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.

1. BIOLOGICAL
NETWORKS
Woochang Hwang

2. BIOLOGICAL NETWORKS
 Introduction
 Biological Networks
 Protein-Protein Interaction Networks
 Signaling & Metabolic Pathway Networks
 Expression Networks
 Biological Networks’ Properties
 Databases
 Discussion
 STM Clustering Model

3. Introduction

4. 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

5. Proteomics
Genomics
Proteomics
Structural Proteomics Functional Proteomics
Structure Determination
Database
/ Knowledge Source
Homology Modeling
Protein-Protein Interaction
& Networking
Protein Expression
Post-tranlational
Modification
Database
/ Knowledge Source

6. From the particular to the universal
A.-L- Barabasi & Z. Oltvai, Science, 2002

7. Genome Size

8. Proteom Size (PDB)

9. 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
BIOLOGICAL NETWORK

10. 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.

11. 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.

12. 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.)

13. Protein Interaction Network

14. 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”.

15. 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.

16. Protein Interactions
P. Uetz, et al. Nature, 2000; Ito et al., PNAS, 2001; …

17. Yeast Protein Interaction Network
Nodes: proteins
Links: physical
interactions (binding)

18. Pathway Networks

19. 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

20. A Pathway Example

21. A Pathway Example

22. A Pathway Example

23. 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.

24. Regulatory Network

25. Expression Network
 A network representation of genomic data.
 Inferred from genomic data, i.e. microarray.

26. BIOLOGICAL NETWORK
PROPERTY
 Interaction Network
 Pathway Network
 Regulatory Network
 Expression Network

27. 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

28.  PREFERENTIAL ATTACHMENT on Growth: the probability that a
new vertex will be connected to vertex i depends on the connectivity
of that vertex:
( ) i
i
j
j
k
k
k
 

Power Law Network

29. The Barabási-Albert [BA] model
ER Model WS Model Actors Power Grid www
 The probability of finding a
highly connected node decreases
exponentially with k:
( ) ~
P K K 

(a) Random Networks (b) Power law Networks
Power Law Network (Scale Free)

30. Small World Property
 A small average path length
 Any node can be reached within a small
number of edges, 4~5 hops.

31.  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
Power Law Network

32. Attack Tolerance
 Complex systems maintain their basic functions
even under errors and failures
(cell  mutations; Internet  router breakdowns)
node failure

33. Attack Tolerance
 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

34. Protein Interaction Network
)
exp(
)
(
~
)
( 0
0


k
k
k
k
k
k
P


 
H. Jeong, S.P. Mason, A.-L. Barabasi & Z.N. Oltvai, Nature, 2001

35. 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.

36. Hierarchical Modularity
E. Ravasz et al., Science, 2002

37. Hierarchical Modularity
Metabolic Networks Protein Networks
E. Ravasz et al., Science, 2002

38. 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.

39. Databases

40. 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 Databases

41. Protein Interaction Databases
 Species-specific
 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

42. Protein Interaction Databases
 Interaction type-specific
 DIP - Database of Interacting Proteins
 DPInteract - DNA-protein interactions
 Inter-Chain Beta-Sheets (ICBS) - A database of protein-
protein 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)

43. 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

44. 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

49. 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.

50. 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

51. Contents
 Introduction
 Protein Interaction Networks
 Functional Categories
 Functional Module Detection Algorithm
 Signal Transduction Model (STM)
 Experimental Results
 Discussion
 Future Works

52. 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.

53. Cluster Assessment
 Clustering Coefficient:
 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:
 is the number of shortest paths from node s to t and (v) the
number of shortest paths from s to t that pass through the node v.
 P-value:
 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:
 n is the number of proteins and e is the number of interactions in a
sub graph s of a PPI network.
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54. 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

55. 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

56. 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

57. 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

58. 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.

59. Contribution
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.
 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.

60. 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.

61. Statistical Signal Transduction Model
 Signal transduction behavior of the network is modeled by
the Erlang distribution, a special case of the Gamma
distribution.
(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.
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62. 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.

63. Topologically Modified Signal
Transduction Model
 The Erlang distribution was further weighted to reflect network
topology.
(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.
 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.
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64. 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.

65. 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.

66. 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.

67. 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.

68. 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.

69. 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.

70. Cluster Merge
 Similarity of two clusters i and 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.
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71. 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.

72. 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.

73. 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 well-
studied 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.

