An LMI Approach to Stability Analysis of Delayed Genetic Regulatory Networks

1. An LMI Approach to Stability Analysis of Delayed Genetic Regulatory Networks 授課老師: 曾慶耀 教授 學生: 鍾予軒 Department of Communications, Navigation and Control Engineering National Taiwan Ocean University

2. Outline • Definition of genetic regulatory networks • Basis of biology (transcription and translation) • Structure of genetic regulatory networks • Motivations • Model of genetic regulatory networks • Stability Analysis with Time-varying Delays • Simulation • Conclusions

3. Definition of Genetic Regulatory Networks • Biological cells • Interaction between genes and poteins • Start from transcription and end to translation to gain potein DNA transcription mRNA translation Protein

4. Transcription • The mRNA template is generated by the genomic containing a protein sequence for translation • Promoter can be recognized by mRNA polymerase

5. Translation • In the translation process, decoded by the ribosome to produce protein • The ribosome can provide places, make tRNA and mRNA binding

6. Structure of Genetic Regulatory Networks Node‧n Node‧4 Node‧1 Node‧2 Node‧3

7. Motivations • Develop mathematical quantitative analysis of genetic regulatory networks • Time delays exist in genetic regulatory networks due to chemical reactions • Construct new stability criteria based on Lyapunov theorem

8. Model of Genetic Regulatory Networks the concentrations of mRNA the concentrations of protein the Hill function

9. Hill Function • transcription factor j is an activator of gene i • transcription factor j is a repressor of gene i

10. From other genes Degradation rate c Degradation rate a ‧ ‧ ‧ To other genes or mRNAs Transcription processes mRNAs Proteins Gene‧ i

11. Mathematics • Lyapunovstability theorem • Inequality bounding technique and free weighting matrices • Schur complement • Linear matrix inequality(LMI)

12. Stability Analysis with Time-varying Delays

14. The above conditions hold, the genetic regulatory network with time varying delay is asymptotically stable.

15. Simulation Time delay parameters

18. Model of Genetic Regulatory Networks with Uncentainties

21. Simulation

23. Conclusions • The problem of the genetic regulatory network with time-varying delays has been solved • New robust stability criteria based on Lyapunov functional have been developed • All the proposed stability conditions are in terms of linear matrix inequalities (LMIs)

24. The End Thanks for your Attention