/* * Dynamical modeling of syncytial mitotic cycles in Drosophila * embryos * * Model Status * * This CellML version of the model runs in PCEnv but requires * initial conditions and 'switches' in order to reproduce the * published results. The set of parameters used to produce figure * 3 of the published paper is implemented in this version. The * doubling of N and rescaling of other variables at division are * not included in this CellML description. * * ValidateCellML verifies this model as valid CellML with fully * consistent units. * * Model Structure * * ABSTRACT: Immediately following fertilization, the fruit fly * embryo undergoes 13 rapid, synchronous, syncytial nuclear division * cycles driven by maternal genes and proteins. During these mitotic * cycles, there are barely detectable oscillations in the total * level of B-type cyclins. In this paper, we propose a dynamical * model for the molecular events underlying these early nuclear * division cycles in Drosophila. The model distinguishes nuclear * and cytoplasmic compartments of the embryo and permits exploration * of a variety of rules for protein transport between the compartments. * Numerical simulations reproduce the main features of wild-type * mitotic cycles: patterns of protein accumulation and degradation, * lengthening of later cycles, and arrest in interphase 14. The * model is consistent with mutations that introduce subtle changes * in the number of mitotic cycles before interphase arrest. Bifurcation * analysis of the differential equations reveals the dependence * of mitotic oscillations on cycle number, and how this dependence * is altered by mutations. The model can be used to predict the * phenotypes of novel mutations and effective ranges of the unmeasured * rate constants and transport coefficients in the proposed mechanism. * * The complete original paper reference is cited below: * * Dynamical modeling of syncytial mitotic cycles in Drosophila * embryos, Laurence Calzone, Denis Thieffry, John J Tyson, Bela * Novak, 2007, Molecular Systems Biology , 3, 131. PubMed ID: * 17667953 * * figure1 * * [[Image file: calzone_2007.png]] * * Dynamical model of nuclear division cycles during early embryogenesis * of Drosophila. */ import nsrunit; unit conversion on; 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 MPF_n(time) dimensionless; when(time=time.min) MPF_n=0; real k_in first_order_rate_constant; k_in=0.15; real k_out first_order_rate_constant; k_out=0; real k_dn_v1 first_order_rate_constant; k_dn_v1=0.01; real k_dn_v2 first_order_rate_constant; k_dn_v2=1.5; real k_wee_v1 first_order_rate_constant; k_wee_v1=0.005; real k_wee_v2 first_order_rate_constant; k_wee_v2=1; real k_stg_v1_1 first_order_rate_constant; k_stg_v1_1=0.2; real k_stg_v2 first_order_rate_constant; k_stg_v2=2; real MPF_c(time) dimensionless; when(time=time.min) MPF_c=1; real FZY(time) dimensionless; when(time=time.min) FZY=0; real Wee1_n(time) dimensionless; when(time=time.min) Wee1_n=0; real StgP_n(time) dimensionless; when(time=time.min) StgP_n=0; real preMPF_n(time) dimensionless; when(time=time.min) preMPF_n=0; real preMPF_c(time) dimensionless; when(time=time.min) preMPF_c=0; real k_sc first_order_rate_constant; k_sc=0.01; real k_dc_ first_order_rate_constant; k_dc_=0.01; real epsilon dimensionless; epsilon=0.00007; real N(time) dimensionless; when(time=time.min) N=1; real StgP_c(time) dimensionless; when(time=time.min) StgP_c=0; real Wee1_c(time) dimensionless; when(time=time.min) Wee1_c=0; real IE(time) dimensionless; when(time=time.min) IE=0; real j_aie dimensionless; j_aie=0.01; real j_iie dimensionless; j_iie=0.01; real k_aie first_order_rate_constant; k_aie=1; real k_iie first_order_rate_constant; k_iie=0.4; real j_afz dimensionless; j_afz=0.01; real j_ifz dimensionless; j_ifz=0.01; real k_afz first_order_rate_constant; k_afz=1; real