- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-04-06 12:59:19+12:00
- Desc:
- Fixed broken documentation and RDF.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/ueda_hagiwara_kitano_2001/rawfile/8f858539c90901b4872a9d5b5caf099a11838ff1/ueda_hagiwara_kitano_2001.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : ueda_model_2001.xml
CREATED : 23rd September 2003
LAST MODIFIED : 23rd September 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 Ueda et al.'s mathematical model of circadian rhythms in Drosophila.
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#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" name="ueda_2001" cmeta:id="ueda_2001">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model is known to run in both OpenCell and COR to replicate the published results. The units have been checked and they are consistent.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A mechanism for generating circadian rhythms has been of major interest in recent years. After the discovery of per and tim, a model with a simple feedback loop involving per and tim has been proposed. However, it is recognized that the simple feedback model cannot account for phenotypes generated by various mutants. A recent report by Glossop, Lyons and Hardin [Science286, 766 (1999)] on Drosophila suggests involvement of another feedback loop by dClk that is interlocked with per-tim feedback loop. In order to examine whether interlocked feedback loops can be a basic mechanism for circadian rhythms, a mathematical model was created and examined. Through extensive simulation and mathematical analysis, it was revealed that the interlocked feedback model accounts for the observations that are not explained by the simple feedback model. Moreover, the interlocked feedback model has robust properties in oscillations.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm, Hiroki R. Ueda, Masatoshi Hagiwara, and Hiroaki Kitano, 2001, <emphasis>Journal of Theoretical Biology</emphasis>, 210, 401-406. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/11403560">PubMed ID: 11403460</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="ueda_2001.png"/>
</imageobject>
</mediaobject>
<caption>The interlocked feedback model of Drosophila circadian rhythm.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="hour">
<unit units="second" multiplier="3600.0"/>
</units>
<units name="flux">
<unit units="nanomolar"/>
<unit units="hour" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="hour" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="nanomolar" exponent="-1"/>
<unit units="hour" exponent="-1"/>
</units>
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<variable units="hour" public_interface="out" name="time" cmeta:id="environment_time"/>
</component>
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<rdf:RDF>
<rdf:Description rdf:about="#Per_m">
<dc:title>Per_m</dc:title>
<dcterms:alternative>Per mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" cmeta:id="Per_m_Per_m" name="Per_m" initial_value="0.5"/>
<variable units="dimensionless" name="B1" initial_value="0.0"/>
<variable units="flux" name="C1" initial_value="0.0"/>
<variable units="flux" name="S1" initial_value="1.45"/>
<variable units="flux" name="D1" initial_value="0.94"/>
<variable units="nanomolar" name="L1" initial_value="0.3"/>
<variable units="nanomolar" name="R1" initial_value="1.02"/>
<variable units="nanomolar" name="A1" initial_value="0.45"/>
<variable units="nanomolar" public_interface="in" name="PT_n"/>
<variable units="nanomolar" public_interface="in" name="CC_n"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
<variable units="dimensionless" public_interface="in" name="a"/>
<variable units="dimensionless" public_interface="in" name="r"/>
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<eq/>
<apply>
<diff/>
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<ci>time</ci>
</bvar>
<ci>Per_m</ci>
</apply>
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<apply>
<plus/>
<ci> C1 </ci>
<apply>
<times/>
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<apply>
<divide/>
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<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci> CC_n </ci>
<ci> A1 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B1 </ci>
</apply>
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<apply>
<power/>
<apply>
<divide/>
<ci> PT_n </ci>
<ci> R1 </ci>
</apply>
<ci> r </ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> CC_n </ci>
<ci> A1 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B1 </ci>
</apply>
</apply>
</apply>
</apply>
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<plus/>
<apply>
<times/>
<ci> D1 </ci>
<apply>
<divide/>
<ci> Per_m </ci>
<apply>
<plus/>
<ci> L1 </ci>
<ci> Per_m </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> Per_m </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Per_c" cmeta:id="Per_c">
<rdf:RDF>
<rdf:Description rdf:about="#Per_c">
<dc:title>Per_c</dc:title>
<dcterms:alternative>cytosolic Per protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Per_c" initial_value="0.6"/>
<variable units="first_order_rate_constant" name="S2" initial_value="0.48"/>
<variable units="first_order_rate_constant" name="D2" initial_value="0.44"/>
<variable units="nanomolar" name="L2" initial_value="0.2"/>
<variable units="nanomolar" name="Dbt_c" initial_value="1.0"/>
