/* * Cell Size at S Phase Initiation: An Emergent Property of the * G1/S Network * * Model Status * * This CellML version of the model runs in PCEnv and COR to produce * graphs that are similar in shape but not in magnitude to the * graphs in figure 3 of the published paper. This could possibly * be due to a missing variable k55 in the equation for cdk1_c. * The units have been checked and are consistent. * * Model Structure * * ABSTRACT: The eukaryotic cell cycle is the repeated sequence * of events that enable the division of a cell into two daughter * cells. It is divided into four phases: G1, S, G2, and M. Passage * through the cell cycle is strictly regulated by a molecular * interaction network, which involves the periodic synthesis and * destruction of cyclins that bind and activate cyclindependent * kinases that are present in nonlimiting amounts. Cyclin-dependent * kinase inhibitors contribute to cell cycle control. * * Budding yeast is an established model organism for cell cycle * studies, and several mathematical models have been proposed * for its cell cycle. An area of major relevance in cell cycle * control is the G1 to S transition. In any given growth condition, * it is characterized by the requirement of a specific, critical * cell size, PS, to enter S phase. The molecular basis of this * control is still under discussion. * * The authors report a mathematical model of the G1 to S network * that newly takes into account nucleo/cytoplasmic localization, * the role of the cyclin-dependent kinase Sic1 in facilitating * nuclear import of its cognate Cdk1-Clb5, Whi5 control, and carbon * source regulation of Sic1 and Sic1- containing complexes. The * model was implemented by a set of ordinary differential equations * that describe the temporal change of the concentration of the * involved proteins and protein complexes. The model was tested * by simulation in several genetic and nutritional setups and * was found to be neatly consistent with experimental data. To * estimate PS, the authors developed a hybrid model including * a probabilistic component for firing of DNA replication origins. * Sensitivity analysis of PS provides a novel relevant conclusion: * PS is an emergent property of the G1 to S network that strongly * depends on growth rate. * * The complete original paper reference is cited below: * * Cell Size at S Phase Initiation: An Emergent Property of the * G1/S Network, Matteo Barberis, Edda Klipp, Marco Vanoni, Lilia * Alberghina, 2007, PLOS Computational Biology PubMed ID: 17432928 * * figure1 * * [[Image file: barberis_2007.png]] * * Main Events That Occur during the Yeast Cell Cycle */ import nsrunit; unit conversion on; // unit nanomolar predefined unit minute=60 second^1; unit first_order_rate_constant=.01666667 second^(-1); unit flux=1.6666667E-8 meter^(-3)*second^(-1)*mole^1; unit second_order_rate_constant=1.6666667E4 meter^3*second^(-1)*mole^(-1); math main { realDomain time minute; time.min=0; extern time.max; extern time.delta; real v_c(time) nanomolar; when(time=time.min) v_c=0.5; real dv_c_dt(time) flux; real k_growth first_order_rate_constant; k_growth=0.0051; real v_n(time) nanomolar; when(time=time.min) v_n=0.5; real k_volume(time) dimensionless; real mcln2_c(time) nanomolar; when(time=time.min) mcln2_c=0; real k_50 first_order_rate_constant; k_50=0.6; real k_10 first_order_rate_constant; k_10=0.12; real mcln2_n(time) nanomolar; when(time=time.min) mcln2_n=0; real