Gene Network Modeling

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Gene Network Modeling

• Prof. Yasser Kadah
• Eng. Fadhl Al-Akwaa

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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

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From The Last Lecture

• DNA sequence A,T,C,G
• ATCGAATCGA
• Protein sequence except B, J, O, U, X, Z
• KMLSLLMARTYW

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The Central DogmaProtein Synthesis
Cell Function
Transcriptome
Proteome
Genome
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Bioinformatics Important Challenges
Protein Function Protein 3D Structure
Gene Predication
Gene Function
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Public Data Base
Protein sequence KMLSLLMARTYW
DNA sequence A,T,C,G
Microarray
Gene Expression Level
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Gene Expression
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Microarray Technology
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Translation Rate
Protein Level
Gene Expression Level
Transcription Rate
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Translation Rate


Protein Level
Gene Expression Level

Transcription Rate
-
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Translation Rate


Protein Level
Gene Expression Level

Transcription Rate
-
?
?
?
?
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OUTLINES

• What is the Gene Regulatory Network?
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Future work
• Reference

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What is Gene Regulatory Network?
(GRN)
Gene A
Gene C
Gene D
Gene B
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GRN An example Fission yeast
Lackner DH ,2007
http//www.sanger.ac.uk/Info/News-releases/2007/07
0413.shtml
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http//en.wikipedia.org/wiki/Metabolic_network_mod
elling
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http//www.enm.bris.ac.uk/anm/summerschools/comple
xity/imagery/191.html
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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

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Why build a Gene Network? Functional Genomics

• Allow researchers to make predictions about gene
  function that can then be tested at the bench.
• The Focus is gradually shifting to Functional
  Genomics.

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Application of GRN Translational Genomics

• we can study the effects of a compound (such as a
  drug) on the level of expression of many genes.
• Translational Genomics
• The mission of the Translational Genomics
  is
• to translate genomic discoveries into
  advances
• in human health.

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Application of GRN Understanding Experimental
data

• Biologists are expecting powerful computational
  tools to extract functional
• information from the Experimental data.

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GRN Model Objective

• Construct a gene network model that
• Describes known genes interactions well
• Predicts interactions not known so far
• Allows for Drug effect simulation
• Understand the otology of the Disease

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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

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GRN Construction Methodology

• Forward Engineering
• Inverse Engineering Traditional methodology

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Forward Engineering
Hard
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Reverse Engineering
Model Gene Network
very difficultinverse problem
Possible forward problem
Microaary Data
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Reverse Engineering
Boolean networks
easy
Boolean data
easy
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Data Required DNA Microarray
gene 1 gene 2 gene 3
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Data Required Gene Expression Matrix
t1 t2 t3 t4
g1 0 1 2 1
g2 1 2 1 0
g3 0 1 1 1.
g4 1 2 1 0
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Data Required Gene Expression Matrix
t1 t2 t3 t4
g1 0 1 2 1
g2 1 2 1 0
g3 0 1 1 1.
g4 1 2 1 0
a1 a2 a3 a4
g1 0 3 1 1
g2 1 2 1 0
g3 0 1 1 1.
g4 1 2 1 0
Time serious
Snap Shot
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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN Modeling Steps
• GRN Models
• GRS Software
• Next work
• Reference

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Overview of steps in modeling and control of
Probabilistic Boolean networks Ranadip Pal,2007
Microarray Image
Data Extraction
Discretization
A3
A1
A2
C
Gene Expression Extraction
B
Discretization
Grid Alignment
Segmentation
Hypothesis testing
Upregulated
1
99

t1
0
1.72 2.25 0.94 1.56
t2
-1
Down regulated
t1
t2
Application of Stationary Policy
Design of Optimal Control Policy
Gene Selection
BN generation
(I) Penalty Assignment
Seed Algorithm
Y
PBN steady state matched
(II) Formulation of Optimal Control
Problem
Dynamic Programming
Original Steady State
Optimal Control Policy
F
E
Prior Biological Knowledge
D
Gene Selection
Steady State using Control
Network Generation
G
H
Control of Network
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GRN modeling steppes Discretization
gene 1 gene 2 gene 3
assume that genes exist in two states on and off
if expression of gene i is above level ti
consider it on, otherwise, consider it off
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GRN modeling steppes Discretization
t1
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GRN modeling steppes Discretization
on
on
on
on
on
on
on
t1
off
off
off
off
off
off
off
off
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GRN modeling steppes Discretization
gene 1 gene 2 gene 3
t1
t2
t3
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GRN modeling steppes Discretization
gene 1 gene 2 gene 3
on
on
on
on
on
on
on
on
on
t1
on
on
on
t2
off
on
on
t3
off
off
off
off
off
off
off
off
off
off
off
off
off
off
off
off
off
off
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GRN modeling steppes Discretization

