# AKT Model # y(1) AKT/Xt between 0 and 1 # y(2) pIRS/Xt # time in secs # Parameters p d1ak=0.0909/60 p k1ak=0.9091/60 p KK1ak=0.05 p KK2ak=0.05 p betaak=1 p k2ak=0.9091/60 p deltaak=1/60 p phiak=1/60( p epsak=0.01/60 p psi=0.559 p E2T=1 p lamda=.1 p TSC1=1 p TSC2=1 p TOR=5 p GDP=50 p GTP=50 p k5ak=.01 p k7ak=0.1 p k7bak=0.1 p k6ak=0.1 p k6bak=0.1 p k8ak=8.65 p k8bak=.33 p a1ak=0.21 p d11ak=6.72 p k11ak=0.1 p k9ak=0.01 p k9bak=0.01 p a2ak=0.16 p d2ak=1.86 p k22ak=0.45 p a3ak=0.013 p d3ak=1 p k3ak=2.25 p KTOR=1 p kmtor=300 p Kerk=1 p kneg2=0.1 p kneg3=0.2 # Definitions of concentrations #y3=TSC1TSC2 #y4=TSC1TSC2pAKT #y5=R or Rheb #y6=RGTPTSC1TSC2 #y7=RGTPTOR #y8=aTOR #in nanomolar: p XTak=58 # pAKT=(1-y1)*XT #ODES y3'=(k8ak*TSC1*TSC2-k8bak*y3+(d11ak*y4-a1ak*y3*XTak*(1-y1))-kneg2*x14*y3/(Kerk+y3))/60 y4'=(-(d11ak+k11ak)*y4+a1ak*y3*XTak*(1-y1))/60 y5'=(-k6ak*GDP*y5+k6bak*RGDP-k7ak*GTP*y5+k7bak*RGTP)/60 RGTP'=(k7ak*GTP*y5-k7bak*RGTP-k9ak*RGTP+k9bak*RGDP-a2ak*RGTP*y3+d2ak*y6)/60 y6'=(a2ak*RGTP*y3-(d2ak+k22ak)*y6)/60 y7'=(a3ak*RGTP*TOR-(d3ak+k3ak)*y7)/60 y8'=(k3ak*y7-k5ak*y8)/60 #Rtot=0.01 RGDP=0.01-y5-y6-y7-RGTP #PI3K Model: Steady state is assumed. p b1=1 p b4=1 p KKb1=100 p b2=1 p b3=1 p KKb2=100 p KKb3=1 p P1t=1 p Pt=100 p PIPt=100 #y10=aPI3k/Xt #y2=pIRS/Xt #y9=PIP3/Xt y10=(b1/b4)*(Pt/KKb1)*y2/(1+(b1/b4)*(1/KKb1)*y2) y9=(KKb3/b3)*(b2/KKb2)*(PIPt/P1t)*y10/(1+(KKb3/b3)*(b2/KKb2)*(1/P1t)*y10) #pIRS and AKT y1'=(-((d1ak+k1ak)/KK1ak)*y1*(y9-y9*y1/(KK1ak+y1))+d1ak*y1*y9/(KK1ak+y1)+k2ak*E2T*(1-y1)/(KK2ak+(1-y1)))/60 y2'=(lamda+(phiak)*(1-y1)-kmtor*y8*y2/(KTOR+y2)-deltaak*y2)/60 # MAPK Model # z1 EGF_EGFR # z2 (EGF_EGFR)2 # z3 (EGF_EGFR)2-P # z4 (EGF_EGFR)2_PLCg # z5 (EGF_EGFR)2_PLCg-P # z6 (EGF_EGFR)2_Grb2 # z7 (EGF_EGFR)2_Grb2_SOS # z8 (EGF_EGFR)2_Shc # z9 (EGF_EGFR)2_Shc-P # z10 (EGF_EGFR)2_Shc_Grb2 # z11 (EGF_EGFR)2_Shc_Grb2_Sos # z12 Grb2_SOS # z13 Shc-P # z14 Shc_Grb2 # z15 PLCg-P # z16 PLCg-P-I # z17 Shc_Grb2_SOS # z18 EGFR # z19 EGF # z20 PLCg # z21 Grb2 # z22 Shc # z23 SOS # x(1) [KKK_E1] # x(2) [KKK*] # x(3) [KKK*_E2] # x(4) [KK_KKK*] # x(5) [KK-P] # x(6) [KK-P_KKP'ase] # x(7) [KK-P_KKK*] # x(8) [KK-PP] # x(9) [KK-PP_KKP'ase] # x(10) [K_KK-PP] # x(11) [K-P] # x(12) [K-P_KP'ase] # x(13) [K-P_KK-PP] # x(14) [K-PP] # x(15) [K-PP_KP'ase] # x(16) [KKK] # x(17) [KK] # x(18) [K] # x(19) [E1](RasGTP) # x(20) [E2] # x(21) [KKP'ase] # x(22) [KP'ase] #Source: Quantification of Short Term