// This model generated automatically from SBML

// unit definitions
import nsrunit;
unit conversion off;
unit item = dimensionless;
unit substance = 1 item;

// SBML property definitions
property sbmlRole=string;
property sbmlName=string;
property sbmlCompartment=string;

// SBML reactions
// Reaction1: X 
// Reaction2: Y 
// Reaction3: Z 
// Reaction4: <=> PX 
// Reaction5: <=> PY 
// Reaction6: <=> PZ 
// Reaction7: PX 
// Reaction8: PY 
// Reaction9: PZ 
// Reaction10: <=> X 
// Reaction11: <=> Y 
// Reaction12: <=> Z 

math main {
  realDomain time second;
  time.min=0;
  extern time.max;
  extern time.delta;

  // variable definitions
  real cell = 1 femtoliter;
  real beta(time);
  real alpha0(time);
  real alpha(time);
  real eff = 20;
  real n = 2;
  real KM = 40;
  real tau_mRNA = 2;
  real tau_prot = 10;
  real t_ave(time);
  real kd_mRNA(time);
  real kd_prot(time);
  real k_tl(time);
  real a_tr(time);
  real ps_a = .5;
  real ps_0 = 5E-4;
  real a0_tr(time);
  real PX(time) substance;
  real PY(time) substance;
  real PZ(time) substance;
  real X(time) substance;
  real Y(time) substance;
  real Z(time) substance;
  real Reaction1(time) substance/min;
  real Reaction2(time) substance/min;
  real Reaction3(time) substance/min;
  real Reaction4(time) substance/min;
  real Reaction5(time) substance/min;
  real Reaction6(time) substance/min;
  real Reaction7(time) substance/min;
  real Reaction8(time) substance/min;
  real Reaction9(time) substance/min;
  real Reaction10(time) substance/min;
  real Reaction11(time) substance/min;
  real Reaction12(time) substance/min;

  // equations
  beta = tau_mRNA/tau_prot;
  alpha0 = a0_tr*eff*tau_prot/(ln(2)*KM);
  alpha = a_tr*eff*tau_prot/(ln(2)*KM);
  t_ave = tau_mRNA/ln(2);
  kd_mRNA = ln(2)/tau_mRNA;
  kd_prot = ln(2)/tau_prot;
  k_tl = eff/t_ave;
  a_tr = (ps_a-ps_0)*60;
  a0_tr = ps_0*60;
  when (time=time.min) PX = 0;
  PX:time = Reaction4 + -1*Reaction7;
  when (time=time.min) PY = 0;
  PY:time = Reaction5 + -1*Reaction8;
  when (time=time.min) PZ = 0;
  PZ:time = Reaction6 + -1*Reaction9;
  when (time=time.min) X = 0;
  X:time = -1*Reaction1 + Reaction10;
  when (time=time.min) Y = 20;
  Y:time = -1*Reaction2 + Reaction11;
  when (time=time.min) Z = 0;
  Z:time = -1*Reaction3 + Reaction12;
  Reaction1 = kd_mRNA*X;
  Reaction2 = kd_mRNA*Y;
  Reaction3 = kd_mRNA*Z;
  Reaction4 = k_tl*X;
  Reaction5 = k_tl*Y;
  Reaction6 = k_tl*Z;
  Reaction7 = kd_prot*PX;
  Reaction8 = kd_prot*PY;
  Reaction9 = kd_prot*PZ;
  Reaction10 = a0_tr+a_tr*KM^n/(KM^n+PZ^n);
  Reaction11 = a0_tr+a_tr*KM^n/(KM^n+PX^n);
  Reaction12 = a0_tr+a_tr*KM^n/(KM^n+PY^n);

  // variable properties
  cell.sbmlRole="compartment";
  beta.sbmlRole="parameter";
  alpha0.sbmlRole="parameter";
  alpha.sbmlRole="parameter";
  eff.sbmlRole="parameter";
  eff.sbmlName="translation efficiency";
  n.sbmlRole="parameter";
  KM.sbmlRole="parameter";
  tau_mRNA.sbmlRole="parameter";
  tau_mRNA.sbmlName="mRNA half life";
  tau_prot.sbmlRole="parameter";
  tau_prot.sbmlName="protein half life";
  t_ave.sbmlRole="parameter";
  t_ave.sbmlName="average mRNA life time";
  kd_mRNA.sbmlRole="parameter";
  kd_prot.sbmlRole="parameter";
  k_tl.sbmlRole="parameter";
  a_tr.sbmlRole="parameter";
  ps_a.sbmlRole="parameter";
  ps_a.sbmlName="tps_active";
  ps_0.sbmlRole="parameter";
  ps_0.sbmlName="tps_repr";
  a0_tr.sbmlRole="parameter";
  PX.sbmlRole="species";
  PX.sbmlCompartment="cell";
  PY.sbmlRole="species";
  PY.sbmlCompartment="cell";
  PZ.sbmlRole="species";
  PZ.sbmlCompartment="cell";
  X.sbmlRole="species";
  X.sbmlCompartment="cell";
  Y.sbmlRole="species";
  Y.sbmlCompartment="cell";
  Z.sbmlRole="species";
  Z.sbmlCompartment="cell";
  Reaction1.sbmlRole="rate";
  Reaction2.sbmlRole="rate";
  Reaction3.sbmlRole="rate";
  Reaction4.sbmlRole="rate";
  Reaction5.sbmlRole="rate";
  Reaction6.sbmlRole="rate";
  Reaction7.sbmlRole="rate";
  Reaction8.sbmlRole="rate";
  Reaction9.sbmlRole="rate";
  Reaction10.sbmlRole="rate";
  Reaction11.sbmlRole="rate";
  Reaction12.sbmlRole="rate";
}