- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:22:43+12:00
- Desc:
- committing version01 of tyson_1991
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/tyson_1991/rawfile/31e71d0e397c7a62f9b6149670f4353ff7750fad/tyson_1991.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : tyson_model_1991.xml
CREATED : 21st April 2003
LAST MODIFIED : 21st April 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
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.
DESCRIPTION : This file contains a CellML description of John Tyson's
1991 model of the cell division cycle.
CHANGES:
--><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#" cmeta:id="tyson_1991_version01" name="tyson_1991_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Cell Division Cycle: cdc2 and Cyclin Interactions</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The cell cycle is an ordered set of events which results in cell growth and division into two identical daughter cells (somatic cell division). This sequence of specific events includes cell growth, protein, DNA, and organelle replication, and nuclear (chromosomes separate during mitosis) and cellular (the cytoplasm divides during cytokinesis) division. The control of cell division, and thus tissue growth, is complex. Maturation promoting factor (MPF) plays an important role in the control of the cell cycle. This enzyme is a heterodimer composed of cyclin and a protein kinase called cdc2. The interplay between cyclin and cdc2 in generating MPF activity is understood in some detail (see <xref linkend="fig_cell_diagram"/> below). Cyclin and cdc2 bind to form an inactive MPF complex. This complex is then activated by auto-dephosphorylation of the cdc2 subunit. Active MPF stimulates several processes which are known to be essential for nuclear and cell division. MPF then dissociates and cyclin is degraded. The cycle then repeats itself. </para>
<para>
In a study published by John Tyson in 1991, a mathematical model of the cell cycle is developed. The author acknowledges that the model is a simplification of the real biological situation, but he explains that it is a sufficient first approximation to the cell cycle regulatory network. Agreement between experimental data and simulation results provide support for the overall scheme of the model, even if specific details are questioned. However, as understanding of the mechanisms underlying cell cycle regulation improves, mathematical models will play an increasingly important role in integrating molecular level events with cell level division.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.pnas.org/cgi/content/abstract/88/16/7328">Modeling the cell division cycle: cdc2 and cyclin interactions</ulink>, John J. Tyson, 1991, <ulink url="http://www.pnas.org/">
<emphasis>Proceedings of the National Academy of Sciences</emphasis>
</ulink>, 88, 7328-7332. (A <ulink url="http://www.pnas.org/cgi/reprint/88/16/7328.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&db=PubMed&list_uids=1831270&dopt=Abstract">PubMed ID: 1831270</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="tyson_1991.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the interactions between cyclin and cdc2 during the cell cycle.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model.
-->
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</units>
<units name="flux">
<unit units="millimolar"/>
<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="millimolar" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="third_order_rate_constant">
<unit units="millimolar" exponent="-2"/>
<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="C2" name="C2">
<variable units="millimolar" public_interface="out" name="C2"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn_6"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn_8"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn_9"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C2</ci>
</apply>
<apply>
<plus/>
<ci>delta_C2_rxn_6</ci>
<ci>delta_C2_rxn_8</ci>
<ci>delta_C2_rxn_9</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="CP" name="CP">
<rdf:RDF>
<rdf:Description rdf:about="CP">
<dc:title>CP</dc:title>
<dcterms:alternative>cdc2-P</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="CP"/>
<variable units="flux" public_interface="in" name="delta_CP_rxn_8"/>
<variable units="flux" public_interface="in" name="delta_CP_rxn_9"/>
<variable units="flux" public_interface="in" name="delta_CP_rxn_3"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CP</ci>
</apply>
<apply>
<plus/>
<ci>delta_CP_rxn_8</ci>
<ci>delta_CP_rxn_9</ci>
<ci>delta_CP_rxn_3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="pM" name="pM">
<rdf:RDF>
<rdf:Description rdf:about="pM">
<dc:title>pM</dc:title>
<dcterms:alternative>preMPF</dcterms:alternative>
<dcterms:alternative>P-cyclin-cdc2-P</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="pM"/>
<variable units="flux" public_interface="in" name="delta_pM_rxn_3"/>
<variable units="flux" public_interface="in" name="delta_pM_rxn_4"/>
<variable units="flux" public_interface="in" name="delta_pM_rxn_5"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pM</ci>
</apply>
<apply>
<plus/>
<ci>delta_pM_rxn_3</ci>
<ci>delta_pM_rxn_4</ci>
<ci>delta_pM_rxn_5</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="M" name="M">
