- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-05-23 23:06:22+12:00
- Desc:
- committing version02 of goldbeter_1991
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/goldbeter_1991/rawfile/d2bbfb040e8200d89f5ff03a2c085b00fac0c6f1/goldbeter_1991.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : goldbeter_model_1991.xml
CREATED : 24th May 2007
LAST MODIFIED : 24th May 2007
AUTHOR : James Lawson
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification. This file is known to run in PCEnv.
DESCRIPTION : This file contains a CellML description of Albert Goldbeter's
1991 minimal model for the mitotic oscillator invoving cyclin and cdc2 kinase.
CHANGES: James Lawson rebuilt this model, using the differential expressions in the paper to define the reactions, rather than using reaction elements.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="goldbeter_1991_version01" name="goldbeter_1991_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Minimal Cascade Model for the Mitotic Oscillator Involving Cyclin and cdc2 Kinase</title>
<author>
<firstname>James</firstname>
<surname>Lawson</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 by James Lawson (24/05/07) with the differential expressions in Goldbeter's 1991 paper, instead of reaction elements. The output of the model is similar to that shown in the paper. This file is known to run in PCEnv.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Better understanding of the molecular mechanisms underlying the cell cycle has given rise to the theory that there may be one universal, homologous mechanism controlling the onset of mitosis. Studies with yeast and embryonic cells suggest that mitosis is triggered by the periodic activation of cdc2 kinase. Using this experimental data, Albert Goldbeter developed a minimal mathematical model which describes the mitotic oscillator involving cyclin and cdc2 kinase (see <xref linkend="fig_reaction_diagram"/> below). This model is based on the situation in amphibian embryos. As cyclin, a protein signalling molecule, accumulates and exceeds a certain threshold concentration, mitosis is triggered. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation. In the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. Since cyclin activates cdc2 kinase, and in turn, active cdc2 kinase indirectly triggers the degradation of cyclin, cyclin oscillations may originate from a negative feedback loop.
</para>
<para>
Model simulations support this theory. Oscillations can arise as long as thresholds exist in the activation of cdc2 kinase by cyclin, and in the activation of cyclin protease by cdc2 kinase. Time lags associated with these thresholds, together with the delayed negative feedback from the cdc2-induced cyclin degradation, can readily lead to sustained mitotic oscillations.
</para>
<para>
Albert Goldbeter acknowledges that the model is a simplification of the biological situation, and it is based on a number of assumptions, but in its simplified form, the model highlights the conditions in which the cyclin-cdc2 kinase system can operate as an autonomous oscillator. The model is also useful in considering the mechanisms underlying the more complex situation in yeast and somatic cells. By highlighting the ways in which oscillations may be stopped, the models suggests how the products of other genes could play a role in the control of mitosis.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.pnas.org/cgi/content/abstract/88/20/9107">A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase</ulink>, Albert Goldbeter, 1991, <ulink url="http://www.pnas.org/">
<emphasis>Proceedings of the National Academy of Sciences</emphasis>
</ulink>, 88, 9107-9111. (A <ulink url="http://www.pnas.org/cgi/reprint/88/20/9107.pdf">PDF version</ulink> of the article is available to subscribers on the journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=1833774&amp;dopt=Abstract">PubMed ID: 1833774</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="reaction_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>Minimal cascade model for the mitotic oscillations between cyclin and cdc2 kinase (M) during the cell cycle. X represents the fraction of active (phosphorylated) cyclin protease. * represents the fraction of inactive enzymes.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model.
