LECTURE 2

1.Complex Network Models

2.Properties of Protein-Protein Interaction Networks

3.Usage of KNApSack Database

Complex Network Models:

Average Path length L, Clustering coefficient C, Degree Distribution P(k) help understand the structure of the network.

Some well-known types of Network Models are as follows:

•Regular Coupled Networks

•Random Graphs

•Small world Model

•Scale-free Model

•Hierarchical Networks

Regular networks

Diamond Crystal

Graphite Crystal

Regular networks

Both diamond and graphite are carbon

Regular network (A ring lattice)

Average path length L is high

Clustering coefficient C is high

Degree distribution is delta type.

1 2 43

1P(k)

5

Random Graph

Erdos and Renyi introduced the concept of random graph around 40 years ago.

Random Graph

p=0 p=0.1

p=0.15 p=0.25

N=10

Emax = N(N-1)/2

=45

p=0.25

Average path length L is Low

Clustering coefficient C is low

Degree distribution is exponential type.

( )!

k

P k ek

Random Graph

Usually to compare a real network with a random network we first generate a random network of the same size i.e. with the same number of nodes and edges.

Other than Erdos Reyini random graphs there are other type of random graphs

A Random graph can be constructed such that it matches the degree distribution or some other topological properties of a given graph

Geometric random graphs

Random Graph

Small world model (Watts and Strogatz)Oftentimes,soon after meeting a stranger, one is surprised to find that they have a common friend in between; so they both cheer:

“What a small world!”

What a small world!!

Small world model (Watts and Strogatz)

Begin with a nearest-neighbor coupled network

Randomly rewire each edge of the network with some probability p

Small world model (Watts and Strogatz)

Average path length L is Low

Clustering coefficient C is high

Degree distribution is exponential type.

P(k)

Start with a small number of nodes; at every time step, a new node is introduced and is connected to already-existing nodes following Preferential Attachment (probability is high that a new node be connected to high degree nodes)

Scale-free model (Barabási and Albert)

Average path length L is Low

Clustering coefficient C is not clearly known.

Degree distribution is power-law type.

0.0001

0.001

0.01

0.1

1

10 100 10001

γ=3

γ=2

P(k) ~ k-γ

Scale-free networks exhibit robustnessRobustness – The ability of complex systems to maintain their function even when the structure of the system changes significantlyTolerant to random removal of nodes (mutations)

Vulnerable to targeted attack of hubs (mutations) – Drug targets

The term “scale-free” refers to any functional form f(x) that remains unchanged to within a multiplicative factor under a rescaling of the independent variable x i.e. f(ax) = bf(x).

This means power-law forms (P(k) ~ k-γ), since these are the only solutions to f(ax) = bf(x), andhence “power-law” is referred to as “scale-free”.

Scale-free model (Barabási and Albert)

Hierarchical Graphs

The starting point of this construction is a small cluster of four densely linked nodes (see the four central nodes in figure).Next, three replicas of this module are generated and the three external nodes of the replicated clusters connected to the central node of the old cluster, which produces a large 16-node module. Three replicas of this 16-node module are then generated and the 12 peripheral nodes connected to the central node of the old module, which produces a new module of 64 nodes.

NETWORK BIOLOGY: UNDERSTANDING THE CELL’S FUNCTIONAL ORGANIZATIONAlbert-László Barabási & Zoltán N. Oltvai

NATURE REVIEWS | GENETICS VOLUME 5 | FEBRUARY 2004 | 101

Hierarchical Graphs

The hierarchical network model seamlessly integrates a scale-free topology with an inherent modular structure by generating a network that has a power-law degree distribution with degree exponent γ = 1 +ln4/ln3 = 2.26 and a large, system-size independent average clustering coefficient <C> ~ 0.6. The most important signature of hierarchical modularity is the scaling of the clustering coefficient, which follows C(k) ~ k –1 a straight line of slope –1 on a log–log plot

NETWORK BIOLOGY: UNDERSTANDING THE CELL’S FUNCTIONAL ORGANIZATIONAlbert-László Barabási & Zoltán N. Oltvai

NATURE REVIEWS | GENETICS VOLUME 5 | FEBRUARY 2004 | 101

NETWORK BIOLOGY: UNDERSTANDING THE CELL’S FUNCTIONAL ORGANIZATIONAlbert-László Barabási & Zoltán N. Oltvai

NATURE REVIEWS | GENETICS VOLUME 5 | FEBRUARY 2004 | 101

Comparison of random, scale-free and hierarchical networks

Typical protein-protein interaction

A protein binds with another or several other proteins in order to perform different biological functions---they are called protein complexes.

protein-protein interaction

PROTEIN-PROTEIN INTERACTIONSby Catherine RoyerBiophysics Textbook Online

protein-protein interaction

This complex transport oxygen from lungs to cells all over the body through blood circulation

PROTEIN-PROTEIN INTERACTIONSby Catherine RoyerBiophysics Textbook Online

protein-protein interaction

•Usually protein-protein interaction data are produced by Laboratory experiments (Yeast two-hybrid, pull-down assay etc.)

