- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:31:38+12:00
- Desc:
- committing version01 of gardner_dolnik_collins_1998
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/gardner_dolnik_collins_1998/rawfile/c30d309dc9418aac3ee93ceaa7903336b2e3e942/gardner_dolnik_collins_1998.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : gardner_model_1998.xml
CREATED : 1st May 2003
LAST MODIFIED : 1st May 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 Gardner et al.'s
1998 mathematical model of controlling cell cycle dynamics using a reversibly binding inhibitor.
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="gardner_dolnik_collins_1998_version01" name="gardner_dolnik_collins_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Controlling Cell Cycle Dynamics Using a Reversibly Binding Inhibitor</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>
Experimental analysis of the cell division cycle has lead to the elucidation of many of the genes and proteins that control cell division. In turn, this has allowed scientists to manipulate the cycle, usually by mutating the regulatory genes. However, this often results in unpredictable responses, such as uncontrolled cell division, inhibited cell division, or fatal errors during the cell cycle. A more controlled way to manipulate the cell cycle is to add a reversibly binding inhibitor. In this study described here, Timothy Gardner, Milos Dolnik and James Collins develop a mathematical model of cell division cycle dynamics under the influence of an inhibitory protein. This protein reversibly binds to cyclin (one of the key cell cycle proteins), and acts to alter the frequency of the cell cycle oscillations.
</para>
<para>
In order to characterise the features of their model, Gardner <emphasis>et al.</emphasis> applied it to two previously published models of the cell cycle. The specific model discussed here is the model developed by Goldbeter in 1991 (for more details of this model please see <ulink url="${HTML_EXMPL_GOLDBETER_MODEL}">Goldbeter, 1991</ulink>). Although this model is based on certain assumptions and is a simplification of the biological cell cycle, it has sufficient detail to describe the dynamics of the molecular mechanisms underlying the cell cycle oscillations. The model reduces the cell cycle to cyclin, cdc2 kinase and cyclin protease. Cyclin is continually synthesised, and once it exceeds a threshold concentration, activates cdc2 kinase, which activates cyclin protease, witch in turn degrades cyclin, and creates a negative feedback loop (see <xref linkend="fig_reaction_diagram"/> below). Cycle oscillations are generated by threshold mechanisms for the activation of cdc2 kinase and cyclin protease, and also the time lags associated with these threshold mechanisms.
</para>
<para>
Simulations of the combined model show that the frequency of the cell cycle oscillations can be altered by regulating the rate of inhibitor synthesis, the inhibitor-cyclin binding rate, or the equilibrium constant of the of the inhibitor binding protein.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.pnas.org/cgi/content/abstract/95/24/14190">A theory for controlling cell cycle dynamics using a reversibly binding inhibitor</ulink>, Timothy S. Gardner, Milos Dolnik and James J. Collins, 1998, <ulink url="http://www.pnas.org/">
<emphasis>Proceedings of the National Academy of Sciences</emphasis>
</ulink>, 95, 14190-14195. (A <ulink url="http://www.pnas.org/cgi/reprint/95/24/14190.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=9826676&dopt=Abstract">PubMed ID: 9826676</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>Control of the Goldbeter 1991 model with a cyclin inhibitor. M represents cdc2 kinase, X represents the fraction of active (phosphorylated) cyclin protease, and * represents the fraction of inactive enzymes. The Goldbeter model is outlined by the dashed box. Solid arrows indicate protein synthesis, degradation or enzymatic conversion. Dashed arrows represent activation.</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"/>
<variable units="second_order_rate_constant" name="vi" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="in" name="kd"/>
<variable units="flux" public_interface="in" name="delta_C_rxn_5"/>
<variable units="flux" public_interface="in" name="delta_C_rxn_6"/>
<variable units="flux" public_interface="in" name="delta_C_rxn_7"/>
<variable units="flux" public_interface="in" name="delta_C_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>C</ci>
</apply>
