Minimal Mitotic Oscillator

Citation
Goldbeter, A. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl. Acad. Sci. USA 88: 9107-1101 (1991). http://www.pnas.org/cgi/content/abstract/88/20/ 9107
Description
This is a widely cited minimal (3-variable) model for a mitotic oscillator. The three variables represent Cyclin ( C), inactive cdc-2 Kinase (M) and an active cdc-2 Kinase (X).
Rate constant       Reaction
K1 = 0.1 (hill khalf) Comp[M] -> M
K2 = 0.1 (hill khalf) M -> EmptySet
K3 = 0.1 (hill khalf) Comp[X] -> X
K4 = 0.1 (hill khalf) X -> EmptySet
Kc = 0.3 (hill vmax) Comp[M] -> M
kd = 0.00333 C -> EmptySet
kd = 0.00333 (hill khalf) C + X -> X + EmptySet
V2 = 0.167 (hill vmax) M -> EmptySet
V4 = 0.1 (hill vmax) X -> EmptySet
vd = 0.1 (hill vmax) C + X -> X + EmptySet
vi = 0.023 EmptySet -> C
VM1 = 0.5 (hill vmax) Comp[M] -> M
VM3 = 0.2 (hill vmax) Comp[X] -> X
Variable IC   ODE
C 0 C'[t] == vi - kd*C[t] - (vd*C[t]*X[t])/( kd + C[t])
M 0 M'[t] == (VM1*C[t]*(1 - M[t]))/((Kc + C[t])*( 1 + K1 - M[t])) - (V2*M[t])/(K2 + M[t])
X 0 X'[t] == (VM3*M[t]*(1 - X[t]))/(1 + K3 -  X[t]) - (V4*X[t])/(K4 + X[t])
Generated by Cellerator Version 1.0 update 3.0216 using Mathematica 4.2 for Mac OS X (June 4, 2002), February 18, 2003 12:15:11