Network of interactions and complexes

•The results of the experiments are converted to binary interactions.•The binary interactions can be represented as a network/graph where a node represents a protein and an edge represents an interaction.

AD

F

BC

E

Bait protein

Interacted protein

A

B FD EC

Spoke approachC

B

D

F

E

A

Matrix approach

detected complex data

AtpB AtpAAtpG AtpEAtpA AtpHAtpB AtpHAtpG AtpHAtpE AtpH

0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0

List of interactions

Corresponding network

Adjacency matrix

Network of interactions

The yeast protein interaction network evolves rapidly and contain few redundant duplicate genes by A. Wagner.

Mol. Biology and Evolution. 2001

985 proteins and 899 interactions

S. Cerevisiae

giant component consists of 466 proteins

The yeast protein interaction network evolves rapidly and contain few redundant duplicate genes by A. Wagner.

Mol. Biol. Evol. 2001

Average degree ~ 2

Clustering co-efficient = 0.022

Degree distribution is scale free

An E. coli interaction network from DIP (http://dip.mbi.ucla.edu/).

300 proteins and 287 interactions

E. coli

Giant component

93 proteins

Components of this graph has been determined by applying Depth First Search Algorithm

There are total 62 components

An E. coli interaction network from DIP (http://dip.mbi.ucla.edu/).

Average degree ~ 1.913

Clustering co-efficient = 0.29

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2

Log(Degree)

Lo

g(N

o. o

f N

od

e)

Degree distribution ~ scale free

Lethality and Centrality in protein networks byH. Jeong, S. P. Mason, A.-L. Barabasi, Z. N. OltvaiNature, May 2001

1870 proteins and 2240 interactions

S. Cerevisiae

Almost all proteins are connected

Degree distribution is scale free

Average degree 5.42

Clustering co-efficient = 0.18

Giant component consists of

4385 proteins

PPI network based on MIPS database consisting of 4546 proteins12319 interactions

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5 3

Degree distribution ~ scale free

PPI network based on MIPS database consisting of 4546 proteins12319 interactions

# of

proteins

# of

Interac.

Average degree

Clustering Coeffi.

Giant

Compo.

Degree Distribu.

985 899 ~2 0.022 Exist

47.3%

Power

law

300 287 1.913 0.29 Exist

31%

Almost

Power

law

1870 2240 ______ ______ Exist

~100%

Power

law

4546 12319 5.42 0.18 Exist

~96%

Not exactly

Power

law

A complete PPI network tends to be a connected graph

And tends to have Power law distribution

Introduction to KNApSaCK database

http://kanaya.aist-nara.ac.jp/KNApSAcK/

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0

600

±1 ±0.1 ±0.01 ±0.001

# of candidates for molecular formula

accurate mass: 226.0477

251

321

Chorismic acid Isochorismic acid

597

FT-MS high accurate MW for metabolites [molecular weight (ppm)]

KNApSAcK: Species-metabolite relation DB

±1 ±0.1 ±0.01 ±0.001

C10H10O6

Error level for FT-MS

Molecular formulaCandidatesof Metabolites

Since 2004

(Mw margin )

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Now!

Since 2004

Species Metabolite

Last updata 2010/3/31 50,054 unique metabolites102,005 species-metabolite relations

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Current Status of KNApSAcK project

Plant kingdom (Predicted)-- 200,000 D. Strack and R. Dixon (2003)

Known NPs (Predicted)-- 50,000 /Plants, Luca and Pierre, (2000)

KNApSAcK(last updata 2009/5/21)-- 50,054 unique metabolites 102,005 species-metabolite relations

Model speciesArabidopsis thaliana-- 5,000 ca. 1/3 of 1200 protein typesHuman-- 2,500 Ryals (2004)Bacteria (E. coli, B. subtilis)-- 800 – 1700

Systematization of Species-metabolite relation DB(KNApSAcK)

Basic study:--Metabolomics (Systems Biol)-- Evolution of NPs-- Gene to metabolite relations

Applied works:-- Food Sciences 　-- Health creation-- Herbal medicine-- Drug development by Herb.

