Gene and Protein Networks I Wednesday, April CSCI 4830: Algorithms for Molecular Biology Debra Goldberg

Outline 1. Introduction 2. Network models 3. Implications from topology 4. Confidence assessment, edge prediction

Outline 1. Introduction 2. Network models 3. Implications from topology 4. Confidence assessment, edge prediction

What is a network? A collection of objects (nodes, vertices) Binary relationships (edges) May be directed Also called a graph

Networks are everywhere

Social networks from Nodes: People Edges: Friendship

Sexual networks Nodes: People Edges: Romantic and sexual relations

Transportation networks Nodes: Locations Edges: Roads

Power grids Nodes: Power station Edges: High voltage transmission line

Airline routes Nodes: Airports Edges: Flights

Internet Nodes: MBone Routers Edges: Physical connection

World-Wide-Web Nodes: Web documents Edges: Hyperlinks

Gene and protein networks

Metabolic networks Nodes: Metabolites Edges: Biochemical reaction (enzyme) from web.indstate.edu

Protein interaction networks Gene function predicted from Nodes: Proteins Edges: Observed interaction

Gene regulatory networks Inferred from error-prone gene expression data from Wyrick et al Nodes: Genes or gene products Edges: Regulation of expression

Signaling networks Nodes: Molecules ( e.g., Proteins or Neurotransmitters) Edges: Activation or Deactivation from pharyngula.org

Signaling networks Nodes: Molecules (e.g., Proteins or Neurotransmitters) Edges: Activation or Deactivation from

Synthetic sick or lethal (SSL) Cells live (wild type) Cells live Cells die or grow slowly X Y X Y X Y X Y

SSL networks Gene function, drug targets predicted Nodes: Nonessential genes Edges: Genes co-lethal from Tong et al X Y

Other biological networks Coexpression –Nodes: genes –Edges: transcribed at same times, conditions Gene knockout / knockdown –Nodes: genes –Edges: similar phenotype (defects) when suppressed

What they really look like…

We need models!

Outline 1. Introduction 2. Network models 3. Implications from topology 4. Confidence assessment, edge prediction

Traditional graph modeling RandomRegular from GD2002

Introduce small-world networks

Small-world Networks Six degrees of separation 100 – 1000 friends each Six steps: But… We live in communities

Small-world measures Typical separation between two vertices –Measured by characteristic path length Cliquishness of a typical neighborhood –Measured by clustering coefficient v C v = 1.00 v C v = 0.33

Watts-Strogatz small-world model

Measures of the W-S model Path length drops faster than cliquishness Wide range of p has both small-world properties

Small-world measures of various graph types Cliquishness Characteristic Path Length Regular graph HighLong Random graph LowShort Small-world graph HighShort

Another network property: Degree distribution P (k) The degree (notation: k ) of a node is the number of its neighbors The degree distribution is a histogram showing the frequency of nodes having each degree

Degree distribution of E-R random networks Binomial degree distribution, well-approximated by a Poisson Degree = k P( k) Erdös-Rényi random graphs Network figures from Strogatz, Nature 2001

Degree distribution of many real-world networks Scale-free networks Degree distribution follows a power law P (k = x) =  x -  Degree = k P( k) log k log P( k)

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?

Another scale-free network model Duplication and divergence –New nodes are copies of existing nodes –Same neighbors, then some gain/loss Solé, Pastor-Satorras, et al. (2002)

Other degree distributions Amaral, Scala, et al., PNAS (2000)

Hierarchical Networks Ravasz, et al., Science 2002

3. Scaling clustering coefficient (DGM) 2. Clustering coefficient independent of N Properties of hierarchical networks 1. Scale-free

C of 43 metabolic networks Independent of N Ravasz, et al., Science 2002

Scaling of the clustering coefficient C(k) Metabolic networks Ravasz, et al., Science 2002

Summary of network models Random Poisson degree distribution Small world high CC, short pathlengths Scale-free power law degree distribution Hierarchical high CC, modular, power law degree distribution

Many real-world networks are small-world, scale-free World-wide-web Collaboration of film actors (Kevin Bacon) Mathematical collaborations (Erdös number) Power grid of US Syntactic networks of English Neural network of C. elegans Metabolic networks Protein-protein interaction networks

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”

Outline 1. Introduction 2. Network models 3. Implications from topology 4. Confidence assessment, edge prediction

SSL “hubs” might be good cancer drug targets (Tong et al, Science, 2004) Normal cell Cancer cells w/ random mutations Alive Dead

Lethality Hubs are more likely to be essential Jeong, et al., Nature 2001

Degree anti-correlation Few edges directly between hubs Edges between hubs and low-degree genes are favored Maslov and Sneppen, Science 2002

Outline 1. Introduction 2. Network models 3. Implications from topology 4. Confidence assessment, edge prediction

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) | Normalization factor? N(x) = the neighborhood of node x y x v w v w...

Mutual clustering coefficient Jaccard Index:Meet / Min:Geometric: |N(v)  N(w)| |N(v)  N(w)| |N(v)  N(w)| |N(v)| · |N(w)| |N(v)  N(w)| min ( |N(v)|, |N(w)| ) Hypergeometric: a p-value

Mutual clustering coefficient Hypergeometric: P (intersection at least as large by chance) -log = neighbors of node v = neighbors of node w = nodes in graph

Prediction A v-w edge would have a high clustering coefficient v w

Interaction generality Confidence measure for edge based on topology around neighbors. Saito, Suzuki, and Hayashizaki 2002,2003

Confidence assessment Integrate experimental details with local topology –Degree –Clustering coefficient –Degree of neighbors –Etc. Used logistic regression Bader, et al., Nature Biotechnology 2003

The synthetic lethal network has many triangles Xiaofeng Xin, Boone Lab

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) v w S:Synthetic sickness or lethality (SSL) H:Sequence homology X:Correlated expression P:Stable physical interaction Wong, et al., PNAS 2004

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