BIOLOGICAL NETWORKS

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BIOLOGICAL NETWORKS

• Woochang Hwang

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BIOLOGICAL NETWORKS

• Introduction
• Biological Networks
• Protein-Protein Interaction Networks
• Signaling Metabolic Pathway Networks
• Expression Networks
• Biological Networks Properties
• Databases
• Discussion
• STM Clustering Model

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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

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Proteomics
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From the particular to the universal
A.-L- Barabasi Z. Oltvai, Science, 2002
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Genome Size
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Proteom Size (PDB)
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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

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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.

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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.

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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.)

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Protein Interaction Network
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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.

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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.

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Protein Interactions
P. Uetz, et al. Nature, 2000 Ito et al., PNAS,
2001
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Yeast Protein Interaction Network
Nodes proteins Links
physical interactions (binding)
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Pathway Networks
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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

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A Pathway Example
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A Pathway Example
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A Pathway Example
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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.

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Regulatory Network
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Expression Network

• A network representation of genomic data.
• Inferred from genomic data, i.e. microarray.

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BIOLOGICAL NETWORK PROPERTY

• Interaction Network
• Pathway Network
• Regulatory Network
• Expression Network

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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 nodes neighbors are connected to
  each other

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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

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The Barabási-Albert BA model
ER Model
WS Model
Actors
Power Grid
www
(a) Random Networks
(b) Power law Networks
Power Law Network (Scale Free)

• The probability of finding a highly connected
  node decreases exponentially with k

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Small World Property

• A small average path length
• Any node can be reached within a small number of
  edges, 45 hops.

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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

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Attack Tolerance

• Complex systems maintain their basic functions
  even under errors and
  failures
  (cell ? mutations Internet ?
  router breakdowns)

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Attack Tolerance

• Robust. For ?lt3, removing nodes does not break
  network into islands.
• Very resistant to random attacks, but attacks
  targeting key nodes are more dangerous.

Max Cluster Size
Path Length
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Protein Interaction Network
H. Jeong, S.P. Mason, A.-L. Barabasi Z.N.
Oltvai, Nature, 2001
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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.

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

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Databases
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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.

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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

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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)

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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

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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

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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

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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

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Contents

• Introduction
• Protein Interaction Networks
• Functional Categories
• Functional Module Detection Algorithm
• Signal Transduction Model (STM)
• Experimental Results
• Discussion
• Future Works

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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.

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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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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

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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
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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

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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

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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.

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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 networks topological
  properties into the model.

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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.

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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 gt 0 is the shape parameter, b gt 0 is the
  scale parameter, x gt 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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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.
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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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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.
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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.
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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.
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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.
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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.
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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.

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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)gtminsize(i,
  j), clusters i and j have substantial
  interconnections.

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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.
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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.

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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.

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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
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Comparative Analysis
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.

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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(V2logVVE) 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(V2logVVE).

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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.

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Thanks!