- Author:
- Dougal Cowan <devnull@localhost>
- Date:
- 2011-05-16 09:01:54+12:00
- Desc:
- relativized the import
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/goldbeter_dupont_berridge_1990/rawfile/e803177d4571e14e2c20dc71b0ab57eecfa60c11/goldbeter_dupont_berridge_1990.cellml
<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="goldbeter_model_1990" name="goldbeter_model_1990">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation</title>
<author>
<firstname>Mark</firstname>
<surname>Hanna</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>Runs in PCEnv and COR. Reproduces published output (figures 2a, 2b when the value of 'k' is changed to 6, 4a, 4b when the value of 'beta' is changed to 0.644)</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: In a variety of cells, hormonal or neurotransmitter signals elicit a train of intracellular Ca2+ spikes. The analysis of a minimal model based on Ca2+-induced Ca2+ release from intracellular stores shows how sustained oscillations of cytosolic Ca2+ may develop as a result of a rise in inositol 1,4,5-trisphosphate (InsP3) triggered by external stimulation. This rise elicits the release of a certain amount of Ca2+ from an InsP3-sensitive intracellular store. The subsequent rise in cytosolic Ca2+ in turn triggers the release of Ca2+ from a second store insensitive to InsP3. In contrast to the model proposed by Meyer and Stryer [Meyer, T. & Stryer, L. (1988) <emphasis>Proc. Matl. Acad. Sci. USA 85, 5051-5055</emphasis>], the present model, which contains only two variable, predicts the occurrence of periodic Ca2+ spikes in the absence of InsP3 oscillations. Such results indicate that repetitive Ca2+ spikes evoked by external stimuli do not necessarily require the concomitant, periodic variation of InsP3. The model is closely related to that proposed by Kuba and Takeshita [Kuba, K. & Takeshita, S. (1981) <emphasis>J. Theor. Biol. 93, 1009-1031</emphasis>] for Ca2+ oscillations in sympathetic neurones, based on Ca2+-induced Ca2+ release. We extend their results by showing the minimal conditions in which the latter process gives rise to periodic behaviour and take into account the role of the rise in InsP3 caused by external stimulation. The analysis further shows how signal-induced Ca2+ oscillations might be effectively encoded in terms of their frequency through the phospohorylation of a cellular substrate by a protein kinase activated by cytosolic Ca2+.</para>
<para>Minimla model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation, Albert Goldbeter, Genevieve Dupont, Michael J. Berridge, 1990, <emphasis>Biophysics</emphasis>, 87, 1461-1465. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=2304911&dopt=Abstract">PubMed ID: 2304911</ulink></para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="goldbeter_1990.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of the mechanism generating Ca2+ oscillations, based on the self-amplified release of Ca2+ from intracellular stores.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!-- Units -->
<units name="s">
<!-- time: second -->
<unit units="second"/>
</units>
<units name="per_s">
<!-- time^-1: per second -->
<unit exponent="-1" units="s"/>
</units>
<units name="uM">
<!-- concentration: micromolar -->
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="uM_per_s">
<!-- flux: micromolar per second -->
<unit units="uM"/>
<unit exponent="-1" units="s"/>
</units>
<!-- Components -->
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="s"/>
</component>
<component cmeta:id="Ca_component" name="Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Ca_component">This component stores information about Calcium ion (Ca2+) concentrations in various cellular compartments</rdf:Description>
<rdf:Description rdf:about="#Z">Ca2+ concentration in the cytosol</rdf:Description>
<rdf:Description rdf:about="#Y">Ca2+ concentration in the IP3-insensitive intracellular Ca2+ pool</rdf:Description>
<rdf:Description rdf:about="#v_0">Influx of Ca2+ into the cell</rdf:Description>
<rdf:Description rdf:about="#k">Efflux of Ca2+ out of the cell</rdf:Description>
<rdf:Description rdf:about="#k_f">Rate constant for leaky transport of Ca2+ from the IP3-insensitive intracellular Ca2+ pool into the cytosol</rdf:Description>
<rdf:Description rdf:about="#beta">Level of external stimulation</rdf:Description>
<rdf:Description rdf:about="#v_1">Activated flux from extracellular medium into cytosol</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="s"/>
<variable cmeta:id="Z" initial_value="0.5" name="Z" private_interface="out" public_interface="out" units="uM"/>
<variable cmeta:id="Y" initial_value="1.75" name="Y" private_interface="out" units="uM"/>
<variable cmeta:id="v_0" initial_value="1" name="v_0" units="uM_per_s"/>
