Chapter 8: The Topology of Biological Networks Overview

Chapter 8: The Topology of Biological Networks

8.1 Introduction

Prof. Yechiam Yemini (YY)

Computer Science Department Columbia University

Overview  A gallery of networks  Scale-free network models

2

1

A Gallery of Networks

3

Introduction  Network abstractions  Node: biological object  Edge: interaction between nodes

 Regulatory networks  Node: genes; edge: regulatory interaction

 Metabolic networks  Node: metabolite; edge: reaction

 Protein networks    

Node: protein; edge: interaction Node: module; edge: interaction Node: complex; edge: sharing a protein Node: residue; edge: folding neighbors

What Can Network Abstractions Teach Us About Biological Systems? 4

2

The E.Coli Regulatory Network http://www.biomedcentral.com/1471-2105/5/199

Node= TFs Edge= Regulatory interaction

UNORGANIZED VIEW

HIERARCHICAL VIEW

MODULAR VIEW Hierarchical structure and modules in the Escherichia coli regulatory network. Hong-Wu Ma , Jan Buer, and An-Ping Zeng

5

Regulatory Network Of E.Coli E.coli: 105 TFs affect 749 genes 7 TFs regulate >0.5 genes Connectivity distribution  Egress: follows a power-law  Ingress: follows exponential (Shen-Orr).

Martinez-Antonio, Collado-Vides, Curr Opin Microbiol 6, 482 (2003)

6

3

Yeast Regulation

http://www.biochemj.org/bj/381/0001/bj3810001.htm

Node= TFs Edge= Regulatory interaction

Charting gene regulatory networks: strategies, challenges and perspectives Gong-Hong WEI, De-Pei LIU1 and ChihChuan LIANG ; Biochem J. 2004 (381)

The colour scheme depicts functional category: orange, mitotic cell cycle; pink, budding and filament formation; green, amino acid metabolism; yellow, nitrogen and sulphur utilization; blue, C-compound and carbohydrate utilization; red, TFs; grey, unspecific or several functional categories.

7

Yeast Regulatory Network http://www.cmth.bnl.gov/~maslov/rockefeller_2002_networks.ppt

Sergei Maslov

8

4

Metabolic Network Node= Metabolites Edge= Reaction

Human

E-Coli

Ravasz et al…Science Vol 297, 2002

9

Signaling Networks

MAPK signaling pathway

http://www.cs.tau.ac.il/~spike/

www.bioscience.org/1998/v3/d/malumbre/fig2.jpg

10

5

Yeast P2P Interaction Network Node= proteins Edge= interaction

http://www.imb-jena.de/tsb/yeast.html http://www.macdevcenter.com/pub/a/mac/2004/08/20/bioinformatics.html

11

Yeast P2P Domain Interaction Network Node= domain Edge= interaction

http://www.utoronto.ca/boonelab/proteomics.htm

(A) Yeast SH3 domain protein-protein network; proteins are colored according to their k-core value (6-core = black, 5-core = cyan, 4-core = blue, 3-core = red, 2- core = green, 1-core = yellow), identifying subnets in which each protein has at least k interactions. By definition, lower core numbers encompass all higher core numbers (e.g. 4-core subgraph includes 4-core, 5core and 6-core). The 6-core subgraph is highlighted in red and depicted in (B).

12

6

A Network of Protein Complexes http://www.genomenewsnetwork.org/articles/01_02/Yeast_proteins_image1.shtml

Node=complex Edge=shared proteins Color=role Red, cell cycle; dark green, signalling; dark blue, transcription, DNA maintenance, chromatin structure; pink, protein and RNA transport; orange, RNA metabolism; light green, protein synthesis; brown, cell polarity and structure; violet, intermediate and energy metabolism; light blue, membrane biogenesis and traffic. Lowe panel is an example of a complex (yeast TAPC212) linked to two other complexes (yeast TAP-C77 and TAP-C110) by shared components.

13

Key Question: Are Biological Networks Random? Or do they reflect hidden organizational principles? First answer: biological network are random  Are organized through scale-free random evolution  Barabasi group: Jeong et al. Nature 407, 651-654 (2000).

Second answer: regulatory networks are not random  Are organized from statistically-significant motifs  Uri Alon’s group: Shen-Orr et al. Nature Gen. 31, 64 (2002)

Both can be correct  Contradiction is only seeming

14

7

Statistical Topology Features

15

Random Networks (Erdos Renyi, 1959)  G(n,p) a graph on n nodes where an edge has probability p  Toss a coin with probability p to select an edge  Average degree d=p(n-1)~pn m pk(1-p)[m-k] ~ (dk /k!)exp(-d)  Probability of k edges (m=n(n-1)/2): p(k)=

k

 G(n,p(n)) has a property F, if p(G(n,p(n)∈F)1 when n∞  Main result: many properties F have threshold behavior  There exists p*(n) such that if p(n)/p*(n)>1 p(G(n,p(n)∈F)1 and if p(n)/p*(n) p(αk)/p(k)=γ(α−1)k(k!/(αk)!)

 Topological features of SF nets  γ=2 hub-and-spoke topology  2