k_ifz first_order_rate_constant; k_ifz=0.2; real Stg_m(time) dimensionless; when(time=time.min) Stg_m=1; real k_dm_v1 first_order_rate_constant; k_dm_v1=0.002; real k_dm_v2 first_order_rate_constant; k_dm_v2=0.2; real j_m dimensionless; j_m=0.05; real Xp(time) dimensionless; when(time=time.min) Xp=0; real Xm(time) dimensionless; when(time=time.min) Xm=0; real k_sxm first_order_rate_constant; k_sxm=0.0005; real k_sxp first_order_rate_constant; k_sxp=0.001; real k_ins first_order_rate_constant; k_ins=0.08; real k_outs first_order_rate_constant; k_outs=0.02; real k_astg_v1 first_order_rate_constant; k_astg_v1=0; real k_astg_v2 first_order_rate_constant; k_astg_v2=1; real k_istg first_order_rate_constant; k_istg=0.3; real k_dstg first_order_rate_constant; k_dstg=0.015; real j_astg dimensionless; j_astg=0.05; real j_istg dimensionless; j_istg=0.05; real Stg_n(time) dimensionless; when(time=time.min) Stg_n=0; real Stg_c(time) dimensionless; when(time=time.min) Stg_c=1; real k_sstg first_order_rate_constant; k_sstg=0.02; real k_inw first_order_rate_constant; k_inw=0.04; real k_outw first_order_rate_constant; k_outw=0.01; real k_awee first_order_rate_constant; k_awee=0.3; real k_iwee_v1 first_order_rate_constant; k_iwee_v1=0.01; real k_iwee_v2 first_order_rate_constant; k_iwee_v2=1; real j_awee dimensionless; j_awee=0.05; real j_iwee dimensionless; j_iwee=0.05; real Wee1P_n(time) dimensionless; when(time=time.min) Wee1P_n=0; real Wee1P_c(time) dimensionless; real Wee1_T dimensionless; Wee1_T=0.8; real CycB_T(time) dimensionless; real Stg_T(time) dimensionless; real StgP_T(time) dimensionless; real k_ez first_order_rate_constant; k_ez=0.5; // // MPF_n:time=(k_in*MPF_c-k_out*MPF_n-(k_dn_v1+k_dn_v2*FZY)*MPF_n-(k_wee_v1+k_wee_v2*Wee1_n)*MPF_n+(k_stg_v1_1+k_stg_v2*StgP_n)*preMPF_n); // preMPF_n:time=(k_in*preMPF_c-k_out*preMPF_n-(k_dn_v1+k_dn_v2*FZY)*preMPF_n+(k_wee_v1+k_wee_v2*Wee1_n)*MPF_n-(k_wee_v1+k_stg_v2*StgP_n)*preMPF_n); // MPF_c:time=(k_sc-epsilon*N*(k_in*MPF_c-k_out*MPF_n)/(1-N*epsilon)-k_dc_*MPF_c+(k_stg_v1_1+k_stg_v2*StgP_c)*preMPF_c-(k_wee_v1+k_wee_v2*Wee1_c)*MPF_c); // preMPF_c:time=((-1)*epsilon*N*(k_in*preMPF_c-k_out*preMPF_n)/(1-N*epsilon)-k_dc_*preMPF_c-(k_stg_v1_1+k_stg_v2*StgP_c)*preMPF_c+(k_wee_v1+k_wee_v2*Wee1_c)*MPF_c); // IE:time=(k_aie*(1-IE)*MPF_n/(j_aie+1-IE)-k_iie*IE/(j_iie+IE)); // FZY:time=(k_afz*IE*(1-FZY)/(j_afz+1-FZY)-k_ifz*FZY/(j_ifz+FZY)); // Stg_m:time=((-1)*(k_dm_v1/(j_m+Stg_m)+k_dm_v2*Xp)*Stg_m); // Xm:time=(k_sxm*N); // Xp:time=(k_sxp*Xm); // StgP_n:time=(k_ins*StgP_c-k_outs*StgP_n+(k_astg_v1+k_astg_v2*MPF_n)*Stg_n/(j_astg+Stg_n)-k_istg*StgP_n/(j_istg+StgP_n)-k_dstg*StgP_n); // Stg_n:time=(k_ins*Stg_c-k_outs*Stg_n-(k_astg_v1+k_astg_v2*MPF_n)*Stg_n/(j_astg+Stg_n)+k_istg*StgP_n/(j_istg+StgP_n)-k_dstg*Stg_n); // StgP_c:time=((-1)*k_dstg*StgP_c-epsilon*N*(k_ins*StgP_c-k_outs*StgP_n)/(1-N*epsilon)+(k_astg_v1+k_astg_v2*MPF_c)*Stg_c/(j_astg+Stg_c)-k_istg*StgP_c/(j_istg+StgP_c)); // Stg_c:time=(k_sstg*Stg_m-k_dstg*Stg_c-epsilon*N*(k_ins*Stg_c-k_outs*Stg_n)/(1-N*epsilon)-(k_astg_v1+k_astg_v2*MPF_c)*Stg_c/(j_astg+Stg_c)+k_istg*StgP_c/(j_istg+StgP_c)); // Wee1_n:time=(k_inw*Wee1_c-k_outw*Wee1_n+k_awee*Wee1P_n/(j_awee+Wee1P_n)-(k_iwee_v1+k_iwee_v2*MPF_n)*Wee1_n/(j_iwee+Wee1_n)); // Wee1_c:time=((-1)*(k_inw*Wee1_c-k_outw*Wee1_n)*N*epsilon/(1-N*epsilon)+k_awee*Wee1P_c/(j_awee+Wee1P_c)-(k_iwee_v1+k_iwee_v2*MPF_c)*Wee1_c/(j_iwee+Wee1_c)); // Wee1P_n:time=(k_inw*Wee1P_c-k_outw*Wee1P_n-k_awee*Wee1P_n/(j_awee+Wee1P_n)+(k_iwee_v1+k_iwee_v2*MPF_n)*Wee1_n/(j_iwee+Wee1_n)); // Wee1P_c=((Wee1_T-N*epsilon*(Wee1_n+Wee1P_n))/(1-N*epsilon)-Wee1_c); // N:time=(0 first_order_rate_constant); // CycB_T=((1-N*epsilon)*(MPF_c+preMPF_c)+N*epsilon*(MPF_n+preMPF_n)); // Stg_T=((1-N*epsilon)*(Stg_c+StgP_c)+N*epsilon*(Stg_n+StgP_n)); // StgP_T=((1-N*epsilon)*StgP_c+N*epsilon*StgP_n); // }