(* 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 = {
alpha[t], beta[t], gamma[t]
};

initialValues = {
alpha[0] == 29.19988, beta[0] == 188.8, gamma[0] == 0.3367
};

rates = {
r1, r2, r3, r4
};

rateEquations = {
r1 -> r1\[LetterSpace]v\[LetterSpace]Km1, r2 -> (r2\[LetterSpace]sigma1*alpha[t]*(1 + alpha[t])*(1 + beta[t])^2)/(r2\[LetterSpace]L1 + (1 + alpha[t])^2*(1 + beta[t])^2), r3 -> (r3\[LetterSpace]sigma2*beta[t]*(1 + r3\[LetterSpace]d*beta[t])*(1 + gamma[t])^2)/(r3\[LetterSpace]L2 + (1 + r3\[LetterSpace]d*beta[t])^2*(1 + gamma[t])^2), r4 -> r4\[LetterSpace]ks*gamma[t]
};

parameters = {
r1\[LetterSpace]v\[LetterSpace]Km1 -> 0.45, r2\[LetterSpace]L1 -> 500000000.0, r2\[LetterSpace]sigma1 -> 10.0, r3\[LetterSpace]L2 -> 100.0, r3\[LetterSpace]d -> 0.0, r3\[LetterSpace]sigma2 -> 10.0, r4\[LetterSpace]ks -> 1.99, cell -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
alpha'[t] == 1.0*r1 -1.0*r2, beta'[t] == 50.0*r2 -1.0*r3, gamma'[t] == 0.02*r3 -1.0*r4
};
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]}]