Transcript BIOLOGICAL NETWORK

BIOLOGICAL
NETWORKS
Woochang Hwang
BIOLOGICAL NETWORKS
Introduction
 Biological Networks




Protein-Protein Interaction Networks
Signaling & Metabolic Pathway Networks
Expression Networks
Biological Networks’ Properties
 Databases
 Discussion
 STM Clustering Model

Introduction
Bioinformatics

Informatics
Its carrier is a set of digital
codes and a language.
In its manifestation in the
space-time continuum, it
has utility (e.g. to
decrease entropy of an
open system).

Bioinformatics
The essence of life is
information (i.e. from digital
code to emerging properties
of biosystems.)
Bioinformatics is the study
of information content of life
Proteomics
Genomics
Proteomics
Structural Proteomics
Functional Proteomics
Structure Determination
Protein-Protein Interaction
& Networking
Database
/ Knowledge Source
Protein Expression
Homology Modeling
Post-tranlational
Modification
Database
/ Knowledge Source
From the particular to the universal
A.-L- Barabasi & Z. Oltvai, Science, 2002
Genome Size
Proteom Size (PDB)
BIOLOGICAL NETWORK
Networks are found in biological systems of
varying scales:
1. Evolutionary tree of life
2. Ecological networks
3. Expression networks
4. Regulatory networks
- genetic control networks of organisms
5. The protein interaction network in cells
6. The metabolic network in cells
… more biological networks
Why Study Networks?
It is increasingly recognized that complex
systems cannot be described in a
reductionist view.
 Understanding the behavior of such
systems starts with understanding the
topology of the corresponding network.
 Topological information is fundamental in
constructing realistic models for the
function of the network.

Biological Network Model

Network


A linked list of interconnected nodes.
Node


Protein, peptide, or non-protein biomolecules.
Edges
 Biological relationships, etc., interactions, regulations, reactions,
transformations, activation, inhibitions.
Biological Network Model

It is usually represented by a 2-D diagram
with characteristic symbols linking the protein
and non-protein entities.

A circle indicates a protein or a non-protein
biomolecule.
An symbol in between indicates the nature of
molecule-molecule process (activation,
inhibition, association, disassociation, etc.)

Protein Interaction Network
Proteins in a cell

There are thousands of different active
proteins in a cell acting as:





enzymes, catalysors to chemical reactions of
the metabolism
components of cellular machinery (e.g.
ribosomes)
regulators of gene expression
Certain proteins play specific roles in special
cellular compartments.
Others move from one compartment to
another as “signals”.
Protein Interactions


Proteins perform a function as a complex rather
as a single protein.
Knowing whether two proteins interact can help
us discover unknown proteins’ functions:
 If the function of one protein is known, the
function of its binding partners are likely to be
related- “guilt by association”.
 Thus, having a good method for detecting
interactions can allow us to use a small number
of proteins with known function to characterize
new proteins.
Protein Interactions
P. Uetz, et al. Nature, 2000; Ito et al., PNAS, 2001; …
Yeast Protein Interaction Network
Nodes: proteins
Links: physical
interactions (binding)
Pathway Networks
Signaling & Metabolic Pathway Network


A Pathway can be defined as a modular unit
of interacting molecules to fulfill a cellular
function.
Signaling Pathway Networks




In biology a signal or biopotential is an electric
quantity (voltage or current or field strength), caused by
chemical reactions of charged ions.
refer to any process by which a cell converts one kind of
signal or stimulus into another.
Another use of the term lies in describing the transfer of
information between and within cells, as in signal
transduction.
Metabolic Pathway Networks

a series of chemical reactions occurring within a cell,
catalyzed by enzymes, resulting in either the formation
of a metabolic product to be used or stored by the cell,
or the initiation of another metabolic pathway
A Pathway Example
A Pathway Example
A Pathway Example
Regulatory Network

a collection of DNA segments (genes) in a cell
which interact with each other and with other
substances in the cell, thereby governing the
rates at which genes in the network are
transcribed into mRNA.
Regulatory Network
Expression Network


A network representation of genomic data.
Inferred from genomic data, i.e. microarray.
BIOLOGICAL NETWORK
PROPERTY
Interaction Network
 Pathway Network
 Regulatory Network
 Expression Network

