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Selkov-Wolf-Heinrich.cps
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Selkov-Wolf-Heinrich.cps
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<body xmlns="http://www.w3.org/1999/xhtml"><h1>Simple model of glycolytic oscillations</h1>
<p>This is the version of Wolf-Heinrich (2000) of the Sel'kov (1968) model of glycolytic oscillations. It is a very simple model with two species, X and Y, where the conversion of X->Y is activated by Y itself. Wolf and Heinrich use this model as a building block for a model of coupled oscillating cells connected by a well-stirred medium. However, the model included here is equivalent to what Sel'kov proposed for a single cell, without export of any species to the medium.</p>
<p><b>References:</b>
<ul>
<li><a href="https://doi.org/10.1111/j.1432-1033.1968.tb00175.x">Sel'kov EE (1968) Self-oscillations in glycolysis. 1. A simple kinetic model. European Journal of Biochemistry 4:79–86</a> </li>
<li><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1220770/">Wolf J, Heinrich R (2000) Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation. Biochemical Journal 345 Pt 2:321–334</a></li>
</ul>
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<p style="font-size:small"><b>CC0 1.0 Universal</b>: To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. Please refer to <a href="http://creativecommons.org/publicdomain/zero/1.0/" title="Creative Commons CC0">CC0 Public Domain Dedication</a> for more information.</p></body>
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<Parameter name="Use Time Sens" type="bool" value="0"/>
<Parameter name="Time-Sens" type="cn" value=""/>
<ParameterGroup name="Experiment Set">
</ParameterGroup>
<ParameterGroup name="Validation Set">
<Parameter name="Weight" type="unsignedFloat" value="1"/>
<Parameter name="Threshold" type="unsignedInteger" value="5"/>
</ParameterGroup>
</Problem>
<Method name="Evolutionary Programming" type="EvolutionaryProgram">
<Parameter name="Log Verbosity" type="unsignedInteger" value="0"/>
<Parameter name="Number of Generations" type="unsignedInteger" value="200"/>
<Parameter name="Population Size" type="unsignedInteger" value="20"/>
<Parameter name="Random Number Generator" type="unsignedInteger" value="1"/>
<Parameter name="Seed" type="unsignedInteger" value="0"/>
<Parameter name="Stop after # Stalled Generations" type="unsignedInteger" value="0"/>
</Method>
</Task>
<Task key="Task_23" name="Metabolic Control Analysis" type="metabolicControlAnalysis" scheduled="false" updateModel="false">
<Report reference="Report_16" target="" append="1" confirmOverwrite="1"/>
<Problem>
<Parameter name="Steady-State" type="key" value="Task_17"/>
</Problem>
<Method name="MCA Method (Reder)" type="MCAMethod(Reder)">
<Parameter name="Modulation Factor" type="unsignedFloat" value="1.0000000000000001e-09"/>
<Parameter name="Use Reder" type="bool" value="1"/>
<Parameter name="Use Smallbone" type="bool" value="1"/>
</Method>
</Task>
<Task key="Task_24" name="Lyapunov Exponents" type="lyapunovExponents" scheduled="false" updateModel="false">
<Report reference="Report_17" target="" append="1" confirmOverwrite="1"/>
<Problem>
<Parameter name="ExponentNumber" type="unsignedInteger" value="3"/>
<Parameter name="DivergenceRequested" type="bool" value="1"/>
<Parameter name="TransientTime" type="float" value="0"/>
</Problem>
<Method name="Wolf Method" type="WolfMethod">
<Parameter name="Orthonormalization Interval" type="unsignedFloat" value="1"/>
<Parameter name="Overall time" type="unsignedFloat" value="1000"/>
<Parameter name="Relative Tolerance" type="unsignedFloat" value="9.9999999999999995e-07"/>
<Parameter name="Absolute Tolerance" type="unsignedFloat" value="9.9999999999999998e-13"/>
<Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
</Method>
</Task>
<Task key="Task_25" name="Time Scale Separation Analysis" type="timeScaleSeparationAnalysis" scheduled="false" updateModel="false">
<Report reference="Report_18" target="" append="1" confirmOverwrite="1"/>
<Problem>
<Parameter name="StepNumber" type="unsignedInteger" value="100"/>
<Parameter name="StepSize" type="float" value="0.01"/>
<Parameter name="Duration" type="float" value="1"/>
<Parameter name="TimeSeriesRequested" type="bool" value="1"/>
<Parameter name="OutputStartTime" type="float" value="0"/>
</Problem>
<Method name="ILDM (LSODA,Deuflhard)" type="TimeScaleSeparation(ILDM,Deuflhard)">
