Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle Camille Nicodemus Auckland Bioengineering Institute, The University of Auckland
Model Status This CellML model runs in OpenCell and COR. It was created from equations [1] to [46]. The model parameters were taken from the Parameters document. The units have been checked and they are consistent. v_sw has been set to 0 in this particular model which means the model is de-coupled from the circadian clock. The CellML model runs to replicate the first part of figure 7B.
Model Structure We propose an integrated computational model for the network of cyclin-dependent kinases (Cdks) that controls the dynamics of the mammalian cell cycle. The model contains four Cdk modules regulated by reversible phosphorylation, Cdk inhibitors, and protein synthesis or degradation. Growth factors (GFs) trigger the transition from a quiescent, stable steady state to self-sustained oscillations in the Cdk network. These oscillations correspond to the repetitive, transient activation of cyclin D/Cdk4-6 in G(1), cyclin E/Cdk2 at the G(1)/S transition, cyclin A/Cdk2 in S and at the S/G(2) transition, and cyclin B/Cdk1 at the G(2)/M transition. The model accounts for the following major properties of the mammalian cell cycle: (i) repetitive cell cycling in the presence of suprathreshold amounts of GF; (ii) control of cell-cycle progression by the balance between antagonistic effects of the tumor suppressor retinoblastoma protein (pRB) and the transcription factor E2F; and (iii) existence of a restriction point in G(1), beyond which completion of the cell cycle becomes independent of GF. The model also accounts for endoreplication. Incorporating the DNA replication checkpoint mediated by kinases ATR and Chk1 slows down the dynamics of the cell cycle without altering its oscillatory nature and leads to better separation of the S and M phases. The model for the mammalian cell cycle shows how the regulatory structure of the Cdk network results in its temporal self-organization, leading to the repetitive, sequential activation of the four Cdk modules that brings about the orderly progression along cell-cycle phases. The original paper reference is cited below: Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Goldbeter A, Gerard C, 2009, Unite de Chronobiologie Theorique , 106(51), 21643-8. PubMed ID: 20007375 reaction diagram GF-induced oscillations in the Cdk network. (A) Below a sharp threshold in the concentration of GF, the Cdk network evolves to a stable steady state, whereas sustained oscillations occur above the threshold that corresponds to a bifurcation beyond which the steady state becomes unstable