Biological Networks Properties




Power law degree distribution: Rich get richer
Small World: A small average path length
 Mean shortest node-to-node path
Robustness: Resilient and have strong
resistance to failure on random attacks and
vulnerable to targeted attacks
Hierarchical Modularity: A large clustering
coefficient
 How many of a node’s neighbors are
connected to each other
Power Law Network
 PREFERENTIAL ATTACHMENT on Growth: the probability that a
new vertex will be connected to vertex i depends on the connectivity
of that vertex:
ki
(ki ) 
kj
j
The Barabási-Albert [BA] model
ER Model
WS Model
(a) Random Networks
Actors
Power Grid
(b) Power law Networks
Power Law Network (Scale Free)
 The probability of finding a
highly connected node decreases
exponentially with k:
P( K ) ~ K 
www
Small World Property


A small average path length
Any node can be reached within a small
number of edges, 4~5 hops.
Power Law Network

Power-law degree distribution & Small world
phenomena also observed in:





communication networks
web graphs
research citation networks
social networks
Classical -Erdos-Renyi type random graphs do not
exhibit these properties:



Links between pairs of fixed set of nodes picked
uniformly:
Maximum degree logarithmic with network size
No hubs to make short connections between nodes
Attack Tolerance
 Complex systems maintain their basic functions
even under errors and failures
(cell  mutations; Internet  router breakdowns)
node failure


Robust. For <3, removing
nodes does not break
network into islands.
Very resistant to random
attacks, but attacks
targeting key nodes are
more dangerous.
Path Length
Attack Tolerance
Protein Interaction Network
k  k0
P(k ) ~ (k  k0 ) exp(
)
k

H. Jeong, S.P. Mason, A.-L. Barabasi & Z.N. Oltvai, Nature, 2001
Protein Interaction Network

The yeast protein interaction network seems to
reveal some basic graph theoretic properties:



The frequency of proteins having interactions with
exactly k other proteins follows a power law.
The network exhibits the small world phenomena: can
reach any node within small number of hops, usually 4
or 5 hops
Robustness: Resilient and have strong resistance to
failure on random attacks and vulnerable to targeted
attacks.
Hierarchical Modularity
E. Ravasz et al., Science, 2002
Hierarchical Modularity
Metabolic Networks
Protein Networks
E. Ravasz et al., Science, 2002
Implications From Observations





Biological complexity: # states ~2# of genes.
Protein hubs critical for cells, 45% .
Infections will target highly connected nodes.
Cascading node failures could cause a critical
problem.
Development of drug and treatment with novel
strategies like targeting effective nodes is
indispensable.
Databases
Protein Databases
Swiss-Prot (non-redundant database):
Release 41.0, 11/4/2003: 124,464 entries.
Release 41.5, 23/4/2002: 125,236 entries.
TrEMBL (translations of EMBL nucleotide sequences
not yet integrated into Swiss-Prot):
Release 23.7, 17/4/2003: 863,248 entries
This number keeps rapidly growing mainly due to large
scale sequencing projects.
Protein Interaction Databases
 Species-specific



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FlyNets - Gene networks in the fruit fly
MIPS - Yeast Genome Database
RegulonDB - A DataBase On Transcriptional Regulation
in E. Coli
SoyBase
PIMdb - Drosophila Protein Interaction Map database
 Function-specific







Biocatalysis/Biodegradation Database
BRITE - Biomolecular Relations in Information
Transmission and Expression
COPE - Cytokines Online Pathfinder Encyclopaedia
Dynamic Signaling Maps
EMP - The Enzymology Database
FIMM - A Database of Functional Molecular Immunology
CSNDB - Cell Signaling Networks Database
Protein Interaction Databases
 Interaction type-specific
 DIP - Database of Interacting Proteins
 DPInteract - DNA-protein interactions
 Inter-Chain Beta-Sheets (ICBS) - A database of proteinprotein interactions mediated by interchain beta-sheet
formation
 Interact - A Protein-Protein Interaction database
 GeneNet (Gene networks)
 General
 BIND - Biomolecular Interaction Network Database
 BindingDB - The Binding Database
 MINT - a database of Molecular INTeractions
 PATIKA - Pathway Analysis Tool for Integration and
Knowledge Acquisition
 PFBP - Protein Function and Biochemical Pathways
Project
 PIM (Protein Interaction Map)
Pathway Databases
 KEGG (Kyoto Encyclopedia of Genes and Genomes)
 http://www.genome.ad.jp/kegg/
 Institute for Chemical Research, Kyoto University
 PathDB
 http://www.ncgr.org/pathdb/index.html
 National Center for Genomic Resources
 SPAD: Signaling PAthway Database
 Graduate School of Genetic Resources Technology. Kyushu
University.
 Cytokine Signaling Pathway DB.
 Dept. of Biochemistry. Kumamoto Univ.
 EcoCyc and MetaCyc
 Stanford Research Institute
 BIND (Biomolecular Interaction Network Database)
 UBC, Univ. of Toronto
KEGG

Pathway Database: Computerize current knowledge of
molecular and cellular biology in terms of the pathway of
interacting molecules or genes.

