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An Application of Bendixson-Boincare Theorem
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What is a gene network and its mathematical model? What is a gene ... some gene networks realistically as a huge amount of experimental data has been accumulate ... – PowerPoint PPT presentation
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Title: An Application of Bendixson-Boincare Theorem
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An Application of Bendixson-Boincare Theorem
- MAT 574- Fall 2003
- Arizona State University
- Math Stat Dept
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What is a gene network and its mathematical model?
- What is a gene network?
- A network which consists of mutual interactions
between products of gene and other chemicals in a
cell. - Nonlinearity, delay and noise.
- Why mathematical model?
- Understanding dynamical aspect of inner cellular
phenomena. - Modeling some gene networks realistically as a
huge amount of experimental data has been
accumulate
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Central Dogma of Molecular Biology
Poly A Site
Termination Site
Exon
DNA
Exon
Intron
Transcription
5Cap
RNA processing (Cleavage Polyadenylation)
Poly A
Primary transcript
Splicing
Functional mRNA
Translation
Degradation
Protein
Degradation
Function
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Two gene of genetic regulatory system.
Protein P
Promoter
Gene Q
Promoter
Gene P
Protein q
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A Limit cycle generated by a two-gene model.
q
A
Slow manifold
B
fast manifold
E
fast manifold
Equilibruim locus of slow system
fast manifold
c
D
Slow manifold
p
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What does that mean?
- The periodic jumping dynamics may exist robustly,
provided that there are two different time scale
dynamics in gene-protein network. - This model act as a genetic oscillator or switch
is robust for parameter variations or environment
variations.
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References
- Chen,L and Aihara .K. A Model of Periodic
Oscillation for Genetic Regulatory Systems, IEEE
Trans. On Circuits and Systems, Part-I, Vol.49,
2002. - Chen,L and Aihara .K. Stability of Genetic
Regulatory Networks with Time Delay, IEEE Trans.
On Circuits and Systems, Part-I, Vol.49, 2002.
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