- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-01-08 13:55:57+13:00
- Desc:
- Added cmeta:ids to CellMl file and added session file
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/borghans_1997/rawfile/2e1c8a539c0c5789a9cd96551da70ff81d7e05a1/borghans_dupont_goldbeter_1997b.cellml
<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:base="file:///Users/Hanne/Desktop/repository%20models/borghans_1997/borghans_dupont_goldbeter_1997b.cellml" cmeta:id="borghans_model_1997b" name="borghans_model_1997b">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms</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 8 and 9)</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: Intracellular Ca2+ oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca2+-induced Ca2+ release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca2+ oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca2+ spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca2+ oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca2+-release channel on a unique intracellular store at high cytosolic Ca2+ concentrations, (ii) taking into account the Ca2+-activated degradation of inositol 1,4,5-trisphosphate (IP3), or (iii) considering explicitly the evolution of the Ca2+ concentration in two different pools, one sensitive and the other one insensitive to IP3. Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP3 into account shows chaotic behaviour.</para>
<para>Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms, Jose A.M. Borghans, Genevieve Dupont, Albert Goldbeter, 1997, <emphasis>Biophysical Chemistry</emphasis>, 66, 25-41. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=17029867&dopt=Abstract">PubMed ID: 17029867</ulink></para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="borghans_1997b.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of the one-pool model based on CICR with Ca2+-stimulated degradation of IP3.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!-- Units -->
<units name="min">
<!-- time: minute -->
<unit multiplier="60" units="second"/>
</units>
<units name="per_min">
<!-- per time: per minute -->
<unit exponent="-1" units="min"/>
</units>
<units name="uM">
<!-- concentration: micromolar -->
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="per_uM4">
<!-- "Fudge factor": micromolar^-4 -->
<unit exponent="-4" units="uM"/>
</units>
<units name="uM_per_min">
<!-- flux: micromolar per minute -->
<unit units="uM"/>
<unit units="per_min"/>
</units>
<!-- Components -->
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="min"/>
</component>
<component cmeta:id="Ca_component" name="Ca">
<variable name="time" private_interface="out" public_interface="in" units="min"/>
<!-- Species -->
<variable cmeta:id="Z" initial_value="0.1" name="Z" private_interface="out" units="uM"/>
<variable cmeta:id="Y" initial_value="1.0" name="Y" private_interface="out" units="uM"/>
<!-- Flux -->
<variable name="V_in" private_interface="in" units="uM_per_min"/>
<variable name="V_2" private_interface="in" units="uM_per_min"/>
<variable name="V_3" private_interface="in" units="uM_per_min"/>
<!-- Rate constants -->
<variable initial_value="1" name="K_f" units="per_min"/>
<variable initial_value="10" name="K" units="per_min"/>
<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/>
<apply><minus/>
<ci>V_in</ci>
<ci>V_2</ci>
</apply>
<ci>V_3</ci>
<apply><minus/>
<apply><times/>
<ci>K_f</ci>
<ci>Y</ci>
</apply>
<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><minus/>
<apply><minus/>
<ci>V_2</ci>
<ci>V_3</ci>
</apply>
<apply><times/>
<ci>K_f</ci>
<ci>Y</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Ca_flux_component" name="Ca_flux">
<variable name="time" private_interface="out" public_interface="in" units="min"/>
<variable cmeta:id="beta" initial_value="0.5" name="beta" private_interface="out" units="dimensionless"/>
<variable name="Z" private_interface="out" public_interface="in" units="uM"/>
<variable name="Y" private_interface="out" public_interface="in" units="uM"/>
<variable name="V_in" private_interface="in" public_interface="out" units="uM_per_min"/>
<variable name="V_2" private_interface="in" public_interface="out" units="uM_per_min"/>
<variable name="V_3" private_interface="in" public_interface="out" units="uM_per_min"/>
</component>
<component cmeta:id="V_in_component" name="V_in">
<variable cmeta:id="V_in" name="V_in" public_interface="out" units="uM_per_min"/>
<variable cmeta:id="v_0" initial_value="2" name="v_0" units="uM_per_min"/>
<variable cmeta:id="v_1" initial_value="1" name="v_1" units="uM_per_min"/>
<variable name="beta" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="V_in_maths">
<apply id="V_in_eq"><eq/>
<ci>V_in</ci>
<apply><plus/>