Signaling by the Epidermal Growth Factor Receptor[Table 2] # Parameters p #Modification: NO - values are same as original ones [No need for conversion of parameters' units] p kf1=0.003 p kb1=0.06 p kf2=0.01 p kb2=0.1 p kf3=1 p kb3=0.01 p Vu4=450 p Ku4=50 p kf5=0.06 p kb5=0.2 p kf6=1 p kb6=0.05 p kf7=0.3 p kb7=0.006 p Vu8=1 p Ku8=100 p kf9=0.003 p kb9=0.05 p kf10=0.01 p kb10=0.06 p kf11=0.03 p kb11=4.5e-3 p kf12=1.5e-3 p kb12=1e-4 p kf13=0.09 p kb13=0.6 p kf14=6 p kb14=0.06 p kf15=0.3 p kb15=9e-4 p Vu16=1.7 p Ku16=340 p kf17=0.003 p kb17=0.1 p kf18=0.3 p kb18=9e-4 p kf19=0.01 p kb19=2.14e-2 p kf20=0.12 p kb20=2.4e-4 p kf21=0.003 p kb21=0.1 p kf22=0.03; p kb22=0.064; p kf23=0.1; p kb23=0.021; p kf24=0.009; p kb24=4.29e-2; p kf25=1; p kb25=0.03; #Source: Digital Signaling and Hysteresis Characterize Ras Activation in Lymphoid Cells. #Modification: Units changed from micro molar and/or sec to nanomolar and/or sec. "mols"=number of molecules. p kfi1=1.125e-4 p kbi1=3 p kfi2=1.0625e-4 p kbi2=0.4 p kcati3=1.75 p kcati4=0.003 p kcati5=0.1 p ki3m=2.7388e3 p ki4m=1.52304e4 p ki5m=1.7869e1 #Source: Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling. p a1=0.00049; p a2=0.0307; p a3=0.0204; p a4=0.0493; p a5=0.0564; p a6=0.0326; p a7=0.0038; p a8=0.0050; p a9=0.0056; p a10=0.0162; p d1=0.049; p d2=3.3078; p d3=10.3862; p d4=2.7167; p d5=10.0885; p d6=0.8134; p d7=11.5688; p d8=5.0182; p d9=8.0892; p d10=9.7908; p k1=0.049; p k2=5.6407; p k3=7.0000; p k4=11.1367; p k5=3.5775; p k6=1.1328; p k7=0.7276; p k8=0.5291; p k9=1.0955; p k10=2.9318; #Negatif Feedback from ERK to SOS. p k_nfb=0.0; p km_nfb=1000; #Parameters for TACE p dT=1; p gpT=10; p grT=0; p KmTACE=1000; #Parameters for ARGOS p kAE=5; p dAE=1; p dA=0.000001; p gpA=0.000001; p KmA=10; p grAE=0; #total concentrations #EGFR p tot1=10; #EGF p tot2=0.1; aux EGFtot=tot2 #PLCg p tot3=105; #Grb2 p tot4=85; #Shc p tot5=150; #SOS p tot6=50 #Ras#betha p tot7=200 p Rgap=0.1 #TOTAL concentrations #Dynamic Modeling and Analysis of the Cross-talk between Insulin/AKT and MAPK/ERK Signaling Pathway Parameters p tot8=9.2235e-001 p tot9=5.1288e+003 p tot10=8.1552e+002 p tot11=5e-002 p tot12=3.2830e-001 p tot13=2.1238e-001 p tot14=5.0345e+002 #Algebraic Equations for conserved moieties z18=tot1-(z1+2*(z2+z3+z4+z5+z6+z7+z8+z9+z10+z11))-grAE*AE