(* Generated by JWS Online *)

(* This is an experimental feature of JWS Online. Please report any mistakes.*)

(* Note that the following notable SBML entities or features are not supported in notebook outputyet: *)
    (* Events *)
    (* Constraints *)
    (* Units and UnitDefinitions *)
    (* AlgebraicRules *)
    (* conversionFactors *)

variables = {
PX[t], PY[t], PZ[t], X[t], Y[t], Z[t]
};

initialValues = {
PX[0] == 0.0, PY[0] == 0.0, PZ[0] == 0.0, X[0] == 0.0, Y[0] == 20.0, Z[0] == 0.0
};

rates = {
Reaction1, Reaction10, Reaction11, Reaction12, Reaction2, Reaction3, Reaction4, Reaction5, Reaction6, Reaction7, Reaction8, Reaction9
};

rateEquations = {
Reaction1 -> kd\[LetterSpace]mRNA*X[t], Reaction10 -> a0\[LetterSpace]tr + (a\[LetterSpace]tr*KM^n)/(KM^n + PZ[t]^n), Reaction11 -> a0\[LetterSpace]tr + (a\[LetterSpace]tr*KM^n)/(KM^n + PX[t]^n), Reaction12 -> a0\[LetterSpace]tr + (a\[LetterSpace]tr*KM^n)/(KM^n + PY[t]^n), Reaction2 -> kd\[LetterSpace]mRNA*Y[t], Reaction3 -> kd\[LetterSpace]mRNA*Z[t], Reaction4 -> k\[LetterSpace]tl*X[t], Reaction5 -> k\[LetterSpace]tl*Y[t], Reaction6 -> k\[LetterSpace]tl*Z[t], Reaction7 -> kd\[LetterSpace]prot*PX[t], Reaction8 -> kd\[LetterSpace]prot*PY[t], Reaction9 -> kd\[LetterSpace]prot*PZ[t]
};

parameters = {
KM -> 40.0, eff -> 20.0, n -> 2.0, ps\[LetterSpace]0 -> 0.0005, ps\[LetterSpace]a -> 0.5, tau\[LetterSpace]mRNA -> 2.0, tau\[LetterSpace]prot -> 10.0, cell -> 1.0
};

assignments = {
alpha0 -> (a0\[LetterSpace]tr*eff*tau\[LetterSpace]prot)/(KM*Log[2]), alpha -> (a\[LetterSpace]tr*eff*tau\[LetterSpace]prot)/(KM*Log[2]), kd\[LetterSpace]mRNA -> Log[2]/tau\[LetterSpace]mRNA, kd\[LetterSpace]prot -> Log[2]/tau\[LetterSpace]prot, a0\[LetterSpace]tr -> 60*ps\[LetterSpace]0, a\[LetterSpace]tr -> 60*(-ps\[LetterSpace]0 + ps\[LetterSpace]a), k\[LetterSpace]tl -> eff/t\[LetterSpace]ave, beta -> tau\[LetterSpace]mRNA/tau\[LetterSpace]prot, t\[LetterSpace]ave -> tau\[LetterSpace]mRNA/Log[2]
};

events = {

};

speciesAnnotations = {
PX[t]->"http://identifiers.org/uniprot/P03023", PY[t]->"http://identifiers.org/uniprot/P04483", PZ[t]->"http://identifiers.org/uniprot/P03034"
};

reactionAnnotations = {

};

units = {
{"time" -> "", "metabolite" -> "", "extent" -> ""}
};

(* Time evolution *)
odes = {
PX'[t] == 1.0*Reaction4 -1.0*Reaction7, PY'[t] == 1.0*Reaction5 -1.0*Reaction8, PZ'[t] == 1.0*Reaction6 -1.0*Reaction9, X'[t] == 1.0*Reaction10 -1.0*Reaction1, Y'[t] == 1.0*Reaction11 -1.0*Reaction2, Z'[t] == 1.0*Reaction12 -1.0*Reaction3
};
timeCourse = NDSolve[Join[odes, initialValues]//.rateEquations//.assignments//.parameters, variables, {t, 0, 100}];

(* Steady-state solution initialized with result of time evolution *)
findRootEquations = odes /.D[_[t],t]->0;
findRootVariables = Partition[Flatten[{#, #/.timeCourse/.t->100} &/@variables],2];
steadyStateVariables = FindRoot[findRootEquations//.rateEquations//.assignments//.parameters, findRootVariables, MaxIterations->100]
fluxes = #//.assignments//.parameters/.steadyStateVariables&/@rateEquations

(* Plot the time evolution of the variables *)
plotTable=Table[Plot[variables[[i]]/.parameters/.timeCourse,{t,0,100},PlotLegends->variables[[i]],PlotRange->Full],{i,Length[variables]}]