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BIOLOGICAL NETWORKS

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Title: BIOLOGICAL NETWORKS


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
6
From the particular to the universal
A.-L- Barabasi Z. Oltvai, Science, 2002
7
Genome Size
8
Proteom Size (PDB)
9
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

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 nodes neighbors are connected to
    each other

28
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

29
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

30
Small World Property
  • A small average path length
  • Any node can be reached within a small number of
    edges, 45 hops.

31
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

32
Attack Tolerance
  • Complex systems maintain their basic functions
    even under errors and
    failures
    (cell ? mutations Internet ?
    router breakdowns)

33
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
34
Protein Interaction Network
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
Protein Networks
Metabolic 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
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.

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

45
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This is the expanded
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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

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

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.

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
  • 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.

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 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.

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.

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

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
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.
  • 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(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).

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!
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