基因调控网络： － 数学模型与仿真

1. 基因调控网络：－数学模型与仿真 马宏宾 系统所 2003.10.30

2. 纲要 • 有向图 • Bayesian网络 • Boolean网络及推广 • 常微分方程 • “定性”微分方程 • 偏微分方程 • 随机模型 • 基于规则的形式方法 • 必要的说明 • 问题与背景 • 模型与仿真 • 总结与展望 • 参考文献

3. 必要的说明 • 我完全不懂生物学； • 我为什么要讲这个？ • 我讲的侧重点在哪？ 内容完全基于：〔童维上传〕 Modeling and Simulation of Genetic Regulatory Systems: A Literature Review

4. 问题与背景 • 什么是基因调控网络？ • 细胞、DNA、蛋白质、基因、基因网络 • 为什么要研究基因调控网络？ • 从分子水平认识细胞组织的功能。 • 基因调控网络与复杂性 • 了解基因调控网络，对我们有什么启发？

5. 问题与背景 • 基因和蛋白质 • Genes code for proteins that are essential for development and functioning of organism: gene expression

6. 问题与背景 • 基因表达的调控：〔不同层次〕 • Gene expression controlled by proteins produced by other genes: regulatory interactions

7. 问题与背景 • 基因调控网络： • Genetic regulatory network consists of set of genes, proteins, small molecules, and their mutual regulatory interactions。 • Development and functioning of organisms cell emerges from interactions in genetic regulatory networks。

8. 问题与背景 Choice between alternative developmental pathways controlled by network of genes, proteins, and mutual regulatory interactions。 • 例子：

9. 问题与背景 • 基因调控网络的复杂性 • Large networks • Complex cells has many components that can interact in complex ways. • Dynamics processes are hard to understand by intuitive approaches alone. • Genetic regulatory networks have complicated interactions far beyond correlation of gene expression patterns. • Clustering cannot reveal causal connections between genes. • 为什么需要数学建模与仿真？ • precise and unambiguous description of network of interactions • systematical derivation of behavioral predictions

10. 问题与背景 • 目标－－我们想知道： • Which genes are expressed?When and where in the organisms?To which extent? • Are there any universal laws? • Can we predict the evolution of the network? • How to predict the evolution of the network?

11. 问题与背景 • 途径－－实验、建模、仿真：

12. 模型：有向图

13. 模型：有向图

14. 模型：Baysian network

15. 模型：Baysian network

16. 模型：Boolean network

17. 模型：Boolean network

18. 模型：Boolean network Truth tables State-transition diagram

19. 模型：Generalized logical network

20. 模型：Nonlinear ODE

21. 模型：Nonlinear ODE • Negative feedback • Gene encodes a protein inhibiting its own expression • important for homeostasis, maintenance of system near a desired state • Steady state analysis • Transient behavior simulation

22. 模型：Nonlinear ODE • Positive feedback • Gene encodes a protein activating its own expression. • important for differentiation, evolution towards one of two alternative states of system • Steady states • Transient behaviors

23. 模型：Nonlinear ODE • Applications:

24. 模型：Piecewise-linear ODE

25. 模型：Qualitative Differential Equation • QDE: • Abstraction of the form • Qualitative valuex: • Qualitative function fi: • QSIM algorithmQualitative behaviors • Qualitative simulation

26. 模型：Spatially Distributed Model • Configuration： • Discrete model: • Continuous model:boundary conditions:

27. 模型：Stochastic Model

28. 模型：Stochastic Model • Time evolution of p(X,t)：master equation: • ＝>Stochastic simulation: use r.v. τand ρ

29. 模型：Stochastic Model • Simulations: • Applications:

30. 模型：Rule-based formalism • Knowledge base 〔Expert system?〕 • Facts： • Rules：

31. 总结与展望

32. 总结与展望 • Computer tools for modeling and simulation will be necessary to understand genetic regulatory processes • Variety of approaches available, representing genetic regulatory systems on different levels of abstraction • Choice of approach depends on aim of analysis and on available information: • knowledge on reaction mechanisms • quantitative data on model parameters and gene expression levels • Serious applications are beginning to emerge

33. 参考文献 • Hidde De Jong, Modeling and Simulation of Genetic Regulatory Systems: A Literature Review, Journal Of Computational Biology, 9 (1), 2002. • Harley H. McAdams, Adam Arkin, Simulation Of Prokaryotic Genetic Circuits, Annu. Rev. Biophys. Biomol. Struct. 1998. 27:199–224. • Paul Smolen, Douglas A. Baxter And John H. Byrne, ModelingTranscriptional Control in Gene Networks—Methods, Recent Results, and Future Directions, Bulletin of Mathematical Biology (2000) 62, 247–292. • Christophe Roos, Facing Biological Complexity – From One Cell to a Multicellular Organism, Technology BIOINFORMATICS. • Eric Alm and Adam P Arkin, Biological networks, Current Opinion in Structural Biology, 2003, 13:193–202. • Olivier Cinquin, Jacques Demongeot, Positive and negative feedback: striking a balance between necessary antagonists, Journal of Theoretical Biology, 216(2), pp229-241 (2002)

34. 谢谢大家！