Clustering of Interaction Network

1
Clustering of Interaction Network

• Definition
• Process to detect densely connected sub-graphs
• Determines protein complexes or functional
  modules
• Difficulties
• Noisy data (too many false positives or false
  negatives)
• Cannot be solved by traditional clustering
  techniques
• Difficult to define the pair-wise distance
  between proteins in the network.
• Protein complexes may overlap.
• Disparate sources of data
• Different reliabilities
• 1750
• Small overlaps
• lt17

2
Protein Interaction Network

• Undirected, unweighted graph
• Node represents protein, edge represents
  interaction

• Example of Yeast protein interaction network
• Importance
• Provide a global view of cellular organizations
  and biological functions
• Applicable to systematic approaches for
  functional knowledge discovery
• Problem
• Large scale
• Complex connectivity

3
Structural Property

• Small-world Phenomenon ( Watts Strogatz )
• Appearance of networks in the middle of regular
  and random networks
• Higher average clustering coefficient than
  expected by random chance
• Significantly small average shortest path length
• Scale-free Distribution ( Barabasi Albert )
• Network growth by preferential attachment
• Power law degree distribution a few high degree
  nodes, many low degree nodes
• Clustering coefficient distribution independent
  to degree

Protein Interaction Database DIP MIPS
density 0.0015 0.0015
average clustering coefficient 0.2283 0.2878
average shortest path length 4.14 4.43
degree distribution (?) 1.77 1.64
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Conventional Graph Clustering Approaches

• Density-based Clustering
• Finding densely connected sub-graphs ( e.g.
  Maximal clique algorithm )
• Hierarchical Clustering
• Top-down approach iteratively partitioning a
  graph
• ( e.g. Minimum cut algorithm )
• Bottom-up approach iteratively merging nodes
• ( e.g. Node merging by common neighbors )
• Problems
• Computationally inefficient
• Unable to detect overlapping clusters
• Discard sparsely connected nodes

5
Functional Influence Model

• Functional Flow
• treat each protein of known functional annotation
  as a source of functional flow for that
  function
• simulating the spread of this functional flow
  through the neighborhoods surrounding the sources
  with random walk.
• functional score the amount of flow that the
  protein has received for that function

u
v
Func(a)
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Functional Influence

• Functional Influence based on Distance.

• Weibull Distribution

• Curve Fitting

d is the distance between two nodes
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Functional Influence Model

• Information Flow Simulation
• Computation of functional influence infs(x) of s
  on x ? V based on Shortest Path
• Input a weighted interaction network and a
  source node s
• Output functional influence pattern of s
• Measurements

• PathRatio
• PathRatio is the natural aging or losing of
  information propagation in the network.
• SPath(s,y) is all the shortest paths
  between node s and node y.
• PR(s,y) is the PathRatio between node s and node
  y.
• PathStrength
• PS(P) measures the strength of path P
  using weights on the edges along the path P.

8
Framework of functional influence simulation

• Algorithm
• Initialize inf(s)
• Compute initial flow I(s ? y) by
• Update inf(y) by
• Repeat 3 for every node in the network.
• Finally, the functional profile,
• is generated for every node in the network.

F(d) is the functional distribution model. d is
the distance between node s and node y. PR(s,y)
is the Path Resistance between node s and node y.
Inf(s) is the initial functional influence from
node s. Infs(y) is the functional influence
received by node y from node s.
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Functional Module Detection (FMD)
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FlowChart for functional module detection
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Functional Modularity Detection

• Experimental Data
• DIP (4935 proteins, 14162 interaction)
• Evaluation
• Functional categories and annotations from MIPS
• Hyper-geometric p-value
• Result

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Computational Epidemiology

• Computational Epidemiology
• is a multidisciplinary field utilizing
  techniques to develop tools and models to aid
  epidemiologists in their study of the spread of
  diseases.

