basic_circadian_clock_models.nb
Author
Tim Breitenbach, Charlotte Helfrich-Förster, Thomas Dandekar
Title
basic_circadian_clock_models.nb
Description
Supplemental notebook to "An effective model of endogenous clocks and external stimuli determining circadian rhythms"
Category
Academic Articles & Supplements
Keywords
circadian endogenous clocks, circadian rhythms, eukaryotic organism
URL
http://www.notebookarchive.org/2022-01-1vufp3h/
DOI
https://notebookarchive.org/2022-01-1vufp3h
Date Added
2022-01-04
Date Last Modified
2022-01-04
File Size
290.09 kilobytes
Supplements
Rights
Redistribution rights reserved
Download
Open in Wolfram Cloud
This file contains supplementary data for Tim Breitenbach, Charlotte Helfrich-Förster and Thomas Dandekar , “An effective model of endogenous clocks and external stimuli determining circadian rhythms,” Scientific Reports, 11(1), 2021 161655. https://www.nature.com/articles/s41598-021-95391-y.
Basic Circadian Clock Models
Basic Circadian Clock Models
Tim Breitenbach, Charlotte Helfrich-Förster and Thomas Dandekar
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(*GeneratetimecurvesoftheagentsoftheoriginalGoldbetermodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
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(*Entrainment*)phi=1*Pi;(*PhaseshiftbetweenthephaseoftheZeitgeberandthemolecularclock*)u[t_]:=(Cos[2*Pi*t/24+phi]+1)s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t])-0.05u[t]*M[t],P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{u[t],M[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{u,,M}]
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Plot[{Evaluate[{u[t],P0[t]}/.s],ZwP0},{t,0,d},PlotRangeAll,PlotLegends{u,,}]
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Plot[{Evaluate[{u[t],P1[t]}/.s],ZwP1},{t,0,d},PlotRangeAll,PlotLegends{u,,}]
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Plot[{Evaluate[{u[t],P2[t]}/.s],ZwP2},{t,0,d},PlotRangeAll,PlotLegends{u,,}]
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Plot[{Evaluate[{u[t],PN[t]}/.s],ZwPN},{t,0,d},PlotRangeAll,PlotLegends{u,,}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];(*FlymodelEntrainment*)phi=1*Pi;(*PhaseshiftbetweenthephaseoftheZeitgeberandthemolecularclock*)u[t_]:=(Cos[2*Pi*t/24+phi]+1)*0.25s=NDSolve[{M'[t]0.76*((1^4)/(1^4+(PN[t])^4))-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]*(1-u[t])-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{u[t]}/.s],Evaluate[{M[t]}/.s],Evaluate[{P0[t]}/.s],ZwM,ZwP0},{t,0,d},PlotRangeAll,PlotLegends{u,,,M,}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
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(*mRNAknockdown*)ts=20;(*Durationoftheinhibition*)u[t_]:=Piecewise[{{5,0≤t≤ts},{0,ts<t≤d}}];s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t])-0.05u[t]*M[t],P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{M[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,M}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
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(*InhibitionperTranscription*)ts=20;(*Durationoftheinhibition*)u[t_]:=Piecewise[{{1,0≤t≤ts},{0,ts<t≤d}}];s=NDSolve[{M'[t]0.76*((1^4)/(1^4+(PN[t])^4))*(1-u[t])-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,120},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{M[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,M}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
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(*InhibitionperTranslationEntrainment*)phi=1*Pi;(*PhaseshiftbetweenthephaseoftheZeitgeberandthemolecularclock*)u[t_]:=(Cos[2*Pi*t/24+phi]+1)*0.25s=NDSolve[{M'[t]0.76*((1^4)/(1^4+(PN[t])^4))-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]*(1-u[t])-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{u[t]}/.s],Evaluate[{M[t]}/.s],Evaluate[{P0[t]}/.s],ZwM,ZwP0},{t,0,d},PlotRangeAll,PlotLegends{u,,,M,}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
