/* * The kinetic origins of the restriction point in the mammalian * cell cycle * * Model Status * * This CellML version of the model has been checked in COR and * PCEnv and the model runs to replicate the original published * results as depicted in figure 5b of the paper. The units have * been checked and are consistent. * * Model Structure * * ABSTRACT: A detailed model mechanism for the G1/S transition * in the mammalian cell cycle is presented and analysed by computer * simulation to investigate whether the kinetic origins of the * restriction point (R-point) can be identified. The R-point occurs * in mid-to-late G1 phase and marks the transition between mitogendependent * to mitogen-independent progression of the cell cycle. For purposes * of computer simulations, the R-point is defined as the first * point in time after mitosis where cutting off mitogen stimulation * does not prevent the cell reaching the threshold activity of * cyclin-E/cdk2 required for entry into S phase. The key components * of the network that generate a dynamic switching behaviour associated * with the R-point include a positive feedback loop between cyclin-E/cdk2 * and Cdc25A, along with the mutually negative interaction between * the cdk inhibitor p27Kip1 and cyclin-E/cdk2. Simulations of * the passage through the R-point were carried out and the factors * affecting the position of the R-point in G1 are determined. * The detailed model also shows various points in the network * where the activation of cyclin-E/cdk2 can be initiated with * or without the involvement of the retinoblastoma protein. * * The complete original paper reference is cited below: * * The kinetic origins of the restriction point in the mammalian * cell cycle, B. D. Aguda and Y. Tang, 1999 (A PDF version of * the article is available to subscribers on the journal website.) * PubMed ID: 10619492 * * Figure 1 * * [[Image file: aguda_1999a.png]] * * A detailed mechanistic model of the GI/S transition in the mammalian * cell cycle. * * Figure 2 * * [[Image file: aguda_1999b.png]] * * pRB-independant pathways leading to activation of CycE/Cdk2. */ import nsrunit; unit conversion on; // unit millimolar predefined unit minute=60 second^1; unit first_order_rate_constant=.01666667 second^(-1); math main { realDomain time minute; time.min=0; extern time.max; extern time.delta; real k1 first_order_rate_constant; k1=0.1; real k1_v1 first_order_rate_constant; k1_v1=0.5; real k1_v2 first_order_rate_constant; k1_v2=0.5; real kn1 first_order_rate_constant; kn1=0.001; real k2 first_order_rate_constant; k2=0.1; real kn2 first_order_rate_constant; kn2=1; real k3 first_order_rate_constant; k3=1.42; real k3_ first_order_rate_constant; k3_=0; real kn4 first_order_rate_constant; kn4=0.016; real k5 first_order_rate_constant; k5=0.02; real kn6 first_order_rate_constant; kn6=5; real k8 first_order_rate_constant; k8=2; real k9 first_order_rate_constant; k9=2; real k10 first_order_rate_constant; k10=0.035; real k17 first_order_rate_constant; k17=3.5; real k18 first_order_rate_constant; k18=0.0001; real k19 first_order_rate_constant; k19=0.05; real k20 first_order_rate_constant; k20=0.01; real k21 first_order_rate_constant; k21=0.1; real k22 first_order_rate_constant; k22=0.001; real k24 first_order_rate_constant; k24=0.1; real k25 