Novak and Tyson Cell Cycle Model (1997)

Citation
Novak B, tyson JJ (1997) Modeling the control of DNA replication in fission yeast, PNAS, USA, 94:9147-9152. http://www.pnas.org/cgi/content/abstract/ 94/17/9147
Description
A cell cycle model with 13 dynamic variables ( Cdc25,G1K,G1R=[Cig2/Cdc2/Rum1],G2K=[Cdc13/Cdc2],G2R=[Cdc13/Cdc2/Rum1],IE=[ Intermediary enzyme],mass,PG2=[Cdc13/P-Cdc2],PG2R=[Cdc13/P-Cdc2/Rum1],R=[ Rum1],UbE,UbE2, Wee1} and two auxilllary variables MPF = G2K+ beta*PG2, SPF=MPF+alpha*G1K+Cig1, (alpha, beta, Cig1 constants) . NOTE: The following switches in the published model are NOT described by the SBML: "Switches(i) When SPF crosses 0.1 from below, S phase is initiated (Start).(ii) When UbE crosses 0.1 from above, the cell divides functionally (mass->mass/2), although visible cytokinesis may be delayed.(iii) 60 min after Start,kp is divided by 2, and at cell division kp is multiplied by 2." ( from Table 1 of the cited reference).
Rate constant       Reaction
0 G1R -> R
0.00175 EmptySet -> G1K
0.00495*mass[t] EmptySet -> mass
0.0075*(1 - UbE[t]) + 0.25*UbE[t] G2K -> EmptySet
0.0075*(1 - UbE[t]) + 0.25*UbE[t] PG2 -> EmptySet
0.015 EmptySet -> G2K
0.025*(1 - Cdc25[t]) + 0.5*Cdc25[t] PG2 -> G2K
0.035*(1 - Wee1[t]) + 0.35*Wee1[t] G2K -> PG2
0.0375*(1 - UbE2[t]) + 7.5*UbE2[t] G1K -> EmptySet
0.05 + 0.0075*(1 - UbE[t]) + 0.25*UbE[t] G2R -> R
0.05 + 0.0075*(1 - UbE[t]) + 0.25*UbE[t] PG2R -> R
0.09375 EmptySet -> R
0.1 G1R -> G1K + R
0.1 G2R -> G2K + R
0.1 PG2R -> PG2 + R
0.1875 G1R -> G1K
0.1875 G2R -> G2K
0.1875 PG2R -> PG2
0.1875 R -> EmptySet
0.4 (G2K[t] + 0.05 PG2[t]) = unassigned ( hill vmax) 1 - IE |-> IE
10 G1K + R -> G1R
100 G2K + R -> G2R
100 PG2 + R -> PG2R
3.25 (0.25 G1K[t] + G2K[t] + 0.05 PG2[t])  = unassigned (hill vmax) mass + R |-> mass + EmptySet
G2K[t] + 0.05 PG2[t] = unassigned ( hill vmax) 1 - Cdc25 |-> Cdc25
G2K[t] + 0.05 PG2[t] = unassigned ( hill vmax) 1 - UbE2 |-> UbE2
G2K[t] + 0.05 PG2[t] = unassigned ( hill vmax) Wee1 |-> EmptySet
Variable IC   ODE
Cdc25 0 Cdc25'[t] == -((kcr*Cdc25[t])/(Kmcr + Cdc25[t])) +  (kc*(1 - Cdc25[t])*(G2K[t] + beta*PG2[t]))/(1 +  Kmc - Cdc25[t])
G1K 0 G1K'[t] == k5 + k4*G1R[t] + k8r*G1R[t] -  k8*G1K[t]*R[t] - G1K[t]*(V6p*(1 - UbE2[t]) +  V6*UbE2[t])
G1R 0 G1R'[t] == -(k4*G1R[t]) - k6p*G1R[t] - k8r* G1R[t] + k8*G1K[t]*R[t]
G2K 0 G2K'[t] == k1 + k4*G2R[t] + k7r*G2R[t] +  (V25p*(1 - Cdc25[t]) + V25*Cdc25[t])*PG2[t] -  k7*G2K[t]*R[t] - G2K[t]*(V2p*(1 - UbE[t]) +  V2*UbE[t]) - G2K[t]*(Vwp*(1 - Wee1[t]) + Vw* Wee1[t])
G2R 0 G2R'[t] == -(k4*G2R[t]) - k7r*G2R[t] + k7*G2K[ t]*R[t] - G2R[t]*(k2p + V2p*(1 - UbE[t]) +  V2*UbE[t])
IE 0 IE'[t] == -((kir*IE[t])/(Kmir + IE[t])) + (ki* (1 - IE[t])*(G2K[t] + beta*PG2[t]))/(1 + Kmi -  IE[t])
mass 0.4 mass'[t] == mu*mass[t]
PG2 0 PG2'[t] == -((V25p*(1 - Cdc25[t]) + V25*Cdc25[ t])*PG2[t]) + k4*PG2R[t] + k7r*PG2R[t] - k7*PG2[t] *R[t] - PG2[t]*(V2p*(1 - UbE[t]) + V2*UbE[t])  + G2K[t]*(Vwp*(1 - Wee1[t]) + Vw*Wee1[t])
PG2R 0 PG2R'[t] == -(k4*PG2R[t]) - k7r*PG2R[t] + k7* PG2[t]*R[t] - PG2R[t]*(k2p + V2p*(1 - UbE[t])  + V2*UbE[t])
R 0 R'[t] == k3 + k6p*G1R[t] + k8r*G1R[t] +  k7r*G2R[t] + k7r*PG2R[t] - k4*R[t] - k8*G1K[ t]*R[t] - k7*G2K[t]*R[t] - k7*PG2[t]*R[t] - (kp* mass[t]*(Cig1 + alpha*G1K[t] + G2K[t] + beta*PG2[t])*R[t] )/(Kmp + R[t]) + G2R[t]*(k2p + V2p*(1 -  UbE[t]) + V2*UbE[t]) + PG2R[t]*(k2p + V2p*( 1 - UbE[t]) + V2*UbE[t])
UbE 0 UbE'[t] == (ku*IE[t]*(1 - UbE[t]))/(1 +  Kmu - UbE[t]) - (kur*UbE[t])/(Kmur + UbE[t])
UbE2 0 UbE2'[t] == (ku2*(G2K[t] + beta*PG2[t])*(1 -  UbE2[t]))/(1 + Kmu2 - UbE2[t]) - (kur2*UbE2[ t])/(Kmur2 + UbE2[t])
Wee1 0 Wee1'[t] == (kwr*(1 - Wee1[t]))/(1 +  Kmwr - Wee1[t]) - (kw*(G2K[t] + beta*PG2[t])* Wee1[t])/(Kmw + Wee1[t])

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