- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:24:42+12:00
- Desc:
- committing version01 of ueda_hagiwara_kitano_2001
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/ueda_hagiwara_kitano_2001/rawfile/4fedfdc4fe9c34bc3e4177c2a0083008d0aba7ec/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#" cmeta:id="ueda_hagiwara_kitano_2001_version01" name="ueda_hagiwara_kitano_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Interlocked Feedback Model of Drosophila Circadian Rhythm</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>
Model is currently non-functional (unsuitably constrained)
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Many living organisms, from bacteria to plants, insects to mammals, display circadian rhythms. These are spontaneously sustained oscillations with a period close to 24 hours. Even in the absence of environmental cues, such as the light changes associated with day and night, organisms have been shown to retain their circadian behaviour, therefore suggesting that the rhythms are endogenous. Experiments with <emphasis>Drosophila</emphasis> (fruit fly), <emphasis>Neurospora</emphasis> (fungus), cyanobacteria, plants and mammals have improved our understanding of the molecular mechanisms underlying circadian rhythms. It seems that they rely on a negative feedback on gene expression. A number of genes involved in circadian rhythms have been identified. These include: <emphasis>Per</emphasis> (period), <emphasis>Tim</emphasis> (timeless), <emphasis>Cyc</emphasis> (cycle), <emphasis>Clk</emphasis> (clock), <emphasis>dbt</emphasis> (doubletime), and <emphasis>Cry</emphasis> (cryptochrome). Among these genes, <emphasis>per</emphasis>, <emphasis>tim</emphasis> and <emphasis>Clk</emphasis> are rhythmically expressed. <emphasis>per</emphasis> and <emphasis>tim</emphasis> mRNA levels peak in the evening, where as <emphasis>Clk</emphasis> mRNA levels peak late at night or early in the morning.
</para>
<para>
Analysis of <emphasis>per</emphasis> and <emphasis>tim</emphasis> oscillatory expression has revealed a negative feedback loop (<emphasis>
<emphasis>per-tim</emphasis> feedback loop</emphasis> in the figure below). Several mathematical models of this negative feedback loop have been developed, and model simulations have shown that a delayed negative feedback loop is sufficient to produce spontaneous oscillations. However, these models fail to take into account the <emphasis>Clk</emphasis> negative feedback loop. Based on experimental analyses of <emphasis>Clk</emphasis> expression, Ueda <emphasis>et al.</emphasis> have developed a different type of mathematical model which they call an <emphasis>interlocked feedback model</emphasis> (as opposed to a <emphasis>simple model</emphasis>). The interlocked feedback model is composed of two coupled negative feedback loops: a per-tim feedback loop which is activated by CLK-CYC and inhibited by PER-TIM, and a Clk feedback loop, which is inhibited by CLK-CYC and reactivated by PER-TIM.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://linkinghub.elsevier.com/retrieve/pii/S0022519300922264">Robust Oscillations within the Interlocked Feedback Model of <emphasis>Drosophila</emphasis> Circadian Rhythm</ulink>, Hiroki R. Ueda, Masatoshi Hagiwara, and Hiroaki Kitano, 2001, <ulink url="http://www.sciencedirect.com/science/journal/00225193">
<emphasis>Journal of Theoretical Biology</emphasis>
</ulink>, 210, 401-406. (<ulink url="http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WMD-457VD36-24-1&_cdi=6932&_user=140507&_orig=search&_coverDate=06%2F21%2F2001&_sk=997899995&view=c&wchp=dGLzVlz-zSkWz&md5=6924ecbd484d35a98e1e70ee47751f1f&ie=/sdarticle.pdf">A PDF</ulink> version of the article is available on the <emphasis>Journal of Theoretical Biology</emphasis> website.) <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 <emphasis>Drosophila</emphasis> circadian rhythm.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<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"/>
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<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"/>
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<variable units="hour" public_interface="out" name="time"/>
</component>
<component cmeta:id="Per_m" name="Per_m">
<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" name="Per_m"/>
<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"/>
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<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"/>
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<variable units="dimensionless" public_interface="in" name="a"/>
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</bvar>
<ci>Per_m</ci>
</apply>
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<minus/>
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<ci> C1 </ci>
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<times/>
<ci> S1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci> CC_n </ci>
<ci> A1 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B1 </ci>
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<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
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<ci> PT_n </ci>
<ci> R1 </ci>
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<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>
<apply>
<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 cmeta:id="Per_c" name="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"/>
<variable units="first_order_rate_constant" name="S2" initial_value="0.48"/>
<variable units="flux" 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">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Per_c</ci>
</apply>
<apply>
<minus/>
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<plus/>
<apply>
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<ci> S2 </ci>
<ci> Per_m </ci>
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<ci> PT_c </ci>
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<apply>
<plus/>
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<ci> Per_c </ci>
<ci> Tim_c </ci>
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<ci> D2 </ci>
<ci> Dbt_c </ci>
<apply>
<divide/>
<ci> Per_c </ci>
<apply>
<plus/>
<ci> L2 </ci>
<ci> Per_c </ci>
</apply>
</apply>
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<apply>
<times/>
<ci> D0 </ci>
<ci> Per_c </ci>
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</apply>
</math>
</component>
<component cmeta:id="Tim_m" name="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" name="Tim_m"/>
<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"/>
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<variable units="dimensionless" public_interface="in" name="r"/>
<math xmlns="http://www.w2.org/1998/Math/MathML">
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<cn cellml:units="dimensionless"> 1.0 </cn>
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<ci> PT_n </ci>
<ci> R2 </ci>
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<ci> r </ci>
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<apply>
<power/>
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<divide/>
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<ci> A2 </ci>
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<ci> a </ci>
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<ci> B2 </ci>
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<apply>
<times/>
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<ci> Tim_m </ci>
</apply>
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</apply>
</apply>
</math>
</component>
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<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" name="Tim_c"/>
<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"/>
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</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" name="PT_c"/>
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<variable units="nanomolar" public_interface="in" name="Per_c"/>
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<rdf:Description rdf:about="PT_n">
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<dcterms:alternative>nuclear Per-Tim protein complex</dcterms:alternative>
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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"/>
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<variable units="flux" public_interface="in" name="T2"/>
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</bvar>
<ci>PT_n</ci>
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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>
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</rdf:Description>
</rdf:RDF>
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<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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<ci>time</ci>
</bvar>
<ci>Clk_m</ci>
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<ci> C3 </ci>
<apply>
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<ci> S5 </ci>
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<ci> A3 </ci>
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<ci> B3 </ci>
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<cn cellml:units="dimensionless"> 1.0 </cn>
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<ci> R3 </ci>
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<ci> r </ci>
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<ci> A3 </ci>
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<ci> B3 </ci>
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<times/>
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<apply>
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<ci> Clk_m </ci>
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<apply>
<times/>
<ci> D0 </ci>
<ci> Clk_m </ci>
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</component>
<component cmeta:id="Clk_c" name="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" name="Clk_c"/>
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Robust Oscillations within the Interlocked Feedback Model of
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Ueda et al.'s mathematical model of circadian rhythms in Drosophila.
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<dc:creator rdf:resource="rdf:#80c31eab-7206-488c-adcc-38dd92c26456"/>
</rdf:Description>
</rdf:RDF>
</model>
