Boolean dynamics of genetic regulatory networks inferred from

Boolean dynamics of genetic
regulatory networks inferred
from microarray time series data
Wen Wei Rong
Supervisor: Prof. Dr. Heike Siebert
Outline
• Motivation
• Methods
• Algorithm
• Results
• Summary
Motivation
• 1969 – Modeling genetic regulatory networks
• 1998 – Boolean networks to infer genetic
regulatory systems from time series gene
expression data
• 1999 – dynamic Baysian networks
• 2002 – probabilistic Boolean networks
Motivation
• Probabilistic Boolean network
• Dynamic Bayesian network
Computationally complex
Create a single network
-> not realistic!
• Modified methods from Akutsu et al. (2000)
-all possible networks are considered
-networks grouped by attractor basins
Microarray
http://www.fastol.com/~renkwitz/microarray_chips.htm
Microarray
Dataset
Workflow
Normalization
Discretization
Clustering
Normalized
Dataset
A Set of
Possible
Networks
Meta-Genes
Expression
Profiles
Discretized
Expression
Profiles
Algorithm for inferrencing Boolean Dynamics
Clustering with k-mean
• Reducing problem size (Meta-Gene level)
• Analysis of networks tractable
Clustering
Choosing k
http://public.lanl.gov/mewall/kluwer2002.html
Singular Value Decomposition
Singular Value
Decomposition as
measure for internal
consistency
http://smd.stanford.edu/help/svd.shtml
Discretization
http://www.cs.columbia.edu/4761/notes07/chapter7.3-regulation.pdf
Discretization – Step 1
Support Vector Regression
http://www.di.ens.fr/~mschmidt/Software/minFunc/minFunc.html
Support Vector Regression
Kernel Function:
Gaussian kernel with
width σ=1
http://www.cs.columbia.edu/4761/notes07/chapter7.3-regulation.pdf
Gaussian kernel
http://www.didaktik.mathematik.uni-wuerzburg.de/history/ausstell/gauss/geldschein.html
Support Vector Regression
Kernel Function:
Gaussian kernel with
width σ=1
Width ε: 3/2*average
standard deviation
http://www.di.ens.fr/~mschmidt/Software/minFunc/minFunc.html
Average, Standard Deviation
Average:
Stantard
Deviation:
Discretization - Step 2
Thresholding
Full set to reduced set
• Loss of information
• Introduction of error:
 Choosing k-means from a host of algorithms
 Choosing k
 Random starting condition for k means
Algorithm
• Verify that the expression profiles given as
input can be reproduced by these inferred
networks
• Explore the dynamics beyond the time series
that were provided as input
• Predict expression profiles under different
initial conditions
Of particular interest: computing the steady
state or equilibrium dynamic of the networks
INFER_NETWORKS
Input
n nodes {v1, v2, ..., vn}
c Profiles {P1, P2, ..., Pc}
Q ... the biggest number of tuples
INFER_NETWORKS
Runnning Time: O(nq+1)
INFER_NETWORKS
Input
n nodes {v1, v2, ..., vn}
c Profiles {P1, P2, ..., Pc}
Q ... the biggest number of tuples
INFER_FUNCTION
k=1
k=2
RUN_NETWORK
ATTRACTOR
„The time step t1 is the first time step such that the
expression profile of the nodes at time t1 is the same as
the expression profile of the nodes at time T.“
Enumeration of
All Networks
Workflow
ENUMERATE_NETWORKS
INFER_FUNCTION
Expression
Profiles
Boolean
Functions
INFER_NETWORK
Possible
Connections and
Boolean Functions
ATTRACTOR
Attractors
Profile P*
RUN_NETWORK
IL-2-stimulated immune responce
experiment
Three measurements each at twelve different
time points: 39000 transkripts were analyzed
http://www.focusonnature.com/SouthAmericaMammalList.htm
Results
Results
Results
Results
Results
Summary
„Many networks fall into the same attractor
basins, suggesting that many of the networks
are equaly valid. They also have many locally
consistent substructures.“
General intuition: biological system modular,
robust and often function correctly despite
extreme change
Literatur
• Boolean dynamics of genetic regulatory
networks inferred from microarray time series
data – Martin et al. (2007)
• Inferring qualitative relations in genetic
networks and metabolic pathways – Akutsu et
al. (2000)