<apply>
<plus/>
<ci>vi</ci>
<ci>delta_C_rxn_5</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kd</ci>
<ci>C</ci>
</apply>
</apply>
<ci>delta_C_rxn_6</ci>
<ci>delta_C_rxn_7</ci>
<ci>delta_C_rxn_8</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C_deg" name="C_deg">
<variable units="micromolar" public_interface="out" name="C_deg"/>
<variable units="flux" public_interface="in" name="delta_C_deg_rxn_5"/>
<variable units="flux" public_interface="in" name="delta_C_deg_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>C_deg</ci>
</apply>
<apply>
<plus/>
<ci>delta_C_deg_rxn_5</ci>
<ci>delta_C_deg_rxn_9</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>
fraction of inactive cdc2 kinase
</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="M_" initial_value="0.99"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_M__rxn_1"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_M__rxn_2"/>
<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_1</ci>
<ci>delta_M__rxn_2</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>
fraction of active cdc2 kinase
</dcterms:alternative>
<dcterms:alternative>E3</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="M"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_M_rxn_1"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_M_rxn_2"/>
<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_1</ci>
<ci>delta_M_rxn_2</ci>
</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 inactive cyclin protease
</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="X_"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_X__rxn_3"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_X__rxn_4"/>
<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>X_</ci>
</apply>
<apply>
<plus/>
<ci>delta_X__rxn_3</ci>
<ci>delta_X__rxn_4</ci>
</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"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_X_rxn_3"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_X_rxn_4"/>
<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>X</ci>
</apply>
<apply>
<plus/>
<ci>delta_X_rxn_3</ci>
<ci>delta_X_rxn_4</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>
concentration of unbound inhibitor
</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Y"/>
<variable units="second_order_rate_constant" name="vs" initial_value="0.08"/>
<variable units="flux" public_interface="in" name="delta_Y_rxn_10"/>
<variable units="flux" public_interface="in" name="delta_Y_rxn_6"/>
<variable units="flux" public_interface="in" name="delta_Y_rxn_7"/>
<variable units="flux" public_interface="in" name="delta_Y_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>Y</ci>
</apply>
<apply>
<plus/>
<ci>vs</ci>
<ci>delta_Y_rxn_10</ci>
<ci>delta_Y_rxn_6</ci>
<ci>delta_Y_rxn_7</ci>
<ci>delta_Y_rxn_9</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Y_deg" name="Y_deg">
<rdf:RDF>
<rdf:Description rdf:about="Y_deg">
<dc:title>Y_deg</dc:title>
<dcterms:alternative>
concentration of degraded inhibitor
</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Y_deg"/>
<variable units="flux" public_interface="in" name="delta_Y_deg_rxn_8"/>
<variable units="flux" public_interface="in" name="delta_Y_deg_rxn_10"/>
<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_deg</ci>
</apply>
<apply>
<plus/>
<ci>delta_Y_deg_rxn_8</ci>
<ci>delta_Y_deg_rxn_10</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Z" name="Z">
<rdf:RDF>
<rdf:Description rdf:about="Z">
<dc:title>Z</dc:title>
<dcterms:alternative>
concentration of inhibitor-target complex
</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Z"/>
<variable units="flux" public_interface="in" name="delta_Z_rxn_6"/>
<variable units="flux" public_interface="in" name="delta_Z_rxn_7"/>
<variable units="flux" public_interface="in" name="delta_Z_rxn_9"/>
<variable units="flux" public_interface="in" name="delta_Z_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>Z</ci>
</apply>
<apply>
<plus/>
<ci>delta_Z_rxn_6</ci>
<ci>delta_Z_rxn_7</ci>
<ci>delta_Z_rxn_8</ci>
<ci>delta_Z_rxn_9</ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe all the enzymes involved in reactions
-->
<component cmeta:id="E1" name="E1">
<variable units="micromolar" public_interface="out" name="E1"/>
</component>
<component cmeta:id="E2" name="E2">
<variable units="micromolar" public_interface="out" name="E2"/>
</component>
<component cmeta:id="E4" name="E4">
<variable units="micromolar" public_interface="out" name="E4"/>
</component>
<!--
The following component defines the constants of the model.