Genes Database: Maintain gene catalogs of all sequenced
organisms and link each gene product to a pathway
component

Ligand Database: Organize a database of all chemical
compounds in living cells and link each compound to a
pathway component

Pathway Tools: Develop new bioinformatics technologies
for functional genomics, such as pathway comparison,
pathway reconstruction, and pathway design
Discussion
 Problems

Network Inference
 Micro Array, Protein Chips, other high throughput assay methods

Function prediction
 The function of 40-50% of the new proteins is unknown
 Understanding biological function is important for:









Study of fundamental biological processes
Drug design
Genetic engineering
Functional module detection
 Cluster analysis
Topological Analysis
 Descriptive and Structural
 Locality Analysis
 Essential Component Analysis
Dynamics Analysis
 Signal Flow Analysis
 Metabolic Flux Analysis
 Steady State, Response, Fluctuation Analysis
Evolution Analysis
Biological Networks are very rich networks with very limited, noisy, and
incomplete information.
Discovering underlying principles is very challenging.
Signal Transduction Model Based
Functional Module Detection Algorithm
for Protein-Protein Interaction Networks
Woochang Hwang1
Young-Rae Cho1
Aidong Zhang1
Murali Ramanathan2
1Department
of Computer Science and Engineering,
State University of New York at Buffalo
2Department
of Pharmaceutical Sciences,
State University of New York at Buffalo
University at Buffalo The State University of New York
Contents




Introduction
Protein Interaction Networks
Functional Categories
Functional Module Detection Algorithm




Signal Transduction Model (STM)
Experimental Results
Discussion
Future Works
Introduction

Cellular Functions are coordinately carried out by groups of genes and
gene products.

Detection of such functional modules in a complex molecular network
is one of the most challenging problem.

Molecular networks: high data volume, high noise level, sparse
connectivity, etc.

PPI data
 S. Cerevisae full PPI data in DIP: over 4900 proteins and 18000
interactions.
 PPI data provide us the good opportunity to analyze the
underlying principles and the structure of large living systems.
Cluster Assessment

Clustering Coefficient:





C B (v ) 

s  t  vV
 st (v)
 st
 st
(v) the
number of shortest paths from s to t that pass through the node v.
 C  G  C 

 i 

 ni 





P  1 
G 
i 0

n

 
k 1
C is the size of the cluster containing k proteins with a given function; G is
the size of the universal set of proteins of known proteins and contains n
proteins with the function.
The p-value is the probability that a cluster would be enriched with
proteins with a particular function by chance alone.
Density:

d (v )d (v )  1
 st is the number of shortest paths from node s to t and
P-value:

C (v ) 
i , jN ( v )
N(v) is the set of the direct neighbors of node v and d(v) is the
number of the direct neighbors of node v
Betweeness Centrality:

i, j 
2
Density(C ) 
2*e
n(n  1)
n is the number of proteins and e is the number of interactions in a
sub graph s of a PPI network.
Protein-Protein Interaction (PPI) Data & MIPS
Functional Category Data

DIP Yeast Protein Interaction core data
 2521 proteins, 5949 interactions
 Average clustering coefficient: 0.069
 Average path length: 5.47

MIPS Functional Category
 457 Hierarchical Functional Categories
 Sub graphs of each functional categories are
extracted from DIP core data.


Average graph density: 0.0025
Average diameter (longest path in a graph): 4.23
MIPS functional modules in DIP Protein-Protein
Interaction (PPI) Network
Figure 1. (a) Mitochodrial Transport
19 singletons
Diameter: 6
(b) Mitosis
20 singletons
Diameter: 3
Topological Properties of MIPS Functional Modules
in DIP Protein Interaction Data

Sparse connectivity : low density, isolated sub graphs and
singletons existence.

Longish shape: high diameter
Related works

Distance Based Approaches
 Several distance metrics were introduced
 Use traditional clustering algorithms

Graph Based Approaches
 Density based approaches: Maximal Cliques, Quasi
Cliques, RNSC, HCS, MCODE
 Statistical approaches: MCL, Samantha
Related works

Suffered by their limited way of clustering.

identify only the clusters with specific shapes, e.g.,
balanced round shapes, with high density .