<Parameter name="Deuflhard Tolerance" type="unsignedFloat" value="0.0001"/>
</Method>
</Task>
<Task key="Task_26" name="Sensitivities" type="sensitivities" scheduled="false" updateModel="false">
<Report reference="Report_19" target="" append="1" confirmOverwrite="1"/>
<Problem>
<Parameter name="SubtaskType" type="unsignedInteger" value="1"/>
<ParameterGroup name="TargetFunctions">
<Parameter name="SingleObject" type="cn" value=""/>
<Parameter name="ObjectListType" type="unsignedInteger" value="7"/>
</ParameterGroup>
<ParameterGroup name="ListOfVariables">
<ParameterGroup name="Variables">
<Parameter name="SingleObject" type="cn" value=""/>
<Parameter name="ObjectListType" type="unsignedInteger" value="41"/>
</ParameterGroup>
<ParameterGroup name="Variables">
<Parameter name="SingleObject" type="cn" value=""/>
<Parameter name="ObjectListType" type="unsignedInteger" value="0"/>
</ParameterGroup>
</ParameterGroup>
</Problem>
<Method name="Sensitivities Method" type="SensitivitiesMethod">
<Parameter name="Delta factor" type="unsignedFloat" value="0.001"/>
<Parameter name="Delta minimum" type="unsignedFloat" value="9.9999999999999998e-13"/>
</Method>
</Task>
<Task key="Task_27" name="Moieties" type="moieties" scheduled="false" updateModel="false">
<Report reference="Report_20" target="" append="1" confirmOverwrite="1"/>
<Problem>
</Problem>
<Method name="Householder Reduction" type="Householder">
</Method>
</Task>
<Task key="Task_28" name="Cross Section" type="crosssection" scheduled="false" updateModel="false">
<Problem>
<Parameter name="AutomaticStepSize" type="bool" value="0"/>
<Parameter name="StepNumber" type="unsignedInteger" value="100"/>
<Parameter name="StepSize" type="float" value="0.01"/>
<Parameter name="Duration" type="float" value="1"/>
<Parameter name="TimeSeriesRequested" type="bool" value="1"/>
<Parameter name="OutputStartTime" type="float" value="0"/>
<Parameter name="Output Event" type="bool" value="0"/>
<Parameter name="Start in Steady State" type="bool" value="0"/>
<Parameter name="Use Values" type="bool" value="0"/>
<Parameter name="Values" type="string" value=""/>
<Parameter name="LimitCrossings" type="bool" value="0"/>
<Parameter name="NumCrossingsLimit" type="unsignedInteger" value="0"/>
<Parameter name="LimitOutTime" type="bool" value="0"/>
<Parameter name="LimitOutCrossings" type="bool" value="0"/>
<Parameter name="PositiveDirection" type="bool" value="1"/>
<Parameter name="NumOutCrossingsLimit" type="unsignedInteger" value="0"/>
<Parameter name="LimitUntilConvergence" type="bool" value="0"/>
<Parameter name="ConvergenceTolerance" type="float" value="9.9999999999999995e-07"/>
<Parameter name="Threshold" type="float" value="0"/>
<Parameter name="DelayOutputUntilConvergence" type="bool" value="0"/>
<Parameter name="OutputConvergenceTolerance" type="float" value="9.9999999999999995e-07"/>
<ParameterText name="TriggerExpression" type="expression">
</ParameterText>
<Parameter name="SingleVariable" type="cn" value=""/>
</Problem>
<Method name="Deterministic (LSODA)" type="Deterministic(LSODA)">
<Parameter name="Integrate Reduced Model" type="bool" value="0"/>
<Parameter name="Relative Tolerance" type="unsignedFloat" value="9.9999999999999995e-07"/>
<Parameter name="Absolute Tolerance" type="unsignedFloat" value="9.9999999999999998e-13"/>
<Parameter name="Max Internal Steps" type="unsignedInteger" value="100000"/>
<Parameter name="Max Internal Step Size" type="unsignedFloat" value="0"/>
</Method>
</Task>
<Task key="Task_29" name="Linear Noise Approximation" type="linearNoiseApproximation" scheduled="false" updateModel="false">
<Report reference="Report_21" target="" append="1" confirmOverwrite="1"/>
<Problem>
<Parameter name="Steady-State" type="key" value="Task_17"/>
</Problem>
<Method name="Linear Noise Approximation" type="LinearNoiseApproximation">
</Method>
</Task>
<Task key="Task_30" name="Time-Course Sensitivities" type="timeSensitivities" scheduled="false" updateModel="false">
<Problem>
<Parameter name="AutomaticStepSize" type="bool" value="0"/>
<Parameter name="StepNumber" type="unsignedInteger" value="100"/>
<Parameter name="StepSize" type="float" value="0.01"/>
<Parameter name="Duration" type="float" value="1"/>
<Parameter name="TimeSeriesRequested" type="bool" value="1"/>
<Parameter name="OutputStartTime" type="float" value="0"/>
<Parameter name="Output Event" type="bool" value="0"/>
<Parameter name="Start in Steady State" type="bool" value="0"/>
