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1、SUPPLEMENTARYINFORMATIONEFFECTOFPROMOTERARCHITECTUREONTHECELL-TO-CELLVARIABILITYINGENEEXPRESSIONAlvaroSanchez1,HernanG.Garcia2,DanielJones2,RobPhillips3,4,JaneKondev51GraduatePrograminBiophysicsandStructuralBiologyand5DepartmentofPhysics,BrandeisUniversity,Waltham,MA.2De
2、partmentofPhysics,3DepartmentofBioengineeringand4DepartmentofAppliedPhysics,CaliforniaInstituteofTechnology,Pasadena,CA.ThemomentsofthemRNAprobabilitydistributionWestartbyconsideringthesamemechanismasinthetext(seefigure1),inwhichthepromoterswitchesbetweenoneactiveandonei
3、nactivestate.Thereareonlytwostochasticvariablesinthemodel:thenumberofmRNAtranscriptspercell(m),andthestateofthepromoterwhichreflectswhichtranscriptionfactorsareboundwhere.Thepromoterstateisalwaysadiscreteandfinitestochasticvariable(s)(foranexample,seefigure1a).Theexample
4、infigure1aillustratesthesimplestmodeloftranscriptionalactivationbyatranscriptionfactor.Whentheactivatorisboundtothepromoter(state1)mRNAissynthesizedatrate.Whentheactivatorisnotbound(state2)mRNAissynthesizedatalowerrate.Thepromoterswitchesstochasticallyfromstate1tostate2w
5、ithrate,andfromstate2tostate1withrate.EachmRNAmoleculeisdegradedwithrate.Thetimeevolutionforthejointprobabilityofhavingthepromoterinstates1or2,withmRNAsinthecell(whichwewriteasand,respectively),isgivenbyamasterequation,whichwecanbuildbylistingallpossiblereactionsthatlead
6、toachangeincellularstate,eitherbychangingorbychanging(figure1b).Themasterequationtakestheform:(1)Inspectingthissystemofequations,wenoticethatbydefiningthevector:(2)andthematriceswecanrewritethesystemofequations(1)inmatrixform.(3)Thisapproachcanbegeneralizedtoanymechanism
7、oftranscriptionalregulationatthepromoterlevel.Theonlydifferencebetweenthemechanismsrestsontheparticulardimensionalityandformofthethreematricesdefinedabove.ExamplesofthosematricesforallofthearchitecturesandmechanismsinvestigatedonthispaperaregiveninTableS1inTextS1.Instead
8、ystate,thelefthandsideofequation(4)isequalto0:(4)InordertofindthefirsttwomomentsofthesteadystatemRNApro