z19=tot2+grT*TACE-(z1+2*(z2+z3+z5+z4+z8+z9+z6+z7+z10+z11)) z20=tot3-(z4+z5+z15+z16) z21=tot4-(z12+z14+z17+z6+z7+z10+z11+SRd+SRt) z22=tot5-(z13+z14+z17+z8+z9+z10+z11+SRd+SRt) z23=tot6-(z12+z17+z7+z11+SRd+SRt) Rd=tot7-(Rt+SRd+SRt+x1) x16=tot8-(x2+x1+x3+x4+x7) x17=tot9-(x5+x8+x4+x7+x6+x9+x10+x13) x18=tot10-(x11+x14+x10+x13+x12+x15) #x19=tot11-(x1); x20=tot12-(x3) x21=tot13-(x6+x9) x22=tot14-(x12+x15) #Reactions #Source: Quantification of Short Term Signaling by the Epidermal Growth Factor Receptor(No.49) r1=kf1*z18*z19-kb1*z1 r2=kf2*z1*z1-kb2*z2 r3=kf3*z2-kb3*z3 r4=Vu4*z3/(Ku4+z3) r5=kf5*z3*z20-kb5*z4 r6=kf6*z4-kb6*z5 r7=kf7*z5-kb7*z3*z15 r8=Vu8*z15/(Ku8+z15) r9=kf9*z3*z21-kb9*z6 r10=kf10*z6*z23-kb10*z7 r11=kf11*z7-kb11*z3*z12 r12=kf12*z12-kb12*z21*z23 r13=kf13*z3*z22-kb13*z8 r14=kf14*z8-kb14*z9 r15=kf15*z9-kb15*z13*z3 r16=Vu16*z13/(Ku16+z13) r17=kf17*z9*z21-kb17*z10 r18=kf18*z10-kb18*z3*z14 r19=kf19*z10*z23-kb19*z11 r20=kf20*z11-kb20*z17*z3 r21=kf21*z13*z21-kb21*z14 r22=kf22*z14*z23-kb22*z17 r23=kf23*z17-kb23*z13*z12 r24=kf24*z9*z12-kb24*z11 r25=kf25*z15-kb25*z16 #ODEs z1'=r1-2*r2 z2'=r2+r4-r3 z3'=r3+r7+r11+r15+r18+r20-r4-r5-r9-r13 z4'=r5-r6 z5'=r6-r7 z6'=r9-r10 z7'=r10-r11 z8'=r13-r14 z9'=r14-r24-r15-r17 z10'=r17-r18-r19 z11'=r19-r20+r24 z12'=r11+r23-r12-r24 z13'=r15+r23-r21-r16 z14'=r18+r21-r22 z15'=r7-r8-r25 z16'=r25 z17'=-r23+r22+r20-kfi1*z17*Rd+kbi1*SRd-kfi2*z17*Rt+kbi2*SRt-k_nfb*z17*x14/(km_nfb+z17) SRd'=kfi1*z17*Rd-kbi1*SRd SRt'=kfi2*z17*Rt-kbi2*SRt Rt'=-kfi2*z17*Rt+kbi2*SRt+(kcati3*Rd*SRt)/(ki3m+Rd)+(kcati4*Rd*SRd)/(ki4m+Rd)-(kcati5*Rgap*Rt)/(ki5m+Rt)-a1*x16*Rt+(d1+k1)*x1 p Kraf=1 x1'= a1*x16*Rt- (d1+k1)*x1-kneg3*x1*XTak*(1-y1)/(Kraf+x1) x2'= k1*x1- a2*x2*x20+ d2*x3- a3*x2*x17+(k3+d3)*x4- a5*x5*x2+(k5+d5)*x7 x3'= a2*x2*x20-(d2+k2)*x3 x4'= a3*x17*x2-(d3+k3)*x4 x5'= k3*x4-a4*x5*x21+d4*x6-a5*x5*x2+d5*x7+k6*x9 x6'= a4*x5*x21-(d4+k4)*x6 x7'= a5*x5*x2-(d5+k5)*x7 x8'= k5*x7-a6*x8*x21+d6*x9-a7*x8*x18+(d7+k7)*x10-a9*x11*x8+(d9+k9)*x13 x9'= a6*x8*x21-(d6+k6)*x9 x10'=a7*x18*x8-(d7+k7)*x10 x11'=k7*x10-a8*x11*x22+d8*x12-a9*x11*x8+d9*x13+k10*x15 x12'=a8*x11*x22-(d8+k8)*x12 x13'=a9*x11*x8-(d9+k9)*x13 x14'=k9*x13-a10*x14*x22+d10*x15 x15'=a10*x14*x22-(d10+k10)*x15 #Protease-TACE production by ERK TACE'=gpT*x14/(KmTACE+x14)-dT*TACE #ARGOS production ARGOS'=gpA*x14/(KmA+x14)-dA*ARGOS #inhibition of EGF by ARGOS. AE:EGF.ARGOS complex #AE'=kAE*z19*ARGOS-dAE*AE AE'=kAE*z18*ARGOS-dAE*AE @ meth=cvode, toler=1e-8, atol=1e-8 @ bound=600000, yhi=300,ylo=0,xhi=20000,xlo=0,yp=x14,total=20000 done