<ci>v_0</ci>
<apply><times/>
<ci>v_1</ci>
<ci>beta</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="V_2_component" name="V_2">
<variable name="Z" public_interface="in" units="uM"/>
<variable cmeta:id="V_2_V_2" name="V_2" public_interface="out" units="uM_per_min"/>
<variable initial_value="6.5" name="V_M2" units="uM_per_min"/>
<variable initial_value="0.1" name="K_2" units="uM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="V_2_maths">
<apply id="V_2_eq"><eq/>
<ci>V_2</ci>
<apply><times/>
<ci>V_M2</ci>
<apply><divide/>
<apply><power/>
<ci>Z</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_2</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply><power/>
<ci>Z</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="V_3_component" name="V_3">
<variable name="time" private_interface="out" public_interface="in" units="min"/>
<variable name="Z" private_interface="out" public_interface="in" units="uM"/>
<variable name="Y" public_interface="in" units="uM"/>
<variable name="A" private_interface="in" units="uM"/>
<variable cmeta:id="V_3" name="V_3" public_interface="out" units="uM_per_min"/>
<variable cmeta:id="K_y" initial_value="0.2" name="K_y" units="uM"/>
<variable cmeta:id="K_z" initial_value="0.3" name="K_z" units="uM"/>
<variable cmeta:id="K_a" initial_value="0.2" name="K_a" units="uM"/>
<variable initial_value="19.5" name="V_M3" units="uM_per_min"/>
<variable name="beta" private_interface="out" public_interface="in" 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>A</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_a</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply><power/>
<ci>A</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
<apply><divide/>
<apply><power/>
<ci>Y</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_y</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply><power/>
<ci>Y</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply><divide/>
<apply><power/>
<ci>Z</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_z</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply><power/>
<ci>Z</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A_component" name="A">
<variable name="time" public_interface="in" units="min"/>
<variable name="Z" public_interface="in" units="uM"/>
<variable cmeta:id="A" initial_value="0.5" name="A" public_interface="out" units="uM"/>
<variable name="beta" public_interface="in" units="dimensionless"/>
<variable cmeta:id="upsilon_p" initial_value="2.5" name="upsilon_p" units="uM_per_min"/>
<variable cmeta:id="upsilon_d" initial_value="80" name="upsilon_d" units="uM_per_min"/>
<variable cmeta:id="K_p" initial_value="1" name="K_p" units="uM"/>
<variable cmeta:id="K_d" initial_value="0.4" name="K_d" units="uM"/>
<variable initial_value="4" name="n" units="dimensionless"/>
<variable cmeta:id="epsilon" initial_value="0.1" name="epsilon" units="per_min"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="A_maths">
<apply id="dA/dt_eq"><eq/>
<apply><diff/>
<bvar><ci>time</ci></bvar>
<ci>A</ci>
</apply>
<apply><minus/>
<apply><minus/>
<apply><times/>
<ci>beta</ci>
<ci>upsilon_p</ci>
</apply>
<apply><times/>
<ci>upsilon_d</ci>
<apply><divide/>
<apply><power/>
<ci>A</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_p</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply><power/>
<ci>A</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply><divide/>
<apply><power/>
<ci>Z</ci>
<ci>n</ci>
</apply>
<apply><plus/>
<apply><power/>
<ci>K_d</ci>
<ci>n</ci>
</apply>
<apply><power/>
<ci>Z</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><times/>
<ci>epsilon</ci>
<ci>A</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- groups -->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="Ca">
<component_ref component="Ca_flux">
<component_ref component="V_in"/>
<component_ref component="V_2"/>
<component_ref component="V_3">
<component_ref component="A"/>
</component_ref>
</component_ref>
</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="Ca_flux"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V_in" variable_2="V_in"/>
<map_variables variable_1="V_2" variable_2="V_2"/>
<map_variables variable_1="V_3" variable_2="V_3"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="Y" variable_2="Y"/>
</connection>
<connection>
<map_components component_1="Ca_flux" component_2="V_in"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="V_in" variable_2="V_in"/>
</connection>
<connection>
<map_components component_1="Ca_flux" component_2="V_2"/>
<map_variables variable_1="V_2" variable_2="V_2"/>
<map_variables variable_1="Z" variable_2="Z"/>
</connection>
<connection>
<map_components component_1="Ca_flux" component_2="V_3"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="V_3" variable_2="V_3"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="Y" variable_2="Y"/>
