Transcript The Properties of Protein-Protein Interaction Networks and

Course Name:
Systems Biology
Conducted byShigehiko kanaya
&
Md. Altaf-Ul-Amin
Dates of Lectures:
October
9, 15, 16, 22, 23, 30
November
5, 6, 12, 13, 19, 20, 26, 27
Lecture Time: Mondays &Tuesdays 11:0012:30
Website
http://kanaya.naist.jp/Lecture/
Syllabus
Introduction to Graphs/Networks, Different network models, Properties of
Protein-Protein Interaction Networks, Different centrality measures
Protein Function prediction using network concepts, Application of network
concepts in DNA sequencing, Line graphs
Concept and types of metric, Hierarchical Clustering, Finding clusters in
undirected simple graphs: application to protein complex detection
Introduction to KNApSAcK database, Metabolic Reaction system as ordinary
differential equations, Metabolic Reaction system as stochastic process
Metabolic network and stoichiometric matrix, Information contained in
stoichiometric matrix, Elementary flux modes and extreme pathways
Graph spectral analysis/Graph spectral clustering and its application to
metabolic networks
Normalization procedures for gene expression data, Tests for differential
expression of genes, Multiple testing and FDR, Reverse Engineering of genetic
networks
Finding Biclusters in Bipartite Graphs, Properties of transcriptional/gene
regulatory networks, Introduction to software package Expander
Introduction to signaling pathways, Selected biological processes: Glycolytic
oscillations, Sustained oscillation in signaling cascades
Central dogma of molecular biology
The crowded Environment inside the cell
Some of the physical
characteristics are as follows:
Viscosity > 100 × μ H20
Osmotic pressure < 150 atm
Electrical gradient ~300000 V/cm
Near crystalline state
The osmotic pressure of ocean
water is about 27 atm and that
of blood is 7.7 atm at 25oC
Without a complicated
regulatory system all the
processes inside the cell cannot
be controlled properly.
Source: Systems biology by
Bernhard O. Palsson
From Genome to Phenome
(Dynamic)
Phenome
Metabolome
Metabolites (Bio-chemical molecules)
Proteome
Proteins-Amino Acid Sequences
Transcriptome
mRNA and other RNAs - Nucleotide
sequence-Single Stranded
Genome (Gene set)
DNA –Nucleotide sequenceATCTGAT……Double Helix
(Statiic)
Progressing genome projects: many kinds of “–omics” works have progressed such as
genomics, transcriptomics, proteomics, metabolomics ….
These are dynamic information reflecting to Phenome.
Bioinofomatics
Genome:
5’
3’
a
b
c
b
c
d
e
f
g
Integration of omics
i
k
m
to define
elements
j
l
(genome, mRNAs,
Activation (+)
Proteins,
metabolites)
A
h
Transcriptome：
5’
3’
a
Repression (-) G
h
d
e
D
E
f
i
k
G
g
j
m
l
Proteome, Interactome
A
B
Function
A
Unit
B C
Protein
C
D E
F
Metabolome
FT-MS
Metabolite 1
Metabolic Pathway
F
G
H
G
H K
I
J
K
L organism
M
Understanding
as a system
I L
M J
(Systems
Biology)
comprehensive and global analysis of diverse metabolites produced in
cells and organisms
B C
Metabolite 2
D E
F
Metabolite 3
Metabolite 4
I L
Metabolite 5
Understanding speciesHspecies
K
relations
Metabolite 6
(Survival Strategy)
3’
5’
3’
5’
Introduction to Graphs/Networks
Representing as a network often helps to
understand a system
Konigsberg bridge problem
Konigsberg was a city in present day Germany encompassing two
islands and the banks of Pregel River. The city was connected by
7 bridges.
Problem: Start at any point, walk over each bridge exactly once
and return to the same point. Possible?
Konigsberg bridge problem
Konigsberg was a city in present day Germany including two
islands and the banks of Pregel River. The city was connected by
7 bridges.
Problem: Start at any point, walk over each bridge exactly once
and return to the same point. Possible?
Konigsberg bridge problem
Konigsberg was a city in present day Germany including two
islands and the banks of Pregel River. The city was connected by
7 bridges.
Problem: Start at any point, walk over each bridge exactly once
and return to the same point. Possible?
Konigsberg bridge problem
Problem: Start at any point, walk over each bridge exactly once
and return to the same point. Possible?
This problem was solved by Leonhard Eular in 1736 by means of
a graph.