<variable cmeta:id="v_1" initial_value="7.3" name="v_1" units="uM_per_s"/>
<variable name="v_2" private_interface="in" units="uM_per_s"/>
<variable name="v_3" private_interface="in" units="uM_per_s"/>
<variable cmeta:id="k" initial_value="10" name="k" units="per_s"/>
<variable cmeta:id="k_f" initial_value="1" name="k_f" units="per_s"/>
<variable cmeta:id="beta" initial_value="0.301" name="beta" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="Ca_maths">
<apply id="dZ/dt_eq"><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Z</ci>
</apply>
<apply><plus/>
<ci>v_0</ci>
<apply><times/>
<ci>v_1</ci>
<ci>beta</ci>
</apply>
<apply><minus/>
<ci>v_2</ci>
</apply>
<ci>v_3</ci>
<apply><times/>
<ci>k_f</ci>
<ci>Y</ci>
</apply>
<apply><minus/>
<apply><times/>
<ci>k</ci>
<ci>Z</ci>
</apply>
</apply>
</apply>
</apply>
<apply id="dY/dt_eq"><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>Y</ci>
</apply>
<apply><plus/>
<ci>v_2</ci>
<apply><minus/>
<ci>v_3</ci>
</apply>
<apply><minus/>
<apply><times/>
<ci>k_f</ci>
<ci>Y</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="v_2_component" name="v_2">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#v_2_component">Component for the calculation of v_2</rdf:Description>
<rdf:Description rdf:about="#v_2">Rate of ATP-driven pumping of Ca2+ from the cytosol into the IP3-insensitive store</rdf:Description>
<rdf:Description rdf:about="#V_M2">Maximum rate for v_2</rdf:Description>
<rdf:Description rdf:about="#K_2">Threshold concentration for pumping of Ca2+ from the cytosol into the IP3-insensitive store</rdf:Description>
</rdf:RDF>
<variable name="Z" public_interface="in" units="uM"/>
<variable cmeta:id="v_2" name="v_2" public_interface="out" units="uM_per_s"/>
<variable cmeta:id="V_M2" initial_value="65" name="V_M2" units="uM_per_s"/>
<variable cmeta:id="K_2" initial_value="1" name="K_2" units="uM"/>
<variable initial_value="2" name="n" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="v_2_maths">
<apply id="v_2_id"><eq/>
<ci>v_2</ci>
<apply><times/>
<ci>V_M2</ci>
<apply><divide/>
<apply><power/>
<ci>Z</ci>
<ci>n</ci>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_2</ci>
<ci>n</ci>
</apply>
<apply><power/>
<ci>Z</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#v_3_component">Component for the calculation of v_3</rdf:Description>
<rdf:Description rdf:about="#v_3">Rate of transport from this pool into the cytosol</rdf:Description>
<rdf:Description rdf:about="#V_M3">Maximum rate for v_3</rdf:Description>
<rdf:Description rdf:about="#K_R">Threshold concentration for Ca2+ release</rdf:Description>
<rdf:Description rdf:about="#K_A">Threshold concentration for Ca2+ activation</rdf:Description>
</rdf:RDF>
<variable name="Z" public_interface="in" units="uM"/>
<variable name="Y" public_interface="in" units="uM"/>
<variable cmeta:id="v_3" name="v_3" public_interface="out" units="uM_per_s"/>
<variable cmeta:id="V_M3" initial_value="500" name="V_M3" units="uM_per_s"/>
<variable cmeta:id="K_R" initial_value="2" name="K_R" units="uM"/>
<variable cmeta:id="K_A" initial_value="0.9" name="K_A" units="uM"/>
<variable initial_value="2" name="m" units="dimensionless"/>
<variable initial_value="4" name="p" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="v_3_maths">
<apply id="v_3_eq"><eq/>
<ci>v_3</ci>
<apply><times/>
<ci>V_M3</ci>
<apply><divide/>
<apply><power/>
<ci>Y</ci>
<ci>m</ci>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_R</ci>
<ci>m</ci>
</apply>
<apply><power/>
<ci>Y</ci>
<ci>m</ci>
</apply>
</apply>
</apply>
<apply><divide/>
<apply><power/>
<ci>Z</ci>
<ci>p</ci>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_A</ci>
<ci>p</ci>
</apply>
<apply><power/>
<ci>Z</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="W_star_component" name="W_star">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#W_star_component">Component for the calculation of W_star</rdf:Description>
<rdf:Description rdf:about="#W_star">Fraction of a protein substrate in the phosphorylated form</rdf:Description>
<rdf:Description rdf:about="#W_T">Total amount of protein substrate</rdf:Description>
<rdf:Description rdf:about="#v_P">Maximum rate of phosphatase</rdf:Description>
<rdf:Description rdf:about="#K_1">K_1 = K_m1/W_T, where K_m1 denotes the Michaelis constant of kinase</rdf:Description>
<rdf:Description rdf:about="#K_2">K_2 = K_m2/W_T, where K_m2 denotes the MIchaelis constant of phosphatase</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="s"/>
<variable name="Z" private_interface="out" public_interface="in" units="uM"/>
<variable cmeta:id="W_star" initial_value="0" name="W_star" units="dimensionless"/>
<variable cmeta:id="W_T" initial_value="1" name="W_T" units="uM"/>
<variable cmeta:id="v_P" initial_value="5" name="v_P" units="uM_per_s"/>