<variable units="second_order_rate_constant" public_interface="in" name="V1"/>
<variable units="first_order_rate_constant" public_interface="in" name="V2"/>
<variable units="nanomolar" public_interface="in" name="Per_m"/>
<variable units="nanomolar" public_interface="in" name="Tim_c"/>
<variable units="nanomolar" public_interface="in" name="PT_c"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Per_c</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> S2 </ci>
<ci> Per_m </ci>
</apply>
<apply>
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<ci> V2 </ci>
<ci> PT_c </ci>
</apply>
</apply>
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<plus/>
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<ci> Per_c </ci>
<ci> Tim_c </ci>
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<ci> Dbt_c </ci>
<apply>
<divide/>
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<plus/>
<ci> L2 </ci>
<ci> Per_c </ci>
</apply>
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</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> Per_c </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Tim_m" cmeta:id="Tim_m">
<rdf:RDF>
<rdf:Description rdf:about="#Tim_m">
<dc:title>Tim_m</dc:title>
<dcterms:alternative>Tim mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" cmeta:id="Tim_m_Tim_m" name="Tim_m" initial_value="0.7"/>
<variable units="dimensionless" name="B2" initial_value="0.0"/>
<variable units="flux" name="C2" initial_value="0.0"/>
<variable units="flux" name="S3" initial_value="1.45"/>
<variable units="flux" name="D3" initial_value="0.94"/>
<variable units="nanomolar" name="L3" initial_value="0.3"/>
<variable units="nanomolar" name="R2" initial_value="1.02"/>
<variable units="nanomolar" name="A2" initial_value="0.45"/>
<variable units="nanomolar" public_interface="in" name="PT_n"/>
<variable units="nanomolar" public_interface="in" name="CC_n"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
<variable units="dimensionless" public_interface="in" name="a"/>
<variable units="dimensionless" public_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<ci>time</ci>
</bvar>
<ci>Tim_m</ci>
</apply>
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<minus/>
<apply>
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<ci> C2 </ci>
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<ci> S3 </ci>
<apply>
<divide/>
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<plus/>
<apply>
<power/>
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<divide/>
<ci> CC_n </ci>
<ci> A2 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B2 </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> PT_n </ci>
<ci> R2 </ci>
</apply>
<ci> r </ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> CC_n </ci>
<ci> A2 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B2 </ci>
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</apply>
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<ci> D3 </ci>
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<divide/>
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<ci> Tim_m </ci>
</apply>
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<apply>
<times/>
<ci> D0 </ci>
<ci> Tim_m </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Tim_c" cmeta:id="Tim_c">
<rdf:RDF>
<rdf:Description rdf:about="#Tim_c">
<dc:title>Tim_c</dc:title>
<dcterms:alternative>cytosolic Tim protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" cmeta:id="Tim_c_Tim_c" name="Tim_c" initial_value="0.8"/>
<variable units="first_order_rate_constant" name="S4" initial_value="0.48"/>
<variable units="flux" name="D4" initial_value="0.44"/>
<variable units="nanomolar" name="L4" initial_value="0.2"/>
<variable units="second_order_rate_constant" public_interface="in" name="V1"/>
<variable units="first_order_rate_constant" public_interface="in" name="V2"/>
<variable units="nanomolar" public_interface="in" name="Tim_m"/>
<variable units="nanomolar" public_interface="in" name="Per_c"/>
<variable units="nanomolar" public_interface="in" name="PT_c"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Tim_c</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> S4 </ci>
<ci> Tim_m </ci>
</apply>
<apply>
<times/>
<ci> V2 </ci>
<ci> PT_c </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
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<ci> Per_c </ci>
<ci> Tim_c </ci>
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<ci> D4 </ci>
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<ci> L4 </ci>
<ci> Tim_c </ci>
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</apply>
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<times/>
<ci> D0 </ci>
<ci> Tim_c </ci>
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</apply>
</apply>
</math>
</component>
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<rdf:RDF>
<rdf:Description rdf:about="#PT_c">
<dc:title>PT_c</dc:title>
<dcterms:alternative>cytosolic Per-Tim protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" cmeta:id="PT_c_PT_c" name="PT_c" initial_value="0.9"/>
<variable units="flux" name="D5" initial_value="0.44"/>
<variable units="nanomolar" name="L5" initial_value="0.2"/>
<variable units="nanomolar" public_interface="in" name="K1"/>
<variable units="nanomolar" public_interface="in" name="K2"/>
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<variable units="nanomolar" public_interface="in" name="Per_c"/>