time AP1 v_sap1 GF K_agf GF k_dap1 AP1 eps time pRB v_sprb k_pc1 pRB E2F k_pc2 pRBc1 V_1 pRB K_1 pRB Md Mdp27 V_2 pRBp K_2 pRBp k_dprb pRB eps time pRBc1 k_pc1 pRB E2F k_pc2 pRBc1 eps time pRBp V_1 pRB K_1 pRB Md Mdp27 V_2 pRBp K_2 pRBp V_3 pRBp K_3 pRBp Me V_4 pRBpp K_4 pRBpp k_pc3 pRBp E2F k_pc4 pRBc2 k_dpRBp pRBp eps time pRBc2 k_pc3 pRBp E2F k_pc4 pRBc2 eps time pRBpp V_3 pRBp K_3 pRBp Me V_4 pRBpp K_4 pRBpp k_dpRBpp pRBpp eps time E2F v_se2f k_pc1 pRB E2F k_pc2 pRBc1 k_pc3 pRBp E2F k_pc4 pRBc2 V_1e2f Ma E2F K_1e2f E2F V_2e2f E2Fp K_2e2f E2Fp k_de2f E2F eps time E2Fp V_1e2f Ma E2F K_1e2f E2F V_2e2f E2Fp K_2e2f E2Fp k_de2fp E2Fp eps time Cd k_cd1 AP1 k_cd2 E2F K_i7 K_i7 pRB K_i8 K_i8 pRBp k_com1 Cd Cdk4_tot Mdi Md Mdp27 k_decom1 Mdi V_dd Cd K_dd Cd k_ddd Cd eps time Mdi k_com1 Cd Cdk4_tot Mdi Md Mdp27 k_decom1 Mdi V_m2d Md K_2d Md V_m1d Mdi K_1d Mdi eps time Md V_m1d Mdi K_1d Mdi V_m2d Md K_2d Md k_c1 Md p27 k_c2 Mdp27 eps time Mdp27 k_c1 Md p27 k_c2 Mdp27 eps time Ce k_ce E2F K_i9 K_i9 pRB K_i10 K_i10 pRBp k_com2 Ce Cdk2_tot Mei Me Mep27 Mai Ma Map27 k_decom2 Mei V_de Skp2 K_dceskp2 Skp2 Ce K_de Ce k_dde Ce eps time Mei k_com2 Ce Cdk2_tot Mei Me Mep27 Mai Ma Map27 k_decom2 Mei V_m2e Wee1 i_b1 Me K_2e Me V_m1e Pe Mei K_1e Mei eps time Me V_m1e Pe Mei K_1e Mei V_m2e Wee1 i_b1 Me K_2e Me k_c3 Me p27 k_c4 Mep27 eps time Skp2 v_sskp2 V_dskp2 Skp2 K_dskp2 Skp2 Cdh1a K_cdh1 Cdh1a k_ddskp2 Skp2 eps time Mep27 k_c3 Me p27 k_c4 Mep27 eps time Pei v_spei V_6e x_e1 x_e2 Chk1 Pe K_6e Pe V_m5e Me a_e Pei K_5e Pei k_dpei Pei eps time Pe V_m5e Me a_e Pei K_5e Pei V_6e x_e1 x_e2 Chk1 Pe K_6e Pe k_dpe Pe eps time Ca k_ca E2F K_i11 K_i11 pRB K_i12 K_i12 pRBp k_com3 Ca Cdk2_tot Mei Me Mep27 Mai Ma Map27 k_decom3 Mai V_da Ca K_da Ca Cdc20a K_acdc20 Cdc20a k_dda Ca eps time Mai k_com3 Ca Cdk2_tot Mei Me Mep27 Mai Ma Map27 k_decom3 Mai V_m2a Wee1 i_b2 Ma K_2a Ma V_m1a Pa Mai K_1a Mai eps time Ma V_m1a Pa Mai K_1a Mai V_m2a Wee1 i_b2 Ma K_2a Ma k_c5 Ma p27 k_c6 Map27 eps time Map27 k_c5 Ma p27 k_c6 Map27 eps time p27 v_s1p27 v_s2p27 E2F K_i13 K_i13 pRB K_i14 K_i14 pRBp k_c1 Md p27 k_c2 Mdp27 k_c3 Me p27 k_c4 Mep27 k_c5 Ma p27 k_c6 Map27 k_c7 Mb p27 k_c8 Mbp27 V_1p27 Me p27 K_1p27 p27 V_2p27 p27p K_2p27 p27p k_ddp27 p27 eps time p27p V_1p27 Me p27 K_1p27 p27 V_2p27 p27p K_2p27 p27p V_dp27p Skp2 K_dp27skp2 Skp2 p27p K_dp27p p27p k_ddp27p p27p eps time Cdh1i V_2cdh1 Cdh1a K_2cdh1 Cdh1a Ma Mb V_1cdh1 Cdh1i K_1cdh1 Cdh1i k_dcdh1i Cdh1i eps time Cdh1a v_scdh1a V_1cdh1 Cdh1i K_1cdh1 Cdh1i V_2cdh1 Cdh1a K_2cdh1 Cdh1a Ma Mb k_dcdh1a Cdh1a eps time Pai v_spai V_6a x_a1 