# A model of MPF regulation in frog egg extracts
# after (Novak & Tyson, J. Cell Sci., 1993)

# Warning: WinPP and XPP are case insensitive.

# Differential Equations (Figure 2)

dCyclin/dt = k1 - k2*Cyclin - k3*Cyclin*Cdk
dMPF/dt = k3*cyclin*Cdk - k2*MPF - kwee*MPF + k25*preMPF
dpreMPF/dt = kwee*MPF - k25*preMPF - k2*preMPF
dCdc25P/dt = F(TotCdc25-Cdc25P,MPF,ka,KKa) - F(Cdc25P,PPase,kb,KKb)
dWee1P/dt = F(TotWee1-Wee1P,MPF,ke,KKe) - F(Wee1P,PPase,kf,KKf)
dIEP/dt = F(TotIE-IEP,MPF,kg,KKg) - F(IEP,PPase,kh,KKh)
dAPC/dt = F(TotAPC-APC,IEP,kc,KKc) - F(APC,PPase,kd,KKd)

# Conservation of Cdk subunits

Cdk = TotCdk - MPF - preMPF

# Rate functions embodying the regulatory signals

k25 = V25'*(TotCdc25-Cdc25P) + V25"*Cdc25P
kwee = Vwee'*Wee1P + Vwee"*(TotWee1-Wee1P)
k2 = V2'*(TotAPC-APC) + V2"*APC

# Michaelis-Menten Rate Law

F(S,E,k,Km) = k*E*S/(Km+S)

# Parameter values (from Marlovits et al., Biophys Chem, 1998)

par k1=1, V2'=.005, V2"=.25, k3=.005
par V25'=.017, V25"=.17, Vwee'=.01, Vwee"=1
par ka=.02, KKa=.1, kb=.1, KKb=1
par kc=.13, KKc=.01, kd=.13, KKd=1
par ke=.02, KKe=.1, kf=.1, KKf=1
par kg=.02, KKg=.01, kh=.15, KKh=.01
par TotCdk=100

# These parameters are arbitrarily set to 1.

par TotCdc25=1, TotWee1=1, TotIE=1, TotAPC=1, PPase=1

# Initial conditions

init Cyclin=0, MPF=0, preMPF=0, Cdc25P=0, Wee1P=0, IEP=1, APC=1

# Define "auxiliary" variables for plotting purposes

aux TotCyclin=cyclin+MPF+preMPF
aux Wee1=10*(TotWee1-Wee1P)

# Simulator settings

@ meth=stiff, Total=200, Bounds=1000

# Plotter settings

@ xhi=200, ylo=0, yhi=25
@ nplot=2, yp2=MPF

done