- Author:
- Mona Zhu <devnull@localhost>
- Date:
- 2011-01-21 10:25:06+13:00
- Desc:
- Adding 1.1 models
- Permanent Source URI:
- https://models.cellml.org/workspace/dupont_goldbeter_1992/rawfile/334070f282db73bbab7c5dc4f82171a26be5820f/dupont_1992b.cellml
<?xml version="1.0"?>
<!-- FILE : dupont_1992b.cellml
CREATED : 27th November 2009
LAST MODIFIED : 1st December 2009
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Dupont and Goldbetter's 1992 mathematical model of protein phosphorylation driven by intracellular calcium oscillations.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="dupont_1992b" name="dupont_1992b" 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>Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis</title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The 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 and Goldbeter's 1992 paper. This file is known to run in PCEnv and COR, and variables for constants (vMK) can be altered to produce figure4b, c and figure5b and c (the ratio vMK/vP is held constant at vMK/vP = 20/0.89). The current parameterization is set to reproduce 4b with vMK=100 (note the erratum received in 1995: wT=10 not 1, to replicate figure 5. Initial conditions for Z, Y and Wstar were set by letting the model settle into a steady state.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>Abstract: Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca2+-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca2+-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations.</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="dupont_1992.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the cell model.</caption>
</informalfigure>
<para>The original paper reference is cited below:</para>
<para>
Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis, Dupont G, Goldbeter A 1992, <emphasis>Biophysical Chemistry</emphasis>
41, 257-270. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/1316185">PubMedID: 1316185</ulink>
</para>
</sect1>
</article>
</documentation>
<!--units defined-->
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="liter"/>
</units>
<units name="minute">
<unit multiplier="60" units="second"/>
</units>
<units name="per_minute">
<unit exponent="-1" units="minute"/>
</units>
<units name="micromolar_min">
<unit units="micromolar"/>
<unit units="per_minute"/>
</units>
<!--components-->
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<variable name="VM3" initial_value="500" units="micromolar_min"/>
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<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="minute"/>
<variable name="v0" initial_value="1" units="micromolar_min"/>
<variable name="v1beta" initial_value="2.4" units="micromolar_min"/>
<variable name="v2" public_interface="in" units="micromolar_min"/>
<variable name="v3" public_interface="in" units="micromolar_min"/>
<variable name="kf" public_interface="in" units="per_minute"/>
<variable name="k" public_interface="in" units="per_minute"/>
<variable name="Y" public_interface="in" units="micromolar"/>
<variable name="Z" cmeta:id="Z" initial_value="0.2281" public_interface="out" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
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<ci>time</ci>
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<ci>Z</ci>
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<minus/>
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<ci>v0</ci>
<ci>v1beta</ci>
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<ci>v2</ci>
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<ci>v3</ci>
<apply>
<times/>
<ci>kf</ci>
<ci>Y</ci>
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</apply>
<apply>
<times/>
<ci>k</ci>
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</math>
</component>
<component name="insensitive_pool" cmeta:id="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="minute"/>
<variable name="v2" public_interface="in" units="micromolar_min"/>
<variable name="v3" public_interface="in" units="micromolar_min"/>
<variable name="kf" public_interface="in" units="per_minute"/>
<variable name="Y" cmeta:id="Y" initial_value="1.454" public_interface="out" units="micromolar"/>
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<ci>time</ci>
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<ci>v2</ci>
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<apply>
<times/>
<ci>kf</ci>
<ci>Y</ci>
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</apply>
</apply>
</math>
</component>
<component name="phosphorylation" cmeta:id="phosphorylation">
<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="#phosphorylation">This component incorporates the reversible phosphorylation by taking into account a protein substrate (total amount denoted by WT)</rdf:Description>
<rdf:Description rdf:about="#Wstar">The fraction of phosphorylated protein (Wstar = [Wstar] /[WT])</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="minute"/>
<variable name="K1" initial_value="0.01" units="dimensionless"/>
<variable name="K2" initial_value="0.01" units="dimensionless"/>
<variable name="WT" initial_value="10" units="micromolar"/>
<variable name="vP" units="micromolar_min"/>
<variable name="vK" private_interface="in" units="micromolar_min"/>
<variable name="Z" private_interface="out" public_interface="in" units="micromolar"/>
<variable name="vMK" private_interface="in" units="micromolar_min"/>
<variable name="Wstar" cmeta:id="Wstar" initial_value="0.8916" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>vP</ci>
<apply>
<times/>
<ci>vMK</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.89</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">20</cn>
