The topology and signature of the regulatory interactions predict the expression pattern of the segment polarity genes in Drosophila m elanogaster

Transcription

1 The opology and sgnaure of he regulaory neracons predc he expresson paern of he segmen polary genes n Drosophla m elanogaser Hans Ohmer and Réka Alber Deparmen of Mahemacs Unversy of Mnnesoa

2 Complex bologcal neworks Bologcal sysems form neworks of neracon gene conrol neworks meabolc neworks neworks of sgnal ransducon and response organ and organsm-level neworks populaon level neworks The funcon of hese sysems canno be undersood n a reducons way or by assumng lnear pahways. I s mporan o uncover he opology of he neracon neworks. sascal descrpon of nework opology sudy he nerplay beween opology and funcon n specfc neworks

3 Wha s Drosophla melanogaser?

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6 Drosophla segmenaon s governed by a cascade of genes 2:50 h 1:20 h 2:10 h Segmen polary genes: wngless (wg) engraled (en) hedgehog (hh) pached (pc) smoohened (smo) cubus nerrupus (c) sloppy pared (slp)

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9 Goal: relae he paern of he segmen polary genes o her neracons 1. The segmen polary genes nerac va a complex regulaory nework. 2. I s possble o model hs nework based only on he opology and sgnaure of he neracons. 3. The resuls of he model are n good agreemen wh he observed wld ype and muan paerns. 4. The model reveals a remarkable robusness wh respec o perurbaons n he nal condons.

10 The segmen polary genes are naed by he par-rule genes en hh wg early sages 2:50 h pre-paern 3:00-3:30 h sable paern 4:20-7:20 h 3:30 h c en pc

11 Sable gene paerns en s expressed n he aneror par of he parasegmen. wg s expressed n he poseror par of he parasegmen. The parasegmenal grooves form beween he wg and en srpes. The pc srpes separae no wo. The c paern s complemenary o ha of en. c en

12 The expresson of he segmen polary genes s mananed by a regulaory nework Cross-regulaon and feedback loops make hese neworks complex.

13 Inercellular neracons play a val role Cadgan, Nusse, Genes & Developmen 11, 3286 (1997)

14 Reconsrucng he opology of he segmen polary nework mrna PROTEIN PROT COMPL represson ranslaon, acvaon, modfcaon cell neghbor cell

15 The von Dassow model of he segmen polary genes d[ pro] = T d max ν [ mrna] ν Κ + [ mrna] ν [ pro] τ The opology of he nework s somewha dfferen from our reconsrucon. The model nvolves 48 unknown parameers. The soluons leadng o wld ype seady saes are dsrbued homogenously n he bologcally relevan parameer space. von Dassow e al., Naure 406, 188 (2000)

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18 Does he opology of he segmen polary nework deermne s funcon? Boolean model of he nework dynamcs: Transcrps and proens are eher ON (1) or OFF(0). The expresson of a node a mesep s gven by a logcal rule of he expresson of s effecors a me -1. Transcrpon depends on ranscrpon facors; repressors are domnan. Translaon depends on he presence of he ranscrp. Transcrps and proens decay n one sep f no produced.

19 Rules for ranscrpon and ranslaon en hh pc c + 1 = +1 = +1 = +1 = WG WG ( 1 or + 1 EN CIA no EN = en + 1 WG = EN + 1 CI = c + 1 HH = wg hh + 1 and no and no ) and no CIR EN SLP and no CIR

20 Rules for pos-ranslaonal processes PH = PTC and ( HH 1 or HH + 1) SMO = no PTC or HH or HH nsananeous 1 CIA CI and ( SMO or hh 1or hh 1) + = CIR + 1 = CI and no SMO and no hh and no hh 1 +ε SMO + 1 +

21 The expresson of wg, PTC and SLP s auo-regulaed + 1 wg = ( CIA [ wg and and SLP ( CIA and no or SLP CIR ) or 1 PTC + = pc or ( PTC and no HH 1 and no HH + 1) ) and no CIR Eher of he acvaors can couner mrna decay. Free PTC does no decay. ] SLP = SLP + 1 SLP s a source n he segmen polary nework.

22 Sar he model from an nal sae gvng he expresson of all nodes SLP parasegmen cell wh node ON cell wh node OFF The paerns are assumed o be dencal n each parasegmen. Wld ype nal sae: wg n he las cell of he parasegmen, en/hh n he frs cell of he parasegmen, pc and c complemenary o en

23 The model reproduces he wld ype seady sae Agrees wh he wld ype paern of he segmen polary genes. nal sae seady sae The ne effec of he neracons s enough o capure he funconng of he nework!

