Fragmenting the early EGFR pathway
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Niveau: Supérieur, Licence, Bac+1Fragmenting the early EGFR pathway Jerome Feret February 16, 2011 All along this pratical work, by “fragments”, we mean homogeneous frag- ments (ie. the fragments which can be generated from a non oriented contact map). Heterogeneous fragments are not implemented yet. 1 The model We consider the following rule set: r01: EGF ( r1 ) , EGFR ( l1,r ) ?? EGF (r ) , EGFR(l ,r ) r02: EGF (r ) , EGFR(l ,r ) ?? EGF ( r1 ) , EGFR ( l1,r ) r03: EGF ( r2 ) , EGF ( r1 ) , EGFR ( l2,r ) , EGFR ( l1,r ) ?? EGF ( r3 ) , EGF ( r2 ) , EGFR ( l3,r1 ) , EGFR ( l2,r1 ) r04: EGF ( r3 ) , EGF ( r2 ) , EGFR ( l3,r1 ) , EGFR ( l2,r1 ) ?? EGF ( r2 ) , EGF ( r1 ) , EGFR ( l2,r ) , EGFR ( l1,r ) r05: EGF ( r3 ) , EGF ( r2 ) , EGFR ( l3,r1 ) , EGFR ( Y68u,l 2,r1 ) ?? EGF ( r3 ) , EGFfragment egfr reset-all contact map given final time annotated contact map contact map kappa rule output-scheme egfr
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Fragmenting the early EGFR pathway
J´erˆomeFeret
February 16, 2011
All along this pratical work, by “fragments”, we mean homogeneous frag-ments (ie. the fragments which can be generated from a non oriented contact map). Heterogeneous fragments are not implemented yet.
1Themodel
We consider the following rule set: 1 1 r01:EGF r,EGFR l,r−→EGF(r) ,EGFR(l,r) 1 1 r02:EGF(r) ,EGFR(l,r)−→EGF r,EGFR l,r 2 12 13 2 r03:EGF r,EGF r,EGFR l,r,EGFR l,r−→EGF r,EGF r, 3 12 1 EGFR l,r,EGFR l,r 3 23 12 12 1 r04:EGF r,EGF r,EGFR l,r,EGFR l,r−→EGF r,EGF r, 2 1 EGFR l,r,EGFR l,r 3 23 12 13 r05:EGF r,EGF r,EGFR l,r,EGFR Y68,l,r−→EGF r, u 2 31 21 EGF r,EGFR l,r,EGFR Y68,l,r p r06:EGFR Y68−→EGFR(Y68) p u 3 23 12 13 r07:EGF r,EGF r,EGFR l,r,EGFR Y48,l,r−→EGF r, u 2 31 21 EGF r,EGFR l,r,EGFR Y48,l,r p r08:EGFR Y48−→EGFR(Y48) p u 1−1 1−1 r09:EGFR Y48,r,SHC Y7,pi−→EGFR Y48,r,SHC Y7,pi p up p − − r10:SHC Y7,pi−→SHC(Y7,pi) p u r11:SHC Y7,pi−→SHC(Y7,pi) p u 1 1 r12:EGFR Y68,GRB2(a,b)−→EGFR Y68,GRB2 a,b p p 1 1 r13:EGFR Y68,GRB2 a,b−→EGFR Y68,GRB2(a,b) p p −1 1− r14:EGFR Y68,GRB2(a,b)−→EGFR Y68,GRB2 a,b p p 1 1− − r15:EGFR Y68,GRB2 a,b−→EGFR Y68,GRB2(a,b) p p 1 12 21 r16:EGFR Y68,GRB2 a,b,SOS(d)−→EGFR Y68,GRB2 a,b, p p 1 SOS d 2 21 11 1 r17:EGFR Y68,GRB2 a,b,SOS d−→EGFR Y68,GRB2 a,b, p p SOS(d) 1 1 r18:GRB2(a,b) ,SOS(d)−→GRB2 a,b,SOS d 1 1 r19:GRB2 a,b,SOS d−→GRB2(a,b) ,SOS(d) 1 12 12 r20:GRB2 a,b,SHC Y7,pi,SOS(d)−→GRB2 a,b,SHC Y7,pi, p p 1 SOS d
2 12 11 1 r21:GRB2 a,b,SHC Y7,pi,SOS d−→GRB2 a,b,SHC Y7,pi, p p SOS(d) 1 1−22 1− r22:GRB2 a,b,SHC Y7,pi,SOS(d)−→GRB2 a,b,SHC Y7,pi, p p 1 SOS d 2 12−1 11− r23:GRB2 a,b,SHC Y7,pi,SOS d−→GRB2 a,b,SHC Y7,pi, p p SOS(d) 1 1 r24:EGFR Y48,SHC(Y7,pi)−→EGFR Y48,SHC Y7,pi p up u 1 1 r25:EGFR Y48,SHC Y7,pi−→EGFR Y48,SHC(Y7,pi) p up u 1 1 r26:EGFR Y48,SHC Y7,pi−→EGFR Y48,SHC Y7,pi p pp p 1 1 r27:EGFR Y48,SHC Y7,pi−→EGFR Y48,SHC Y7,pi p pp p 1 12 1 r28:EGFR Y48,GRB2 a,b,SHC Y7,pi−→EGFR Y48,GRB2 a,b, p pp 1 2 SHC Y7,pi p 2 11 21 r29:EGFR Y48,GRB2 a,b,SHC Y7,pi−→EGFR Y48,GRB2 a,b, p pp 1 SHC Y7,pi p 2 12 13 r30:EGFR Y48,GRB2 a,b,SHC Y7,pi,SOS d−→EGFR Y48, p pp 2 12 31 GRB2 a,b,SHC Y7,pi,SOS d p 3 21 23 1 r31:EGFR Y48,GRB2 a,b,SHC Y7,pi,SOS d−→EGFR Y48, p pp 2 12 1 GRB2 a,b,SHC Y7,pi,SOS d p 1 12 1 r32:EGFR Y48,GRB2(a,b) ,SHC Y7,pi−→EGFR Y48,GRB2 a,b, p pp 1 2 SHC Y7,pi p 2 11 21 r33:EGFR Y48,GRB2 a,b,SHC Y7,pi−→EGFR Y48,GRB2(a,b) , p pp 1 SHC Y7,pi p 1 1 r34:GRB2(a,b) ,SHC Y7,pi−→GRB2 a,b,SHC Y7,pi p p 1 1 r35:GRB2 a,b,SHC Y7,pi−→GRB2(a,b) ,SHC Y7,pi p p −1−1 r36:GRB2(a,b) ,SHC Y7,pi−→GRB2 a,b,SHC Y7,pi p p 1−1− r37:GRB2 a,b,SHC Y7,pi−→GRB2(a,b) ,SHC Y7,pi p p 2 12 13 r38:EGFR Y48,GRB2 a,b,SHC Y7,pi,SOS d−→EGFR Y48, p pp 2 12 31 GRB2 a,b,SHC Y7,pi,SOS d p 3 21 23 12 r39:EGFR Y48,GRB2 a,b,SHC Y7,pi,SOS d−→EGFR Y48, p pp 1 21 GRB2 a,b,SHC Y7,pi,SOS d p
