/* * Restriction point control of the mammalian cell cycle via the * cyclin E/Cdk2:p27 complex * * Model Status * * This model has been built using the expressions found in the * Conradie's 2010 paper "Restriction point control of the mammalian * cell cycle via the cyclin E/Cdk2:p27 complex". This model was * produced using the parameter values on page 360. This file is * known to run on COR 0.9 and Open Cell. * * Model Structure * * Numerous top-down kinetic models have been constructed to describe * the cell cycle. These models have typically been constructed, * validated and analyzed using model species (molecular intermediates * and proteins) and phenotypic observations, and therefore do * not focus on the individual model processes (reaction steps). * We have developed a method to: (a) quantify the importance of * each of the reaction steps in a kinetic model for the positioning * of a switch point [i.e. the restriction point (RP)]; (b) relate * this control of reaction steps to their effects on molecular * species, using sensitivity and co-control analysis; and thereby * (c) go beyond a correlation towards a causal relationship between * molecular species and effects. The method is generic and can * be applied to responses of any type, but is most useful for * the analysis of dynamic and emergent responses such as switch * points in the cell cycle. The strength of the analysis is illustrated * for an existing mammalian cell cycle model focusing on the RP * [Novak B, Tyson J (2004) J Theor Biol230, 563-579]. The reactions * in the model with the highest RP control were those involved * in: (a) the interplay between retinoblastoma protein and E2F * transcription factor; (b) those synthesizing the delayed response * genes and cyclin D/Cdk4 in response to growth signals; (c) the * E2F-dependent cyclin E/Cdk2 synthesis reaction; as well as (d) * p27 formation reactions. Nine of the 23 intermediates were shown * to have a good correlation between their concentration control * and RP control. Sensitivity and co-control analysis indicated * that the strongest control of the RP is mediated via the cyclin * E/Cdk2:p27 complex concentration. Any perturbation of the RP * could be related to a change in the concentration of this complex; * apparent effects of other molecular species were indirect and * always worked through cyclin E/Cdk2:p27, indicating a causal * relationship between this complex and the positioning of the * RP. * * Restriction point control of the mammalian cell cycle via the * cyclin E/Cdk2:p27 complex, Conradie R, Bruggeman F J, Ciliberto * A, Csikasz-Nagy A, Novak B, Westerhoff H V, Snoep J L FEB Journal, * 277, 357-367PubMed ID: 20015233 * * Model Diagram * * [[Image file: conradie_2009.png]] * * Time course of the mammalian cell division cycle. A time integration * for 30 h is shown for six of the intermediates of the system. * The G1-, S/G2- and M-phases for one cell cycle are indicated * in the graph. The RP is also depicted in the G1-phase. It should * be noted that, in contrast to other switch points in the model, * the RP is not a hard coded event (i.e. it is not an explicit * function, but rather an emergent property of the model), and * it is empirically defined as the last time point where, upon * cycloheximide (CHX) treatment, the cell would not finish the * division cycle it started with. The CHX treatment was mimicked * in the model by reducing the translation efficiency of the ribosomes * [e or Eps(t)], a parameter found in all synthesis steps of the * model, from 1.0 to 0.5. This definition was taken from the original * publication in which the model was described [5]. */ import nsrunit; unit conversion on; unit hour=3600 second^1; unit per_hour=2.7777778E-4 