Cell Biology. Lecture 1: 10-Oct-12. Marco Grzegorczyk. (Gen-)Regulatory Network. Microarray Chips. (Gen-)Regulatory Network. (Gen-)Regulatory Network

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1 Genetsche Netzwerke Wntersemester 202/203 ell ology Lecture : 0-Oct-2 Marco Grzegorczyk Gen-Regulatory Network Mcroarray hps G G 2 G metabolte metabolte Gen-Regulatory Network Gen-Regulatory Network G G 2 G G G 3 G 2 metabolte metabolte

2 Regulatory networks and sgnallng pathways low cytometry technology Receptor molecules ell membrane ctvaton Interacton n sgnallng pathway hosphorylated proten Inhbton rom Sachs et al Scence 2005 roten actvaton cascade roten actvaton cascade ell membran ell membran phosphorylaton nucleus phosphorylaton nucleus -> cell response -> cell response roten actvaton cascade 2

3 possbly completely unknown possbly completely unknown.g.: low cytometry eperments Here: oncentratons of phosphorylated protens possbly completely unknown Statstcal Task tract a network from a matr.g.: low cytometry eperments varables... n genes/ protens n 2 cells 2 22 n2 m 2m nm Machne Learnng statstcal methods ther m ndependent steady-state observatons of the system N Or tme seres of the system of length m: n t= m lementary molecular bologcal processes escrpton wth dfferental equatons oncentratons Knetc parameters q Rates 3

4 Gven: Gene epresson tme seres arameters q known: Numercally ntegrate the dfferental equatons for dfferent hypothetcal networks an we nfer the correct gene regulatory network? Model selecton for known parameters q Model selecton for unknown parameters q Measured gene epresson tme seres Gene epresson tme seres predcted wth dfferent models Measured gene epresson tme seres Gene epresson tme seres predcted wth dfferent models ompare Hghest lkelhood: best model Hghest lkelhood: over-fttng Model selecton: fnd the best pathway Select the model wth the hghest posteror probablty: Ths requres an ntegraton of the whole parameter space: Statc ayesan networks NOS GS Marrage between theory and probablty theory. rected acyclc G represents condtonal ndependence relatons. Markov assumpton leads to a factorzaton of the ont probablty dstrbuton: Ths ntegral s usually ntractable especally for systems of non-lnear dfferental equatons 4

5 ayesan networks versus causal networks ayesan networks represent condtonal ndependency relatons - not necessarly causal nteractons. quvalence classes of Ns completed partally drected s Gs v-structure = = Y Z ynamc ayesan networks for tme seres Y Y Z Z t t+ Interpretaton: No need for the acyclcty constrant!!! Unfoldng n tme ayesan networks n b N 2 ~ b 0 arametersaton: Gaussan Ge scorng metrc: ~NμΣ wth normal-wshart dstrbuton of the unknown parameters.e.: μ~nμ*vw - and W~WshartT 0 d ayesan networks d Ge metrc: closed form soluton score Ge unform dstrbuton

6 Learnng the network structure n #Gs Idea: Heurstcally searchng for the M* that s most supported by the M*> e.g.: greedy search algorthm score Ge Learnng the network structure strbuton of MM samplng of ayesan networks etter dea: ayesan model averagng va Markov han Monte arlo MM smulatons onstruct and smulate a Markov han M t t n the space of Gs whose dstrbuton converges to the posteror dstrbuton as statonary dstrbuton.e.: M t = t to generate a G sample: G G 2 G 3 G T Structure MM samplng scheme based on sngle edge operatons quvalence classes of Ns completed partally drected s Gs v-structure = =

7 Gs G representatons Gs Utlse the G G sample for estmatng the posteror probablty of edge relaton features: T ˆ I G T nterpretaton superposton where IG s f the G of G contans the drected edge and 0 otherwse MM samplng of ayesan networks The G sample G G 2 G 3 G T s generated va Markov han Monte arlo MM smulatons That s va smulaton of a Markov han M t t n the space of Gs whose dstrbuton converges to the posteror dstrbuton: M t = t MM samplng of ayesan networks The G sample G G 2 G 3 G T s generated va Markov han Monte arlo MM smulatons That s va smulaton of a Markov han M t t n the space of Gs whose dstrbuton converges to the posteror dstrbuton: M t = t In practce: t s not nfnte!!! robablstc nference true regulatory network edge posteror probabltes hgh Thresholdng low T:/2 :0/4 concrete network predctons T:2/2 :/4 7