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<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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</bvar>
<ci>PT_c</ci>
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<ci> Tim_c </ci>
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<ci> PT_c </ci>
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<ci> PT_c </ci>
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<times/>
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<divide/>
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<ci> PT_c </ci>
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<times/>
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<ci> PT_c </ci>
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</apply>
</math>
</component>
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<rdf:RDF>
<rdf:Description rdf:about="#PT_n">
<dc:title>PT_n</dc:title>
<dcterms:alternative>nuclear Per-Tim protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<variable units="flux" name="D6" initial_value="0.29"/>
<variable units="nanomolar" name="L6" initial_value="0.2"/>
<variable units="nanomolar" public_interface="in" name="K1"/>
<variable units="nanomolar" public_interface="in" name="K2"/>
<variable units="flux" public_interface="in" name="T1"/>
<variable units="flux" public_interface="in" name="T2"/>
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<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
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<diff/>
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<ci>time</ci>
</bvar>
<ci>PT_n</ci>
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<divide/>
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<ci> PT_c </ci>
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<ci> PT_n </ci>
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<ci> PT_n </ci>
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<rdf:RDF>
<rdf:Description rdf:about="#Clk_m">
<dc:title>Clk_m</dc:title>
<dcterms:alternative>Clk mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" cmeta:id="Clk_m_Clk_m" name="Clk_m" initial_value="0.1"/>
<variable units="dimensionless" name="B3" initial_value="0.6"/>
<variable units="flux" name="C3" initial_value="0.0"/>
<variable units="flux" name="S5" initial_value="1.63"/>
<variable units="flux" name="D7" initial_value="0.54"/>
<variable units="nanomolar" name="L7" initial_value="0.13"/>
<variable units="nanomolar" name="R3" initial_value="0.89"/>
<variable units="nanomolar" name="A3" initial_value="0.8"/>
<variable units="nanomolar" public_interface="in" name="CC_n"/>
<variable units="nanomolar" public_interface="in" name="PT_n"/>
<variable units="hour" public_interface="in" name="time"/>
<variable units="first_order_rate_constant" public_interface="in" name="D0"/>
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<variable units="dimensionless" public_interface="in" name="r"/>
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<ci> R3 </ci>
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<ci> r </ci>
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<power/>
<apply>
<divide/>
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<ci> A3 </ci>
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<times/>
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<apply>
<divide/>
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<ci> Clk_m </ci>
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<ci> Clk_m </ci>
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</component>
<component name="Clk_c" cmeta:id="Clk_c">
<rdf:RDF>
<rdf:Description rdf:about="#Clk_c">
<dc:title>Clk_c</dc:title>
<dcterms:alternative>cytosolic Clk protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" cmeta:id="Clk_c_Clk_c" name="Clk_c" initial_value="0.2"/>
<variable units="first_order_rate_constant" name="S6" initial_value="0.47"/>
<variable units="flux" name="D8" initial_value="0.6"/>
<variable units="nanomolar" name="L8" initial_value="0.2"/>
<variable units="second_order_rate_constant" public_interface="in" name="V3"/>
<variable units="first_order_rate_constant" public_interface="in" name="V4"/>
<variable units="nanomolar" public_interface="in" name="Clk_m"/>
<variable units="nanomolar" public_interface="in" cmeta:id="Cyc_c_Cyc_c" name="Cyc_c"/>
<variable units="nanomolar" public_interface="in" name="CC_c"/>
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<dcterms:W3CDTF>2008-10-20T14:24:23+13:00</dcterms:W3CDTF>
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<rdf:value>Added initial conditions to all the substrates (these were based on the values used in the corresponding SBML model in the BioModels database), and fixed a typo in the equation for dPTc/dt such that the first term in this equation now reads V1*Perc*Timc rather than V1*Perc*PTc.</rdf:value>
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<vCard:Given>James</vCard:Given>
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<dc:title>Journal of Theoretical Biology</dc:title>
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<dc:title>Ueda et al.'s mathematical model of circadian rhythms in Drosophila.</dc:title>
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<dcterms:W3CDTF>2003-09-23T00:00:00+00:00</dcterms:W3CDTF>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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