(* 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 = {
y1[t], y2[t], y3[t], y4[t], y5[t], y6[t], y7[t]
};

initialValues = {
y1[0] == 0.2, y2[0] == 0.0, y3[0] == 1.1, y4[0] == 0.8, y5[0] == 1.0, y6[0] == 1.0, y7[0] == 1.05
};

rates = {
Active\[LetterSpace]BMAL1\[LetterSpace]degradation, BMAL1\[LetterSpace]activation, BMAL1\[LetterSpace]deactivation, BMAL1\[LetterSpace]nuclear\[LetterSpace]export, BMAL1\[LetterSpace]nuclear\[LetterSpace]import, BMAL1\[LetterSpace]translation, Bmal1\[LetterSpace]mRNA\[LetterSpace]degradation, Bmal1\[LetterSpace]transcription, cytoplasmic\[LetterSpace]BMAL1\[LetterSpace]degradation, cytoplasmic\[LetterSpace]per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]degradation, nuclear\[LetterSpace]BMAL1\[LetterSpace]degradation, nuclear\[LetterSpace]per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]degradation, per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]formation, per2\[LetterSpace]cry\[LetterSpace]mRNA\[LetterSpace]degradation, per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]export, per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]import, per2\[LetterSpace]cry\[LetterSpace]transcription
};

rateEquations = {
Active\[LetterSpace]BMAL1\[LetterSpace]degradation -> k7d*Nucleus*y7[t], BMAL1\[LetterSpace]activation -> k6a*Nucleus*y6[t], BMAL1\[LetterSpace]deactivation -> k7a*Nucleus*y7[t], BMAL1\[LetterSpace]nuclear\[LetterSpace]export -> k6t*Nucleus*y6[t], BMAL1\[LetterSpace]nuclear\[LetterSpace]import -> Cytoplasm*k5t*y5[t], BMAL1\[LetterSpace]translation -> Cytoplasm*k5b*y4[t], Bmal1\[LetterSpace]mRNA\[LetterSpace]degradation -> Cytoplasm*k4d*y4[t], Bmal1\[LetterSpace]transcription -> Cytoplasm*trans\[LetterSpace]Bmal1, cytoplasmic\[LetterSpace]BMAL1\[LetterSpace]degradation -> Cytoplasm*k5d*y5[t], cytoplasmic\[LetterSpace]per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]degradation -> Cytoplasm*k2d*y2[t], nuclear\[LetterSpace]BMAL1\[LetterSpace]degradation -> k6d*Nucleus*y6[t], nuclear\[LetterSpace]per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]degradation -> k3d*Nucleus*y3[t], per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]formation -> Cytoplasm*k2b*y1[t]^q, per2\[LetterSpace]cry\[LetterSpace]mRNA\[LetterSpace]degradation -> Cytoplasm*k1d*y1[t], per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]export -> k3t*Nucleus*y3[t], per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]import -> Cytoplasm*k2t*y2[t], per2\[LetterSpace]cry\[LetterSpace]transcription -> Cytoplasm*trans\[LetterSpace]per2\[LetterSpace]cry
};

parameters = {
c -> 0.01, hill\[LetterSpace]coeff -> 8.0, k1b -> 1.0, k1d -> 0.12, k1i -> 0.56, k2b -> 0.3, k2d -> 0.05, k2t -> 0.24, k3d -> 0.12, k3t -> 0.02, k4b -> 2.16, k4d -> 0.75, k5b -> 0.24, k5d -> 0.06, k5t -> 0.45, k6a -> 0.09, k6d -> 0.12, k6t -> 0.06, k7a -> 0.003, k7d -> 0.09, q -> 2.0, r -> 3.0, v1b -> 9.0, v4b -> 3.6, Cytoplasm -> 1.0, Nucleus -> 1.0
};

assignments = {
y5\[LetterSpace]y6\[LetterSpace]y7 -> y5[t] + y6[t] + y7[t], trans\[LetterSpace]Bmal1 -> (v4b*y3[t]^r)/(k4b^r + y3[t]^r), trans\[LetterSpace]per2\[LetterSpace]cry -> (v1b*(c + y7[t]))/(c + k1b*(1 + (y3[t]/k1i)^hill\[LetterSpace]coeff) + y7[t])
};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
y1'[t] == 1.0*per2\[LetterSpace]cry\[LetterSpace]transcription -1.0*per2\[LetterSpace]cry\[LetterSpace]mRNA\[LetterSpace]degradation, y2'[t] == 1.0*per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]formation +1.0*per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]export -1.0*cytoplasmic\[LetterSpace]per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]degradation -1.0*per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]import, y3'[t] == 1.0*per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]import -1.0*per2\[LetterSpace]cry\[LetterSpace]nuclear\[LetterSpace]export -1.0*nuclear\[LetterSpace]per2\[LetterSpace]cry\[LetterSpace]complex\[LetterSpace]degradation, y4'[t] == 1.0*Bmal1\[LetterSpace]transcription -1.0*Bmal1\[LetterSpace]mRNA\[LetterSpace]degradation, y5'[t] == 1.0*BMAL1\[LetterSpace]translation +1.0*BMAL1\[LetterSpace]nuclear\[LetterSpace]export -1.0*cytoplasmic\[LetterSpace]BMAL1\[LetterSpace]degradation -1.0*BMAL1\[LetterSpace]nuclear\[LetterSpace]import, y6'[t] == 1.0*BMAL1\[LetterSpace]nuclear\[LetterSpace]import +1.0*BMAL1\[LetterSpace]deactivation -1.0*BMAL1\[LetterSpace]nuclear\[LetterSpace]export -1.0*nuclear\[LetterSpace]BMAL1\[LetterSpace]degradation -1.0*BMAL1\[LetterSpace]activation, y7'[t] == 1.0*BMAL1\[LetterSpace]activation -1.0*BMAL1\[LetterSpace]deactivation -1.0*Active\[LetterSpace]BMAL1\[LetterSpace]degradation
};
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]}]