first_order_rate_constant; k25=0.01; real k25_ first_order_rate_constant; k25_=0.02; real k26 first_order_rate_constant; k26=0.01; real k26_ first_order_rate_constant; k26_=0.1; real k28 first_order_rate_constant; k28=0.01; real k29 first_order_rate_constant; k29=0.001; real a_CyclinE_Cdk2(time) dimensionless; when(time=time.min) a_CyclinE_Cdk2=0; real V_2(time) first_order_rate_constant; real V_10(time) first_order_rate_constant; real V_n2(time) first_order_rate_constant; real V_9(time) first_order_rate_constant; real V_21(time) first_order_rate_constant; real i_CyclinE_Cdk2(time) dimensionless; when(time=time.min) i_CyclinE_Cdk2=0.01; real V_3(time) first_order_rate_constant; real V_5(time) first_order_rate_constant; real pRB_E2F(time) dimensionless; when(time=time.min) pRB_E2F=1.95; real V_n1 first_order_rate_constant; real V_1(time) first_order_rate_constant; real E2F(time) dimensionless; when(time=time.min) E2F=0; real V_4 first_order_rate_constant; V_4=0.000001; real V_18(time) first_order_rate_constant; real V_n4(time) first_order_rate_constant; real pRB(time) dimensionless; when(time=time.min) pRB=0.05; real V_27 first_order_rate_constant; V_27=0.01; real V_26(time) first_order_rate_constant; real V_29(time) first_order_rate_constant; real V_28(time) first_order_rate_constant; real CycD_Cdk4(time) dimensionless; when(time=time.min) CycD_Cdk4=0; real V_6 first_order_rate_constant; V_6=0.018; real V_20(time) first_order_rate_constant; real V_n6(time) first_order_rate_constant; real V_19(time) first_order_rate_constant; real V_17(time) first_order_rate_constant; real p27(time) dimensionless; when(time=time.min) p27=5; real V_7 first_order_rate_constant; V_7=0.0001; real V_8(time) first_order_rate_constant; real V_22(time) first_order_rate_constant; real CycE_Cdk2_p27(time) dimensionless; when(time=time.min) CycE_Cdk2_p27=1; real CycD_Cdk4_p27(time) dimensionless; when(time=time.min) CycD_Cdk4_p27=0; real p16(time) dimensionless; when(time=time.min) p16=5; real V_23 first_order_rate_constant; V_23=0.2; real V_25(time) first_order_rate_constant; real V_24(time) first_order_rate_constant; real pRB_P(time) dimensionless; when(time=time.min) pRB_P=0.01; // // // a_CyclinE_Cdk2:time=(V_2+V_10-(V_n2+V_9+V_21)); // i_CyclinE_Cdk2:time=(V_3+V_n2-(V_2+V_5)); // pRB_E2F:time=(V_n1-V_1); // E2F:time=(V_1+V_4+V_18-(V_n1+V_n4)); // pRB:time=(V_27+V_26+V_29-(V_n1+V_28)); // CycD_Cdk4:time=(V_6+V_20-(V_n6+V_19+V_17)); // p27:time=(V_7+V_10+V_20-(V_8+V_9+V_19+V_22)); // CycE_Cdk2_p27:time=(V_9-V_10); // CycD_Cdk4_p27:time=(V_19-V_20); // p16:time=(V_23+V_25-(V_17+V_24)); // pRB_P:time=(V_1-V_29); // V_1=(k1_v1*CycD_Cdk4*pRB_E2F+k1_v2*CycD_Cdk4_p27*pRB_E2F+k1*a_CyclinE_Cdk2*pRB_E2F); // V_n1=kn1; // V_2=(k2*a_CyclinE_Cdk2*i_CyclinE_Cdk2); // V_n2=(kn2*a_CyclinE_Cdk2); // V_3=(k3*E2F+k3_); // V_n4=(kn4*E2F); // V_5=(k5*i_CyclinE_Cdk2); // V_n6=(kn6*CycD_Cdk4); // V_8=(k8*p27*a_CyclinE_Cdk2); // V_9=(k9*p27*a_CyclinE_Cdk2); // V_10=(k10*CycE_Cdk2_p27); // V_17=(k17*p16*CycD_Cdk4); // V_18=(k18*E2F); // V_19=(k19*p27*CycD_Cdk4); // V_20=(k20*CycD_Cdk4_p27); // V_21=(k21*a_CyclinE_Cdk2^2); // V_22=(k22*p27); // V_24=(k24*p16); // V_25=(k25/(((1 first_order_rate_constant)+k25_*pRB)*(1 minute))); // V_26=(k26/(((1 first_order_rate_constant)+k26_*p16)*(1 minute))); // V_28=(k28*pRB); // V_29=(k29*pRB_P); }