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(*InhibitionperTranslation*)ts=20;(*Durationoftheinhibition*)u[t_]:=Piecewise[{{1,0≤t≤ts},{0,ts<t≤d}}];s=NDSolve[{M'[t]0.76*((1^4)/(1^4+(PN[t])^4))-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]*(1-u[t])-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{M[t]}/.s],Evaluate[{P0[t]}/.s],ZwM,ZwP0},{t,0,d},PlotRangeAll,PlotLegends{,,M,}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=220;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*FlymodelEntrainment*)T=26;(*PeriodoftheZeitgeber*)u[t_]:=(Cos[2*Pi*t/T]+1)*0.06s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-2*u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{u[t],M[t]}/.s]},{t,0,d},PlotRangeAll,PlotLegends{u,}]ZwMu=Evaluate[M[t]/.s]
u
M
Out[]=
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Out[]=
InterpolatingFunction
[t]
 |  |
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In[]:=
FindArgMax[ZwMu,{t,170,180}]-FindArgMax[ZwMu,{t,190,210}]
Out[]=
{-25.9753}
In[]:=
(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=220;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*MammalianmodelEntrainment*)T=23;(*PeriodoftheZeitgeber*)u[t_]:=(Cos[2*Pi*t/T]+1)*0.06s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t])+2.5*u[t]*Exp[-M[t]],P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[{Evaluate[{u[t],M[t]}/.s]},{t,0,d},PlotRangeAll,PlotLegends{u,}]ZwMu=Evaluate[M[t]/.s]
u
M
Out[]=
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Out[]=
InterpolatingFunction
[t]
|  |
|
In[]:=
FindArgMax[ZwMu,{t,170,180}]-FindArgMax[ZwMu,{t,190,210}]
Out[]=
{-22.575}
In[]:=
(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*Flymodelconstantlight*)c=0.1;(*Lightintensity*)u[t_]:=cs=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}]
Out[]=
M[t]InterpolatingFunction
[t],P0[t]InterpolatingFunction
[t],P1[t]InterpolatingFunction
[t],P2[t]InterpolatingFunction
[t],PN[t]InterpolatingFunction
[t]
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In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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In[]:=
Plot[{Evaluate[{M[t]}/.s],ZwM},{t,0,120},PlotRangeAll,PlotLegends{,M}]
u
M
Out[]=
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In[]:=
ZwMu=Evaluate[M[t]/.s];FindArgMax[ZwMu,{t,80,95}]-FindArgMax[ZwMu,{t,105,120}]
Out[]=
{-23.5134}
In[]:=
(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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N
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*Mammalianmodelconstantlight*)c=0.1;(*Lightintensity*)u[t_]:=cs=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t])+2*u[t]*Exp[-M[t]],P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}]
Out[]=
M[t]InterpolatingFunction
[t],P0[t]InterpolatingFunction
[t],P1[t]InterpolatingFunction
[t],P2[t]InterpolatingFunction
[t],PN[t]InterpolatingFunction
[t]
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In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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In[]:=
Plot[{Evaluate[{M[t]}/.s],ZwM},{t,0,120},PlotRangeAll,PlotLegends{,M}]ZwMu=Evaluate[M[t]/.s]
u
M
Out[]=
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Out[]=
InterpolatingFunction
[t]
| |
|
In[]:=
FindArgMax[ZwMu,{t,80,95}]-FindArgMax[ZwMu,{t,105,120}]
Out[]=
{-22.7974}
In[]:=
(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
P
0
P
1
P
2
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N
Out[]=