mclb5_c(time) nanomolar; when(time=time.min) mclb5_c=0; real k_51 first_order_rate_constant; k_51=0.6; real k_11 first_order_rate_constant; k_11=0.12; real mclb5_n(time) nanomolar; when(time=time.min) mclb5_n=0; real k_1 first_order_rate_constant; k_1=0.03523; real sbf_n(time) nanomolar; when(time=time.min) sbf_n=0; real k_2 first_order_rate_constant; k_2=0.03523; real k_39 first_order_rate_constant; k_39=1; real k_34 second_order_rate_constant; k_34=8.46; real k_35 first_order_rate_constant; k_35=0.0005; real sbfwhi5p_n(time) nanomolar; when(time=time.min) sbfwhi5p_n=0; real whi5_n(time) nanomolar; when(time=time.min) whi5_n=0; real sbfwhi5_n(time) nanomolar; when(time=time.min) sbfwhi5_n=0.025544; real cln3_c(time) nanomolar; when(time=time.min) cln3_c=0.000485; real k_6 flux; k_6=0.00001; real k_43 first_order_rate_constant; k_43=0.005; real k_15 first_order_rate_constant; k_15=0.01; real cln2_c(time) nanomolar; when(time=time.min) cln2_c=0; real k_3 first_order_rate_constant; k_3=0.32; real k_26 second_order_rate_constant; k_26=2.82; real k_27 first_order_rate_constant; k_27=0.55; real k_12 first_order_rate_constant; k_12=0.1; real cdk1_c(time) nanomolar; when(time=time.min) cdk1_c=0.333333; real cdk1cln2_c(time) nanomolar; when(time=time.min) cdk1cln2_c=0; real clb5_c(time) nanomolar; when(time=time.min) clb5_c=0; real k_4 first_order_rate_constant; k_4=0.32; real k_28 second_order_rate_constant; k_28=2.82; real k_29 first_order_rate_constant; k_29=0.55; real k_13 first_order_rate_constant; k_13=0.35; real cdk1clb5_c(time) nanomolar; when(time=time.min) cdk1clb5_c=0; real k_7 flux; k_7=0.01; real k_44 first_order_rate_constant; k_44=0.005; real k_49 first_order_rate_constant; k_49=0.001; real k_16 first_order_rate_constant; k_16=0.03; real cdk1_n(time) nanomolar; when(time=time.min) cdk1_n=0.0074127; real cln3_n(time) nanomolar; when(time=time.min) cln3_n=0; real k_24 second_order_rate_constant; k_24=2.82; real k_25 first_order_rate_constant; k_25=0.55; real k_20 first_order_rate_constant; k_20=0.01; real cdk1cln3_n(time) nanomolar; when(time=time.min) cdk1cln3_n=0; real k_21 first_order_rate_constant; k_21=0; real k_46 first_order_rate_constant; k_46=0.1; real k_53 first_order_rate_constant; k_53=0.001; real cdk1cln2_n(time) nanomolar; when(time=time.min) cdk1cln2_n=0; real k_33 first_order_rate_constant; k_33=0.55; real k_32 second_order_rate_constant; k_32=84.6; real k_48 first_order_rate_constant; k_48=0.012; real cdk1clb5sic1_c(time) nanomolar; when(time=time.min) cdk1clb5sic1_c=0; real sic1_c(time) nanomolar; when(time=time.min) sic1_c=0.039234; real cdk1clb5_n(time) nanomolar; when(time=time.min) cdk1clb5_n=0; real k_41 first_order_rate_constant; k_41=1; real cdk1clb5sic1p_n(time) nanomolar; when(time=time.min) cdk1clb5sic1p_n=0; real k_31 first_order_rate_constant; k_31=0.55; real k_30 second_order_rate_constant; k_30=42300; real k_40 first_order_rate_constant; k_40=1; real cdk1cln3far1_n(time) nanomolar; when(time=time.min) cdk1cln3far1_n=0; real far1_n(time) nanomolar; when(time=time.min) far1_n=0; real cdk1cln3far1p_n(time) nanomolar; when(time=time.min) cdk1cln3far1p_n=0; real k_36 second_order_rate_constant; k_36=4363.6; real k_37 second_order_rate_constant; k_37=4363.6; real cdk1clb5sic1_n(time) nanomolar; when(time=time.min) cdk1clb5sic1_n=0; real k_47 first_order_rate_constant; k_47=1; real k_38 second_order_rate_constant; k_38=4363.6; real k_9 flux; k_9=0.00005; real k_18 first_order_rate_constant; k_18=0.0008; real