-->
<component name="constants">
<variable units="dimensionless" public_interface="out" name="alpha" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="out" name="d1" initial_value="0.05"/>
<variable units="first_order_rate_constant" public_interface="out" name="kd" initial_value="0.02"/>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="reaction1">
<variable units="dimensionless" public_interface="in" name="M_"/>
<variable units="dimensionless" public_interface="in" name="M"/>
<variable units="micromolar" public_interface="in" name="C"/>
<variable units="micromolar" public_interface="in" name="E1"/>
<variable units="first_order_rate_constant" name="V1"/>
<variable units="first_order_rate_constant" name="V1_" initial_value="0.75"/>
<variable units="micromolar" name="K1" initial_value="0.06"/>
<variable units="micromolar" name="K6" initial_value="0.3"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_M__rxn_1"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_M_rxn_1"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="M_">
<role stoichiometry="1" direction="forward" delta_variable="delta_M__rxn_1" role="reactant"/>
</variable_ref>
<variable_ref variable="M">
<role stoichiometry="1" direction="forward" delta_variable="delta_M_rxn_1" role="product"/>
</variable_ref>
<variable_ref variable="C">
<role role="activator"/>
</variable_ref>
<variable_ref variable="E1">
<role role="catalyst"/>
</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> V1 </ci>
<apply>
<divide/>
<ci> M_ </ci>
<apply>
<plus/>
<ci> K1 </ci>
<ci> M_ </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V1_calculation">
<eq/>
<ci> V1 </ci>
<apply>
<times/>
<ci> V1_ </ci>
<apply>
<divide/>
<ci> C </ci>
<apply>
<plus/>
<ci> K6 </ci>
<ci> C </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="reaction2">
<variable units="dimensionless" public_interface="in" name="M_"/>
<variable units="dimensionless" public_interface="in" name="M"/>
<variable units="first_order_rate_constant" name="V2" initial_value="0.25"/>
<variable units="micromolar" name="K2" initial_value="0.06"/>
<variable units="micromolar" public_interface="in" name="E2"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_M__rxn_2"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_M_rxn_2"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="M">
<role stoichiometry="1" direction="forward" delta_variable="delta_M_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="M_">
<role stoichiometry="1" direction="forward" delta_variable="delta_M__rxn_2" role="product"/>
</variable_ref>
<variable_ref variable="E2">
<role role="catalyst"/>
</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> V2 </ci>
<apply>
<divide/>
<ci> M </ci>
<apply>
<plus/>
<ci> K2 </ci>
<ci> M </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="dimensionless" public_interface="in" name="X_"/>
<variable units="dimensionless" public_interface="in" name="X"/>
<variable units="dimensionless" public_interface="in" name="M"/>
<variable units="first_order_rate_constant" name="V3"/>
<variable units="first_order_rate_constant" name="VM3" initial_value="0.3"/>
<variable units="micromolar" name="K3" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_X__rxn_3"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_X_rxn_3"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="X_">
<role stoichiometry="1" direction="forward" delta_variable="delta_X__rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="X">
<role stoichiometry="1" direction="forward" delta_variable="delta_X_rxn_3" role="product"/>
</variable_ref>
<variable_ref variable="M">
<role role="catalyst"/>
</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> V3 </ci>
<apply>
<divide/>
<ci> X_ </ci>
<apply>
<plus/>
<ci> K3 </ci>
<ci> X_ </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V3_calculation">
<eq/>
<ci> V3 </ci>
<apply>
<times/>
<ci> M </ci>
<ci> VM3 </ci>
</apply>
</apply>
</math>
</component>
<component name="reaction4">
<variable units="dimensionless" public_interface="in" name="X_"/>
<variable units="dimensionless" public_interface="in" name="X"/>
<variable units="first_order_rate_constant" name="V4" initial_value="0.1"/>
<variable units="micromolar" name="K4" initial_value="0.1"/>
<variable units="micromolar" public_interface="in" name="E4"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_X__rxn_4"/>
<variable units="first_order_rate_constant" public_interface="out" name="delta_X_rxn_4"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="X">
<role stoichiometry="1" direction="forward" delta_variable="delta_X_rxn_4" role="reactant"/>
</variable_ref>
<variable_ref variable="X_">
<role stoichiometry="1" direction="forward" delta_variable="delta_X__rxn_4" role="product"/>
</variable_ref>
<variable_ref variable="E4">
<role role="catalyst"/>
</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> V4 </ci>
<apply>
<divide/>
<ci> X </ci>
<apply>
<plus/>
<ci> K4 </ci>
<ci> X </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction5">
<variable units="micromolar" public_interface="in" name="C"/>
<variable units="micromolar" public_interface="in" name="C_deg"/>
<variable units="dimensionless" public_interface="in" name="X"/>
<variable units="first_order_rate_constant" name="vd" initial_value="0.5"/>
<variable units="micromolar" name="Kd" initial_value="0.02"/>
<variable units="flux" public_interface="out" name="delta_C_rxn_5"/>
<variable units="flux" public_interface="out" name="delta_C_deg_rxn_5"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="C">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_rxn_5" role="reactant"/>
</variable_ref>
<variable_ref variable="C_deg">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_deg_rxn_5" role="product"/>
</variable_ref>
<variable_ref variable="X">
<role role="catalyst"/>
</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> vd </ci>
<ci> X </ci>
<apply>
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A theory for controlling cell cycle dynamics using a reversibly
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Gardner et al.'s 1998 mathematical model of controlling cell cycle
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