24 The naure of he neracons can be negraed no he opology The fuure expresson of a node depends on a combnaon of he expresson of oher nodes. hh Inroduce complemenary nodes. Assocae pseudo-nodes o node combnaons. The fuure expresson of nodes depends on he expresson of pseudo-nodes. +1 = EN and no CIR no CIR ( E CR) EN hh +1 = ( ECR) CIR and CIR

25 The funconal opology reveals acvang srucures me-sep complemen Cycles: wg ( wcacr 2 ) 2 wg ( wscr 2 ) 2 PTC P 2 2H1H 3 Clusers deermne segmen polary en, EN, hh, HH c, CI, CIA, wg, WG, pc, PTC

26 Wha happens f he nework s perurbed? The mos severe perurbaon s caused by gene muaons. To model a null muaon, we assume ha he mrna s kep OFF, hus he proen canno be ranslaed. The effecs of he muaon propagae hroughou he nework.

27 wg, en or hh muaons are lehal fnal sae No wg, en and hh srpes, no segmenaon, regardless of nal sae.

28 pc muaon broadens he srpes fnal sae The wg, en and hh srpes broaden, regardless of nal sae.

29 c muaon can preserve he prepaern fnal sae for wld ype prepaern The effec of c muaon depends on he nal sae. For wld ype prepaern, he wg, en, hh srpes reman.

30 Comparson beween hh and c muans predcon for pc pc wg predcon for wg wld ype c muan hh muan Galle e al., Developmen 127, 5509 (2000)

31 Comparson beween c and pc muans wld ype c muan predcon, c muan pc muan predcon, pc muan en hh Tabaa, Eaon, Kornberg, Genes & Developmen 6, 2635 (1992)

32 Wha happens f he nal sae s perurbed? Possble number of prepaerns for a sngle node: 16 and complemens Toal number of nework-wde prepaerns: All red nal saes lead o seady saes. N 13 = 16

33 How many nal saes lead o he wld ype seady sae? mnmal prepaern seady sae Toal number of wld-ype nducng prepaerns: = 10 5 N

34 There are wo oher frequenly occurrng seady saes Broader naon of wg, en or hh leads o broad srpes. Absence of wg leads o a sae wh no segmenaon. 0.98N Galle e al., Developmen 127, 5509 (2000) 10 2 N

35 The seady saes can be deermned analycally In he sable sae x +1 = x Use he fac ha SLP = SLP2 = and SLP3 = SLP The se of equaons reduces o: 1 = wg1 and no wg2 and no wg wg 2 = wg2 and no wg1 and no wg 3 = wg1 or wg3 wg 4 = wg2 or wg4 wg wg PTC 1 = ( no wg2 and no wg4) or ( PTC1 and no wg1 and no wg3) PTC 2 = ( no wg1 and no wg3) or ( PTC2 and no wg2 and no wg4) PTC = PTC = = Reflecs he assumpon of sably of wg and PTC.

36 Possble sable paerns wld ype broad lehal double wg dsplaced dsplaced, 2 wg The laer saes have very small probably.

37 Can he assumpons of he model be changed? 1. Node expresson decays n one sep f no renewed. 1 Assumpon: proens decay n wo seps; EN + = en Same seady saes, only he pah leadng o hem changes. More overall sably. or en 1 2. wg and PTC expresson s easer o manan han ohers. Assumpon: wg and PTC decay f no renewed. c muans have no segmenaon f wg decays; no wld ype seady sae f PTC decays. The model can be modfed o nclude dfferen mescales for ranscrpon, ranslaon, pos-ranscrponal modfcaons, mrna and proen decay.

38 Can we relax assumpons of mendependence? 3. SLP expresson s a necessary npu. No wld ype seady sae n a SLP muan. 4. The parasegmens reman 4 cells wde. Cell dvson can be ncorporaed no he model.

39 Conclusons and oulook 1. Boolean modelng confrms ha he funconng of he segmen polary nework s deermned by s opology. 2. The wld ype seady sae s robus o perurbaons n he nal condons. 3. The nework favors seady saes wh srpes even for ecopc prepaerns. 4. Boolean modelng allows for a sysemac deermnaon of seady saes and he nal saes leadng o hem. can be appled o a varey of neworks provdes a verfcaon of he compleeness of he opologcal nformaon