(* 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 = {
lacz[t], sigb[t], x[t]
};

initialValues = {
lacz[0] == 0.0, sigb[0] == 0.0, x[0] == 0.0
};

rates = {
v1, v2, v3
};

rateEquations = {
v1 -> IPTG*kbs*multiplier - sigb[t]*(kbd + kbx*x[t]), v2 -> -(kzd*lacz[t]) + kzs*sigb[t], v3 -> kxs*sigb[t] - kxd*x[t]
};

parameters = {
kbd -> 5.8*^-09, kbs -> 100.0, kbx -> 8.4*^-05, kxd -> 1.2*^-13, kxs -> 2*^-06, kzd -> 0.052, kzs -> 1.7*^-06, multiplier -> 1.0, IPTG -> 100.0, compartment -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {
IPTG[t]->"http://identifiers.org/chebi/CHEBI:61448", lacz[t]->"http://identifiers.org/obo.go/GO:0015925", sigb[t]->"http://identifiers.org/interpro/IPR006288", x[t]->"http://identifiers.org/chebi/CHEBI:35222"
};

reactionAnnotations = {
v1->"http://identifiers.org/obo.go/GO:0009058", v1->"http://identifiers.org/obo.go/GO:0006508", v2->"http://identifiers.org/obo.go/GO:0009058", v2->"http://identifiers.org/obo.go/GO:0006508", v3->"http://identifiers.org/obo.go/GO:0009058", v3->"http://identifiers.org/obo.go/GO:0006508"
};

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

(* Time evolution *)
odes = {
lacz'[t] == 1.0*v2 , sigb'[t] == 1.0*v1 -1.0*v2 -1.0*v3, x'[t] == 1.0*v3 
};
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]}]