Structure des petits réseaux

Transcription

1 Structure des petits réseux génétiques et évolution in silico Pul Frnçois (thèse) Hervé Rouult (thèse) Lortoire de Physique Sttistique, NRS & ENS, Pris. IHP, jnvier 06.

2 Genetic networks. Dynmics in cell: istility, oscilltions (circdin,...) Sptil ptterns (. elegns, somites,...) oordinted evolution of severl genes/proteins. Design of synthetic modules.

3 synthetic genetic switch Two genes nd tht inhiit ech other. Two stle stedy sttes : [] high with [] low, nd [] high with [] low. Switching cn e induced y n IPTG or temperture pulse. Grdner et l, Nture 403: (2000) istility requires dimeriztions (or other interctions).

4 synthetic genetic ring oscilltor P L lc01 lci lite tetr lite Lc I Tet R λp R λl P L tet01 λl lite The oscilltion is sed on three genes tht repress ech other in circle ( rock-scissor-pper ). M. Elowitz nd S. Leiler, Nture 403: (2000)

5 Wht re the designs tht chieve given function? n one smple them nd dd desired constrints (roustness,...)? Esyness of cretion, evolvility,...? lueprints of useful networks.

6 n overrepresented motif in trnscriptionl networks X Y Z The feedforwrd loop is overrepresented in the trnscriptionl networks of E. oli nd S. erevisie (Milo et l., Science 298: (2002)). Function: persistence detector?

7 Proposl : design y selection in silico. The inverse of the sttisticl pproch: from the desired tsk to the network. To design modules performing given tsks (e.g. switches nd oscilltors), without imposing priori ny structure to the network, one evolves collection of virtul cells. P. Frnçois nd V. Hkim, PNS, (2004).

8 One computer cell consists in

9 One computer cell consists in - collection of genes - nd ssocited proteins First implementtion: trnscription nd trnsltion condensed in one single step. mrn re included in the present version.

10 One computer cell consists in - collection of genes - nd ssocited proteins First implementtion: trnscription nd trnsltion condensed in one single step. mrn re included in the present version. - trnscriptionl regultions - post-trnscriptionl regultions.

11 Representtion orresponding equtions d dt [] = τ [] δ [] d dt [] =θ[ : ] γ[][] d dt [ : ]=γ[][] θ[ : ] d dt [] = τ []τ [ : ]

12 The evolution in silico. c ells c c

13 The evolution in silico. oncentrtion Temps oncentrtion Temps Integrtion of ODEs oncentrtion oncentrtion Temps Temps

14 The evolution in silico. c Selection c c

15 The evolution in silico. c Elimintion c

16 The evolution in silico. c c Dupliction c c

17 The evolution in silico. c c c c Muttions

18 Possile muttions The modifiction of kinetic constnt in n existing rection or the ddition of new trnscriptionl regultion new post-trnscriptionl regultion new gene The process is iterted over severl genertions.

19 Fitness function for oscilltors [] 2 1 t Two concentrtions re fixed 1 nd 2. ODEs re integrted For t = T/2,3T/2,5T/2... fitness is given y the integrl ( 1 ) 2. For t = T,2T,3T... fitness is given y the integrl ( 2 ) 2.

20 Fitness evolution oncentrtion oncentrtion oncentrtion Genertion 49 Genertion 99 Genertion 199 Genertion 249 Genertion time Finl Stte time Score Genertions

21 The oscillting network c

22 purely iochemicl oscilltor

23 creted istle switch Very different from two genes with reciprocl inhiition

24 creted istle switch

25 creted istle switch

26 core genetic circuit: the Mixed Feedck Loop loop comining trnscriptionl nd post-trnscriptionl interction (i.e. protein-protein interction) is t the core of severl of these networks. This Mixed Feedck Loop hs now een found to e over-represented in S. erevisie nd E.oli (Yeger-Lotem et l, PNS 2004).

27 Mthemticl nlysis of the MFL X δ ρ g δ γ ρf g X δ β δr ρ α θ X X g ρ istility high low Oscilltions ρ 1 Reduced prmeters: ρ 0 = βρ f /(ρ δ r ),ρ 1 = βρ /(ρ δ r ) smll prmeter: δ r / ρ γ ( P. Frnçois nd V. Hkim, PRE (2005)

28 omprison with rel networks First switch: lctose operon, with llolctose inding to lc repressor. llolc llolc perm llolc llolc R βgl perm R R r lc lc R Proposed in 1961 y Monod nd Jco (sed on Lc operon) s n lterntive to reciprocl inhiition (Delrück, 1949)!

29 omprison with rel networks Second switch: developpement of competence in.sutilis, omk ctivtes itself nd is repressed y Mec. omk Mec lp Mec lp omk mec omk comk omk comk

30 Endogeneous oscilltor : the circdin clock ircdin ctivities of whole nimls nd single cells Liu et l, ell (1997)

31 The core structure of circdin clocks Froehlich et l, PNS (2003) Orgnism ctivtors Repressors Neurospor rss W-1, W-2 FRQ Drosophil dlk PER, TIM Mmmls LOK, ML PER, RY The creted networks re working exmples without delys or high Hill coefficients motivtion for new models of the circdin rhythms [for Neurospor, P. Frnçois iophys. J. 88, 2369 (2005)].

32 The lgorithm finds known (with complete description) nd originl designs. n importnt lesson: The post-trnscriptionl interctions ply crucil role: the function of the networks cnnot e understood t ll y focusing only on the trnscriptionl regultions (protein sequestrtion in complex ppers to e prticulrly importnt mechnism). Work in progress/perspectives nlysis of specific fetures of some genetic networks (e.g. temperture compenstion). lueprint for new synthetic networks. Evolution of rel genetic networks. Sptil ptterns, morphogenesis.

33 Somites Y. Sg, Nt. Rev. Gen. (2001)

34 Somitogénèse et oscilltions (ooke & Zeemn (1976) Plmeirim et l (1997)) Y. Sg, Nt. Rev. Gen. (2001)

35 Segmenttion s n oscillting/istle trnsition?

36 The End (for tody). Thnk you!

37 Temperture compenstion Selection of ctivtion energies for temperture compenstion: 10 o K increse : T : 300 o K 310 o K the kinetic constnts increse > 30%, period chnge < 3% [] Time

38 Fitness function for the switches The desired two stle sttes re chosen ( 1, 1 ) nd ( 2, 2 ). ODEs re integrted, the fitness is given y the integrl ( 1 ) 2 ( 1 ) 2. Pulse of protein ODEs re integrted, the fitness is given y the integrl ( 2 ) 2 ( 2 ) 2.

39 Trnscriptionl regultions

40 Post-trnscriptionl regultions *

41 Trnscriptionl switches

42 second type of switch

43 second type of switch

44 second type of switch

45 Toggle switch : mthemticl nlysis d dt = α 0 ν δ d dt = β 0 µ δ ν µ must e strictly higher thn 1 to hve istility, which requires t lest four (nd not two ) elementry rections. [herry nd dler, J. Theor. iol. (2000)]