- Author:
- Ethan Choi <mcho099@aucklanduni.ac.nz>
- Date:
- 2009-12-02 12:14:01+13:00
- Desc:
- Created 2 models for Dupont 1991. Models are complete and run on PCEnv and COR.
1991a replicates figure 2 for constant beta. 1991b replicates figure 4 for a transient beta function.
- Permanent Source URI:
- http://models.cellml.org/workspace/dupont_berridge_goldbeter_1991/rawfile/ca8d2b700c53331dc57fd9b687246df810673a41/dupont_1991b.cellml
<?xml version="1.0"?>
<!-- FILE : dupont_1991b.cellml
CREATED : 25th November 2009
LAST MODIFIED : 26th November 2009
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Dupont, Berridge and Goldbetter's 1991 mathematical model of investigating properties of a minimal for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="Dupont_1991b" name="Dupont_1991b" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Signal-induced Ca2+ oscillations: Properties of a model based on (Ca2+)-induced Ca2+ release</title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This model has been built with the differential expressions in Dupont's 1991 paper. This CellML model is known to run in PCEnv and COR to replicate the published results for the response to a transient increase in InsP3 using a pulse and decay of beta at tp=4 (figure 4B).</para>
</section>
<sect1 id="sec_structure">
<title>Paper Abstract</title>
<para>We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.</para>
<para>The complete original paper reference is cited below:</para>
<para>
Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release, Dupont G, Berridge MJ, Goldbeter A, 1991, <emphasis>Cell Calcium</emphasis>
12, 73-85. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/1647878">PubMedID: 1647878</ulink>
</para>
</sect1>
</article>
</documentation>
<!--units defined-->
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="liter"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="micromolar_s">
<unit units="micromolar"/>
<unit units="per_second"/>
</units>
<!--components-->
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="parameters" cmeta:id="parameters">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#parameters">This component stores and calculates various parameters for the cell components</rdf:Description>
</rdf:RDF>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable name="v0" initial_value="1" public_interface="out" units="micromolar_s"/>
<variable name="v1" initial_value="7.3" public_interface="out" units="micromolar_s"/>
<variable name="v2" public_interface="out" units="micromolar_s"/>
<variable name="v3" public_interface="out" units="micromolar_s"/>
<variable name="beta" private_interface="in" public_interface="out" units="dimensionless"/>
<variable name="VM2" initial_value="65" units="micromolar_s"/>
<variable name="VM3" initial_value="500" units="micromolar_s"/>
<variable name="KR" initial_value="2" units="micromolar"/>
<variable name="KA" initial_value="0.9" units="micromolar"/>
<variable name="kf" initial_value="1" public_interface="out" units="per_second"/>
<variable name="k" initial_value="10" public_interface="out" units="per_second"/>
<variable name="K2" initial_value="1" units="micromolar"/>
<variable name="n" initial_value="2" units="dimensionless"/>
<variable name="m" initial_value="2" units="dimensionless"/>
<variable name="p" initial_value="4" units="dimensionless"/>
<variable name="Z" public_interface="in" units="micromolar"/>
<variable name="Y" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>VM2</ci>
<apply>
<power/>
<ci>Z</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K2</ci>
<ci>n</ci>
</apply>
<apply>
<power/>
<ci>Z</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v3</ci>
<apply>
<times/>
<ci>VM3</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>Y</ci>
<ci>m</ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>KR</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>KA</ci>
<ci>p</ci>
</apply>
<apply>
<power/>
<ci>Z</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cytosol" cmeta:id="cytosol">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#cytosol">This component stores information about the cytosolic Ca2+</rdf:Description>
<rdf:Description rdf:about="#Z">Ca2+ in the cytosol</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="second"/>
<variable name="v0" public_interface="in" units="micromolar_s"/>
<variable name="v1" public_interface="in" units="micromolar_s"/>
<variable name="v2" public_interface="in" units="micromolar_s"/>
<variable name="v3" public_interface="in" units="micromolar_s"/>
<variable name="kf" public_interface="in" units="per_second"/>
<variable name="k" public_interface="in" units="per_second"/>
<variable name="beta" public_interface="in" units="dimensionless"/>
<variable name="Z" cmeta:id="Z" initial_value="0.1" public_interface="out" units="micromolar"/>
<variable name="Y" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Z</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v0</ci>
<apply>
<times/>
<ci>v1</ci>
<ci>beta</ci>
</apply>
</apply>
<ci>v2</ci>
</apply>
<ci>v3</ci>
<apply>
<times/>
<ci>kf</ci>
<ci>Y</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k</ci>