But, the actual functional modules are not so densely
connected as they expected.

Some members in functional categories do not have direct
physical interaction with other members of the functional
category they belong to.

Modules that have longish shapes are frequently observed.

The incompleteness of clustering is another distinct
drawback of existing algorithms, which produce many
clusters with small size and singletons.
Contribution
Unexpected properties of functional categories and sparse
connectivity in PPI networks.
A relative excess of emphasis on density in the existing methods
can be preferential for detecting clusters with relatively balanced
round shapes, high discarding rate, and limit performance.


STM Clustering Model


Effective clustering should be able to detect clusters with arbitrary
shape and density if the cluster members share biological and
topological similarities.
To take those unexpected properties of PPI networks and actual
functional modules into consideration and to conquer the
drawbacks of existing approaches effectively:


STM clustering model utilizes a statistical signal transduction model to
find the modules whose members share biological common feature even
though they are sparsely connected.
STM model also adopts the network’s topological properties into the
model.
STM Clustering Model
Process 1: Simulation of dynamic statistical signal
transduction behavior in the network.

STM model simulates dynamic signal transduction behavior to
find the most influential proteins on each protein in PPI network
biologically and topologically.
Process 2: Selection of the putative cluster representatives
on each node.
Process 3: Preliminary clusters formation.

Preliminary clusters will be formed by accumulating each node
toward its chosen representatives.
Process 4: Cluster merge.



So far, STM has considered only the biological features and
topological connectivity of the network and its components, not
similarity among preliminary clusters.
Clusters that have significant interconnections between them
should have substantial similarity.
In process 4, STM will merge the clusters which has substantial
similarity.
Statistical Signal Transduction Model

Signal transduction behavior of the network is modeled by
the Erlang distribution, a special case of the Gamma
distribution.

x
b
c 1
F (c)  1  e  
k 0



x bk
k!
(1)
where c > 0 is the shape parameter, b > 0 is the scale
parameter, x >= 0 is the independent variable, usually time.
The Erlang distribution with x/b = 1 is used and the value of
c is set to the number of nodes between source protein node
and the target protein
Setting the value of x/b to unity assesses the perturbation
at the target protein when the perturbation reaches 1/e of
its initial value at the nearest neighbor of the source protein
node.
Statistical Signal Transduction Model


Statistically, the Erlang distribution represents the time required
to carry out a sequence of c tasks whose durations are identical,
exponential probability distributions.
It represents the chance that the actual time to accomplish c
tasks will be less than or equal to b.
Figure 2. The pharmacodynamic signal transduction model whose bolus
response is an Erlang distribution. The b is the time constant for signal
transfer and c is the number of compartments.
Topologically Modified Signal
Transduction Model

The Erlang distribution was further weighted to reflect network
topology.
S (v  w) 


iP ( v ,w) d (i)
 F (c )
(2)
d(i) is the degree of node i, P(v,w) is the set of all visited nodes
on the shortest path from node v to node w excluding the
source node v and target node w, and F(c) is the signal
transduction behavior function.
The perturbation induced by the source protein node was
assumed to be proportional to its degree and to follow the
shortest path to the target protein node.


d (v )
Our choice of the shortest path is motivated by the finding that the
majority of flux prefers the path of least resistance in many
physicochemical and biological systems.
During transduction to the target protein node, the perturbation
was assumed to be dissipated at each intermediate node visited
in proportion to the reciprocal of the degree of each
intermediate node visited.
Process 1: Signal Transduction Simulation
Figure 3. Blue arrows are signals from node A and Red ones are from node H.
Results for other nodes are not shown.
Process 1: Signal Transduction Simulation
Figure 3. Blue arrows are signal from node A and Red ones are from node H.
Results for other nodes are not shown.
Process 1: Signal Transduction Simulation
Figure 3. Blue arrows are signal from node A and Red ones are from node H.
Results for other nodes are not shown.
Process 1: Signal Transduction Simulation
Figure 3. Blue arrows are signal from node A and Red ones are from node H.
Results for other nodes are not shown.
Process 2: Representatives Selection
Figure 4. A simple network. Each box contains the numerical values obtained from
Equation 2, from source nodes A, F, G, and H to other target nodes although signals
should be propagated from every node in the network. Results for other nodes are
not shown.
Process 3: Preliminary Clusters Formulation
Figure 5. Three preliminary clusters, {A, B, C, D, E, F}, {F, G, L, N}, {G,
H, I, J, K, M}, are obtained after the Process 3.
Cluster Merge

Similarity of two clusters i and j
Similarity(i, j ) 
interconnectivity(i, j )
minsize(i, j )
(3)

where interconnectivity(i, j) is the number of connections
between clusters i and j, and minsize(i, j) is the size of the
smaller cluster among clusters i and j.