whi5_c(time) nanomolar; when(time=time.min) whi5_c=0.073564; real k_8 flux; k_8=0.00004; real k_45 first_order_rate_constant; k_45=0.005; real k_17 first_order_rate_constant; k_17=0.01; real far1_c(time) nanomolar; when(time=time.min) far1_c=0.0037926; real k_5 flux; k_5=0.000042; real k_42 first_order_rate_constant; k_42=0.005; real k_14 first_order_rate_constant; k_14=0.01; real whi5p_c(time) nanomolar; when(time=time.min) whi5p_c=0; real k_52 first_order_rate_constant; k_52=0.005; real whi5p_n(time) nanomolar; when(time=time.min) whi5p_n=0; real sic1P_n(time) nanomolar; when(time=time.min) sic1P_n=0; real far1P_n(time) nanomolar; when(time=time.min) far1P_n=0; real k_22 first_order_rate_constant; k_22=0.01; real k_19 first_order_rate_constant; k_19=0.01; real k_23 first_order_rate_constant; k_23=0.01; // // v_c:time=dv_c_dt; // dv_c_dt=(k_growth*v_c); // v_n:time=(0 flux); // k_volume=(v_n/v_c); // mcln2_c:time=(k_50*mcln2_n*k_volume-k_10*mcln2_c-dv_c_dt/v_c*mcln2_c); // mclb5_c:time=(k_51*mclb5_n*k_volume-k_11*mclb5_c-dv_c_dt/v_c*mclb5_c); // mcln2_n:time=(k_1*sbf_n-k_50*mcln2_n); // mclb5_n:time=(k_2*sbf_n-k_51*mclb5_n); // sbf_n:time=(k_39*sbfwhi5p_n-k_34*sbf_n*whi5_n+k_35*sbfwhi5_n); // cln3_c:time=(k_6-k_43*cln3_c-k_15*cln3_c-dv_c_dt/v_c*cln3_c); // cln2_c:time=(k_3*mcln2_c-k_26*cdk1_c*cln2_c+k_27*cdk1cln2_c-k_12*cln2_c-dv_c_dt/v_c*cln2_c); // clb5_c:time=(k_4*mclb5_c-k_28*clb5_c*cdk1_c+k_29*cdk1clb5_c-k_13*clb5_c-dv_c_dt/v_c*clb5_c); // cdk1_c:time=(k_7-k_44*cdk1_c+k_49*cdk1_n+k_27*cdk1cln2_c-k_26*cdk1_c*cln2_c-k_28*cdk1_c*clb5_c+k_29*cdk1clb5_c-k_16*cdk1_c-dv_c_dt/v_c*cdk1_c); // cln3_n:time=(k_43*cln3_c/k_volume-k_24*cln3_n*cdk1_n+k_25*cdk1cln3_n-k_20*cln3_n); // cdk1_n:time=(k_44*cdk1_c/k_volume-k_49*cdk1_n-k_24*cln3_n*cdk1_n+k_25*cdk1cln3_n-k_21*cdk1_n); // cdk1cln2_c:time=(k_26*cdk1_c*cln2_c-k_27*cdk1cln2_c-k_46*cdk1cln2_c+k_53*cdk1cln2_n*k_volume-dv_c_dt/v_c*cdk1cln2_c); // cdk1clb5_c:time=(k_28*cdk1_c*clb5_c-k_29*cdk1clb5_c+k_33*cdk1clb5sic1_c-k_32*sic1_c*cdk1clb5_c-k_48*cdk1clb5_c-dv_c_dt/v_c*cdk1clb5_c); // cdk1cln2_n:time=(k_46*cdk1cln2_c/k_volume-k_53*cdk1cln2_n); // cdk1clb5_n:time=(k_41*cdk1clb5sic1p_n+k_48*cdk1clb5_c/k_volume); // cdk1cln3_n:time=(k_24*cln3_n*cdk1_n-k_25*cdk1cln3_n+k_31*cdk1cln3far1_n-k_30*far1_n*cdk1cln3_n+k_40*cdk1cln3far1p_n); // sbfwhi5_n:time=(k_34*sbf_n*whi5_n-k_35*sbfwhi5_n-k_36*sbfwhi5_n*cdk1cln3_n); // sbfwhi5p_n:time=(k_36*sbfwhi5_n*cdk1cln3_n-k_39*sbfwhi5p_n); // cdk1cln3far1_n:time=(k_30*far1_n*cdk1cln3_n-k_31*cdk1cln3far1_n-k_37*cdk1cln3far1_n*cdk1cln2_n); // cdk1clb5sic1_n:time=(k_47*cdk1clb5sic1_c/k_volume-k_38*cdk1clb5sic1_n*cdk1cln2_n); // cdk1clb5sic1p_n:time=(k_38*cdk1clb5sic1_n*cdk1cln2_n-k_41*cdk1clb5sic1p_n); // cdk1cln3far1p_n:time=(k_37*cdk1cln3far1_n*cdk1cln2_n-k_40*cdk1cln3far1p_n); // cdk1clb5sic1_c:time=(k_32*sic1_c*cdk1clb5_c-k_33*cdk1clb5sic1_c-k_47*cdk1clb5sic1_c-dv_c_dt/v_c*cdk1clb5sic1_c); // sic1_c:time=(k_9-k_32*sic1_c*cdk1clb5_c+k_33*cdk1clb5sic1_c-k_18*sic1_c-dv_c_dt/v_c*sic1_c); // whi5_c:time=(k_8-k_45*whi5_c-k_17*whi5_c-dv_c_dt/v_c*whi5_c); // far1_c:time=(k_5-k_42*far1_c-k_14*far1_c-dv_c_dt/v_c*far1_c); // whi5p_c:time=(k_52*whi5p_n*k_volume); // sic1P_n:time=(k_41*cdk1clb5sic1p_n); // far1P_n:time=(k_40*cdk1cln3far1p_n); // whi5_n:time=(k_45*whi5_c/k_volume-k_34*whi5_n*sbf_n-k_22*whi5_n); // far1_n:time=(k_42*far1_c/k_volume-k_30*far1_n*cdk1cln3_n+k_31*cdk1cln3far1_n-k_19*far1_n); // whi5p_n:time=(k_39*sbfwhi5p_n-k_52*whi5p_n-k_23*whi5p_n); // }