(* 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 = {
A[t], B[t], I1[t], I2[t], I3[t], L[t], M[t], P[t]
};

initialValues = {
A[0] == 0.038, B[0] == 0.0, I1[0] == 0.0, I2[0] == 0.0, I3[0] == 0.0, L[0] == 0.372, M[0] == 0.000626, P[0] == 0.0149
};

rates = {
r\[LetterSpace]a1, r\[LetterSpace]a2, r\[LetterSpace]a3\[LetterSpace]l1, r\[LetterSpace]b1, r\[LetterSpace]b2\[LetterSpace]i2, r\[LetterSpace]i1, r\[LetterSpace]i2, r\[LetterSpace]i3, r\[LetterSpace]l2, r\[LetterSpace]l3, r\[LetterSpace]l4, r\[LetterSpace]m1, r\[LetterSpace]m2, r\[LetterSpace]m3\[LetterSpace]i1, r\[LetterSpace]p1, r\[LetterSpace]p2\[LetterSpace]i3
};

rateEquations = {
r\[LetterSpace]a1 -> cell*(gamma\[LetterSpace]A + mu)*A[t], r\[LetterSpace]a2 -> (beta\[LetterSpace]A*cell*A[t]*B[t])/(K\[LetterSpace]A + A[t]), r\[LetterSpace]a3\[LetterSpace]l1 -> (alpha\[LetterSpace]A*cell*B[t]*L[t])/(K\[LetterSpace]L + L[t]), r\[LetterSpace]b1 -> cell*(gamma\[LetterSpace]B + mu)*B[t], r\[LetterSpace]b2\[LetterSpace]i2 -> (cell*I2[t])/tau\[LetterSpace]B, r\[LetterSpace]i1 -> (alpha\[LetterSpace]M*cell*(1 + (K\[LetterSpace]1*A[t]^2)/E^(2*mu*tau\[LetterSpace]M)))/(K + (K\[LetterSpace]1*A[t]^2)/E^(2*mu*tau\[LetterSpace]M)), r\[LetterSpace]i2 -> (alpha\[LetterSpace]B*cell*M[t])/E^(mu*tau\[LetterSpace]B), r\[LetterSpace]i3 -> (alpha\[LetterSpace]P*cell*M[t])/E^(mu*(tau\[LetterSpace]B + tau\[LetterSpace]P)), r\[LetterSpace]l2 -> cell*(gamma\[LetterSpace]L + mu)*L[t], r\[LetterSpace]l3 -> (beta\[LetterSpace]L1*cell*L[t]*P[t])/(K\[LetterSpace]L1 + L[t]), r\[LetterSpace]l4 -> (alpha\[LetterSpace]L*cell*L\[LetterSpace]e*P[t])/(K\[LetterSpace]Le + L\[LetterSpace]e), r\[LetterSpace]m1 -> cell*gamma\[LetterSpace]0, r\[LetterSpace]m2 -> cell*(gamma\[LetterSpace]M + mu)*M[t], r\[LetterSpace]m3\[LetterSpace]i1 -> (cell*I1[t])/tau\[LetterSpace]M, r\[LetterSpace]p1 -> cell*(gamma\[LetterSpace]P + mu)*P[t], r\[LetterSpace]p2\[LetterSpace]i3 -> (cell*I3[t])/(tau\[LetterSpace]B + tau\[LetterSpace]P)
};

parameters = {
K -> 7200.0, K\[LetterSpace]1 -> 25200.0, K\[LetterSpace]A -> 1.95, K\[LetterSpace]L -> 0.97, K\[LetterSpace]L1 -> 1.81, K\[LetterSpace]Le -> 0.26, alpha\[LetterSpace]A -> 17600.0, alpha\[LetterSpace]B -> 0.0166, alpha\[LetterSpace]L -> 2880.0, alpha\[LetterSpace]M -> 0.000997, alpha\[LetterSpace]P -> 10.0, beta\[LetterSpace]A -> 21500.0, beta\[LetterSpace]L1 -> 2650.0, gamma\[LetterSpace]0 -> 7.25*^-07, gamma\[LetterSpace]A -> 0.52, gamma\[LetterSpace]B -> 0.000833, gamma\[LetterSpace]L -> 0.0, gamma\[LetterSpace]M -> 0.411, gamma\[LetterSpace]P -> 0.65, mu -> 0.0226, tau\[LetterSpace]B -> 2.0, tau\[LetterSpace]M -> 0.1, tau\[LetterSpace]P -> 0.83, L\[LetterSpace]e -> 0.08, cell -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {
B[t]->"http://identifiers.org/uniprot/P00722", L[t]->"http://identifiers.org/chebi/CHEBI:17716", L[t]->"http://identifiers.org/kegg.compound/C00243", L\[LetterSpace]e[t]->"http://identifiers.org/chebi/CHEBI:17716", L\[LetterSpace]e[t]->"http://identifiers.org/kegg.compound/C00243", M[t]->"http://identifiers.org/chebi/CHEBI:33699", P[t]->"http://identifiers.org/uniprot/P02920"
};

reactionAnnotations = {
r\[LetterSpace]a3\[LetterSpace]l1->"http://identifiers.org/ec-code/3.2.1.108", r\[LetterSpace]a3\[LetterSpace]l1->"http://identifiers.org/go/GO:0004565", r\[LetterSpace]l2->"http://identifiers.org/go/GO:0005990", r\[LetterSpace]l3->"http://identifiers.org/go/GO:0015155", r\[LetterSpace]l4->"http://identifiers.org/go/GO:0015155", r\[LetterSpace]m2->"http://identifiers.org/go/GO:0006402"
};

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

(* Time evolution *)
odes = {
A'[t] == 1.0*r\[LetterSpace]a3\[LetterSpace]l1 -1.0*r\[LetterSpace]a1 -1.0*r\[LetterSpace]a2, B'[t] == 1.0*r\[LetterSpace]b2\[LetterSpace]i2 -1.0*r\[LetterSpace]b1, I1'[t] == 1.0*r\[LetterSpace]i1 -1.0*r\[LetterSpace]m3\[LetterSpace]i1, I2'[t] == 1.0*r\[LetterSpace]i2 -1.0*r\[LetterSpace]b2\[LetterSpace]i2, I3'[t] == 1.0*r\[LetterSpace]i3 -1.0*r\[LetterSpace]p2\[LetterSpace]i3, L'[t] == 1.0*r\[LetterSpace]l4 -1.0*r\[LetterSpace]a3\[LetterSpace]l1 -1.0*r\[LetterSpace]l2 -1.0*r\[LetterSpace]l3, M'[t] == 1.0*r\[LetterSpace]m1 +1.0*r\[LetterSpace]m3\[LetterSpace]i1 -1.0*r\[LetterSpace]m2, P'[t] == 1.0*r\[LetterSpace]p2\[LetterSpace]i3 -1.0*r\[LetterSpace]p1
};
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]}]