<variable name="v_K" private_interface="in" units="uM_per_s"/>
<variable cmeta:id="K_1" initial_value="0.1" name="K_1" units="dimensionless"/>
<variable cmeta:id="K_2" initial_value="0.1" name="K_2" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="W_star_maths">
<apply id="dW_star/dt_eq"><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>W_star</ci>
</apply>
<apply><times/>
<apply><divide/>
<ci>v_P</ci>
<ci>W_T</ci>
</apply>
<apply><minus/>
<apply><times/>
<apply><divide/>
<ci>v_K</ci>
<ci>v_P</ci>
</apply>
<apply><divide/>
<apply><minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>W_star</ci>
</apply>
<apply><plus/>
<ci>K_1</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply><minus/>
<ci>W_star</ci>
</apply>
</apply>
</apply>
</apply>
<apply><divide/>
<ci>W_star</ci>
<apply><plus/>
<ci>K_2</ci>
<ci>W_star</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="v_K_component" name="v_K">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#v_K_component">Component for the calculation of v_K</rdf:Description>
<rdf:Description rdf:about="#v_K">Maximum rate of kinase</rdf:Description>
<rdf:Description rdf:about="#V_MK">Maximum rate of v_K</rdf:Description>
<rdf:Description rdf:about="#K_a">Constant of activation of the kinase by cytosolic Ca2+</rdf:Description>
</rdf:RDF>
<variable name="Z" public_interface="in" units="uM"/>
<variable cmeta:id="v_K" name="v_K" public_interface="out" units="uM_per_s"/>
<variable cmeta:id="V_MK" initial_value="40" name="V_MK" units="uM_per_s"/>
<variable cmeta:id="K_a" initial_value="2.5" name="K_a" units="uM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="v_K_maths">
<apply id="v_K_eq"><eq/>
<ci>v_K</ci>
<apply><times/>
<ci>V_MK</ci>
<apply><divide/>
<ci>Z</ci>
<apply><plus/>
<ci>K_a</ci>
<ci>Z</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- groups -->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="Ca">
<component_ref component="v_2"/>
<component_ref component="v_3"/>
</component_ref>
<component_ref component="W_star">
<component_ref component="v_K"/>
</component_ref>
</group>
<!-- connections -->
<connection>
<map_components component_1="environment" component_2="Ca"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca" component_2="v_2"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="v_2" variable_2="v_2"/>
</connection>
<connection>
<map_components component_1="Ca" component_2="v_3"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="Y" variable_2="Y"/>
<map_variables variable_1="v_3" variable_2="v_3"/>
</connection>
<connection>
<map_components component_1="Ca" component_2="W_star"/>
<map_variables variable_1="Z" variable_2="Z"/>
</connection>
<connection>
<map_components component_1="environment" component_2="W_star"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="W_star" component_2="v_K"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="v_K" variable_2="v_K"/>
</connection>
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<rdf:Description rdf:about="">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Hanna</vCard:Family>
<vCard:Given>Mark</vCard:Given>
<vCard:Other>James</vCard:Other>
</vCard:N>
<vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<rdf:value>mark@hanna.net.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
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<dcterms:W3CDTF>2009-12-01</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#goldbeter_model_1990">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation</dc:title>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource">
<dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<rdf:value>
<rdf:Bag>
<rdf:li>Calcium Signalling</rdf:li>
<rdf:li>Calcium Oscillations</rdf:li>
<rdf:li>Bursting</rdf:li>
<rdf:li>Calcium Dynamics</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
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<bqs:Pubmed_id>2304911</bqs:Pubmed_id>
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<vCard:Family>Goldbeter</vCard:Family>
<vCard:Given>Albert</vCard:Given>
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<bqs:Person rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Dupont</vCard:Family>
<vCard:Given>Genevieve</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Berridge</vCard:Family>
<vCard:Given>Michael</vCard:Given>
<vCard:Other>J.</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation</dc:title>
<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource">
<dcterms:W3CDTF>1990-02</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Biophysics</dc:title>
</bqs:Journal>
<bqs:volume>87</bqs:volume>
<bqs:first_page>1461</bqs:first_page>
<bqs:last_page>1465</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
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</model>