second^(-1); math main { realDomain time hour; time.min=0; extern time.max; extern time.delta; real eps dimensionless; eps=1; real K1 per_hour; K1=0.6; real K1a per_hour; K1a=0.1; real K2 per_hour; K2=20; real K2a per_hour; K2a=0.05; real K2aa per_hour; K2aa=1; real K3 per_hour; K3=140; real K3a per_hour; K3a=7.5; real K4 per_hour; K4=40; real J1 dimensionless; J1=0.1; real J3 dimensionless; J3=0.01; real J4 dimensionless; J4=0.04; real v_20(time) per_hour; real v_21(time) per_hour; real v_42(time) per_hour; real v_19(time) per_hour; real GA dimensionless; GA=0.3; real GB dimensionless; GB=1; real GE dimensionless; GE=0; real V_2(time) per_hour; real V_4(time) per_hour; real Cdh1(time) dimensionless; when(time=time.min) Cdh1=0.000653278; real Cdc20 dimensionless; Cdc20=0.00220177; real CYCA(time) dimensionless; when(time=time.min) CYCA=1.4094; real CYCB(time) dimensionless; when(time=time.min) CYCB=2.72898; real CYCE(time) dimensionless; when(time=time.min) CYCE=0.0229112; real k15 per_hour; k15=0.25; real k16 per_hour; k16=0.25; real k17 per_hour; k17=10; real k17a per_hour; k17a=0.35; real k18 per_hour; k18=10; real K9 per_hour; K9=2.5; real J17 dimensionless; J17=0.3; real J15 dimensionless; J15=0.1; real v_1(time) per_hour; real v_2(time) per_hour; real v_34(time) per_hour; real v_39(time) per_hour; real v_41(time) per_hour; real DRG(time) dimensionless; when(time=time.min) DRG=0.900533; real ERG(time) dimensionless; when(time=time.min) ERG=0.0121809; real K19 per_hour; K19=20; real K19a per_hour; K19a=0; real K20 per_hour; K20=10; real K21 dimensionless; K21=1; real K22 per_hour; K22=1; real K23a per_hour; K23a=0.005; real K23 per_hour; K23=1; real K26 per_hour; K26=10000; real K26R per_hour; K26R=200; real v_29(time) per_hour; real v_30(time) per_hour; real v_43(time) per_hour; real v_44(time) per_hour; real v_45(time) per_hour; real v_46(time) per_hour; real v_47(time) per_hour; real v_48(time) per_hour; real v_49(time) per_hour; real v_50(time) per_hour; real v_51(time) per_hour; real v_52(time) per_hour; real LA dimensionless; LA=3; real LB dimensionless; LB=5; real LD dimensionless; LD=3.3; real LE dimensionless; LE=5; real FE dimensionless; FE=25; real FB dimensionless; FB=2; real Rb(time) dimensionless; when(time=time.min) Rb=0.000190871; real PPRb(time) dimensionless; when(time=time.min) PPRb=9.97574; real E2F(time) dimensionless; when(time=time.min) E2F=0.989986; real PE2F(time) dimensionless; when(time=time.min) PE2F=3.98594; real E2FRb(time) dimensionless; when(time=time.min) E2FRb=0.00478911; real PE2FRb(time) dimensionless; when(time=time.min) PE2FRb=0.0192822; real PP1A(time) dimensionless; real PP1T dimensionless; PP1T=1; real CYCDT dimensionless; CYCDT=0.010976; real K5 per_hour; K5=20; real K6a per_hour; K6a=10; real K6 per_hour; K6=100; real K7a per_hour; K7a=0; real K7 per_hour; K7=0.6; real K8a per_hour; K8a=0.1; real K8 per_hour; K8=2; real K10 per_hour; K10=5; real k24 per_hour; k24=1000; real k24r per_hour; k24r=10; real K25 per_hour; K25=1000; real K25R per_hour; K25R=10; real K29 per_hour; K29=0.05; real K30 per_hour; K30=20; real J8 dimensionless; J8=0.1; real v_3(time) per_hour; real v_4(time) per_hour; real v_5(time) per_hour; real v_6(time) per_hour; real v_7(time) per_hour; real v_8(time) per_hour; real v_9(time) per_hour; real v_10(time) per_hour; real v_11(time) per_hour; real v_12(time) per_hour; real v_13(time) per_hour; real v_14(time) per_hour; real v_15(time) per_hour; real v_16(time) per_hour; real v_17(time) per_hour; real v_18(time) per_hour; real v_36(time) per_hour; real v_38(time) per_hour; real v_40 per_hour; real HA dimensionless; HA=0.5; real HB dimensionless; HB=1; real HE dimensionless; HE=0.5; real YE dimensionless; YE=1; real YB