Location: Qu, Maclellan, Weiss, 2003 @ 864a5672c293 / qu_maclellan_weiss_2003.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2009-06-17 15:39:10+12:00
Desc:
committing version02 of qu_maclellan_weiss_2003
Permanent Source URI:
https://models.cellml.org/workspace/qu_maclellan_weiss_2003/rawfile/864a5672c29312aa9bc6fad0ceed8fbc319fbe59/qu_maclellan_weiss_2003.cellml

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<!--
This CellML file was generated on 9/01/2009 at 12:22:25 at p.m. using:

COR (0.9.31.1125)
Copyright 2002-2009 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

CellML 1.0 was used to generate this model
http://www.CellML.org/
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	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>Dynamics of the cell cycle: checkpoints, sizers, and timers</title>
				<author>
					<firstname>Jeelean</firstname>
					<surname>Lim</surname>
					<affiliation>
						<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
					</affiliation>
				</author>
			</articleinfo>
			<section id="sec_status">
				<title>Model Status</title>
				<para>
            This CellML version of the model has been checked in COR and PCEnv and the model runs to replicate the results in the original published paper.  The units have been checked and are consistent.
          </para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
ABSTRACT: We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.
</para>
				<para>
The complete original paper reference is cited below:
</para>
				<para>
					<ulink url="http://www.cell.com/biophysj/abstract/S0006-3495(03)74778-X">Dynamics of the Cell Cycle: Checkpoints, Sizers, and Timers</ulink>, Zhilin Qu, W. Robb MacLellan, James N. Weiss, 2003, <ulink url="http://www.cell.com/biophysj/home">
						<emphasis>Biophysical Journal</emphasis>
					</ulink>, 85, 3600-3611. (A <ulink url="http://download.cell.com/biophysj/pdf/PIIS000634950374778X.pdf?intermediate=true">PDF version</ulink> of the article is available to subscribers on the journal website.)  <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/14645053">PubMed ID: 14645053</ulink>
				</para>
				
				<informalfigure float="0" id="fig_reaction_diagram">
					<mediaobject>
						<imageobject>
							<objectinfo>
								<title>Figure 1</title>
							</objectinfo>
							<imagedata fileref="qu_2003a.png"/>
						</imageobject>
					</mediaobject>
					<caption>Signaling networks for cyclin and CDK regulation.</caption>
				</informalfigure>
				<informalfigure float="0" id="fig_reaction_diagram">
					<mediaobject>
						<imageobject>
							<objectinfo>
								<title>Figure 2</title>
							</objectinfo>
							<imagedata fileref="qu_2003b.png"/>
						</imageobject>
					</mediaobject>
					<caption>SKP2 regulation.</caption>
				</informalfigure>
				<informalfigure float="0" id="fig_reaction_diagram">
					<mediaobject>
						<imageobject>
							<objectinfo>
								<title>Figure 3</title>
							</objectinfo>
							<imagedata fileref="qu_2003c.png"/>
						</imageobject>
					</mediaobject>
					<caption>APC/CDC20 regulation.</caption>
				</informalfigure>
				<para>
Please note that equation 2 on page 3604 of the paper describing the cell size is not included in the CellML description.
				</para>
			</sect1>
		</article>
	</documentation>
	
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            <apply>
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      <variable units="dimensionless" name="h_x"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_active"/>
      <variable units="dimensionless" name="a" initial_value="4"/>
      <variable units="minute" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
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            <eq/>
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            <apply>
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                  <power/>
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                     <power/>
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               <plus/>
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      <variable units="minute" public_interface="in" name="time"/>
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            <apply>
               <diff/>
               <bvar>
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               <minus/>
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                        <times/>
                        <ci>k15</ci>
                        <ci>cyclin_CDK_CKI</ci>
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                  <apply>
                     <times/>
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               <apply>
                  <times/>
                  <ci>kplus_i</ci>
                  <ci>cyclin_CDK_CKI</ci>
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      <variable units="first_order_rate_constant" public_interface="in" name="k14"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k15"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k16"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k16u"/>
      <variable units="first_order_rate_constant" public_interface="in" name="kminus_i"/>
      <variable units="first_order_rate_constant" public_interface="in" name="kplus_i"/>
      <variable units="dimensionless" public_interface="in" name="APC"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_CKI"/>
      <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>
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            </apply>
            <apply>
               <minus/>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>kplus_i</ci>
                     <ci>cyclin_CDK_CKI</ci>
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                  <apply>
                     <times/>
                     <ci>kminus_i</ci>
                     <ci>cyclin_CDK_CKI_P</ci>
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               <apply>
                  <times/>
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                     <plus/>
                     <ci>k16</ci>
                     <apply>
                        <times/>
                        <ci>k16u</ci>
                        <ci>APC</ci>
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      <variable units="dimensionless" public_interface="out" name="CDK" cmeta:id="CDK_CDK"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_CKI_P"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_CKI"/>
      <variable units="dimensionless" name="CDK_T" initial_value="200"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_active"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_inactive"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
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            <eq/>
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            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
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                           <ci>cyclin_CDK_active</ci>
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                        <ci>cyclin_CDK_inactive</ci>
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                     <ci>cyclin_CDK_CKI</ci>
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               <ci>CDK_T</ci>
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         </apply>
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      <variable units="dimensionless" public_interface="out" name="cyclin_T"/>
      <variable units="dimensionless" public_interface="in" name="cyclin"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_active"/>
      <variable units="dimensionless" public_interface="in" name="cyclin_CDK_inactive"/>
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            <eq/>
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               <plus/>
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            </apply>
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      <map_variables variable_2="time" variable_1="time"/>
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      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="cyclin_CDK_active"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="Cdc25"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="Cdc25_P"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="Cdc25_2P"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="wee1"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="wee1_P"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="APC"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="CKI"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="cyclin_CDK_CKI"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="environment" component_1="cyclin_CDK_CKI_P"/>
      <map_variables variable_2="time" variable_1="time"/>
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      <map_components component_2="cyclin_CDK_active" component_1="rate_constants"/>
      <map_variables variable_2="cyclin_CDK_active" variable_1="cyclin_CDK_active"/>
      <map_variables variable_2="k5" variable_1="k5"/>
      <map_variables variable_2="k6" variable_1="k6"/>
      <map_variables variable_2="k7" variable_1="k7"/>
      <map_variables variable_2="k7u" variable_1="k7u"/>
      <map_variables variable_2="k14" variable_1="k14"/>
      <map_variables variable_2="k15" variable_1="k15"/>
      <map_variables variable_2="k16" variable_1="k16"/>
      <map_variables variable_2="k16u" variable_1="k16u"/>
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   <connection>
      <map_components component_2="rate_constants" component_1="cyclin"/>
      <map_variables variable_2="k1" variable_1="k1"/>
      <map_variables variable_2="k2" variable_1="k2"/>
      <map_variables variable_2="k2u" variable_1="k2u"/>
      <map_variables variable_2="k3" variable_1="k3"/>
      <map_variables variable_2="k4" variable_1="k4"/>
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      <map_variables variable_2="cyclin_CDK_inactive" variable_1="cyclin_CDK_inactive"/>
      <map_variables variable_2="cyclin" variable_1="cyclin"/>
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      <map_variables variable_2="CDK" variable_1="CDK"/>
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      <map_variables variable_2="APC" variable_1="APC"/>
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      <map_variables variable_2="k4" variable_1="k4"/>
      <map_variables variable_2="k5" variable_1="k5"/>
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      <map_variables variable_2="k9" variable_1="k9"/>
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