-->
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="minute" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<component name="environment">
<variable units="minute" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component cmeta:id="C" name="C">
<variable units="micromolar" public_interface="out" name="C" initial_value="0.01"/>
<variable units="second_order_rate_constant" public_interface="in" name="Vd" initial_value=""/>
<variable units="micromolar" public_interface="in" name="Kd" initial_value=""/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="d(C)/d(time)">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>Vi</ci>
<apply>
<times/>
<ci>Vd</ci>
<ci>X</ci>
<apply>
<divide/>
<ci>C</ci>
<apply>
<plus/>
<ci>Kd</ci>
<ci>C</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kd</ci>
<ci>C</ci>
</apply>
</apply>
</apply>
</math>
<variable units="dimensionless" public_interface="in" name="X"/>
<variable units="second_order_rate_constant" public_interface="in" name="Vi" initial_value=""/>
<variable units="first_order_rate_constant" public_interface="in" name="kd"/>
</component>
<component cmeta:id="M" name="M">
<rdf:RDF>
<rdf:Description rdf:about="M">
<dc:title>M</dc:title>
<dcterms:alternative>
fraction of active cdc2 kinase
</dcterms:alternative>
<dcterms:alternative>E3</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="M" initial_value="0.01"/>
<variable units="minute" public_interface="in" name="V1"/>
<variable units="micromolar" public_interface="in" name="K1"/>
<variable units="first_order_rate_constant" public_interface="in" name="V2"/>
<variable units="micromolar" public_interface="in" name="K2"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="d(M)/d(time)">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>V1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>M</ci>
</apply>
<ci>K1</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>M</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>V2</ci>
<apply>
<divide/>
<ci>M</ci>
<apply>
<minus/>
<ci>K2</ci>
<ci>M</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="X" name="X">
<rdf:RDF>
<rdf:Description rdf:about="X">
<dc:title>X</dc:title>
<dcterms:alternative>
fraction of active cyclin protease
</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="X" initial_value="0.01"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="K3"/>
<variable units="micromolar" public_interface="in" name="K4"/>
<variable units="first_order_rate_constant" public_interface="in" name="V3"/>
<variable units="first_order_rate_constant" public_interface="in" name="V4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="d(X)/d(time)">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>V3</ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>X</ci>
</apply>
<apply>
<plus/>
<ci>K3</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>X</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>V4</ci>
<apply>
<divide/>
<ci>X</ci>
<apply>
<plus/>
<ci>K4</ci>
<ci>X</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="kinetics">
<variable units="first_order_rate_constant" public_interface="out" name="V1"/>
<variable units="first_order_rate_constant" public_interface="out" name="V3"/>
<variable units="micromolar" public_interface="in" name="C"/>
<variable units="micromolar" name="Kc" initial_value="0.5"/>
<variable units="dimensionless" public_interface="in" name="M"/>
<variable units="first_order_rate_constant" name="VM1" initial_value="3"/>
<variable units="first_order_rate_constant" name="VM3" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="V1">
<apply>
<eq/>
<ci>V1</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>C</ci>
<apply>
<plus/>
<ci>Kc</ci>
<ci>C</ci>
</apply>
</apply>
<ci>VM1</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="V3">
<apply>
<eq/>
<ci>V3</ci>
<apply>
<times/>
<ci>M</ci>
<ci>VM3</ci>
</apply>
</apply>
</math>
<variable units="first_order_rate_constant" public_interface="out" name="V2" initial_value="1.5"/>
<variable units="first_order_rate_constant" public_interface="out" name="V4" initial_value="0.5"/>
<variable units="second_order_rate_constant" public_interface="out" name="Vd" initial_value="0.25"/>
<variable units="micromolar" public_interface="out" name="Kd" initial_value="0.02"/>
<variable units="micromolar" public_interface="out" name="K1" initial_value="0.005"/>
<variable units="micromolar" public_interface="out" name="K2" initial_value="0.005"/>
<variable units="micromolar" public_interface="out" name="K3" initial_value="0.005"/>
<variable units="micromolar" public_interface="out" name="K4" initial_value="0.005"/>
<variable units="second_order_rate_constant" public_interface="out" name="Vi" initial_value="0.025"/>
<variable units="first_order_rate_constant" public_interface="out" name="kd" initial_value="0.01"/>
</component>
<connection>
<map_components component_2="environment" component_1="C"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="M"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="X"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C" component_1="kinetics"/>
<map_variables variable_2="Vi" variable_1="Vi"/>
<map_variables variable_2="Vd" variable_1="Vd"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="kd" variable_1="kd"/>
</connection>
<connection>
<map_components component_2="C" component_1="X"/>
<map_variables variable_2="X" variable_1="X"/>
</connection>
<connection>
<map_components component_2="M" component_1="kinetics"/>
<map_variables variable_2="V1" variable_1="V1"/>
<map_variables variable_2="V2" variable_1="V2"/>
<map_variables variable_2="K1" variable_1="K1"/>
<map_variables variable_2="K2" variable_1="K2"/>
</connection>
<connection>
<map_components component_2="X" component_1="kinetics"/>
<map_variables variable_2="V3" variable_1="V3"/>
<map_variables variable_2="V4" variable_1="V4"/>
<map_variables variable_2="K3" variable_1="K3"/>
<map_variables variable_2="K4" variable_1="K4"/>
</connection>
<connection>
<map_components component_2="kinetics" component_1="C"/>
<map_variables variable_2="C" variable_1="C"/>
</connection>
<connection>
<map_components component_2="kinetics" component_1="M"/>
<map_variables variable_2="M" variable_1="M"/>
</connection>
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<rdf:value>This model was rebuilt without reaction components by James Lawson, 24/05/07. The output is not satisfactory, however. Contact with the model author is pending.</rdf:value>
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<dcterms:W3CDTF>1991-10</dcterms:W3CDTF>
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<dc:title>Proceedings of the National Academy of Sciences USA</dc:title>
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<dc:title>A Minimal Cascade Model for the Mitotic Oscillator Involving Cyclin
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model for the mitotic oscillator invoving cyclin and cdc2 kinase.</rdf:value>
</rdf:Description>
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<dcterms:alternative>phosphatase</dcterms:alternative>
<dc:title>E1</dc:title>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dc:title>Albert Goldbeter's 1991 minimal model for the mitotic oscillator
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