| Citation |
|---|
| Gardner TS, Dolnik M, Collins JJ (1998) A theory for controlling cell cycle dynamics using a reversibly binding inhibitor. PNAS 95: 14190-14195. http://www.pnas.org/cgi/content/abstract/95/24/14190 |
| Description |
|---|
| This is a modification of the widely cited ( Goldbeter 1991) 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) .Two additional variables Y, Z control the dynamics of the inhibitor. |
| Rate constant | Reaction |
|---|---|
| a1 = 0.5 | C + Y -> Z |
| a2 = 0.5 | Z -> C + Y |
| d1 = 0.05 | Y -> EmptySet |
| K1 = 0.005 (hill khalf) | Comp[M] -> M |
| K2 = 0.005 (hill khalf) | M -> EmptySet |
| K3 = 0.005 (hill khalf) | Comp[X] -> X |
| K4 = 0.005 (hill khalf) | X -> EmptySet |
| Kc = 0.3 (hill vmax) | Comp[M] -> M |
| kd = 0.01 | C -> EmptySet |
| kd = 0.01 (hill khalf) | C + X -> X + EmptySet |
| V2 = 1.5 (hill vmax) | M -> EmptySet |
| V4 = 0.5 (hill vmax) | X -> EmptySet |
| vd = 0.25 (hill vmax) | C + X -> X + EmptySet |
| vi = 0.025 | EmptySet -> C |
| VM1 = 3 (hill vmax) | Comp[M] -> M |
| VM3 = 1 (hill vmax) | Comp[X] -> X |
| VS = 0 | EmptySet -> Y |
| alpha = 0.1 | Z -> C |
| alpha = 0.1 | Z -> Y |
| Variable | IC | ODE |
|---|---|---|
| C | 0 | C'[t] == vi - kd*C[t] - (vd*C[t]*X[t])/( kd + C[t]) - a1*C[t]*Y[t] + a2*Z[t] + alpha* Z[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]) |
| Y | 1 | Y'[t] == VS - d1*Y[t] - a1*C[t]*Y[t] + a2*Z[t] + alpha*Z[t] |
| Z | 1 | Z'[t] == a1*C[t]*Y[t] - a2*Z[t] - 2*alpha*Z[t] |