基因调控网络：－数学模型与仿真

马宏宾系统所

2003.10.30

纲要• 必要的说明• 问题与背景• 模型与仿真• 总结与展望• 参考文献

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• 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

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？

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

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

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 。

问题与背景• 例子：

Choice between alternative developmental pathways controlled by network of genes, proteins, and mutual regulatory interactions 。

• 基因调控网络的复杂性– Large networks– Complex cells has many components that can interact in comple

x ways.– Dynamics processes are hard to understand by intuitive app

roaches alone.– Genetic regulatory networks have complicated interactions far bey

ond 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 interacti

ons– systematical derivation of behavioral predictions

问题与背景

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?

问题与背景• 途径－－实验、建模、仿真：

模型：有向图

模型：有向图

模型： Baysian network

模型： Baysian network

模型： Boolean network

模型： Boolean network

模型： Boolean network

Truth tables

State-transition diagram

模型： Generalized logical network

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

模型： Nonlinear ODE

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

模型： Nonlinear ODE

Applications:

模型： Piecewise-linear ODE

模型： Qualitative Differential Equation

• QDE:– Abstraction of the form

– Qualitative value x:– Qualitative function fi:– QSIM algorithmQualitative behaviors– Qualitative simulation

模型： Spatially Distributed Model

o Configuration ：o Discrete model:

o Continuous model:

boundary conditions:

模型： Stochastic Model

模型： Stochastic Model

• Time evolution of p(X,t)：

master equation:

• ＝ >Stochastic simulation: use r.v. τand ρ

模型： Stochastic ModelSimulations:

Applications:

模型： Rule-based formalism

• Knowledge base 〔 Expert system? 〕– Facts ：– Rules ：

总结与展望

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

参考文献• Hidde De Jong, Modeling and Simulation of Genetic Regulatory S

ystems: 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, Modeling Transcriptional 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)