x_a2 Chk1 Pa K_6a Pa V_m5a Ma a_a Pai K_5a Pai k_dpai Pai eps time Pa V_m5a Ma a_a Pai K_5a Pai V_6a x_a1 x_a2 Chk1 Pa K_6a Pa k_dpa Pa eps time Cb v_cb k_com4 Cb Cdk1_tot Mbi Mb Mbp27 k_decom4 Mbi V_db Cb K_db Cb Cdc20a K_dbcdc20 Cdc20a Cdh1a K_dbcdh1 Cdh1a k_ddb Cb eps time Mbi k_com4 Cb Cdk1_tot Mbi Mb Mbp27 k_decom4 Mbi V_m2b Wee1 i_b3 Mb K_2b Mb V_m1b Pb Mbi K_1b Mbi eps time Mb V_m1b Pb Mbi K_1b Mbi V_m2b Wee1 i_b3 Mb K_2b Mb k_c7 Mb p27 k_c8 Mbp27 eps time Mbp27 k_c7 Mb p27 k_c8 Mbp27 eps time Cdc20i v_scdc20i V_m3b Mb Cdc20i K_3b Cdc20i V_m4b Cdc20a K_4b Cdc20a k_dcdc20i Cdc20i eps time Cdc20a V_m3b Mb Cdc20i K_3b Cdc20i V_m4b Cdc20a K_4b Cdc20a k_dcdc20a Cdc20a eps time Pbi v_spbi V_6b x_b1 x_b2 Chk1 Pb K_6b Pb V_m5b Mb a_b Pbi K_5b Pbi k_dpbi Pbi eps time Pb V_m5b Mb a_b Pbi K_5b Pbi V_6b x_b1 x_b2 Chk1 Pb K_6b Pb k_dpb Pb eps time Wee1 v_swee1 k_sw Mw V_m7b Mb i_b Wee1 K_7b Wee1 V_m8b Wee1p K_8b Wee1p k_dwee1 Wee1 eps time Wee1p V_m7b Mb i_b Wee1 K_7b Wee1 V_m8b Wee1p K_8b Wee1p k_dwee1p Wee1p eps time Cdc45 V_1cdc45 Me Cdc45_tot Cdc45 K_1cdc45 Cdc45_tot Cdc45 V_2cdc45 Cdc45 K_2cdc45 Cdc45 k_spol Pol_tot Pol Cdc45 k_dpol Pol eps time Pol k_spol Pol_tot Pol Cdc45 k_dpol Pol eps time Primer k_sprim Pol k_dprim Primer k_aatr ATR_tot ATR Primer k_datr ATR eps time ATR k_aatr ATR_tot ATR Primer k_datr ATR eps time Chk1 V_1chk ATR Chk1_tot Chk1 K_1chk Chk1_tot Chk1 V_2chk Chk1 K_2chk Chk1 eps time Mw v_sw BN n_gerard K_iw n_gerard BN n_gerard v_dw Mw K_dw Mw time X V_1x Ma X_tot X K_1x X_tot X V_2x X K_2x X eps time CbA v_cb X 1 k_com4 CbA Cdk1_tot Mbi Mb Mbp27 k_decom4 Mbi V_db CbA K_db CbA Cdc20a K_dbcdc20 Cdc20a Cdh1a K_dbcdh1 Cdh1a k_ddb CbA eps time MP vsP BN n KAP n BN n vmP MP KmP MP kdmp MP time MC vsC BN n KAC n BN n vmC MC KmC MC kdmc MC time MB vsB KIB m KIB m RN m vmB MB KmB MB kdmb MB time MR vsR BN h KAR h BN h vmR MR KmR MR kdmr MR time PC ksP MP V2P PCP Kdp PCP k4 PCC V1P PC Kp PC k3 PC CC kdn PC time CC ksC MC V2C CCP Kdp CCP k4 PCC V1C CC Kp CC k3 PC CC kdnc CC time RC ksR MR k10 RN k9 RC vdRC RC Kd RC kdn RC time PCP V1P PC Kp PC V2P PCP Kdp PCP vdPC PCP Kd PCP kdn PCP time CCP V1C CC Kp CC V2C CCP Kdp CCP vdCC CCP Kd CCP kdn CCP time PCC V2PC PCCP Kdp PCCP k3 PC CC k2 PCN V1PC PCC Kp PCC k4 PCC k1 PCC kdn PCC time PCN V4PC PCNP Kdp PCNP k1 PCC k8 IN V3PC PCN Kp PCN k2 PCN k7 BN PCN kdn PCN time RN k9 RC k10 RN vdRN RN Kd RN kdn RN time PCCP V1PC PCC Kp PCC V2PC PCCP Kdp PCCP vdPCC PCCP Kd PCCP kdn PCCP time PCNP V3PC PCN Kp PCN V4PC PCNP Kdp PCNP vdPCN PCNP Kd PCNP kdn PCNP time BC V2B BCP Kdp BCP k6 BN ksB MB V1B BC Kp BC k5 BC kdn BC time BCP V1B BC Kp BC V2B