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(a) Name(Organism, Metabolite)

(b) Mw margin

(c) Molecular formula

(d) Taxonomic hierarchy

(e) Ion mass of FT-MSwith ionization mode

(h) Mode selection

(g) A list of retrieved metabolites

We can retrieve metabolite information by:

Substrucutre 　

Main window http://kanaya.naist.jp/KNApSAcK/

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Metabolites can be linked to KNApSAcK easily by Keywords (Organism, Metabolite, Molecular Formula)

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(+)-Sesamin is reported in 122 species

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Input: Allium cepa38 Metabolites

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KNApSAcK （ http:/kanaya.naist.jp/KNApSAcK ） (Since 2004)

0 5 10 15 20

Bioinformatics Methodology Development

Review Article

Metabolomics Non-targeted Analysis

Target of Research

0 5 10

Rattus norvegicus

Curcuma longa

E. coli

Salanum lycopersicum

Fragaria x ananassa

Arabidopsis thaliana

Brassica oleracea

Papers utilized KNApSAcK DB to examine metabolomics ( Thanks!) Davey, M.P., et al., Metabolomics, (2009)

Hounsome, N. et al., Postharvest Biol. Technol., (2009) 6 papers-2009 (Red, Foreign country)Xie,Z., et al., J.Exp.Botany,60, 87-97, (2009) Giavalisco, Anal.Chem.(2009)Draper et al., BMC Bioinformatics, (2009)

Shroff et al., PNAS (2009)

Malitsky, S.,., et al., Plant Physiol., (2008) 17 papers-2008 (Red, Foreign country)

Warner, E., et al., J.Chromatography B,(2008)Fait, A., et al., Plant Physiol., 148, 730-750 (2008)Mintz-Oron, S., et al., Plant Physiol., 147, 823-851, (2008)Hanhineva, K., et al., Phytochemistry, 69, 2463-2481 (2008)Bottcher,C., et al., Plant Physiol.,147,2107-2120, (2008)Farder, A. et al., J. Nutrition, 138, 1282-1287, (2008) 　　Mintz-Oron, S., et al., Plant Physiol.,147,823-825, (2008)

Overy, D.P., et al., Nature Protocols, 3, 471-485, (2008)

Dunn, W.B., Physical Biol.,5, 1-24, (2008)Akiyama, K., In Silico Biol., 8, 27, (2008)Sawada, Plant Cell Physiol., (2008)Arita,M. and Suwa, K., BioData Mining, 1,7.1-8 (2008)Saito, K. et al., Trends in Plant Sci.,13, 36-43, (2008)Akiyama, K., et al., In Silico Biol., 8, 339-345, (2008)Takahashi, H., Anal. Bioanal Chem. (in press) (2008)Iijima, Y., et al., Plant J., 54, 949-962, (2008)

Want, E.J. et al., J. Proteome Res., 6, 459-468, (2007) 10 papers-2007Sofia, M., et al., Trends in Anal. Chem., 26, 855-866, (2007)Hummel, J., et al., Topics in Curr. Genet., 18, 75-95, (2007)Gaida, A., and Neumann, S., J. Int. Bioinf., (2007)Griffiths,W.J.,Metabolomics,Metabolonomics and Metabolite Profiling,(Royal Soc.Chem.),2007Ohta, D., et al., Anal.Biol. Chem.(2007)Nakamura, Y., et al., Planta, (2007)Suzuki, H., et al., Phytochemistry, (2007)Sakakibara, K., et al., , J .Biol. Chem.,282, 14932-14941, (2007)Saito, K. et al., Trends in Plant Sci., 13, 36-42, (2007)

Kikuchi, K and Kakeya, H., Natuure Chem. Biol., 2, 392-394, (2006) 　　　4 papers-2006Oikawa, A.,et al., Plant Physiol., 142, 398-413, (2006)Shinbo, Y., et al., Biotchnol. Agric. Forestry, 57, 166-181, (2006)Shinbo, Y., et al., J. Comput. Aided Chem., 7, 94-101, (2006)since 2004Web-sites linked to KNApSAcK(WikiBook) http://en.wikibooks.org/wiki/Metabolomics/Databases (UC Davis ）　 http://fiehnlab.ucdavis.edu/staff/kind/Metabolomics/Structure_Elucidation/(KEGG) http://fire3.scl.genome.ad.jp/dbget-bin/www_bfind?knapsack(TAIR-Metabolomics Resource – Databases) http://www.arabidopsis.org/portals/metabolome/metabolome_database.jsp/（ LECO manual ） Form No. 203-821-333(PubMed) referred by C-IDhttp://metabolomics.jp/wiki/

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We learnt

1.Properties of some complex network models

2.Properties of Protein-Protein Interaction Networks

3.Usage of KNApSack Database