MAPK cascade in solution (no scaffold)

Citation
Levchenko, A., Bruck, J., Sternberg, P.W. (2000) .Scaffold proteins may biphasically affect the levels of mitogen- activated protein kinase signaling and reduce its threshold properties. Proc. Natl. Acad. Sci. USA 97( 11):5818-5823. http://www.pnas.org/cgi/content/abstract/97/11/5818
Description
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) cascade in solution. This cascade is typically expressed as RAF= =>MEK==>MAPK (alternative forms are K3==>K2==> K1 and KKK==>KK==>K) . The input signal is RAFK (RAF Kinase) and the output signal is MAPKpp ( doubly phosphorylated form of MAPK) . RAFK phosphorylates RAF once to RAFp. RAFp, the phosphorylated form of RAF induces two phoshporylations of MEK, to MEKp and MEKpp. MEKpp, the doubly phosphorylated form of MEK, induces two phosphorylations of MAPK to MAPKp and MAPKpp.
Rate constant       Reaction
a10 = 5. MAPKPH + MAPKpp -> MAPKppMAPKPH
a1 = 1. RAF + RAFK -> RAFRAFK
a2 = 0.5 RAFp + RAFPH -> RAFpRAFPH
a3 = 3.3 MEK + RAFp -> MEKRAFp
a4 = 10. MEKp + MEKPH -> MEKpMEKPH
a5 = 3.3 MEKp + RAFp -> MEKpRAFp
a6 = 10. MEKPH + MEKpp -> MEKppMEKPH
a7 = 20. MAPK + MEKpp -> MAPKMEKpp
a8 = 5. MAPKp + MAPKPH -> MAPKpMAPKPH
a9 = 20. MAPKp + MEKpp -> MAPKpMEKpp
d10 = 0.4 MAPKppMAPKPH -> MAPKPH + MAPKpp
d1 = 0.4 RAFRAFK -> RAF + RAFK
d2 = 0.5 RAFpRAFPH -> RAFp + RAFPH
d3 = 0.42 MEKRAFp -> MEK + RAFp
d4 = 0.8 MEKpMEKPH -> MEKp + MEKPH
d5 = 0.4 MEKpRAFp -> MEKp + RAFp
d6 = 0.8 MEKppMEKPH -> MEKPH + MEKpp
d7 = 0.6 MAPKMEKpp -> MAPK + MEKpp
d8 = 0.4 MAPKpMAPKPH -> MAPKp + MAPKPH
d9 = 0.6 MAPKpMEKpp -> MAPKp + MEKpp
k10 = 0.1 MAPKppMAPKPH -> MAPKp + MAPKPH
k1 = 0.1 RAFRAFK -> RAFK + RAFp
k2 = 0.1 RAFpRAFPH -> RAF + RAFPH
k3 = 0.1 MEKRAFp -> MEKp + RAFp
k4 = 0.1 MEKpMEKPH -> MEK + MEKPH
k5 = 0.1 MEKpRAFp -> MEKpp + RAFp
k6 = 0.1 MEKppMEKPH -> MEKp + MEKPH
k7 = 0.1 MAPKMEKpp -> MAPKp + MEKpp
k8 = 0.1 MAPKpMAPKPH -> MAPK + MAPKPH
k9 = 0.1 MAPKpMEKpp -> MAPKpp + MEKpp
Variable IC   ODE
MAPK 0.3 MAPK'[t] == d7*MAPKMEKpp[t] + k8*MAPKpMAPKPH[t] -  a7*MAPK[t]*MEKpp[t]
MAPKMEKpp 0 MAPKMEKpp'[t] == -(d7*MAPKMEKpp[t]) - k7*MAPKMEKpp[t]  + a7*MAPK[t]*MEKpp[t]