BCP Kdp BCP vdBC BCP Kd BCP kdn BCP time BN V4B BNP Kdp BNP k5 BC k8 IN V3B BN Kp BN k6 BN k7 BN PCN kdn BN time BNP V3B BN Kp BN V4B BNP Kdp BNP vdBN BNP Kd BNP kdn BNP time IN k7 BN PCN k8 IN vdIN IN Kd IN kdn IN The University of Auckland Auckland Bioengineering Institute Active, phosphorylated form of phosphatase Cdc25 acting on cyclin B/Cdk1 (including cyclin B1,B2 and B3) Retinoblastoma protein phosphorylated once Inactive, phosphorylated form of kinase Wee1 Complex cyclin B/Cdk1/p27 (includes cyclin B1,B2 and B3) Cyclin B (contain cyclin B1, B2 and B3) Active complex cyclin D/Cdk4-6 (includes cyclinD1,D2 and D3) Unphosphorylated Retinoblastoma protein Active form of Cdc20 Active complex cyclin B/Cdk1 (includes cyclin B1, B2 and B3) Active complex cyclin A/Cdk2 (includes A1, A2) Active form of Cdh1 (epithelial cadherin) Wee1 mRNA induced by the circadian clock Inactive complex cyclin A/Cdk2 (includes cyclin A1, A2) Active, dephosphorylated form of kinase Wee1 Complex cyclin D/Cdk4-6/p27 (including cyclin D1,D2 and D3) Complex between Retinoblastoma protein phosphorylated once/Transcription factor E2F Cyclin A (includes both cyclin A1 and cyclin A2) transcription factor X Inactive complex cyclin B/Cdk1 (includes cyclin B1,B2 and B3) Cyclin-dependent kinase inhibitor p27 (or p21) Active complex cyclin E/Cdk2 (includes cyclin E1 and E2) Complex cyclin A/Cdk2/p27 (includes cyclin A1, A2) Phosphorylated transcription factor E2F Inactive complex cyclin D/Cdk4-6 (includes cyclin D1,D2 and D3) Complex cyclin E/Cdk2/p27 (includes cyclin E1 and E2) Inactive, dephosphorylated form of phosphatase Cdc25 acting on cyclin A/Cdk2 (includes cyclin A1 and A2) DNA polymerase α Inactive form of Cdc20 Cyclin E (includes cyclin E1 and E2) Inactive complex cyclin E/Cdk2 (includes cyclin E1 and E2) Inactive form of Cdh1 (epithelial cadherin) Active, phosphorylated form of phosphatase Cdc25 acting on cyclin E/Cdk2 (includes cyclin E1 and E2) DNA anchor factor Phosphorylated form of cyclin-dependent kinase inhibitor p27(or p21) Cyclin D (includes cyclin D1,D2 and D3) Active, phosphorylated form of phosphatase Cdc25 acting on cyclin A/Cdk2 (including cyclin A1 and A2) RNA primer Inactive, dephosphorylated form of phosphatase Cdc25 acting on cyclin E/Cdk2 (includes cyclin E1 and E2) Inactive, dephosphorylated form of phosphatase Cdc25 acting on cyclin B/Cdk1 (includes cyclin B1,B2 and B3) Retinoblastoma protein phosphorylated twice Mammalian cell 20007375 Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle Unite de Chronobiologie Theorique 106(51) 21643 21648 keyword circadian rhythms mitotic oscillation