Cell Cycle Model; Tyson (1991, 2 variables)

Citation
Tyson JJ, (1991) . Modeling the cell division cycle: cdc2 and cyclin interactions. PNAS, 88: 7328-7332. http://www.pnas.org/cgi/content/abstract/88/16/7328
Description
This is a two variable reduction of the larger 6- variable model published in the same paper.The published equations are u'= k4(v-u)(alpha+u^2)-k6*u, v'=Kappa-k6* u. In the present implementation, the change of variables z=v-u is made, so that the system becomes the more symmetric system u'= k4*z*(alpha+u^2)-k6*u, z'=Kappa-z*(alpha+u^2) . The variables can be interpreted as follows: u=[activeMPF]/[CT], v=([cyclin]+[preMPF]+[activeMPF])/[CT], z=([ cyclin]+[preMPF])/[CT], where [CT]=[CDC2]+{CDC2P]+[preMPF]+[aMPF].
Rate constant       Reaction
k4*(k4prime/k4 + u[t]^2) z -> u
k6 = 1 u -> EmptySet
kappa = 0.015 EmptySet -> z
Variable IC   ODE
u 0 u'[t] == -(k6*u[t]) + k4*(k4prime/k4 + u[t]^2) *z[t]
z 0 z'[t] == kappa - k4*(k4prime/k4 + u[t]^2)*z[t]

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