应用动态流平衡分析对代谢网络初步建模仿真

华中科技大学硕士学位论文应用动态流平衡分析对代谢网络初步建模仿真姓名：陶冠阳申请学位级别：硕士专业：生物医学工程指导教师：骆清铭20060511I*DynamicFluxBalanceAnalysisDFBA-DFBA*2003AA231011505010IIAbstractAlargenumberofmathematicians,physicists,mechanicsandcyberneticexpertshavepaymoreattentiontotheresearchareaofbiologicalsciencesfromtheresearchsectorofspacescience,nuclearphysics,andsoonfromthe1960'sinthiscentury.Asthepenetrationofdifferentdisciplinestobiologicalsciences,biologyhasbeengreatlydevelopedandmathematicalmodelingplayedanimportantrole.Withwealthybiologicalinformationandcreationofthedatabaseofmetabolicnetworkinsomeorganisms’cells,itispossiblefordescribingcells’metabolicnetworksysteminmathematicalmodel.Nowadays,peoplehasknownmoreandmoreknowledgeabouttheorganismsmetabolicnetworksandtheaccuracyhasimprovedconsiderablybecauseofthemodernbiologicalinformationtechnology,particularlyasthedevelopmentofhigh-throughbiochiptechnology.Soitisrequiredthatcomprehendingthemetabolicnetworksinthesightofsystemaspectall-aroundandaccurately.Asthedevelopmentofsystembiology,itbecomesahotspotwhichusingsystembiologyapproachestomodelandstudymetabolicnetwork.Thismodelingapproachcanavoidtheshortcomingsoftraditionalmethodsthatneedingthematuritydynamicsconstants.Ithasanimportantroleandsignificanceforsuchworkinrevealingdeep-seatedmetabolicmechanisms,thenatureoflife,aswellastheinteractionadaptationtoenvironmentintheprocessofevolutionofspecies.Inthispaper,itexaminedmathematicaltheoreticalbasisofthesystemsbiologyapproachdynamicflowbalanceanalysis(DynamicFluxBalanceAnalysisDFBA)anditsnumericalsolutionalgorithm.DFBAbasesondynamicoptimalcontroltheory,hasemphasizedtheintegrationofbiologicalinformationthroughreconstructionbiologicalmetabolicnetworks,andsimulatedthedynamicpropertiesoftheentirenetworkusingstoichiometricmatrix.ThenDFBAwasappliedtomodeltheorganismmetabolicnetworkasviewedfromtheperspectiveofadynamicoptimalcontrolsystem.IntheresearchofEscherichiacolimetabolicnetworks,diauxgrowthwassimulatedbyDFBAmodelinthesimplifiedEscherichiacolimetabolicnetwork.ForthecentercarbonmetabolismofE.network,itintegrateddynamicinformationequationsconstrainconditiontoextendtheIIIDFBAmodel.Thesimulationresultscoincidewiththetrendsofthedynamicspropertiesinthemetabolicnetwork.Finally,thispaperdiscussedsomeproblemsencounteredinmodelingprocessandpossiblyfuturedevelopment.Keywords:SystemsbiologyDynamicflowbalanceanalysisMetabolicnetworksOptimalcontrolMathematicalmodeling_____11[1]1.160H-HHartline[2]1.121.11.1Figure1.1Thediagramofmodelingprocessinmetabolicnetwork1)2)3)()3[3]1.2[4]””MetabolicControlAnalysis,MCA[5](MetabolicFluxAnalysis,MFA)[6]BiochemicalSystemTheory,BST[7](ControlModel,MC)[8]MCABSTPalsson[9]1.2.1(MCA)MCAMCA4MCAQuant[10]MCAMCAPissara[11]Penicillium-chrysogenum1.2.2(MFA)0nnJF=J-nF1.1()()0mbArtbtR++=1.1Ar(t)b(t)Rmbb(t)[12]MFA5(NMR)1.2.3(BST)(BST)MCA2070[13]1.2/pcdXdtrr=-1.2XrprcPapoutsakisMeyer[14,15]Nestor[16]S-1.2.4[17]6/CPiVLiao[18]()TCASeressiotis[19]1.2.5(CM)Ramkrishna7[20]“”VamerRamkrishna-Varner[20]Ramakrishna[21]1.3[22]invitroinvivo8[23]Palsson[24]FBAFBAFBAFBA[25,26]FBAEdwardsDynamicFluxBalanceAnalysis,DFBA[25][27]DFBA1.4[28]EdwardsPalssonFBAMG1655[29]PramanikKeasling[30][31]KEGG[32]FBAMFAFBADFBA[24]2.1DFBAuu*[33]1951R.Beuman11kSkuk(Sk)kSk1()kkkSuS+=k()kkuS1kS+,,11(,,,,)knknkkknVVSuSS++=L(),1(,,,)(,)nknkknjjjjkVSuSVSu+==∑L(2.1)(2.1)(,)jjjVSvjkk+11(){(,())(())}kkkkkkkkfSOPtimizationvSuSfus+=+(2.2)(){,1,1}kkkuDSknn∈∈-L11()0nnfS++=(2.3)12(2.2)()kkfS,1()(,,)kkknkknfsVSuS+=L(2.4)2.11,1()(,,,)(,)nknkknjjjjkVSuSvSudjd++=∫L(2.5)2.5()jdDelta2.5kn+12.52.22.41n232.52.5[27]132.22.22.22.6max(,,)(,,)()ToObjectFtyudeyftyuyoA=′==∫(2.6)2.6yu(,,)yftyu′=DEA2.22.6y[(,,)]ftyuy′-[0,T]t0()[(,,)]tftyuyl′⋅-t[0,T]t[0,T]t()[(,,)]tftyuyl′-0()[(,,)]0Ttftyuydtl′-=∫2.72.72.6(2.7)(,,)()[(,,)]{(,,)()[(,,)]}TTooToObjectFtyudetftyuydtFtyutftyuydtll′=+-′=+-∫∫∫2.82.6(,,,)(,,)()(,,)HtyuFtyutftyull≡+2.92.92.82.814(,,,)()TTooObjectHtyudttydtll′=-∫∫2.102.100()()(0)()TTTootydtTyyytdtllll′′-=-++∫∫2.112.112.8()[(,,,)()]()TToooObjectHtyuytdtTyyllll′=+-+∫2.12lyu(,,)yftyu′=Hyddl′=2.13()tl*()utP(t)*()ut“”*()()()ututPte=+2.14e(,,)yftyu′=ey*()()()ytytqte=+2.15TTy**TTTTTTyyyee=+Δ=+Δ2.162.142.15uy()***00{[,(),(),][()]}()(0)TTObjectHtyqtuptyqtdtTyyeeellell′=++++-+∫2.17Object0dObjectde=()0{[()()]()}()TTHHqtptqtdtTyTyuell∂∂′′+++Δ∂∂∫2.18152.17e()()()()TTTTdydTdTTyTyyTTddTdllllee′--⋅=-Δ-Δ2.192.182.190[()()()][]()0TtTTdobjecttHqtptdtHTTydtyull=∂∂′=+++Δ-Δ=∂∂∫2.200dobjectdt=2.20Hyl-∂′=∂0Hu-∂=∂2.21()tlyl2.9(,,,)[0,]()0MaxHtyutTHyHyTllll∈∂′=∂∂′=-∂=2.222.3BST16173[34]3.1:{,(0,1)(0)(1)0uuxxuu′′-+=∈==3.13.1:122011()()22Iuuuxudx⎡⎤′=+-⎢⎥⎣⎦∫3.21,20((0,1))W1,20((0,1))WBanachFourier12sinsin2sinkaxaxakxppp++++KK1,20((0,1))W:1212{sinsin2sin,,,},kkkSaxaxakaaaRppp=+++∈KK(3.3183.2Sk3.11,20((0,1))WVk3.2Vk3.1Vk[0,1]k+1[xi,xi+1](I=0,1,2…,k)x0,x1,x2…xk+1[xi,xi+1]hi=xi+1-xi(0=I=k)xiui(I=0,1,2,…,k+1)u0=uk+1=0u(x)x,u(x0,u0),(x1,u1),(x2,u2),…,(xk+1,vk+1)u=u(x)[xi,xi+1]xi,ui,(xi+1,ui+1)111,[,].iiiiiiiiuuxxxxxuuxx+++--=∈--3.3:111