dimensionless; YB=0.05; real p27(time) dimensionless; when(time=time.min) p27=0.00922806; real V_6(time) per_hour; real V_8(time) per_hour; real MASS(time) dimensionless; when(time=time.min) MASS=1.68776; real CA(time) dimensionless; when(time=time.min) CA=0.0356927; real CD(time) dimensionless; when(time=time.min) CD=0.010976; real CE(time) dimensionless; when(time=time.min) CE=0.000542587; real CYCD(time) dimensionless; when(time=time.min) CYCD=0.43929; real CYCET dimensionless; CYCET=0.000542587; real K27 per_hour; K27=0.2; real K28 per_hour; K28=0.2; real v_31(time) per_hour; real v_32(time) per_hour; real v_33(time) per_hour; real r31switch dimensionless; r31switch=1; real MU per_hour; MU=0.061; real GM(time) dimensionless; when(time=time.min) GM=1.35565; real K11a per_hour; K11a=0; real K11 per_hour; K11=1.5; real K12 per_hour; K12=1.5; real K13 per_hour; K13=5; real K14 per_hour; K14=2.5; real K31 per_hour; K31=0.7; real K32 per_hour; K32=1.8; real K33 per_hour; K33=0.05; real K34 per_hour; K34=0.05; real J13 dimensionless; J13=0.005; real J14 dimensionless; J14=0.005; real J31 dimensionless; J31=0.01; real J32 dimensionless; J32=0.01; real v_22(time) per_hour; real v_23(time) per_hour; real v_24(time) per_hour; real v_25(time) per_hour; real v_26(time) per_hour; real v_27 per_hour; real v_28 per_hour; real v_35(time) per_hour; real v_37 per_hour; real IEP(time) dimensionless; when(time=time.min) IEP=0.154655; real PPX(time) dimensionless; when(time=time.min) PPX=1; real Cdc20T(time) dimensionless; when(time=time.min) Cdc20T=2.36733; // // v_42=(eps*(K1*(CYCB/J1)^2/((CYCB/J1)^2+1)+K1a)); v_19=(V_2*CYCB); v_21=(V_4*Cdh1/(J4+Cdh1)); v_20=((K3a+K3*Cdc20)*(1-Cdh1)/(J3-Cdh1+1)); V_2=(K2aa*Cdc20+K2a*(1-Cdh1)+K2*Cdh1); V_4=(K4*(GA*CYCA+GB*CYCB+GE*CYCE)); Cdh1:time=(v_20-v_21); CYCB:time=(v_42-v_19); // v_39=(eps*K9*DRG); v_41=(eps*(k17*(DRG/J17)^2/((DRG/J17)^2+1)+k17a*ERG)); v_2=(k18*DRG); v_34=(eps*k15/((DRG/J15)^2+1)); v_1=(k16*ERG); DRG:time=(v_41-v_2); ERG:time=(v_34-v_1); // PP1A=(PP1T/(K21*FE*(CYCA+CYCE+FB*CYCB)+1)); v_29=(E2FRb*K20*(CYCDT*LD+LA*CYCA+LB*CYCB+LE*CYCE)); v_30=(PE2FRb*K20*(CYCDT*LD+LA*CYCA+LB*CYCB+LE*CYCE)); v_43=(Rb*K20*(CYCDT*LD+LA*CYCA+LB*CYCB+LE*CYCE)); v_44=(PPRb*(K19a*(PP1T-PP1A)+K19*PP1A)); v_45=(E2FRb*K26R); v_46=(E2F*(K23a+K23*(CYCA+CYCB))); v_47=(PE2F*K22); v_48=(E2F*Rb*K26); v_49=(PE2FRb*K26R); v_50=(Rb*PE2F*K26); v_51=(PE2FRb*K22); v_52=(E2FRb*(K23a+K23*(CYCA+CYCB))); PPRb:time=(v_29+v_30+v_43-v_44); E2F:time=(v_29+v_45+v_47-v_46-v_48); PE2F:time=(v_30+v_49+v_46-v_47-v_50); Rb:time=(v_44+v_45+v_49-v_48-v_50-v_43); E2FRb:time=(v_51+v_48-v_52-v_29-v_45); PE2FRb:time=(v_52+v_50-v_51-v_30-v_49); // V_6=(K6a+K6*(HA*CYCA+HB*CYCB+HE*CYCE)); V_8=(K8*(YE*(CYCA+CYCE)+YB*CYCB)/(CYCET+J8)+K8a); v_3=(K10*CD); v_4=(K10*CYCD); v_5=(K25*p27*CYCE); v_6=(K25*p27*CYCA); v_7=(k24*p27*CYCD); v_8=(k24r*CD); v_9=(K30*Cdc20*CYCA); v_10=(K30*Cdc20*CA); v_11=(K25R*CE); v_12=(K25R*CA); v_13=(V_8*CE); v_14=(V_8*CYCE); v_15=(V_6*p27); v_16=(V_6*CE); v_17=(V_6*CD); v_18=(V_6*CA); v_36=(eps*K29*E2F*MASS); v_38=(eps*(K7a+K7*E2F)); v_40=(eps*K5); CA:time=(v_6-v_12-v_18-v_10); CD:time=(v_7-v_8-v_17-v_3); CE:time=(v_5-v_11-v_13-v_16); CYCA:time=(v_36-v_9-v_6+v_12+v_18); CYCD:time=(v_39+v_17+v_8-v_7-v_4); CYCE:time=(v_38-v_14-v_5+v_11+v_16); p27:time=(v_40+v_3+v_8-v_15-v_5-v_6-v_7+v_11+v_12+v_13+v_10); // v_31=(K27*MASS*r31switch); v_32=(K28*GM); v_33=(eps*MU*GM); GM:time=(v_31-v_32); MASS:time=v_33; // v_22=(K34*PPX); v_23=(K31*CYCB*(1-IEP)/(J31-IEP+1)); v_24=(K32*PPX*IEP/(J32+IEP)); v_25=(K12*Cdc20T); v_26=(K13*IEP*(Cdc20T-Cdc20)/(J13-Cdc20+Cdc20T)); v_27=(K14*Cdc20/(J14+Cdc20)); v_28=(K12*Cdc20); v_35=(eps*K11a+K11*CYCB); v_37=(eps*K33); Cdc20T:time=(v_35-v_25); IEP:time=(v_23-v_24); PPX:time=(v_37-v_22); }