The pair of clusters that have the highest similarity are merged in
each iteration and the merge process iterates until the highest
similarity of all cluster pairs is less than a given threshold.

We see when interconnectivity(i, j)>=minsize(i, j), clusters i and
j have substantial interconnections.
Process 4: Cluster Merge
Figure 6. Two clusters, {A, B, C, D, E, F, G, L, N}, {G, H, I, J, K, M}, are
obtained after the Merge process when 1.0 is used as the merge
threshold.
Process 4: Cluster Merge
Figure 7. Three clusters, {A, B, C, D, E, F}, {F, G, L, N}, {G, H, I, J, K,
M}, are obtained after the Process 4 when 2.0 is used as the merge
threshold.
Experimental Results

Protein Interaction Data

The core data of S. Cerevisiae was obtained from the
DIP database.


2526 proteins and 5949 filtered reliable physical
interactions.
Species such as S. Cerevisae provide important test
beds for the study of the PPI networks since it is a wellstudied organism for which most proteomics data is
available for the organism, by virtue of the availability
of a defined and relatively stable proteome, full genome
clone libraries, established molecular biology
experimental techniques and an assortment of well
designed genomics databases.
Clustering
Performance
Analysis
60 clusters
Average size: 40.1
Average Density: 0.2145
Average P-value: 13.7
Average Hit %: 51.7
Average Unknown %: 5.1
Table 1. all 60 clusters that
have more than 4 proteins
Cluster
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Protein
Density Distribution (%)
no
H
D
U
214
0.019
24.7
69.6
5.6
188
0.015
69.1
25
5.8
181
0.022
22.0
72.3
5.5
170
0.028
46.4
42.9
10.5
131
0.028
37.4
55.7
6.8
125
0.030
60.8
33.6
5.6
113
0.027
19.4
71.6
8.8
79
0.045
17.7
73.4
8.8
78
0.033
26.9
62.8
10.2
76
0.041
38.1
59.2
2.6
72
0.030
5.55
84.7
9.7
68
0.064
66.1
25
8.8
61
0.041
40.9
52.4
6.5
58
0.064
72.4
27.5
0
53
0.048
15.0
71.6
13.2
50
0.064
66
32
2
45
0.055
24.4
73.3
2.2
44
0.058
59.0
36.3
4.5
39
0.072
10.2
89.7
0
36
0.125
58.3
36.1
5.5
29
0.091
55.1
44.8
0
28
0.074
14.2
78.5
7.1
27
0.119
29.6
66.6
3.7
26
0.153
53.8
46.1
0
25
0.09
28
68
4
25
0.116
68
28
4
22
0.151
59.0
36.3
4.5
21
0.147
76.1
19.0
4.7
20
0.2
75
20
5
19
0.228
78.9
15.7
5.2
17
0.220
70.5
29.4
0
17
0.183
23.5
76.4
0
15
0.304
86.6
13.3
0
14
0.142
50
42.8
7.1
13
0.564
76.9
23.0
0
13
0.358
84.6
15.3
0
13
0.410
69.2
23.0
7.6
13
0.179
61.5
30.7
7.6
12
0.196
16.6
75
8.3
12
0.363
58.3
41.6
0
12
0.166
16.6
75
8.3
11
0.218
54.5
45.4
0
11
0.2
72.7
27.2
0
10
0.466
80
20
0
9
0.361
77.7
22.2
0
8
0.321
50
37.5
12.5
8
0.321
75
25
0
8
0.321
37.5
62.5
0
7
0.333
42.8
57.1
0
7
0.333
57.1
28.5
14.2
7
0.285
28.5
71.4
0
6
0.333
50
33.3
16.6
5
0.4
100
0
0
5
0.6
100
0
0
5
0.4
100
0
0
5
0.4
20
40
40
5
0.5
40
40
20
5
0.5
80
20
0
5
0.6
40
60
0
5
0.4
60
40
0
P-value
Function
(-log10)
43.9 Nuclear transport
36.4 Cell cycle and DNA processing
17.2 Cytoplasmic and nuclear protein degradation
31.6 Transported compounds (substrates)
28.6 Vesicular transport (Golgi network, etc.)
32.2 tRNA synthesis
11.8 Actin cytoskeleton
12.3 Homeostasis of protons
12.5 Ribosome biogenesis
20.2 rRNA processing
6.23 Calcium binding
44.5 mRNA processing
11.5 Cytoskeleton
37.4 General transcription activities
7.93 MAPKKK cascade
33.5 rRNA processing
11.1 Metabolism of energy reserves
5.08 Metabolism
7.33 Cell-cell adhesion
16.9 Vesicular transport
8.29 Phosphate metabolism
4.49 Lysosomal and vacuolar protein degradation
7.28 Cytokinesis (cell division) /septum formation
28.6 Peroxisomal transport
4.59 Regulation of C-compound and carbohydrate utilization
