(* 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 = {
S0[t], S1[t], back\[LetterSpace]step1[t], back\[LetterSpace]step2[t], fwd\[LetterSpace]step1[t], fwd\[LetterSpace]step2[t]
};

initialValues = {
S0[0] == 10.0, S1[0] == 0.0, back\[LetterSpace]step1[0] == 0.0, back\[LetterSpace]step2[0] == 0.0, fwd\[LetterSpace]step1[0] == 0.0, fwd\[LetterSpace]step2[0] == 0.0
};

rates = {
Bw\[LetterSpace]1st\[LetterSpace]step, Bw\[LetterSpace]2nd\[LetterSpace]step, Fw\[LetterSpace]1st\[LetterSpace]step, Fw\[LetterSpace]2nd\[LetterSpace]step
};

rateEquations = {
Bw\[LetterSpace]1st\[LetterSpace]step -> ATP*E^((d*Force*th\[LetterSpace]3)/kT)*k\[LetterSpace]3*S0[t], Bw\[LetterSpace]2nd\[LetterSpace]step -> E^((d*Force*th\[LetterSpace]4)/kT)*k\[LetterSpace]4*S1[t], Fw\[LetterSpace]1st\[LetterSpace]step -> (ATP*k\[LetterSpace]1*S0[t])/E^((d*Force*th\[LetterSpace]1)/kT), Fw\[LetterSpace]2nd\[LetterSpace]step -> (k\[LetterSpace]2*S1[t])/E^((d*Force*th\[LetterSpace]2)/kT)
};

parameters = {
Force -> 0.0, d -> 36.0, kT -> 4.1164, k\[LetterSpace]1 -> 0.7, k\[LetterSpace]2 -> 12.0, k\[LetterSpace]3 -> 5*^-06, k\[LetterSpace]4 -> 6*^-06, th\[LetterSpace]1 -> -0.01, th\[LetterSpace]2 -> 0.045, th\[LetterSpace]3 -> 0.58, th\[LetterSpace]4 -> 0.385, ADP -> 0.0, ATP -> 20.0, Pi\[LetterSpace] -> 0.0, compartment\[LetterSpace] -> 1*^-15
};

assignments = {
tau -> ((ATP*k\[LetterSpace]1)/E^((d*Force*th\[LetterSpace]1)/kT) + k\[LetterSpace]2/E^((d*Force*th\[LetterSpace]2)/kT) + ATP*E^((d*Force*th\[LetterSpace]3)/kT)*k\[LetterSpace]3 + E^((d*Force*th\[LetterSpace]4)/kT)*k\[LetterSpace]4)/(ATP*E^(-((d*Force*th\[LetterSpace]1)/kT) - (d*Force*th\[LetterSpace]2)/kT)*k\[LetterSpace]1*k\[LetterSpace]2 + ATP*E^((d*Force*th\[LetterSpace]3)/kT + (d*Force*th\[LetterSpace]4)/kT)*k\[LetterSpace]3*k\[LetterSpace]4), V\[LetterSpace]ave -> (d*((-back\[LetterSpace]step1[t] - back\[LetterSpace]step2[t])/2 + (fwd\[LetterSpace]step1[t] + fwd\[LetterSpace]step2[t])/2))/(S\[LetterSpace]tot*t), V -> (d*((-Bw\[LetterSpace]1st\[LetterSpace]step - Bw\[LetterSpace]2nd\[LetterSpace]step)/2 + (Fw\[LetterSpace]1st\[LetterSpace]step + Fw\[LetterSpace]2nd\[LetterSpace]step)/2))/S\[LetterSpace]tot, S\[LetterSpace]tot -> S0[t] + S1[t]
};

events = {

};

speciesAnnotations = {
ADP[t]->"http://identifiers.org/kegg.compound/C00008", ADP[t]->"http://identifiers.org/chebi/CHEBI:16761", ADP[t]->"http://identifiers.org/pubchem.substance/3310", ATP[t]->"http://identifiers.org/chebi/CHEBI:15422", ATP[t]->"http://identifiers.org/kegg.compound/C00002", ATP[t]->"http://identifiers.org/pubchem.substance/3304", Pi\[LetterSpace][t]->"http://identifiers.org/chebi/CHEBI:18367", Pi\[LetterSpace][t]->"http://identifiers.org/kegg.compound/C00009", S0[t]->"http://identifiers.org/go/GO:0031475"
};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
S0'[t] == 1.0*Fw\[LetterSpace]2nd\[LetterSpace]step +1.0*Bw\[LetterSpace]2nd\[LetterSpace]step -1.0*Fw\[LetterSpace]1st\[LetterSpace]step -1.0*Bw\[LetterSpace]1st\[LetterSpace]step, S1'[t] == 1.0*Fw\[LetterSpace]1st\[LetterSpace]step +1.0*Bw\[LetterSpace]1st\[LetterSpace]step -1.0*Fw\[LetterSpace]2nd\[LetterSpace]step -1.0*Bw\[LetterSpace]2nd\[LetterSpace]step, back\[LetterSpace]step1'[t] == 1.0*Bw\[LetterSpace]1st\[LetterSpace]step , back\[LetterSpace]step2'[t] == 1.0*Bw\[LetterSpace]2nd\[LetterSpace]step , fwd\[LetterSpace]step1'[t] == 1.0*Fw\[LetterSpace]1st\[LetterSpace]step , fwd\[LetterSpace]step2'[t] == 1.0*Fw\[LetterSpace]2nd\[LetterSpace]step 
};
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]}]