<Parameter name="Use Values" type="bool" value="0"/>
<Parameter name="Values" type="string" value=""/>
<ParameterGroup name="ListOfParameters">
</ParameterGroup>
<ParameterGroup name="ListOfTargets">
</ParameterGroup>
</Problem>
<Method name="LSODA Sensitivities" type="Sensitivities(LSODA)">
<Parameter name="Integrate Reduced Model" type="bool" value="0"/>
<Parameter name="Relative Tolerance" type="unsignedFloat" value="9.9999999999999995e-07"/>
<Parameter name="Absolute Tolerance" type="unsignedFloat" value="9.9999999999999998e-13"/>
<Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
<Parameter name="Max Internal Step Size" type="unsignedFloat" value="0"/>
</Method>
</Task>
</ListOfTasks>
<ListOfReports>
<Report key="Report_11" name="Steady-State" taskType="steadyState" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Footer>
<Object cn="CN=Root,Vector=TaskList[Steady-State]"/>
</Footer>
</Report>
<Report key="Report_12" name="Time-Course" taskType="timeCourse" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Time-Course],Object=Description"/>
</Header>
<Footer>
<Object cn="CN=Root,Vector=TaskList[Time-Course],Object=Result"/>
</Footer>
</Report>
<Report key="Report_13" name="Elementary Flux Modes" taskType="fluxMode" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Footer>
<Object cn="CN=Root,Vector=TaskList[Elementary Flux Modes],Object=Result"/>
</Footer>
</Report>
<Report key="Report_14" name="Optimization" taskType="optimization" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Optimization],Object=Description"/>
<Object cn="String=\[Function Evaluations\]"/>
<Object cn="Separator=	"/>
<Object cn="String=\[Best Value\]"/>
<Object cn="Separator=	"/>
<Object cn="String=\[Best Parameters\]"/>
</Header>
<Body>
<Object cn="CN=Root,Vector=TaskList[Optimization],Problem=Optimization,Reference=Function Evaluations"/>
<Object cn="Separator=	"/>
<Object cn="CN=Root,Vector=TaskList[Optimization],Problem=Optimization,Reference=Best Value"/>
<Object cn="Separator=	"/>
<Object cn="CN=Root,Vector=TaskList[Optimization],Problem=Optimization,Reference=Best Parameters"/>
</Body>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Optimization],Object=Result"/>
</Footer>
</Report>
<Report key="Report_15" name="Parameter Estimation" taskType="parameterFitting" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Object=Description"/>
<Object cn="String=\[Function Evaluations\]"/>
<Object cn="Separator=	"/>
<Object cn="String=\[Best Value\]"/>
<Object cn="Separator=	"/>
<Object cn="String=\[Best Parameters\]"/>
</Header>
<Body>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Problem=Parameter Estimation,Reference=Function Evaluations"/>
<Object cn="Separator=	"/>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Problem=Parameter Estimation,Reference=Best Value"/>
<Object cn="Separator=	"/>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Problem=Parameter Estimation,Reference=Best Parameters"/>
</Body>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Object=Result"/>
</Footer>
</Report>
<Report key="Report_16" name="Metabolic Control Analysis" taskType="metabolicControlAnalysis" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Metabolic Control Analysis],Object=Description"/>
</Header>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Metabolic Control Analysis],Object=Result"/>
</Footer>
</Report>
<Report key="Report_17" name="Lyapunov Exponents" taskType="lyapunovExponents" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Lyapunov Exponents],Object=Description"/>
</Header>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Lyapunov Exponents],Object=Result"/>
</Footer>
</Report>
<Report key="Report_18" name="Time Scale Separation Analysis" taskType="timeScaleSeparationAnalysis" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Time Scale Separation Analysis],Object=Description"/>
</Header>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Time Scale Separation Analysis],Object=Result"/>
</Footer>
</Report>
<Report key="Report_19" name="Sensitivities" taskType="sensitivities" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Sensitivities],Object=Description"/>
</Header>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Sensitivities],Object=Result"/>
</Footer>
</Report>
<Report key="Report_20" name="Moieties" taskType="moieties" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Moieties],Object=Description"/>
