SMPGD Rennes

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Nonlinear stochastic differential equation model
to infer gene regulatory network architecture
A. Climescu-Haulica
Laboratoire Jean Kuntzmann Grenoble

• work partially supported by

Laboratoire BIM iRTSV CEA Grenoble
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Outline

• How difficult is to model the transcriptional
  regulatory network
• Stochasticity of microarray data
• A nonlinear SDE model
• Statistical Analysis
• Results analysis
• Conclusions

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Why a Transcriptional Regulatory Network
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From genes to proteins
Central Dogma
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From Essential Cell Biology B. Alberts et. all
(fig.7-19)
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Eukaryote gene organization
Transcript Region
Promoter Region
DNA
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3
Exon 1
e2
e3
Intron 1
3
5
-2000
-200
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TRANSCRIPTION in mRNA
Trans regulatory factors
Start Transcription Stop
Transcription factors

Start Translation Stop
R
A
-35
-95
TAAA
AATG
UAG
5
3
Exon 1
e2
e3
TATA
_
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Constitutive Promoter
Cis-regulatory elements
Poly A
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Transcription Regulation for eukaryotes
Regulator Control gene expression
Transcription Initiation Complex
From Essential Cell Biology B. Alberts et. all
(fig.8-25)
RNA Polymerase
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Remarks

• 1) A full bunch of information is needed to
  describe the complex relationships occurring in
  transcription and regulation
• - gene promoter regions
• - DNA binding sites
• - DNA transcriptional and regulatory
  factors
• A large scale analysis based on quantitative
  methods will generate hypotheses to be validated
  thru qualitative methods.
• To reverse engineering the transcriptional
  regulatory network
• the exhaustive use of dynamical data is
  expected.

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Microarray gene expression data
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Microarray Technique

• Technique used to test molecular biology targets
  by means of a chip.
• The target is immobilised on chip and hybridized
  with probed sample.
• The color obtained from the chip after
  hybridisation is scanned and the
• image data is analysed to find the
  expression levels from the target.

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Stochastic character of expression levels
from microarrays
Daprès http//www.medicine.man.ac.uk/esrg/jdavis.
htm
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Stochastic character of expression levels
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Example Spellman data

• Organism S. Cerevisiae
• mRNA expression levels of 6178 genes under alpha
  factor syncronisation method for 17 times points

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The nonlinear SDE Model

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SDE Model
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Itô formula application
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Local transcriptional regulatory network
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SDE Model
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MERCI!
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Nonlinear SDE model
where F_i are beta sigmoid functions
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Beta sigmoid function
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Beta sigmoid function plot
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Statistical Analysis
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Statistical Techniques

• Maximum Likelihood
• Akaike Information Criterion

3) Forward Selection Strategy The regulator
with the biggest log-likelihood with respect to
the target gene is selected. A new regulator is
added if it will increase the AIC more than any
other single regulator outside the current
combination.
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RESULTS ANALYSIS
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Example of genes better fittedwith respect to
previous model
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Model estimation for gene ASH1
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(No Transcript)
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Model estimation for gene SPT15
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(No Transcript)
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(No Transcript)
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1885 genes with qe less than 0.5
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Conclusions

• I. Dynamics of the expression level
• well fitted by SDE.
• II. The kinetic considerations improved
  previous results.
• III. Good fitting of expression level may yield
• information about the activators and the
  repressors of a
• target gene.
• IV. Model to be explored for different
  experimental conditions and different organisms.

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The most important

• From this method we propose a tool
• easy to use which reduces considerably the
  complexity of the investigation of the
• space of genes with bioinformatics methods
• - promoter analysis
• - binding factors

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Joint work with Michelle Quirk at LANL
to appear in Computational Methodologies in
Gene Regulatory Networks S. Das et all
(ed) IGI Science Publishers 2008
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Thank you