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*PhaseresponseFlymodel*)t0=14;(*Timewhenlightpulseisgiven*)c=1;(*Lightintensity*)u[t_]:=Piecewise[{{0,t0-1≤t≤t0},{c,t0≤t≤t0+1},{0,t0+1<t≤d}}]s=NDSolve[{M'[t](0.76)*((1)^4)/((1)^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-(3.2)*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-2*u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];ZwMu=Evaluate[M[t]/.s];-FindArgMax[ZwMu,{t,85,95}]+FindArgMax[ZwM,{t,80,90}]
Out[]=
{-3.38822}
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
u
M
u
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2
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In[]:=
Plot[{Evaluate[{M[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,M}]
u
M
Out[]=
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In[]:=
(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
P
0
P
1
P
2
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N
Out[]=
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*PhaseresponseMammalianmodel*)t0=5+21;(*Timewhenlightpulseisgiven*)c=1;(*Lightintensity*)u[t_]:=Piecewise[{{0,t0-1≤t≤t0},{c,t0≤t≤t0+1},{0,t0+1<t≤d}}]s=NDSolve[{M'[t](0.76)*((1)^4)/((1)^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t])+2.5*u[t]*Exp[-M[t]],P0'[t]0.38*M[t]-(3.2)*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];ZwMu=Evaluate[M[t]/.s];-FindArgMax[ZwMu,{t,85,95}]+FindArgMax[ZwM,{t,80,90}]
Out[]=
{3.16413}
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
u
M
u
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Out[]=
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In[]:=
Plot[{Evaluate[{M[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,M}]
u
M
Out[]=
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In[]:=
(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
P
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];(*Anti-phasecoupling*)u[t_]:=(Cos[2*Pi*t/24+Pi]+1)*0.25s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MB'[t]0.76*(1^4)/(1^4+(PBN[t])^4)-0.65*MB[t]/(0.5+MB[t]),PB0'[t]0.38*MB[t]-3.2*PB0[t]/(2+PB0[t])+1.58*PB1[t]/(2+PB1[t])-0.5*P0[t]*PB0[t],PB1'[t]3.2*PB0[t]/(2+PB0[t])-1.58*PB1[t]/(2+PB1[t])-5PB1[t]/(2+PB1[t])+2.5*PB2[t]/(2+PB2[t]),PB2'[t]5*PB1[t]/(2+PB1[t])-2.5*PB2[t]/(2+PB2[t])-1.9*PB2[t]+1.3*PBN[t]-0.95*PB2[t]/(0.2+PB2[t]),PBN'[t]1.9*PB2[t]-1.3PBN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5,MB[0]0.5,PB0[0]0.5,PB1[0]0.5,PB2[0]0.6,PBN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t],MB[t],PB0[t],PB1[t],PB2[t],PBN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[Evaluate[{MB[t],PB0[t],PB1[t],PB2[t],PBN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{OverTilde[M],,,,}]
OverTilde[P]
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Plot[{Evaluate[{M[t],u[t],MB[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,u,OverTilde[M],M}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=150;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];(*Inphasecoupling*)u[t_]:=(Cos[2*Pi*t/24+Pi]+1)*0.25s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MB'[t]0.76*(1^4)/(1^4+(PBN[t])^4)-0.65*MB[t]/(0.5+MB[t]),PB0'[t]0.38*MB[t]-3.2*PB0[t]/(2+PB0[t])+1.58*PB1[t]/(2+PB1[t])-0.5*Exp[-2*P0[t]]*PB0[t],PB1'[t]3.2*PB0[t]/(2+PB0[t])-1.58*PB1[t]/(2+PB1[t])-5PB1[t]/(2+PB1[t])+2.5*PB2[t]/(2+PB2[t]),PB2'[t]5*PB1[t]/(2+PB1[t])-2.5*PB2[t]/(2+PB2[t])-1.9*PB2[t]+1.3*PBN[t]-0.95*PB2[t]/(0.2+PB2[t]),PBN'[t]1.9*PB2[t]-1.3PBN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5,MB[0]0.5,PB0[0]0.5,PB1[0]0.5,PB2[0]0.6,PBN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t],MB[t],PB0[t],PB1[t],PB2[t],PBN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[Evaluate[{MB[t],PB0[t],PB1[t],PB2[t],PBN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{OverTilde[M],,,,}]
OverTilde[P]
