- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-05 13:07:36+13:00
- Desc:
- Added annotations to borghans_dupont_goldbeter_1997.cellml models
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/borghans_1997/rawfile/27b0c76f3984d60237968f86af1704b4a091e2b5/borghans_dupont_goldbeter_1997c.cellml
<?xml version='1.0'?>
<model name="borghans_model_1997c" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<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>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This CellML model runs in both OpenCell and COR to reproduce the published output (figure 12). The units have been checked and they are consistent.</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_1997c.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of the two-pool model for complex Ca2+ oscillations.</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 -->
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</component>
<component cmeta:id="Ca_component" name="Ca">
<variable name="time" private_interface="out" public_interface="in" units="min"/>
<!-- Species -->
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<variable initial_value="0.0" name="Y" private_interface="out" units="uM"/>
<variable initial_value="0.5" name="X" private_interface="out" units="uM"/>
<!-- Flux -->
<variable name="V_in" private_interface="in" units="uM_per_min"/>
<variable name="V_2i" private_interface="in" units="uM_per_min"/>
<variable name="V_3i" private_interface="in" units="uM_per_min"/>
<variable name="V_2s" private_interface="in" units="uM_per_min"/>
<variable name="V_3s" private_interface="in" units="uM_per_min"/>
<!-- Rate constants -->
<variable initial_value="0.5" name="K_f" units="per_min"/>
<variable initial_value="1" name="K" units="per_min"/>
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<eq/>
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<diff/>
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<ci>V_2i</ci>
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<ci>V_3i</ci>
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<ci>K_f</ci>
<ci>Y</ci>
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<apply>
<minus/>
<ci>V_2s</ci>
</apply>
<ci>V_3s</ci>
<apply>
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<eq/>
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<diff/>
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<apply>
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<apply>
<minus/>
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<ci>K_f</ci>
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<eq/>
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<minus/>
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</apply>
<apply>
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<times/>
<ci>K_f</ci>
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</apply>
</apply>
</math>
</component>
<component cmeta:id="Ca_flux_component" name="Ca_flux">
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<variable initial_value="1" 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="X" 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_2i" private_interface="in" public_interface="out" units="uM_per_min"/>
<variable name="V_3i" private_interface="in" public_interface="out" units="uM_per_min"/>
<variable name="V_2s" private_interface="in" public_interface="out" units="uM_per_min"/>
<variable name="V_3s" private_interface="in" public_interface="out" units="uM_per_min"/>
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<component name="V_in">
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<variable initial_value="0.012" name="v_1" units="uM_per_min"/>
<variable name="beta" public_interface="in" units="dimensionless"/>
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<plus/>
<ci>v_0</ci>
<apply>
<times/>
<ci>v_1</ci>
<ci>beta</ci>
</apply>
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<power/>
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<variable name="Y" public_interface="in" units="uM"/>
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<variable name="V_2s" public_interface="out" units="uM_per_min"/>
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<eq/>
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<times/>
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<divide/>
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<power/>
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<cn cellml:units="dimensionless" xmlns:cellml="http://www.cellml.org/cellml/1.0#">2</cn>
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<apply>
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<!-- groups -->
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<component_ref component="Ca_flux">
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<component_ref component="V_2i"/>
<component_ref component="V_3i"/>
<component_ref component="V_2s"/>
<component_ref component="V_3s"/>
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<!-- connections -->
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<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca" component_2="Ca_flux"/>
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<map_variables variable_1="V_3s" variable_2="V_3s"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="Y" variable_2="Y"/>
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<connection>
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<map_variables variable_1="V_in" variable_2="V_in"/>
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<connection>
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<map_variables variable_1="V_2i" variable_2="V_2i"/>
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<connection>
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<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="Y" variable_2="Y"/>
<map_variables variable_1="V_3i" variable_2="V_3i"/>
</connection>
<connection>
<map_components component_1="Ca_flux" component_2="V_2s"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="V_2s" variable_2="V_2s"/>
</connection>
<connection>
<map_components component_1="Ca_flux" component_2="V_3s"/>
<map_variables variable_1="X" variable_2="X"/>
<map_variables variable_1="V_3s" variable_2="V_3s"/>
<map_variables variable_1="beta" variable_2="beta"/>
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<rdf:Description rdf:nodeID="n1">
<rdf:type>
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<title xml:lang="en" xmlns="http://purl.org/dc/elements/1.1/">Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms (Model C)</title>
<creator xmlns="http://purl.org/dc/elements/1.1/">
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