<rdf:RDF>
<rdf:Description rdf:about="M">
<dc:title>M</dc:title>
<dcterms:alternative>active MPF</dcterms:alternative>
<dcterms:alternative>P-cyclin-cdc2</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="M"/>
<variable units="flux" public_interface="in" name="delta_M_rxn_4"/>
<variable units="flux" public_interface="in" name="delta_M_rxn_5"/>
<variable units="flux" public_interface="in" name="delta_M_rxn_6"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M</ci>
</apply>
<apply>
<plus/>
<ci>delta_M_rxn_4</ci>
<ci>delta_M_rxn_5</ci>
<ci>delta_M_rxn_6</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Y" name="Y">
<rdf:RDF>
<rdf:Description rdf:about="Y">
<dc:title>Y</dc:title>
<dcterms:alternative>cyclin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="Y"/>
<variable units="flux" public_interface="in" name="delta_Y_rxn_1"/>
<variable units="flux" public_interface="in" name="delta_Y_rxn_2"/>
<variable units="flux" public_interface="in" name="delta_Y_rxn_3"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Y</ci>
</apply>
<apply>
<plus/>
<ci>delta_Y_rxn_1</ci>
<ci>delta_Y_rxn_2</ci>
<ci>delta_Y_rxn_3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="YP" name="YP">
<rdf:RDF>
<rdf:Description rdf:about="YP">
<dc:title>YP</dc:title>
<dcterms:alternative>cyclin-P</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="YP"/>
<variable units="flux" public_interface="in" name="delta_YP_rxn_6"/>
<variable units="flux" public_interface="in" name="delta_YP_rxn_7"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>YP</ci>
</apply>
<apply>
<plus/>
<ci>delta_YP_rxn_6</ci>
<ci>delta_YP_rxn_7</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="aa" name="aa">
<rdf:RDF>
<rdf:Description rdf:about="aa">
<dc:title>aa</dc:title>
<dcterms:alternative>amino acid</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="aa"/>
<variable units="flux" public_interface="in" name="delta_aa_rxn_1"/>
<variable units="flux" public_interface="in" name="delta_aa_rxn_2"/>
<variable units="flux" public_interface="in" name="delta_aa_rxn_7"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>aa</ci>
</apply>
<apply>
<plus/>
<ci>delta_aa_rxn_1</ci>
<ci>delta_aa_rxn_2</ci>
<ci>delta_aa_rxn_7</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Pi" name="Pi">
<rdf:RDF>
<rdf:Description rdf:about="Pi">
<dc:title>Pi</dc:title>
<dcterms:alternative>inorganic phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="Pi"/>
<variable units="flux" public_interface="in" name="delta_Pi_rxn_4"/>
<variable units="flux" public_interface="in" name="delta_Pi_rxn_7"/>
<variable units="flux" public_interface="in" name="delta_Pi_rxn_9"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Pi</ci>
</apply>
<apply>
<plus/>
<ci>delta_Pi_rxn_4</ci>
<ci>delta_Pi_rxn_7</ci>
<ci>delta_Pi_rxn_9</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ATP" name="ATP">
<rdf:RDF>
<rdf:Description rdf:about="ATP">
<dc:title>ATP</dc:title>
<dcterms:alternative>adenosine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ATP"/>
<variable units="flux" public_interface="in" name="delta_ATP_rxn_3"/>
<variable units="flux" public_interface="in" name="delta_ATP_rxn_5"/>
<variable units="flux" public_interface="in" name="delta_ATP_rxn_8"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ATP</ci>
</apply>
<apply>
<plus/>
<ci>delta_ATP_rxn_3</ci>
<ci>delta_ATP_rxn_5</ci>
<ci>delta_ATP_rxn_8</ci>
</apply>
</apply>
</math>
</component>
<component name="CT">
<variable units="millimolar" public_interface="out" name="CT"/>
<variable units="millimolar" public_interface="in" name="C2"/>
<variable units="millimolar" public_interface="in" name="CP"/>
<variable units="millimolar" public_interface="in" name="pM"/>
<variable units="millimolar" public_interface="in" name="M"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CT_calculation">
<eq/>
<ci> CT </ci>
<apply>
<plus/>
<ci> C2 </ci>
<ci> CP </ci>
<ci> pM </ci>
<ci> M </ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="reaction1">
<variable units="millimolar" public_interface="in" name="aa"/>
<variable units="millimolar" public_interface="in" name="Y"/>
<variable units="millimolar" public_interface="in" name="CT"/>
<variable units="first_order_rate_constant" name="k1"/>
<variable units="flux" public_interface="out" name="delta_aa_rxn_1"/>
<variable units="flux" public_interface="out" name="delta_Y_rxn_1"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="aa">
<role stoichiometry="1" direction="forward" delta_variable="delta_aa_rxn_1" role="reactant"/>
</variable_ref>
<variable_ref variable="Y">
<role stoichiometry="1" direction="forward" delta_variable="delta_Y_rxn_1" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k1 </ci>
<ci> aa </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k1_calculation">
<eq/>
<ci> k1 </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant"> 0.015 </cn>
<ci> CT </ci>
</apply>
<ci> aa </ci>
</apply>
</apply>
</math>
</component>
<component name="reaction2">
<variable units="millimolar" public_interface="in" name="aa"/>
<variable units="millimolar" public_interface="in" name="Y"/>
<variable units="first_order_rate_constant" name="k2" initial_value="0.0"/>
<variable units="flux" public_interface="out" name="delta_aa_rxn_2"/>
<variable units="flux" public_interface="out" name="delta_Y_rxn_2"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="Y">
