(* 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 = {
bound[t], bulk[t], free[t], lytic[t], translocate[t]
};

initialValues = {
bound[0] == 0.0, bulk[0] == 1.0, free[0] == 0.0, lytic[0] == 0.0, translocate[0] == 0.0
};

rates = {
binding, bulk\[LetterSpace]movement, endocytosis, translocation
};

rateEquations = {
binding -> binding\[LetterSpace]kB*extracellular*free[t], bulk\[LetterSpace]movement -> bulk\[LetterSpace]movement\[LetterSpace]kS*extracellular*bulk[t], endocytosis -> endocytosis\[LetterSpace]kT*extracellular*bound[t], translocation -> endosome*translocation\[LetterSpace]kL*translocate[t]
};

parameters = {
endocytosis\[LetterSpace]kT -> 0.141, translocation\[LetterSpace]kL -> 0.013, binding\[LetterSpace]kB -> 0.058, bulk\[LetterSpace]movement\[LetterSpace]kS -> 0.00015, endosome -> 1.0, extracellular -> 1.0, neuroplasm -> 1.0
};

assignments = {
BoNT -> bulk[t] + free[t], tension -> 1 - lytic[t]
};

events = {

};

speciesAnnotations = {
BoNT[t]->"http://identifiers.org/kegg.compound/C07946", bulk[t]->"http://identifiers.org/kegg.compound/C07946", free[t]->"http://identifiers.org/kegg.compound/C07946"
};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
bound'[t] == 1.0*binding -1.0*endocytosis, bulk'[t] ==  -1.0*bulk\[LetterSpace]movement, free'[t] == 1.0*bulk\[LetterSpace]movement -1.0*binding, lytic'[t] == 1.0*translocation , translocate'[t] == 1.0*endocytosis -1.0*translocation
};
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]}]