We start with the following initial state:
2000∗(EGFR(l,r,Y48,Y68)) u u 2000∗(EGF(r)) 2000∗(GRB2(a,b)) 1000∗(SOS(d)) 1000∗(SHC(pi,Y7)) u
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2Firstintuitionsaboutthemodel
(i)Compute the contact map for this model.
In this model, some receptorsEGFRrecruit some proteinsSOS. This can be done in two different ways:
–a receptorEGFRcan be bound to a proteinGRB2that is bound to a protein SOS (short arm); –a receptorEGFRcan be bound to a proteinSHCthat is bound to a protein GRB2, that is bound to a proteinSOS (long arm).
(ii)Compute thestoriesthat describe how a receptorEGFRcan recruit a proteinSOS. (iii)Compute the number of reachable species. (iv)Is it possible for a receptorEGFRto be bound to another receptorEGFR while not being bound to a ligandEGF?
3 Internalcoarse graining
(i)Use the software to compute the reduced differential systems that is associ-ated with our rule set. How many fragments are there? hint:complx egfr.ka --reset-all --do-ODE --output-scheme egfr --final-time 6 (ODE files have the prefixegfr plx ODE). (ii)Argue that the ruler04can be replaced with a simpler rule without modi-fying the behaviour of the model. (iii)Use the software to compress the rule set. hint:complx --reset-all --compute-quantitative-compression egfr.ka --output-quantitative-compression egfrcompressed.ka (iv)Explain the kinetic factor of the ruler04in the compressed rule set. (v)Use the software to compute the reduced differential systems that is associ-ated with compressed rule set. How many fragments are there?
The reduction used the annotated contact map that is given in Fig. 1.
(vi)Motivate each solid/strong edge and each covering class. (vii)Which subspecies in Fig. 2 are fragments with respect to the annotated contact map given Fig. 1 ? (viii)Explain why, with the initial rule set, the edge between the siterof the agentEGFRand itself, should be solid/strong. (ix)Plot the concentration of the proteinsSOSthat are attached to a receptor according to the simulation time. hint:Use eitherOctaveorMatlabto run the fileegfr plx ODE system.m. It will generate the filesegfr plx.data,egfr plx head.dataandegfr plx ODE.gplot.
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d
SOS
b
GRB2
a
Y68
EGF
r
l
Y7 GFR Y48 p
SHC
r
Fig. 1.annotated contact map.
4 Morecomplex example Now, we consider that the bond between a ligandEGFand a receptorEGFR can be broken even if the receptor is bound to another receptor. (i)Encode this assumption as a kappa rule. (ii)How is modified the annotated contact map and the set of fragments? Do you think the reduction that is obtained thanks to the application is optimal?
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SOS d
GRB2 a b
GRB2 a b SHC Y7 GRB2SHC a b Y7
GRB2SHC a b Y7pi
Fig. 2.fragment candidates
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