74. 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
Distribution (%)
Cluster Protein
no
Density
H D U
P-value
(-log10)
Function
1 214 0.019 24.7 69.6 5.6 43.9 Nuclear transport
2 188 0.015 69.1 25 5.8 36.4 Cell cycle and DNA processing
3 181 0.022 22.0 72.3 5.5 17.2 Cytoplasmic and nuclear protein degradation
4 170 0.028 46.4 42.9 10.5 31.6 Transported compounds (substrates)
5 131 0.028 37.4 55.7 6.8 28.6 Vesicular transport (Golgi network, etc.)
6 125 0.030 60.8 33.6 5.6 32.2 tRNA synthesis
7 113 0.027 19.4 71.6 8.8 11.8 Actin cytoskeleton
8 79 0.045 17.7 73.4 8.8 12.3 Homeostasis of protons
9 78 0.033 26.9 62.8 10.2 12.5 Ribosome biogenesis
10 76 0.041 38.1 59.2 2.6 20.2 rRNA processing
11 72 0.030 5.55 84.7 9.7 6.23 Calcium binding
12 68 0.064 66.1 25 8.8 44.5 mRNA processing
13 61 0.041 40.9 52.4 6.5 11.5 Cytoskeleton
14 58 0.064 72.4 27.5 0 37.4 General transcription activities
15 53 0.048 15.0 71.6 13.2 7.93 MAPKKK cascade
16 50 0.064 66 32 2 33.5 rRNA processing
17 45 0.055 24.4 73.3 2.2 11.1 Metabolism of energy reserves
18 44 0.058 59.0 36.3 4.5 5.08 Metabolism
19 39 0.072 10.2 89.7 0 7.33 Cell-cell adhesion
20 36 0.125 58.3 36.1 5.5 16.9 Vesicular transport
21 29 0.091 55.1 44.8 0 8.29 Phosphate metabolism
22 28 0.074 14.2 78.5 7.1 4.49 Lysosomal and vacuolar protein degradation
23 27 0.119 29.6 66.6 3.7 7.28 Cytokinesis (cell division) /septum formation
24 26 0.153 53.8 46.1 0 28.6 Peroxisomal transport
25 25 0.09 28 68 4 4.59 Regulation of C-compound and carbohydrate utilization
26 25 0.116 68 28 4 12.9 Cell fate
27 22 0.151 59.0 36.3 4.5 11.4 DNA conformation modification
28 21 0.147 76.1 19.0 4.7 23.9 Mitochondrial transport
29 20 0.2 75 20 5 24.0 rRNA synthesis
30 19 0.228 78.9 15.7 5.2 17.9 Splicing
31 17 0.220 70.5 29.4 0 19.7 Microtubule cytoskeleton
32 17 0.183 23.5 76.4 0 8.17 Regulation of nitrogen utilization
33 15 0.304 86.6 13.3 0 31.3 Energy generation
34 14 0.142 50 42.8 7.1 8.98 Small GTPase mediated signal transduction
35 13 0.564 76.9 23.0 0 15.9 Mitosis
36 13 0.358 84.6 15.3 0 12.4 DNA conformation modification
37 13 0.410 69.2 23.0 7.6 17.6 3'-end processing
38 13 0.179 61.5 30.7 7.6 6.70 DNA recombination and DNA repair
39 12 0.196 16.6 75 8.3 3.92 Unspecified signal transduction
40 12 0.363 58.3 41.6 0 14.7 Posttranslational modification of amino acids
41 12 0.166 16.6 75 8.3 2.35 Autoproteolytic processing
42 11 0.218 54.5 45.4 0 2.91 Transcriptional control
43 11 0.2 72.7 27.2 0 8.16 Enzymatic activity regulation / enzyme regulator
44 10 0.466 80 20 0 14.8 Translation initiation
45 9 0.361 77.7 22.2 0 12.8 Translation initiation
46 8 0.321 50 37.5 12.5 5.60 Metabolism of energy reserves
47 8 0.321 75 25 0 9.00 Modification by ubiquitination, deubiquitination
48 8 0.321 37.5 62.5 0 3.66 Mitosis
49 7 0.333 42.8 57.1 0 3.46 DNA damage response
50 7 0.333 57.1 28.5 14.2 4.09 Vacuolar transport
51 7 0.285 28.5 71.4 0 4.41 Biosynthesis of serine
52 6 0.333 50 33.3 16.6 2.38 Modification by phosphorylation, dephosphorylation, etc.
53 5 0.4 100 0 0 6.99 Meiosis
54 5 0.6 100 0 0 7.01 Vacuolar transport
55 5 0.4 100 0 0 8.53 ER to Golgi transport
56 5 0.4 20 40 40 1.81 cAMP mediated signal transduction
57 5 0.5 40 40 20 3.11 Oxidative stress response
58 5 0.5 80 20 0 4.43 Intracellular signalling
59 5 0.6 40 60 0 4.19 Tetracyclic and pentacyclic triterpenes
60 5 0.4 60 40 0 4.11 Mitochondrial transport
Table 1. all 60 clusters that
have more than 4 proteins

75. Comparative Analysis
Table 2. Performance analyses of the clusters more than size 4.
Methods Number of
Clusters
Avg. size of
Clusters
Percent of
Discarded
Nodes (%)
Avg. P-Score
Based on
Functions
(-log10P)
Avg. P-Score
Based on
Localizations
(-log10P)
STM 60 40.1 7.8 13.7 7.42
Maximal Clique 120 5.65 98.4 10.61 7.93
Quasi Clique 103 11.2 80.8 11.50 6.58
Samantha 64 7.9 79.9 9.16 4.89
Minimum Cut 114 13.5 35.0 8.36 4.75
Betweeness Cut 180 10.26 21.0 8.19 4.18
MCL 163 9.79 36.7 8.18 3.97
 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.

76. 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 heap-
based 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).

77. 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 protein-
protein interactions.

78. Thanks!