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UEBiophysics Regula'onofgeneexpression DanielJost CNRS,LaboratoireTIMC-IMAG,Grenoble Contact:[email protected] Web:hOp://membres-Qmc.imag.fr/Daniel.Jost/ MasterdegreeinPhysics2016/2017–ENSLyon Modelinggeneexpression v Aims:explainthephysicalandmathema7calbasisofmodelscurrentlyusedinsystems biologytomodelGNR Ø Modelingthecentraldogmaofmolecularbiology 1)DeterminisQcmodeling 2)StochasQcmodeling Ø Beyondthecentraldogma: 1)interacQonbetweengenes 2)MoQfanalysis 3)Networkinference Modelingthecentraldogma:stochas'capproach v RecalldeterminisiQcpart:«InallthissecQon,wewillassumethatthenumberof involvedmoleculesishigh(withweakfluctuaQons),sowecanmodelmRNAor proteinnumbersasconQnuousvariablesrepresenQngtheaveragevalueswithinthe cellpopulaQon.» v Geneexpressionisintrinsicallystochas7c/probabilis7c ExpressionofareportergeneexpressedinE.coli Modelingthecentraldogma:stochas'capproach v Geneexpressionisintrinsicallystochas7c/probabilis7c Ø Intrinsicvariability:biochemicalreacQonsareintrinsicallystochasQcandmay involveasmallnumberofelements.Thenumbersofmoleculesinacellarediscrete andtheyfluctuateinQme,evenundersteady-statecondiQons. Tyagi,2015 factorX promoterregion gene Bionumbers.org Ø Extrinsicvariability:fluctuaQonsduetoenvironment/intra-cellularheterogeneiQes Modelingthecentraldogma:stochas'capproach v Stochas7cmodelsaimtodescribesuchdiscretenessandnoise. v Twomainapproaches: Ø Computeprobabilitydistribu7onsasafuncQonofQme Ø Computepossibletrajectoriesofthebiochemicalsystem Modelingthecentraldogma:stochas'capproach v mRNAproduc7on:weaimtodescribetheprobabilityP(m,t)ofhavingmmRNAin acellatQmet. Ø α mRNA(m) β Ø Modelingthecentraldogma:stochas'capproach v Stochas7csimula7on:theGillespiealgorithm:simulaQngexactstochasQctrajectories m(t) m(t) +1 -1 +1 -1 t1 t2 t3 Qme t1 +1 +1 t2 t3 Qme Ø Fromthe(many)trajectories:esQmatePorcomputeaverage,noise,etc. Whenwillthenextreac7onoccur? Whatisthereac7on? Modelingthecentraldogma:stochas'capproach TD3:extrinsicnoiseandmodelforproteins Modelingthecentraldogma:stochas'capproach v Transcrip7onbursts:Inregulatedpromoters,transcripQonmaybealsobursty.Promoter statealternatebetweenanONandOFFstate,leadingtoenhancednoiseiftheswitching rateislow. Kimetal,2013 factorX promoterregion gene