Konigsberg bridge problem
Problem: Start at any point, walk over each bridge exactly once
and return to the same point. Possible?
This problem was solved by Leonhard Eular in 1736 by means of
a graph.
A
B
C
D
Konigsberg bridge problem
Problem: Start at any point, walk over each bridge exactly once
and return to the same point. Possible?
A
B
A, B, C, D circles represent
land masses and each line
represent a bridge
D
The necessary condition for the
existence of the desired route is
that each land mass be connected
to an even number of bridges.
C
The graph of Konigsberg bridge problem does not hold the necessary
condition and hence there is no solution of the above problem.
This notion has been used in solving DNA sequencing problem
Definition
A graph G=(V,E) consists of a set of vertices V={v1,
v2,…) and a set of edges E={e1,e2, …..) such that each
edge ek is identified by a pair of vertices (vi, vj) which
are called end vertices of ek.
A graph is an abstract representation of almost any
physical situation involving discrete objects and a
relationship between them.
It is immaterial whether the vertices are drawn rectangular or
circular or the edges are drawn staright or curved, long or
short.
A
B
C
A
D
B
C
Both these graphs are the same
D
Many systems in nature can be represented as networks
The internet is a network of computers
Many systems in nature can be represented as networks
Road Network
No such node exists
Air route Network
Very high degree node
Many systems in nature can be represented as networks
Printed circuit boards are networks
Network theory is extensively used to design the wiring and
placement of components in electronic circuits
Many systems in nature can be represented as networks
Protein-protein interaction network of e.coli
Some Basic Concepts regarding networks:
•Average Path length
•Diameter
•Eccentricity
•Clustering Coefficient
•Degree distribution
Average Path length
Distance between node u and v called d(u,v) is the least length of a
path from u to v.
d(a,e) = ?
a
c
d
b
f
e
Average Path length
Distance between node u and v called d(u,v) is the least distance of
a path from u to v.
d(a,e) = ?
Length of a-b-c-d-f-e path is 5
a
c
d
b
f
e
Average Path length
Distance between node u and v called d(u,v) is the least distance of
a path from u to v.
d(a,e) = ?
Length of a-b-c-d-f-e path is 5
a
Length of a-c-d-f-e path is 4
c
d
b
f
e
Average Path length
Distance between node u and v called d(u,v) is the least length of a
path from u to v
d(a,e) = ?
Length of a-b-c-d-f-e path is 5
a
c
Length of a-c-d-f-e path is 4
d
b
f
Length of a-c-d-e path is 3
e
The minimum length of a path from a to e is 3 and therefore
d(a,e) = 3.
Average Path length
Average path length L of a network is defined as the mean
distance between all pairs of nodes.
a
c
There are 6 nodes and
d
b
f
e
6C
2
= (6!)/(2!)(4!)=15
distinct pairs for example
(a,b), (a,c)…..(e,f).
We have to calculate distance between each of these 15 pairs and
average them
Average Path length
Average path length L of a network is defined as the mean
distance between all pairs of nodes.
a
c
d
b
f
e
L=27/15=1.8
Average path length of most
real complex network is small
a to b
1
a to c
1
a to d
2
a to e
3
a to f
3
------------------------------------------____________________
15 pairs
27(total length)
Average Path length
Finding average path length is not easy when the
network is big enough. Even finding shortest path
between any two pair is not easy.
A well known algorithm is as follows:
Dijkstra E.W., A note on two problems in connection
with Graphs”, Numerische Mathematik, Vol. 1, 1959,
269-271.
Dijkstra’s algorithm can be found in almost every
book of graph theory.
There are other algorithms for finding shortest paths
between all pairs of nodes.
Diameter
Distance between node u and v called d(u,v) is the least length of a
path from u to v.
The longest of the distances between any two node is called
Diameter
a to b
1
a
a to c
1
c
a to d
2
d
b
f
a to e
3
e
Diameter of this graph is 3
a to f
3
------------------------------------------15 pairs
Eccentricity And Radius
Eccentricity of a node u is the maximum of the distances of any
other node in the graph from u.
The radius of a graph is the minimum of the eccentricity
values among all the nodes of the graph.
a to b
1
2
a 3
a to c
1
c
2
3
a to d
2
d
b
f
a to e
3
3
a to f
3
e
3
Therefore eccentricity of
node a is 3
Radius of this graph is 2
Degree Distribution
The degree distribution is the probability
distribution function P(k), which shows the
probability that the degree of a randomly
selected node is k.