• we obtain the following discretized gene
  expression data

time 0 5 10 15 20 25 30 35 40 45 50 55
gene 1 0 0 0 0 0 0 1 1 1 1 1 1
gene 2 0 0 0 0 0 0 0 1 1 0 0 0
gene 3 1 1 1 1 1 1 1 0 0 0 0 0

• the gene expression data is now in the form of
  bit streams

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GRN modeling steppes Discretization
Up-regulated 1
Unchanged 0
Down-regulated -1
assume that genes exist in three states
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GRN modeling steppes Gene SelectionClustring
a1 a2 a3 a4
g1 0 1 2 1
g2 1 2 1 0
g3 0 1 1 1.
g4 1 2 1 0
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Clustering Steps Correlation

• Choose a similarity metric to compare the
  transcriptional response or the expression
  profiles
• Pearson Correlation
• Spearman Correlation
• Euclidean Distance

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Clustering Steps Correlation Algorithm

• Correlation coefficients are values from 1 to 1,
  with 1 indicating a similar behavior, 1
  indicating an opposite behavior and 0 indicating
  no direct relation.

g1 g2 g3 g4 g5
g1 1 0.23 0.00 0.95 -0.63
g2 -1 1 0.91 0.56 0.56
g3 0 0.23 1 0.32 0.77
g4 1 0.5 0.56 1 -0.36
g5 -1 0.91 0.32 0.4 1
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Clustering Steps Clustering Algorithm

• Choose a clustering algorithm
• Hierarchical
• K-means

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Hierarchical Clustering
g1 g2 g3 g4 g5
g1 0.23 0.00 0.95 -0.63
g2 0.91 0.56 0.56
g3 0.32 0.77
g4 -0.36
g5
g1 g2 g3 g4 g5
g1 0.23 0.00 0.95 -0.63
g2 0.91 0.56 0.56
g3 0.32 0.77
g4 -0.36
g5

• Find largest value in similarity matrix.

• Join clusters together.

• Recompute matrix and iterate.

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Hierarchical Clustering
g1 , g4 g2 g3 g5
g1 , g4 0.37 0.16 -0.52
g2 0.91 0.56
g3 0.77
g5
g1 , g4 g2 g3 g5
g1 , g4 0.37 0.16 -0.52
g2 0.91 0.56
g3 0.77
g5

• Find largest value is similarity matrix.

• Join clusters together.

• Recompute matrix and iterate.

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Hierarchical Clustering
g1 , g4 g2 , g3 g5
g1 , g4 0.27 -0.52
g2 , g3 0.68
g5
g1 , g4 g2 , g3 g5
g1 , g4 0.27 -0.52
g2 , g3 0.68
g5

• Find largest value is similarity matrix.

• Join clusters together.

• Recompute similarity matrix and iterate.

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Clustering Example
Eisen et al. (1998), PNAS, 95(25) 14863-14868
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GRN Modeling Steppes GRN Generation
t1 t2 t3 t4
g1 0 1 2 1
g2 1 2 1 0
g3 0 1 1 1.
g4 1 2 1 0
Statistical Signal Processing Technique
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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

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GRN Models

• Directed and undirected graphs
• Bayesian networks
• Boolean networks
• Generalized logical networks
• Non-linear ordinary differential equations
• Piecewise linear differential equations
• Qualitative differential equations
• Partial differential equations
• Stochastic master equations
• Rule based formalisms

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GRN Models

• Hidde de Jong, Modeling and simulation of
  genetic regulatory systems a literature review
• J Comput Biol. 20029(1)67-103. Review. 

Node States
Computation
Data
Complexity
Dynamics
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What class of modelsshould be chosen?

• The selection should be made in view of
• data requirements
• goals of modeling and analysis.

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Classical Tradeoff

• A fine model with many parameters
• may be able to capture detailed low-level
  phenomena (protein concentrations, reaction
  kinetics)
• requires very large amounts of data for
  inference, lest the model be overfit.
• A coarse model with lower complexity
• may succeed in capturing high-level phenomena
  (which genes are ON/OFF)
• requires smaller amounts of data.