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Plot[{Evaluate[{M[t],u[t],MB[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,u,OverTilde[M],M}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=120;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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In[]:=
ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*Intermediate-phasecoupling*)u[t_]:=(Cos[2*Pi*t/24+Pi]+1)*0.25s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MB'[t]0.76*(1^4)/(1^4+(PBN[t])^4)-0.65*MB[t]/(0.5+MB[t]),PB0'[t]0.38*MB[t]-3.2*PB0[t]/(2+PB0[t])+1.58*PB1[t]/(2+PB1[t])-0.5*P2[t]*PB0[t],PB1'[t]3.2*PB0[t]/(2+PB0[t])-1.58*PB1[t]/(2+PB1[t])-5PB1[t]/(2+PB1[t])+2.5*PB2[t]/(2+PB2[t]),PB2'[t]5*PB1[t]/(2+PB1[t])-2.5*PB2[t]/(2+PB2[t])-1.9*PB2[t]+1.3*PBN[t]-0.95*PB2[t]/(0.2+PB2[t]),PBN'[t]1.9*PB2[t]-1.3PBN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5,MB[0]0.5,PB0[0]0.5,PB1[0]0.5,PB2[0]0.6,PBN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t],MB[t],PB0[t],PB1[t],PB2[t],PBN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[Evaluate[{MB[t],PB0[t],PB1[t],PB2[t],PBN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{OverTilde[M],,,,}]
OverTilde[P]
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Plot[{Evaluate[{M[t],u[t],MB[t]}/.s],ZwM},{t,0,d},PlotRangeAll,PlotLegends{,u,,M}]
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(*Generateunperturbedtimecurvesoftheagentsofthemodel*)d=300;(*timeHorizonforthesimulation*)s=NDSolve[{MD'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*MD[t]/(0.5+MD[t]),P0'[t]0.38*MD[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t]),P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MD[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5},{MD[t],P0[t],P1[t],P2[t],PN[t]},{t,0,d}];
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Plot[Evaluate[{MD[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{M,,,,}]
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ZwM=Evaluate[MD[t]/.s];ZwP0=Evaluate[P0[t]/.s];ZwP1=Evaluate[P1[t]/.s];ZwP2=Evaluate[P2[t]/.s];ZwPN=Evaluate[PN[t]/.s];
In[]:=
(*Modelforfoodentrainableperipheralclocks*)u[t_]:=(Cos[2*Pi*t/24]+1)*0.25u1[t_]:=Piecewise[{{0.25*(Cos[2*Pi*t/24+1*Pi]+1),0≤t≤160},{u[t],160<t≤d}}]s=NDSolve[{M'[t]0.76*(1^4)/(1^4+(PN[t])^4)-0.65*M[t]/(0.5+M[t]),P0'[t]0.38*M[t]-3.2*P0[t]/(2+P0[t])+1.58*P1[t]/(2+P1[t])-u[t]*P0[t],P1'[t]3.2*P0[t]/(2+P0[t])-1.58*P1[t]/(2+P1[t])-5P1[t]/(2+P1[t])+2.5*P2[t]/(2+P2[t]),P2'[t]5*P1[t]/(2+P1[t])-2.5*P2[t]/(2+P2[t])-1.9*P2[t]+1.3*PN[t]-0.95*P2[t]/(0.2+P2[t]),PN'[t]1.9*P2[t]-1.3PN[t],MB'[t]0.76*(1^4)/(1^4+(PBN[t])^4)-0.65*MB[t]/(0.5+MB[t]),PB0'[t]0.38*MB[t]-3.2*PB0[t]/(2+PB0[t])+1.58*PB1[t]/(2+PB1[t])-0.3*Exp[-2P0[t]]*PB0[t]-0.4*u1[t]*PB0[t],PB1'[t]3.2*PB0[t]/(2+PB0[t])-1.58*PB1[t]/(2+PB1[t])-5PB1[t]/(2+PB1[t])+2.5*PB2[t]/(2+PB2[t]),PB2'[t]5*PB1[t]/(2+PB1[t])-2.5*PB2[t]/(2+PB2[t])-1.9*PB2[t]+1.3*PBN[t]-0.95*PB2[t]/(0.2+PB2[t]),PBN'[t]1.9*PB2[t]-1.3PBN[t],M[0]0.5,P0[0]0.5,P1[0]0.5,P2[0]0.6,PN[0]1.5,MB[0]0.5,PB0[0]0.5,PB1[0]0.5,PB2[0]0.6,PBN[0]1.5},{M[t],P0[t],P1[t],P2[t],PN[t],MB[t],PB0[t],PB1[t],PB2[t],PBN[t]},{t,0,d}];
In[]:=
Plot[Evaluate[{M[t],P0[t],P1[t],P2[t],PN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{,,,,}]
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Plot[Evaluate[{MB[t],PB0[t],PB1[t],PB2[t],PBN[t]}/.s],{t,0,d},PlotRangeAll,PlotLegends{OverTilde[M],,,,}]
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Plot[{Evaluate[{M[t],u[t],u1[t],MB[t]}/.s],ZwM},{t,0,300},PlotRangeAll,PlotStyle{Red,Orange,Blue,Green,Black},PlotLegends{,u,OverTilde[u],OverTilde[M],M}]
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Cite this as: Tim Breitenbach, Charlotte Helfrich-Förster, Thomas Dandekar, "basic_circadian_clock_models.nb" from the Notebook Archive (2022), https://notebookarchive.org/2022-01-1vufp3h
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