1. Developing a virus spread and containment
respond model
4. Analyzing results of the containment strategy
(death toll vs. strategies)
2. Understanding virus spread and identifying
critical properties
3. Utilizing this finding into real infectious
virus spread
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Virus Spread Network Model

• What represent nodes and edges in virus spread
  network model?
• Node
• Person (community network)
• Town or place (road network)
• Edge
• Interaction (community network)
• Pathway (road network)
• Weight of nodes and edges
• Changed by time t based on virus spread dynamics
  model
• Node weight Status of health (0 1)
• Edge weight Status of strength (0 1)

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Model Scheme

• Spread Model
• Spreading phase edges which are in the region of
  spreading will be damaged
• Defense Model
• Signaling and propagation phase nodes which have
  a certain number of damaged edges will send
  signals to neighbor nodes
• Defense action phase nodes which have a certain
  level of signals from neighbor nodes will remove
  all edges of those nodes

Virus progression to neighbor nodes
Signaling alarms to neighbor nodes from infected
neighbor node
Culling nodes to prevent from virus progression
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Spread Model

• Spreading Model
• Simulating disease spreading
• Damaging nodes and edges which are in a virus
  spread radius from center
• Virus Spread by r(t)

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Defense Model

• Defense Model
• Simulating defense system of disease spreading
  and message spreading
• Culling interactions from damaged nodes in order
  to stop spreading (Edge Culling in Green Circles)

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Problem / Solution Approach

• Which element of virus spread system has the
  greatest impact on containment campaign?
• Identifying critical element of system by
  computational modeling and stochastic simulation.
• How to plan a effective containment campaign for
  minimizing damages by virus spread?
• Mining best combination of critical parameters
  under certain conditions.

Parameters
Critical parameter
Simulation Analysis
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Application

• Virus Spread Simulation on the road network at
  the city of Oldenburg, German
• Green edges Healthy edges
• Red edges Damaged edges by spread process
• Blue edges Damaged edges by defense process

Uncontrolled ? 0.02
Intermediate ? 0.12
Controlled ? 0.22


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Osteoporosis

• Osteoporosis
• Definition a systemic skeletal disease
  characterized by low bone mass and
  micro-architectural deterioration of bone tissue
  leading to enhanced bone fragility and a
  consequent increase in fracture risk
• 25 million people in the United States are
  suffered.
• 10 billion dollars are expended by medical
  charges including rehabilitation and treatment
  facilities.
• Research Funding will be 200 billion by the year
  of 2040

Normal
Osteoporosis
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Challenges

• Diagnosis of Osteoporosis?
• Traditional method of evaluating bone strength is
  by assessing bone mineral density (BMD).
• Limitations on BMD
• A major limitation of BMD is that it incompletely
  reflects variation in bone strength.
• Other factors like bone microarchitecture
  contribute substantially to bone strength
• By evaluating bone microstructure we can improve
  determination of bone quality and strength

Computational Model on Bone Microstructure
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Computational Model on Bone Microstructure

• Questions
• What is the better way to evaluate bone strength?
• How can we identify fragile locations of the bone
  structure?
• Why dont we think this problem in a new
  direction?
• Let me think this problem with the structural
  point of view.
• Graph-based approach of bone microstructure
• Bone microstructure contributes on bone strength.
• We suppose rod-like mineral fibers represented by
  edges in a graph.
• It is capable of quantitative
• assessment of bone mineral
• density and bone micro-architecture

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Model Approach

• Bone is not a uniformly solid material, but
  rather has some spaces between its hard elements.
• Designing a network approach model for the bone
  microstructure.
• Quantitative assessment of bone mineral density
  could be successfully done with this approach.

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Bone Network Model

• Creating Bone Network
• A femur bone image from patients with
  osteoporosis by DXA scan.
• By image profiling on DXA scan image, we create
  bone network based on the bone density.
• What represent nodes and edges in bone network
  model?
• Node fiber binding point for bone cell movements
  and biochemical interactions
• Edge a group of mineralized fibers
• Weight of nodes and edges
• Node weight average weight of directly connected
  edges
• Edge weight Strength status of mineralized fibers

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Problem / Solution Approach

• What alternative ways for determining the
  strength of bone rather than Bone Mineral Density
  (BMD)?
• ?Designing a computational model of bone
  microstructure.
• How can we identify fragile locations of the bone
  structure?
• ?Creating algorithms for mining weak locations
  from a computational model of bone microstructure.

Human Bone
Bone Model
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Identifying Critical Locations

• Information Propagation Model
• An algorithm to find critical edges in bone
  network
• Measuring the quantity of stress energy in each
  edge
• Cutting the most critical edge by Information
  Propagation Model
• Iteratively run to find the next critical edges.
• It stops at the first isolated network

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Conclusions

• Various applications are generating data very
  rapidly and in great volume, demanding data
  mining approaches.
• Network-based approaches look promising to solve
  complex problems.
• This research requires close collaboration among
  multidisciplinary groups.
• Semi-supervised approaches to integrate domain
  knowledge into data mining tools are important to
  the success of the research.