<role stoichiometry="1" direction="forward" delta_variable="delta_Y_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="aa">
<role stoichiometry="1" direction="forward" delta_variable="delta_aa_rxn_2" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k2 </ci>
<ci> Y </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="millimolar" public_interface="in" name="CP"/>
<variable units="millimolar" public_interface="in" name="Y"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="millimolar" public_interface="in" name="pM"/>
<variable units="millimolar" public_interface="in" name="CT"/>
<variable units="third_order_rate_constant" name="k3"/>
<variable units="flux" public_interface="out" name="delta_CP_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_Y_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_pM_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_ATP_rxn_3"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="CP">
<role stoichiometry="1" direction="forward" delta_variable="delta_CP_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="Y">
<role stoichiometry="1" direction="forward" delta_variable="delta_Y_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="pM">
<role stoichiometry="1" direction="forward" delta_variable="delta_pM_rxn_3" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k3 </ci>
<ci> CP </ci>
<ci> Y </ci>
<ci> ATP </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k3_calculation">
<eq/>
<ci> k3 </ci>
<apply>
<divide/>
<cn cellml:units="first_order_rate_constant"> 200.0 </cn>
<ci> CT </ci>
</apply>
</apply>
</math>
</component>
<component name="reaction4">
<variable units="millimolar" public_interface="in" name="pM"/>
<variable units="millimolar" public_interface="in" name="M"/>
<variable units="millimolar" public_interface="in" name="Pi"/>
<variable units="millimolar" public_interface="in" name="CT"/>
<variable units="first_order_rate_constant" name="F_M"/>
<variable units="first_order_rate_constant" name="k4" initial_value="10.0"/>
<variable units="first_order_rate_constant" name="k4_" initial_value="0.018"/>
<variable units="flux" public_interface="out" name="delta_pM_rxn_4"/>
<variable units="flux" public_interface="out" name="delta_M_rxn_4"/>
<variable units="flux" public_interface="out" name="delta_Pi_rxn_4"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="pM">
<role stoichiometry="1" direction="forward" delta_variable="delta_pM_rxn_4" role="reactant"/>
</variable_ref>
<variable_ref variable="M">
<role stoichiometry="1" direction="forward" delta_variable="delta_M_rxn_4" role="product"/>
</variable_ref>
<variable_ref variable="Pi">
<role stoichiometry="1" direction="forward" delta_variable="delta_Pi_rxn_4" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> F_M </ci>
<ci> pM </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="F_M_calculation">
<eq/>
<ci> F_M </ci>
<apply>
<plus/>
<ci> k4_ </ci>
<apply>
<times/>
<ci> k4 </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> M </ci>
<ci> CT </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="reaction5">
<variable units="millimolar" public_interface="in" name="pM"/>
<variable units="millimolar" public_interface="in" name="M"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="second_order_rate_constant" name="k5"/>
<variable units="flux" public_interface="out" name="delta_pM_rxn_5"/>
<variable units="flux" public_interface="out" name="delta_M_rxn_5"/>
<variable units="flux" public_interface="out" name="delta_ATP_rxn_5"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="M">
<role stoichiometry="1" direction="forward" delta_variable="delta_M_rxn_5" role="reactant"/>
</variable_ref>
<variable_ref variable="ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn_5" role="reactant"/>
</variable_ref>
<variable_ref variable="pM">
<role stoichiometry="1" direction="forward" delta_variable="delta_pM_rxn_5" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k5 </ci>
<ci> M </ci>
<ci> ATP </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k5_calculation">
<eq/>
<ci> k5 </ci>
<apply>
<divide/>
<cn cellml:units="first_order_rate_constant"> 0.0 </cn>
<ci> ATP </ci>
</apply>
</apply>
</math>
</component>
<component name="reaction6">
<variable units="millimolar" public_interface="in" name="M"/>
<variable units="millimolar" public_interface="in" name="C2"/>
<variable units="millimolar" public_interface="in" name="YP"/>
<variable units="first_order_rate_constant" name="k6" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="delta_M_rxn_6"/>
<variable units="flux" public_interface="out" name="delta_C2_rxn_6"/>
<variable units="flux" public_interface="out" name="delta_YP_rxn_6"/>
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Proceedings of the National Academy of Sciences USA
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The University of Auckland, Bioengineering Institute
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Modeling the Cell Division Cycle:cdc2 and Cyclin Interactions
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John Tyson's 1991 model of the cell division cycle.
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This is the CellML description of John Tyson's 1991 model of the cell
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