</connection>
<connection>
<map_components component_1="V_3" component_2="A"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="A" variable_2="A"/>
<map_variables variable_1="beta" variable_2="beta"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="#borghans_model_1997b"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms</title><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n1"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n2"/></reference></rdf:Description><rdf:Description rdf:nodeID="n3"><rdf:value xml:lang="en">mark@hanna.net.nz</rdf:value><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n4"><rdf:_2><rdf:Description rdf:nodeID="n5"/></rdf:_2><rdf:_3><rdf:Description rdf:nodeID="n6"/></rdf:_3><rdf:_1><rdf:Description rdf:nodeID="n7"/></rdf:_1><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n8"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n9"/></N></rdf:Description><rdf:Description rdf:nodeID="n10"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">1997-01-16</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n1"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n11"/></subject></rdf:Description><rdf:Description rdf:nodeID="n12"><rdf:_5 xml:lang="en">Calcium Dynamics</rdf:_5><rdf:_2 xml:lang="en">Calcium Oscillations</rdf:_2><rdf:_4 xml:lang="en">Chaos</rdf:_4><rdf:_3 xml:lang="en">Bursting</rdf:_3><rdf:_1 xml:lang="en">Calcium Signalling</rdf:_1><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n7"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n13"/></Person></rdf:Description><rdf:Description rdf:nodeID="n14"><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n15"/></ORG><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n16"/></N><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n3"/></EMAIL></rdf:Description><rdf:Description rdf:nodeID="n17"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Biophysical Chemistry</title></rdf:Description><rdf:Description rdf:nodeID="n2"><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n18"/></JournalArticle><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">17029867</Pubmed_id></rdf:Description><rdf:Description rdf:nodeID="n13"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n19"/></N></rdf:Description><rdf:Description rdf:nodeID="n20"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n21"/></N></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n14"/></creator><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n22"/></created></rdf:Description><rdf:Description rdf:nodeID="n9"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Albert</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Goldbeter</Family></rdf:Description><rdf:Description rdf:nodeID="n15"><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Auckland Bioengineering Institute</Orgunit></rdf:Description><rdf:Description rdf:nodeID="n23"><rdf:type><rdf:Description rdf:about="http://www.example.org/foo/bar/bazfoo"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n6"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n8"/></Person></rdf:Description><rdf:Description rdf:nodeID="n11"><rdf:value><rdf:Description rdf:nodeID="n12"/></rdf:value></rdf:Description><rdf:Description rdf:nodeID="n16"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">James</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Mark</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Hanna</Family></rdf:Description><rdf:Description rdf:nodeID="n18"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms</title><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n10"/></issued><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n4"/></creator><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n17"/></Journal><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">66</volume><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">41</last_page><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">25</first_page></rdf:Description><rdf:Description rdf:nodeID="n22"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2009-11-30</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n5"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n20"/></Person></rdf:Description><rdf:Description rdf:nodeID="n19"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">O.M.</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Jose</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Borghans</Family></rdf:Description><rdf:Description rdf:nodeID="n21"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Genevieve</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Dupont</Family></rdf:Description></rdf:RDF></model>
