Science 2002 Coulomb, et al., Proceedings of the Royal Society B 2005 Methods: predicting function Predicting protein function Homology Machine Learning Graph-theoretic methods Direct methods Module-assisted methods Review: Sharan, Ulitsky, Shamir. Molecular Systems Biology, 2007 10
Direct methods: Neighborhood Majority method Schwikowski, Uetz, et al., Nat Biotechnol 18, 2000 Neighborhood method How does frequency affect assignment? Hishigaki, Nakai, et al., Yeast 18, 2001 Minimum cut (graph-theoretic) methods Vazquez, Flammini, et al. (2003) globally tries to minimize the number of protein interactions between different annotations Karaoz, Murali, et al. (2004) incorporates gene-expression data for better performance Nabieva, Jim, et al. (2005) reformulated as an integer linear programming problem Functional flow Nabieva, Jim, et al., Bioinformatics 21 Suppl 1, 2005 A Markov random field method Letovsky and Kasif, Bioinformatics 19 Suppl 1, 2003 Derive marginal probabilities given other proteins putative assignment Statistically, neighbors often share label Applies p(l N, k) = p(k L,N) p(l) p(k N) iteratively to propagate probabilities L is a Boolean random variable that indicates whether or not a node has a that label N is the number of neighbors k is the number of neighbors with that label Module-assisted methods Spirin and Mirny, PNAS 2003 Find fully connected subgraphs (cliques), OR Find subgraphs that maximize density: 2m/(n(n 1)) Bader and Hogue, BMC Bioinformatics 2003 Weight vertices: neighborhood density, connectedness Find connected communities with high weights MCODE : Molecular COmplex DEtection Girvan and Newman, PNAS 2002 Betweenness centrality Removes edges likely to go between communities Confidence assessment, edge prediction 11
Confidence assessment Traditionally, biological networks determined individually High confidence Slow New methods look at entire organism Lower confidence ( 50% false positives) Inferences made based on this data Confidence assessment Can use topology to assess confidence if true edges and false edges have different network properties Assess how well each edge fits topology of true network Can also predict unknown relations Goldberg and Roth, PNAS 2003 Use clustering coefficient, a local property Number of triangles = N(v) N(w) y x v w Normalization factor? N(x) = the neighborhood of node x v w. Mutual clustering coefficient (MCC) Jaccard Index: Meet / Min: Geometric: N(v) N(w) ---------------- N(v) N(w) N(v) N(w) ------------------------ min ( N(v), N(w) ) Hypergeometric: a p-value N(v) N(w) 2 ------------------ N(v) N(w) Prediction A v-w edge would have a high MCC Questions Degree distribution? v w Clustering coefficient? 2, 5, 9 Mutual clustering coefficient: 2 & 7 Use Meet/Min definition 60 12
Overview Networks, protein interaction networks (PINs) Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words Protein Complexes Groups of proteins that bind together to perform a specific task. Examples: Ribosomes Proteasomes Replication complexes GINS complex, DNA polymerase Image from: Computation site for bioinformatics at Charité, Universitätsmedizin Berlin Found at http://bioinf.charite.de/hergo/intro.htm Finding protein compexes Protein-Protein Interaction Network Dense regions may be an indication of a protein complex from Girvan and Newman, PNAS 2002 Image from Yeast Proteomics, Genome News Network, 1-18-02 Looking for Complexes One goal of studying the interaction network is to discover previously unknown protein complexes. Methods: Look for cliques or near cliques Look for vertices with high clustering Community structure: Partitioning methods 13
Community structure Proteins in a community may be involved in a common process or function Finding the communities Hierarchical clustering Betweenness centrality Dense subgraphs Similar subgraphs Spectral clustering Party and date hubs from Girvan and Newman, PNAS 2002 Hierarchical clustering (1) Using natural edge weights Gene co-expression e.g., Eisen MB, et al., PNAS 1998 Hierarchical clustering (2) Topological overlap A measure of neighborhood similarity l i,j is 1 if there is a direct link between i and j, 0 otherwise Ravasz, et al., Science 2002 from www.medscape.com Hierarchical clustering (3) Adjacency vector Function cluster: Tong et al., Science 2004 Find drug targets: Parsons et al., Nature Biotechnology 2004 Party and date hubs Protein interaction network Partition hubs by expression correlation of neighbors Han, et al., Nature 2004 14
Network connectivity Scale-free networks are: Robust to random failures Vulnerable to attacks on hubs Removing hubs quickly disconnects a network and reduces the size of the largest component Removing date hubs shatters network into communities Date Hubs" Party Hubs" Many sub-networks" Albert, et al., Nature 2000 A single main component" Similar subgraphs Across species Interaction network and genome sequence e.g., Ogata, et al., Nucleic Acids Research 2000 Betweenness centrality Consider the shortest path(s) between all pairs of nodes Betweenness centrality of an edge is a measure of how many shortest paths traverse this edge Edges between communities have higher centrality Girvan, et al., PNAS 2002 Spectral clustering Compute adjacency matrix eigenvectors Each eigenvector defines a cluster: Proteins with high magnitude contributions Bu, et al., Nucleic Acids Research 2003 Overview Networks, protein interaction networks (PINs) Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words positive eigenvalue negative eigenvalue 15
Questions How does the WWW evolve? How might protein interaction networks (PINs) evolve? How can we determine if our model is incorrect? Model for scale-free networks Growth and preferential attachment New node has edge to existing node v with probability proportional to degree of v Biologically plausible? Gene duplication gives functional diversity A primary mechanism for diversity After duplication, 2 routes to diversity: Subfunctionalization: function loss yields complementary subsets of original functions Neofunctionalization: de novo acquisition of functions Protein interactions are convenient proxy for functions Edge Loss Edge Gain Gene duplication in a PIN Barabási and Oltvai, Nature Reviews Genetics (2004) Another scale-free network model Advantages of this model Duplication and divergence New nodes are copies of existing nodes Same neighbors, then some gain/ loss This model generates networks that are: scale-free highly clustered PINs are also scale-free, highly clustered Solé, Pastor-Satorras, et al. (2002)" 16
Question Paralogs: x & w or y & t y v x w t Overview Networks, protein interaction networks (PINs) Network models What can we learn from PINs Discovering protein complexes PIN evolution Final words Final words Network analysis has become an essential tool for analyzing complex systems There is still much biologists can learn from scientists in other disciplines There is much other scientists can learn from us An exciting new direction 17