MAPKp 0 MAPKp'[t] == k7*MAPKMEKpp[t] - a8*MAPKp[t]*MAPKPH[t]  + d8*MAPKpMAPKPH[t] + d9*MAPKpMEKpp[t] + k10* MAPKppMAPKPH[t] - a9*MAPKp[t]*MEKpp[t]
MAPKPH 0.3 MAPKPH'[t] == -(a8*MAPKp[t]*MAPKPH[t]) + d8*MAPKpMAPKPH[ t] + k8*MAPKpMAPKPH[t] - a10*MAPKPH[t]*MAPKpp[t] +  d10*MAPKppMAPKPH[t] + k10*MAPKppMAPKPH[t]
MAPKpMAPKPH 0 MAPKpMAPKPH'[t] == a8*MAPKp[t]*MAPKPH[t] - d8* MAPKpMAPKPH[t] - k8*MAPKpMAPKPH[t]
MAPKpMEKpp 0 MAPKpMEKpp'[t] == -(d9*MAPKpMEKpp[t]) - k9*MAPKpMEKpp[t]  + a9*MAPKp[t]*MEKpp[t]
MAPKpp 0 MAPKpp'[t] == k9*MAPKpMEKpp[t] - a10*MAPKPH[t]*MAPKpp[t]  + d10*MAPKppMAPKPH[t]
MAPKppMAPKPH 0 MAPKppMAPKPH'[t] == a10*MAPKPH[t]*MAPKpp[t] - d10* MAPKppMAPKPH[t] - k10*MAPKppMAPKPH[t]
MEK 0.2 MEK'[t] == k4*MEKpMEKPH[t] + d3*MEKRAFp[t] -  a3*MEK[t]*RAFp[t]
MEKp 0 MEKp'[t] == -(a4*MEKp[t]*MEKPH[t]) + d4*MEKpMEKPH[t]  + k6*MEKppMEKPH[t] + d5*MEKpRAFp[t] + k3*MEKRAFp[ t] - a5*MEKp[t]*RAFp[t]
MEKPH 0.2 MEKPH'[t] == -(a4*MEKp[t]*MEKPH[t]) + d4*MEKpMEKPH[t]  + k4*MEKpMEKPH[t] - a6*MEKPH[t]*MEKpp[t] + d6* MEKppMEKPH[t] + k6*MEKppMEKPH[t]
MEKpMEKPH 0 MEKpMEKPH'[t] == a4*MEKp[t]*MEKPH[t] - d4*MEKpMEKPH[t]  - k4*MEKpMEKPH[t]
MEKpp 0 MEKpp'[t] == d7*MAPKMEKpp[t] + k7*MAPKMEKpp[t] +  d9*MAPKpMEKpp[t] + k9*MAPKpMEKpp[t] - a7*MAPK[t]* MEKpp[t] - a9*MAPKp[t]*MEKpp[t] - a6*MEKPH[t]*MEKpp[t]  + d6*MEKppMEKPH[t] + k5*MEKpRAFp[t]
MEKppMEKPH 0 MEKppMEKPH'[t] == a6*MEKPH[t]*MEKpp[t] - d6*MEKppMEKPH[ t] - k6*MEKppMEKPH[t]
MEKpRAFp 0 MEKpRAFp'[t] == -(d5*MEKpRAFp[t]) - k5*MEKpRAFp[t]  + a5*MEKp[t]*RAFp[t]
MEKRAFp 0 MEKRAFp'[t] == -(d3*MEKRAFp[t]) - k3*MEKRAFp[t] +  a3*MEK[t]*RAFp[t]
RAF 0.4 RAF'[t] == -(a1*RAF[t]*RAFK[t]) + k2*RAFpRAFPH[t] +  d1*RAFRAFK[t]
RAFK 0.1 RAFK'[t] == -(a1*RAF[t]*RAFK[t]) + d1*RAFRAFK[t] +  k1*RAFRAFK[t]
RAFp 0 RAFp'[t] == d5*MEKpRAFp[t] + k5*MEKpRAFp[t] +  d3*MEKRAFp[t] + k3*MEKRAFp[t] - a3*MEK[t]*RAFp[t]  - a5*MEKp[t]*RAFp[t] - a2*RAFp[t]*RAFPH[t] + d2* RAFpRAFPH[t] + k1*RAFRAFK[t]
RAFPH 0.3 RAFPH'[t] == -(a2*RAFp[t]*RAFPH[t]) + d2*RAFpRAFPH[t]  + k2*RAFpRAFPH[t]
RAFpRAFPH 0 RAFpRAFPH'[t] == a2*RAFp[t]*RAFPH[t] - d2*RAFpRAFPH[t]  - k2*RAFpRAFPH[t]
RAFRAFK 0 RAFRAFK'[t] == a1*RAF[t]*RAFK[t] - d1*RAFRAFK[t] -  k1*RAFRAFK[t]
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