</apply>
</apply>
</apply>
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<eq/>
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<diff/>
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<ci>time</ci>
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<ci>Wstar</ci>
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<ci>WT</ci>
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<ci>vK</ci>
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<minus/>
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<ci>Wstar</ci>
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<minus/>
<apply>
<plus/>
<ci>K1</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<ci>Wstar</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>Wstar</ci>
<apply>
<plus/>
<ci>K2</ci>
<ci>Wstar</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="kinase_reaction" cmeta:id="kinase_reaction">
<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="#kinase_reaction">This component gives the expression for the kinase reaction rate (vK) assuming kinase is activated by cytosolic Ca2+. In this model (dupont_1992b) the ratio vMK/vP is held constant at vMK/vP = 20/0.89</rdf:Description>
<rdf:Description rdf:about="#vK">kinase reaction rate</rdf:Description>
<rdf:Description rdf:about="#vMK">maximal rate of the kinase</rdf:Description>
</rdf:RDF>
<variable initial_value="100" name="vMK" cmeta:id="vMK" public_interface="out" units="micromolar_min"/>
<variable initial_value="1" name="Ka" units="micromolar"/>
<variable initial_value="4" name="q" units="dimensionless"/>
<variable name="Z" public_interface="in" units="micromolar"/>
<variable name="vK" cmeta:id="vK" public_interface="out" units="micromolar_min"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<ci>vK</ci>
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<times/>
<ci>vMK</ci>
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<divide/>
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<power/>
<ci>Z</ci>
<ci>q</ci>
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<plus/>
<apply>
<power/>
<ci>Ka</ci>
<ci>q</ci>
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<apply>
<power/>
<ci>Z</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--groups-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="phosphorylation">
<component_ref component="kinase_reaction"/>
</component_ref>
</group>
<!--connections-->
<connection>
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<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="insensitive_pool"/>
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</connection>
<connection>
<map_components component_1="environment" component_2="phosphorylation"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="parameters" component_2="cytosol"/>
<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"/>
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<connection>
<map_components component_1="parameters" component_2="insensitive_pool"/>
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<map_variables variable_1="kf" variable_2="kf"/>
<map_variables variable_1="Y" variable_2="Y"/>
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<connection>
<map_components component_1="insensitive_pool" component_2="cytosol"/>
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<connection>
<map_components component_1="cytosol" component_2="phosphorylation"/>
<map_variables variable_1="Z" variable_2="Z"/>
</connection>
<connection>
<map_components component_1="phosphorylation" component_2="kinase_reaction"/>
<map_variables variable_1="vK" variable_2="vK"/>
<map_variables variable_1="Z" variable_2="Z"/>
<map_variables variable_1="vMK" variable_2="vMK"/>
</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:title> Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis (Model B)</dc:title>
<dc:creator rdf:parseType="Resource">
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<vCard:Family>Choi</vCard:Family>
<vCard:Given>Ethan</vCard:Given>
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<rdf:Description rdf:about="#dupont_1992b">
<dc:title> Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis</dc:title>
<cmeta:comment rdf:parseType="Resource">
<rdf:value> This is the CellML description of Dupont and Goldbeter's mathematical model Protein phosphorylation driven by intracellular calcium oscillations. </rdf:value>
<dc:creator rdf:parseType="Resource">
<vCard:FN>Ethan Choi</vCard:FN>
</dc:creator>
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<!-- Keyword(s) -->
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:Bag>
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<rdf:li>Calcium regulation</rdf:li>
<rdf:li>Kinase</rdf:li>
<rdf:li>Calmodulin</rdf:li>
<rdf:li>Frequency coding</rdf:li>
<rdf:li>Biochemical oscillations</rdf:li>
</rdf:Bag>
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<vCard:Family>Dupont</vCard:Family>
<vCard:Given>Genevieve</vCard:Given>
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<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Goldbeter</vCard:Family>
<vCard:Given>Albert</vCard:Given>
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<dc:title> Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis </dc:title>
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<dcterms:W3CDTF>1992-04</dcterms:W3CDTF>
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<dc:title>Biophysical Chemistry</dc:title>
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<bqs:volume>42</bqs:volume>
<bqs:first_page>257</bqs:first_page>
<bqs:last_page>270</bqs:last_page>
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</model>