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Occams Razor
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Model Reliability and Adequacy

• P is the set of all possible observations
• S set of all observations made on the study
  system
• M is the set of all model outputs
• QS ?M

P
S
M
Q
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Model Reliability and Adequacy


S
P
P
M
S
M
Q
Useless Model
Dream Model
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Model Reliability and Adequacy


P
P
M
S
Q
Q
M
S
Complete, but erring model
Incomplete model
Model reliability Q/M Model adequacy Q/S
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GRN Models

• Directed and undirected graphs
• Bayesian networks
• Boolean networks
• Generalized logical networks
• Non-linear ordinary differential equations
• Piecewise linear differential equations
• Qualitative differential equations
• Partial differential equations
• Stochastic master equations
• Rule based formalisms

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Directed and undirected Graphs

• Probably most straightforward way to model a GRN
• GltV,Egt
• V set of vertices
• Set of edges Elti,jgt where i,j ? V, head and tail
  of edge
• Additional labels denote positive/negative
  influence

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Directed and undirected Graphs

• Advantages
• Intuitive way of visualization
• Common and well explored graph algorithms can
  make biologically relevant predictions about
  GRSes
• paths between genes may reveal missing regulatory
  interactions or provide clues about redundancy
• cycles in the network point at feedback relations
• connectivity characteristics give indication of
  the complexity
• loosely connected subgraphs point at functional
  modules
• Disadvantages
• Time does not play a role
• Too much abstraction very simplified model far
  from reality

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GRN Models

• Directed and undirected graphs
• Bayesian networks
• Boolean networks
• Generalized logical networks
• Non-linear ordinary differential equations
• Piecewise linear differential equations
• Qualitative differential equations
• Partial differential equations
• Stochastic master equations
• Rule based formalisms

More popular and efficient
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Boolean Network Model

• A Boolean network is defined by a set of
• nodes, V x1, x2, . . . , xn, and a list
  of
• Boolean functions, F f1, f2, . . . , fn
• Each xk represents the state (expression) of
• a gene, gk, where xk 1 the gene is
  expressed
• or xk 0, the gene is not expressed

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Boolean Network
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 1
x3 1 0 1 1 1
GAP
At any given time, combining the gene states
gives a gene activity pattern (GAP).
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Boolean Network

• Given a GAP at time t, a deterministic function
  (a set of logical rules) provides the GAP at time
  t 1.

t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
GAPt1
GAPt
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Boolean Network
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
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Boolean Network
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
x1
x2
x3
t
x1
t1
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
x1
x2
x3
t
x1
t1
or
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
x1
x2
x3
t
x1
t1
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
x1
x2
x3
t
x1
t1
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
x1
x2
x3
t
x1
t1
or
For each node there will be 22k possible
functions
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Boolean Network Example
t 0 1 2 3 4
x1 1 1 0 1 1
x2 1 0 0 0 0
x3 1 0 1 1 0
x1
x2
x3
t
x2
x1
x3
t1
or
nor
nand
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Boolean Network Example
I. Shmulevich et al., Bioinformatics (2002), 18
(2) 261-274
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Boolean Networks Summary

• Advantages
• Efficient analysis of large RN
• Positive/negative feedback-cycles can be modeled
  with BNs
• Disadvantages
• Strong simplifying assumptions gene is either
  on or off, no in between states
• The computation time is very high or often
  impractical to construct large-scale gene
  networks
• Very susceptible to noise
• There are situations where boolean idealisation
  is not appropriate more general methods required

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Bayesian Networks

• A gene regulatory network is represented by
  directed acyclic graph
• Vertices correspond to genes.
• Edges correspond to direct influence or
  interaction.
• For each gene xi, a conditional distribution
  p(xi ancestors(xi) ) is defined.
• The graph and the conditional distributions,
  uniquely specify the joint probability
  distribution.

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Bayesian Network Example
Conditional distributions p(x1), p(x2), p(x3
x2), p(x4 x1,x2), p(x5 x4)
p(X) p(X) p(x1) p(x2) p(x3 x2) p(x4 x1,x2)
p(x5 x4)
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Learning Bayesian Models

• Using gene expression data, the goal is to find
  the bayesian network that best matches the data.
• Recovering optimal conditional probability
  distributions when the graph is known is easy.
• Recovering the structure of the graph is NP hard
• (non-deterministic polynomial ).
• But, good statistics are available
• What is the likelihood of a specific assignment?
• What is the distribution of xi given xj?

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Issues with Bayesian Models

• Computationally intensive.
• Requires lots of data.
• Does not allow for feedback loops which are known
  to play an important role in biological networks.
• Does not make use of the temporal aspect of the
  data.
• Dynamical Bayesian Networks aim at solving some
  of these issues but they require even more data.

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Differential Equations

• Typically uses linear differential equations to
  model the gene trajectoriesdxi(t) / dt a0
  ai,1 x1(t) ai,2 x2(t) ai,n xn(t)
• Several reasons for that choice
• lower number of parameters implies that we are
  less likely to over fit the data
• sufficient to model complex interactions between
  the genes

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Small Network Example
dx1(t) / dt 0.491 - 0.248 x1(t) dx2(t) / dt
-0.473 x3(t) 0.374 x4(t) dx3(t) / dt -0.427
0.376 x1(t) - 0.241 x3(t) dx4(t) / dt 0.435
x1(t) - 0.315 x3(t) - 0.437 x4(t)
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Small Network Example
_
x1
_

