系统生物学数学基础

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1、系统生物学数学基础(初稿)雷锦誌清华大学周培源应用数学研究中心2007年9月系统生物学数学基础前言什么是系统生物学?“Systemsbiologyisthescienceofdiscovering,modeling,understandingandultimatelyengineer-ingatthemolecularlevelthedynamicrelationshipsbetweenthebiologicalmoleculesthatdefinelivingorganisms.”LeroyHood,Ph.D.,M.D.,P

2、residentInstituteforSystemsBiologyAllbiologicalphenomena,whetherit’sdigestionofasugarmolecule,beatingofthehumanheart,orneutralizinganinvadingvirus,aretheresultofcomplexsystems.Thusourapproachistofocusresearchonbiologicalsystemsasawhole,ratherthanpursuethetraditiona

3、lapproachoffocusingonindividualgenes,proteins,orpartsofanorganism.系统生物学的研究内容?系统生物学研究方法?Scientistsfrommultipledisciplines(biology,chemistry,mathematics,physics,etc.)workcloselytogethertofullyunderstandallaspectsoftheinherentlycomplexsystemsintrinsictolivingorganisms

4、.Suchin-depthunderstandingisultimatelyessentialtorealizingourgoalofpredictive,preventive,personalizedmedicine.系统生物学与数学?•“它(物理学)的范畴可定义为我们全部知识中能够用数学语言表发的那个部分”－－爱因斯坦•统计，模型，分析，模拟......总结定性、半定建立数学模收集经验数据--性规律型@I@@@?用经验资料验证求解、发展数学模型理论“Mostreadersofthispublicationwi

5、llknowthat‘post-genomics’and‘proteomics’arephrasesthatmeanlittlethatisspecificbutheraldanencyclopaediceraofinformationaboutthewaybiologicalcellsandtheirgenesandproteinsbehave.Buthowbesttomakesenseofitall?Itis,atlast,possibletoanticipatemathematicsbecomingusefulinthe

6、modellingofthesystems.”–Nature4072000,819.内容简介?•基因表达•基因调控网络–Toggleswitches–生物振荡2系统生物学数学基础–生命节律–胚胎发育•细胞分裂与分化•系统生物学前沿介绍•随机过程(Masterequation,Langevinequation,Fokker-Plankequation)•微分方程(建模，定性理论，数值求解)•随机微分方程(建模，数值求解，稳定性分析)•反应扩散方程(建模，数值求解)补充阅读材料:1.Mackey,M.C.,Santillan,M

7、.,Mathematics,Biology,andPhysicss:Interactionsandinterepen-dence,NoticesAMS,52(2005)(8).2.Sontga,E.D.,Molecularsystemsbiologyanddynamics:anintroductionfornon-biologists.3.Alon,U.,Anintroductiontosystemsbiology,Chapman&Hall/CRC,London,2007.4.Fall,C.P.,Marland,E.S.,W

8、agner,J.M.,Tyson,J.J.,(Eds.)Computationalcellbiology,Springer-Verlag,NewYork,2001.5.Alberghina,L.,Westerhoff,H.V.(Eds.)Systemsbiology:Definitionsan