</Header>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Moieties],Object=Result"/>
</Footer>
</Report>
<Report key="Report_21" name="Linear Noise Approximation" taskType="linearNoiseApproximation" separator="	" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Linear Noise Approximation],Object=Description"/>
</Header>
<Footer>
<Object cn="String=
"/>
<Object cn="CN=Root,Vector=TaskList[Linear Noise Approximation],Object=Result"/>
</Footer>
</Report>
</ListOfReports>
<ListOfPlots>
<PlotSpecification name="Time course" type="Plot2D" active="1" taskTypes="">
<Parameter name="log X" type="bool" value="0"/>
<Parameter name="log Y" type="bool" value="0"/>
<Parameter name="plot engine" type="string" value="QCustomPlot"/>
<Parameter name="x axis" type="string" value="time"/>
<Parameter name="y axis" type="string" value="concentration"/>
<Parameter name="z axis" type="string" value=""/>
<ListOfPlotItems>
<PlotItem name="[X]" type="Curve2D">
<Parameter name="Line type" type="unsignedInteger" value="0"/>
<Parameter name="Line subtype" type="unsignedInteger" value="0"/>
<Parameter name="Line width" type="unsignedFloat" value="1.2"/>
<Parameter name="Symbol subtype" type="unsignedInteger" value="0"/>
<Parameter name="Color" type="string" value="auto"/>
<Parameter name="Recording Activity" type="string" value="during"/>
<ListOfChannels>
<ChannelSpec cn="CN=Root,Model=Simple model of glycolytic oscillations,Reference=Time"/>
<ChannelSpec cn="CN=Root,Model=Simple model of glycolytic oscillations,Vector=Compartments[Cell],Vector=Metabolites[X],Reference=Concentration"/>
</ListOfChannels>
</PlotItem>
<PlotItem name="[Y]" type="Curve2D">
<Parameter name="Line type" type="unsignedInteger" value="0"/>
<Parameter name="Line subtype" type="unsignedInteger" value="0"/>
<Parameter name="Line width" type="unsignedFloat" value="1.2"/>
<Parameter name="Symbol subtype" type="unsignedInteger" value="0"/>
<Parameter name="Color" type="string" value="auto"/>
<Parameter name="Recording Activity" type="string" value="during"/>
<ListOfChannels>
<ChannelSpec cn="CN=Root,Model=Simple model of glycolytic oscillations,Reference=Time"/>
<ChannelSpec cn="CN=Root,Model=Simple model of glycolytic oscillations,Vector=Compartments[Cell],Vector=Metabolites[Y],Reference=Concentration"/>
</ListOfChannels>
</PlotItem>
</ListOfPlotItems>
</PlotSpecification>
<PlotSpecification name="Phase plane" type="Plot2D" active="1" taskTypes="">
<Parameter name="log X" type="bool" value="0"/>
<Parameter name="log Y" type="bool" value="0"/>
<Parameter name="x axis" type="string" value="X"/>
<Parameter name="y axis" type="string" value="Y"/>
<Parameter name="z axis" type="string" value=""/>
<Parameter name="plot engine" type="string" value="QWT"/>
<ListOfPlotItems>
<PlotItem name="orbit" type="Curve2D">
<Parameter name="Line type" type="unsignedInteger" value="0"/>
<Parameter name="Line subtype" type="unsignedInteger" value="0"/>
<Parameter name="Line width" type="unsignedFloat" value="1.2"/>
<Parameter name="Symbol subtype" type="unsignedInteger" value="0"/>
<Parameter name="Color" type="string" value="auto"/>
<Parameter name="Recording Activity" type="string" value="during"/>
<ListOfChannels>
<ChannelSpec cn="CN=Root,Model=Simple model of glycolytic oscillations,Vector=Compartments[Cell],Vector=Metabolites[X],Reference=Concentration"/>
<ChannelSpec cn="CN=Root,Model=Simple model of glycolytic oscillations,Vector=Compartments[Cell],Vector=Metabolites[Y],Reference=Concentration"/>
</ListOfChannels>
</PlotItem>
</ListOfPlotItems>
</PlotSpecification>
</ListOfPlots>
<GUI>
<ListOfSliders>
<Slider key="Slider_0" associatedEntityKey="Task_18" objectCN="CN=Root,Model=Simple model of glycolytic oscillations,Vector=Values[k],Reference=InitialValue" objectType="float" objectValue="2.64442" minValue="0.384" maxValue="38.4" tickNumber="1000" tickFactor="100" scaling="logarithmic"/>
<Slider key="Slider_1" associatedEntityKey="Task_18" objectCN="CN=Root,Model=Simple model of glycolytic oscillations,Vector=Values[v],Reference=InitialValue" objectType="float" objectValue="4.04689" minValue="0.03" maxValue="30" tickNumber="1000" tickFactor="100" scaling="logarithmic"/>
</ListOfSliders>
</GUI>
<ListOfUnitDefinitions>
<UnitDefinition key="Unit_15" name="dimensionless" symbol="1">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_14">
</rdf:Description>
</rdf:RDF>
</MiriamAnnotation>
<Expression>
1
</Expression>
</UnitDefinition>
</ListOfUnitDefinitions>
</COPASI>