<ci>Z</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="insensitive_pool">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#insensitive_pool">This component stores information about the InsP3-insensitive intracellular store and the Ca2+ in this pool</rdf:Description>
<rdf:Description rdf:about="#Y">Ca2+ in the intracellular Ca2+ pool</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="second"/>
<variable name="v2" public_interface="in" units="micromolar_s"/>
<variable name="v3" public_interface="in" units="micromolar_s"/>
<variable name="kf" public_interface="in" units="per_second"/>
<variable name="Y" cmeta:id="Y" initial_value="0.64" public_interface="out" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Y</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v2</ci>
<ci>v3</ci>
</apply>
<apply>
<times/>
<ci>kf</ci>
<ci>Y</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="beta_pulse" cmeta:id="beta_pulse">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_pulse">This component stores information about saturation function beta when it is given a transient function </rdf:Description>
<rdf:Description rdf:about="#beta">saturation function of the InsP3 receptor</rdf:Description>
<rdf:Description rdf:about="#tp">time of instantaneous increase in beta</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="second"/>
<variable name="betaf" initial_value="0.96" units="dimensionless"/>
<variable name="tp" cmeta:id="tp" initial_value="4" units="second"/>
<variable name="beta" cmeta:id="beta" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>beta</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>time</ci>
<ci>tp</ci>
</apply>
</piece>
<piece>
<apply>
<times/>
<ci>betaf</ci>
<apply>
<exp/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">-0.2</cn>
<apply>
<minus/>
<ci>time</ci>
<ci>tp</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>time</ci>
<ci>tp</ci>
</apply>
</piece>
</piecewise>
</apply>
</math>
</component>
<!--groups-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="parameters">
<component_ref component="beta_pulse"/>
</component_ref>
</group>
<!--connections-->
<connection>
<map_components component_1="environment" component_2="parameters"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="cytosol"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="insensitive_pool"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="insensitive_pool"/>
<map_variables variable_1="v2" variable_2="v2"/>
<map_variables variable_1="v3" variable_2="v3"/>
<map_variables variable_1="kf" variable_2="kf"/>
<map_variables variable_1="Y" variable_2="Y"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="cytosol"/>
<map_variables variable_1="v0" variable_2="v0"/>
<map_variables variable_1="v1" variable_2="v1"/>
<map_variables variable_1="v2" variable_2="v2"/>
<map_variables variable_1="v3" variable_2="v3"/>
<map_variables variable_1="kf" variable_2="kf"/>
<map_variables variable_1="k" variable_2="k"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="Z" variable_2="Z"/>
</connection>
<connection>
<map_components component_1="insensitive_pool" component_2="cytosol"/>
<map_variables variable_1="Y" variable_2="Y"/>
</connection>
<connection>
<map_components component_1="parameters" component_2="beta_pulse"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="beta" variable_2="beta"/>
</connection>
<!--rdf description-->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<foo xmlns="http://www.example.org/foo/bar/baz" />
<rdf:Description rdf:about="">
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Choi</vCard:Family>
<vCard:Given>Ethan</vCard:Given>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>mcho099@aucklanduni.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2009-11-25</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#Dupont_1991b">
<dc:title>Signal-induced Ca2+ oscillations: Properties of a model based on (Ca2+)-induced Ca2+ release </dc:title>
<cmeta:comment rdf:parseType="Resource">
<rdf:value> This is the CellML description of Dupont, Berridge, and Goldbeter's mathematical model of Ca2+ oscillations based on (Ca2+)-induced Ca2+ release. </rdf:value>
<dc:creator rdf:parseType="Resource">
<vCard:FN>Ethan Choi</vCard:FN>
</dc:creator>
</cmeta:comment>
<cmeta:species>Xenopus oocytes</cmeta:species>
<cmeta:bio_entity>Various cells</cmeta:bio_entity>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>Calcium Dynamics </rdf:li>
<rdf:li>Ca2+</rdf:li>
<rdf:li>Insp3</rdf:li>
<rdf:li>cytosol</rdf:li>
<rdf:li>insensitive</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>1647878</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Dupont</vCard:Family>
<vCard:Given>G</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Berridge</vCard:Family>
<vCard:Given>M</vCard:Given>
<vCard:Other>J</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Goldbetter</vCard:Family>
<vCard:Given>A</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title> Signal-induced Ca2+ oscillations: Properties of a model based on (Ca2+)-induced Ca2+ release </dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1991-02</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Cell Calcium</dc:title>
</bqs:Journal>
<bqs:volume>12</bqs:volume>
<bqs:first_page>73</bqs:first_page>
<bqs:last_page>85</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
</model>