12.9 Cell fate
11.4 DNA conformation modification
23.9 Mitochondrial transport
24.0 rRNA synthesis
17.9 Splicing
19.7 Microtubule cytoskeleton
8.17 Regulation of nitrogen utilization
31.3 Energy generation
8.98 Small GTPase mediated signal transduction
15.9 Mitosis
12.4 DNA conformation modification
17.6 3'-end processing
6.70 DNA recombination and DNA repair
3.92 Unspecified signal transduction
14.7 Posttranslational modification of amino acids
2.35 Autoproteolytic processing
2.91 Transcriptional control
8.16 Enzymatic activity regulation / enzyme regulator
14.8 Translation initiation
12.8 Translation initiation
5.60 Metabolism of energy reserves
9.00 Modification by ubiquitination, deubiquitination
3.66 Mitosis
3.46 DNA damage response
4.09 Vacuolar transport
4.41 Biosynthesis of serine
2.38 Modification by phosphorylation, dephosphorylation, etc.
6.99 Meiosis
7.01 Vacuolar transport
8.53 ER to Golgi transport
1.81 cAMP mediated signal transduction
3.11 Oxidative stress response
4.43 Intracellular signalling
4.19 Tetracyclic and pentacyclic triterpenes
4.11 Mitochondrial transport
Comparative Analysis
Methods
Number of
Avg. size of
Clusters
Clusters
Percent of
Discarded
Nodes (%)
STM
Maximal Clique
Quasi Clique
Samantha
Minimum Cut
Betweeness Cut
MCL
60
120
103
64
114
180
163
7.8
98.4
80.8
79.9
35.0
21.0
36.7
40.1
5.65
11.2
7.9
13.5
10.26
9.79
Avg. P-Score
Based on
Functions
(-log10P)
13.7
10.61
11.50
9.16
8.36
8.19
8.18
Avg. P-Score
Based on
Localizations
(-log10P)
7.42
7.93
6.58
4.89
4.75
4.18
3.97
Table 2. Performance analyses of the clusters more than size 4.
 Other methods can only detect the clusters with small size.
 Relatively high P-scores regarding their high discarding rates on other
methods (e.g., Maximal Clique, Quasi Clique, Samantha)
 Due to the mass production of small size clusters which have less
than 5 members
 Due to the discard of sparsely connected proteins.
 Due to high overlaps among many small clusters which are highly
enriched for the same function.
Computational Complexity




Our signal transduction based model is fundamentally
established on all pairs shortest path searching
algorithm to measure the distance between all pairs of
nodes: O(V2logV+VE) where V is the number of nodes
and E is the number of edges in a network.
The time required to find the best cluster pair that has
the most interconnections is O(k2logk) by using heapbased priority queue, where k is the number of
preliminary clusters.
But k is much smaller than V in sparse networks like the
Yeast PPI network.
So the total time complexity of our algorithm is
bounded by the time consumed in measuring the
distance between all pairs of nodes, which is
O(V2logV+VE).
Discussion





In head-to-head comparisons, our algorithm
outperformed competing approaches and is capable of
effectively detecting both dense and sparsely connected,
biologically relevant functional modules with fewer
discards.
The clusters identified had p-values that are 2.2 orders
of magnitude or approximately 125-fold lower than
Quasi clique, the best performing alternative clustering
method, on biological function.
The incompleteness of clustering is another distinct
drawback of existing algorithms, which produce many
clusters with small size and singletons.
Our method discarded only about 7.8% of proteins
which is tremendously lower than the other approaches
did, 59% in average.
In conclusion, our method has strong
pharmacodynamics-based underpinnings and is an
effective, versatile approach for analyzing proteinprotein interactions.
Thanks!