MAP-Kinase in Solution

References
(1) 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. USA97(11):5818–5823.
(2) Shapiro, B, Leevchenko A., Mjolsness E. (2001) Automatic Equation Generation for Signal Transduction with Applications to MAP-Kinase, in Foundations of Systems  Biology, Edited by H. Kitano, MIT Press.

<<xlr8r.m

Canonical Form

{{(Underoverscript[RAF⇄RAFp, RAFPH, RAFK])},{(Underoverscript[MEK⇄MEKp⇄MEKpp, MEKPH, RAFp])},{(Underoverscript[MAPK⇄MAPKp⇄MAPKpp, MAPKPH, MEKpp]) }};

Define the System

stn={
{(Underoverscript[RAF⇄RAFp, RAFPH, RAFK]), a1,d1,k1, a2,d2,k2},{(Underoverscript[MEK⇄MEKp⇄MEKpp, MEKPH, RAFp]), a3,d3,k3,a4,d4,k4,a5,d5,k5,a6,d6,k6 },
{(Underoverscript[MAPK⇄MAPKp⇄MAPKpp, MAPKPH, MEKpp]), a7,d7,k7,a8,d8,k8,a9,d9,k9,a10,d10,k10 }};

myrates={a1-> 1.,a2-> 0.5, a3-> 3.3,a4-> 10., a5-> 3.3,
a6-> 10., a7-> 20., a8-> 5., a9->20.,a10-> 5., d1->.4, d2->.5,  d3-> .42, d4-> .8, d5-> .4,
d6-> .8, d7-> .6, d8-> .4, d9-> .6, d10-> .4,k1-> .1,k2-> .1,k3-> .1,k4-> .1, k5-> .1,k6-> .1,k7-> .1,k8-> .1,k9-> .1,k10-> .1,
v1-> 0.1, K-> 0.3, k11-> .005};

myic={MEK->  0.2,MAPK-> 0.3,RAF-> 0.4,RAFPH-> .3,
MEKPH->  0.2 ,MAPKPH->0.3 ,RAFK-> 0.1};

Translate reactions into differential equations

ODE[stn]//TableForm

Predict a Time Course

sim=run[stn,"IC"->myic,"rates"->myrates,
timeSpan->100,MaxSteps->25000];

gridPlot[sim,plotColumns-> 5,ImageSize-> 800]