_
x2
x3


_
x4
one interaction coefficient
_
dx1(t) / dt 0.491 - 0.248 x1(t) dx2(t) / dt
-0.473 x3(t) 0.374 x4(t) dx3(t) / dt -0.427
0.376 x1(t) - 0.241 x3(t) dx4(t) / dt 0.435
x1(t) - 0.315 x3(t) - 0.437 x4(t)
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Small Network Example
constant coefficients
dx1(t) / dt 0.491 - 0.248 x1(t) dx2(t) / dt
-0.473 x3(t) 0.374 x4(t) dx3(t) / dt -0.427
0.376 x1(t) - 0.241 x3(t) dx4(t) / dt 0.435
x1(t) - 0.315 x3(t) - 0.437 x4(t)
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Problem Revisited
a0,i a1,i a2,i a3,i a4,i
x1 .431 -.248 0 0 0
x2 0 0 0 -.473 .374
x3 -.427 .376 0 -.241 0
x4 0 .435 0 -.315 -.437
Given the time-series data, can we find the
interactions coefficients?
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Issues with Differential Equations

• Even under the simplest linear model, there are
  m(m1) unknown parameters to estimate
• m(m-1) directional effects
• m self effects
• m constant effects
• Number of data points is mn and we typically have
  that n ltlt m (few time-points).
• To avoid over fitting, extra constraints must be
  incorporated into the model such as
• Smoothness of the equations
• Sparseness of the network (few non-null
  interaction coefficients)

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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

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GRN Software

• GNA Genetic Network Analyzer
• Helix Bioinformatics

http//www-helix.inrialpes.fr/article122.html
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GRN Software

• Probabilistic Boolean Networks (PBN)
• Matlab Tool Box
• Ilya Shmulevich
• Institute for Systems Biology

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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

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Future Work Literature Review

• Study the noisy natural of Microarray Data.
• Study in depth the existing modeling methodology.
• Focus on specialized problem like cancer.

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Future Work GSP Statistics Books

• Genomics signal processing and statistics,
• Edward,2006
• Introduction to genomics signal processing with
  control, Ily,2006
• Computational and Statistical Approaches to
  Genomics (Springer, 2006), Ily

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Future Work Statistics Books

• Handbook of Computational Statistics
• An Introduction to Statistical Signal Processing,
  Robert M. Gray,2007
• fundamentals of statistical signal processing
  estimation theory, steven kay
• nonlinear signal processing a statistical
  approach, Gonzalo R,2005
• Inference_in_HMM, Olivier Cappe,2005

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Future Work Modeling Books

• Modeling and Control of Complex Systems (Control
  Engineering) by Petros A. Ioannou, Andreas
  Pitsillides,2008 
• MODELING BIOLOGICAL SYSTEMS Principles and
  Applications2005
• gene regulation and metabolism postgenomic
  computational approaches, Julio, 2000

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Future Work Resources

• IEEE Transactions on Computational Biology and
  Bioinformatics
• IEEE International Workshop on Genomic Signal
  Processing and Statistics
• IEEE Journal of Selected Topics in Signal
  Processing Special Issue on Genomic and
  Proteomic Signal Processing
• EURASIP Journal of Bioinformatics and Systems
  Biology Special issue of the on Genetic
  Regulatory Networks
• IEEE Signal Processing Magazine on Signal
  Processing Special issue of the Methods in
  Genomics and Proteomics
• IEEE Transactions on Signal Processing Special
  Genomic Signal Processing issue of the
• Workshop on Discrete Models for Genetic
  Regulatory Networks

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OUTLINES

• What is the Gene Regulatory Network? GRN
• Application of GRN
• GRN Construction Methodology
• GRN modeling steps
• GRN Models
• GRS Software
• Next work
• Reference

97
Reference

• Hidde de Jong, Modeling and simulation of genetic
  regulatory systems a literature review J Comput
  Biol. 20029(1)67-103. Review. 
• BAYESIAN ROBUSTNESS IN THE CONTROL OF GENE
  REGULATORY NETWORKS Ranadip Pal1, Aniruddha
  Datta2, Edward R. Dougherty
• Anastassiou, D. (2001). Genomic Signal
  Processing. IEEE Signal Processing
• Dougherty, E. R. and A. Datta (2005). "Genomic
  signal processing diagnosis and therapy." Signal
  Processing Magazine, IEEE 22(1) 107 - 112.
• Vaidyanathan, P. P. (2004). Genomics and
  Proteomics A Signal Processorapos's Tour.
  Circuits and Systems Magazine, IEEE. 4 1-1.

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Reference

• Vaidyanathan, P. P. and B.-J. Yoon (2004). "The
  role of signal-processing concepts in genomics
  and proteomics." Journal of the Franklin
  Institute.(Special Issue on Genomics).

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