# of nodes
having degree k
Degree Distribution
10
1
2
Degree
3 4
P(k)
Degree Distribution
1
1
Any randomness in the network will broaden
the shape of this peak
2
Degree
3 4
# of nodes
having degree k
Degree Distribution
4
2
1
2
Degree
3 4
P(k)
Degree Distribution
0.5
0.25
1
2
Degree
3 4
Degree Distribution
P(k )  e


k
k!
Poisson’s Distribution
e = 2.71828..., the
Base of natural
Logarithms
Degree distribution of random graphs follow Poisson’s
distribution
Degree Distribution
P(k)
P(k) ~ k-γ
Power Law Distribution
Connectivity k
Degree distribution of
many biological
networks follow Power
Law distribution
Power Law Distribution on log-log plot is a straight line
Clustering coefficient
2 Ei
Ci 
ki (ki  1)
1
C
N
N
C
i 1
i
ki = # of neighbors of node i
Ei = # of edges among the
neighbors of node i
a
c
d
b
f
e
Clustering coefficient
2 Ei
Ci 
ki (ki  1)
1
C
N
N
C
i 1
i
Ca=2*1/2*1= 1
ki = # of neighbors of node i
Ei = # of edges among the
neighbors of node i
a
c
d
b
f
e
Clustering coefficient
2 Ei
Ci 
ki (ki  1)
1
C
N
N
Ca=2*1/2*1= 1
C
i 1
i
Cb=2*1/2*1= 1
ki = # of neighbors of node i
Cc=2*1/3*2= 0.333
Ei = # of edges among the
neighbors of node i
Cd=2*1/3*2= 0.333
Ce=2*1/2*1= 1
Cf=2*1/2*1= 1
a
c
Total
= 4.666
d
b
f
e
C =4.666/6= 0.7776
Clustering coefficient
By studying the average clustering C(k) of nodes with a
given degree k, information about the actual modular
organization can be extracted.
C =2*1/2*1= 1
a
Cb=2*1/2*1= 1
Cc=2*1/3*2= 0.333
Cd=2*1/3*2= 0.333
a
Ce=2*1/2*1= 1
c
Cf=2*1/2*1= 1
d
b
f
C(1)=0
C(2)=(Ca+Cb+Ce+Cf)/4=1
e
C(3)=(Cc+Cd)/2=0.333
Clustering coefficient
By studying the average clustering C(k) of nodes with a given
degree k, information about the actual modular organization
can be extracted.
For most of the known metabolic networks the average
clustering follows the power-law.
C(k) ~ k-γ
Power Law Distribution
Subgraphs
Consider a graph G=(V,E). The graph G'=(V',E') is a
subgraph of G if V' and E' are respectively subsets of V and E.
a
c
b
a
Subgraph of G
c
d
b
f
e
Graph G
c
d
Subgraph of G
f
Induced Subgraphs
An induced subgraph on a graph G on a subset S of nodes of G
is obtained by taking S and all edges of G having both endpoints in S.
a
c
b
a
c
d
b
Graph G
c
f
e
Induced subgraph of
G for S={a, b, c}
d
Induced subgraph of f
G for S={c, d, f}
Graphlets
Graphlets are non-isomprphic induced subgraphs of large
networks
T. Milenkovic, J. Lai, and N. Przulj, GraphCrunch: A Tool for Large Network
Analyses, BMC Bioinformatics, 9:70, January 30, 2008.
Partial subgraphs/Motifs
A partial subgraph on a graph G on a subset S of nodes of G is
obtained by taking S and some of the edges in G having both
end-points in S. They are sometimes called edge subgraphs.
a
c
b
a
c
Partial subgraph of G
d
b
f
e
Graph G
For S={a, b, c}
Partial subgraphs/Motifs
Genomic analysis of regulatory network dynamics reveals
large topological changes
Nicholas M. Luscombe, M. Madan Babu, Haiyuan Yu, Michael Snyder, Sarah
A. Teichmann & Mark Gerstein, NATURE | VOL 431| 2004
SIM
MIM
FFL
SIM=Single input motif
MIM= Multiple input motif
FFL=Feed forward loop
This paper searched for these motifs in transcriptional
regulatory network of Saccharomyces cerevisiae
Partial subgraphs/Motifs
Genomic analysis of regulatory network dynamics reveals
large topological changes
Nicholas M. Luscombe, M. Madan Babu, Haiyuan Yu, Michael Snyder, Sarah
A. Teichmann & Mark Gerstein, NATURE | VOL 431| 2004