- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-07-29 10:33:56+12:00
- Desc:
- Tidied session file
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/ueda_hagiwara_kitano_2001/rawfile/09b8be6010363d54693f325ce06a0d9c12fa0d23/ueda_hagiwara_kitano_2001.cellml
<?xml version="1.0"?>
<!-- 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#" cmeta:id="ueda_2001" name="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: 11403560</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 prefix="nano" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="hour">
<unit multiplier="3600.0" units="second"/>
</units>
<units name="flux">
<unit units="nanomolar"/>
<unit exponent="-1" units="hour"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="hour"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="nanomolar"/>
<unit exponent="-1" units="hour"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="hour"/>
</component>
<component cmeta:id="Per_m" name="Per_m">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Per_m">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Per_m</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Per mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Per_m_Per_m" initial_value="0.5" name="Per_m" public_interface="out" units="nanomolar"/>
<variable initial_value="0.0" name="B1" units="dimensionless"/>
<variable initial_value="0.0" name="C1" units="flux"/>
<variable initial_value="1.45" name="S1" units="flux"/>
<variable initial_value="0.94" name="D1" units="flux"/>
<variable initial_value="0.3" name="L1" units="nanomolar"/>
<variable initial_value="1.02" name="R1" units="nanomolar"/>
<variable initial_value="0.45" name="A1" units="nanomolar"/>
<variable name="PT_n" public_interface="in" units="nanomolar"/>
<variable name="CC_n" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<variable name="a" public_interface="in" units="dimensionless"/>
<variable name="r" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Per_m</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> C1 </ci>
<apply>
<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>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
<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>
<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 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Per_c">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Per_c</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">cytosolic Per protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable initial_value="0.6" name="Per_c" public_interface="out" units="nanomolar"/>
<variable initial_value="0.48" name="S2" units="first_order_rate_constant"/>
<variable initial_value="0.44" name="D2" units="first_order_rate_constant"/>
<variable initial_value="0.2" name="L2" units="nanomolar"/>
<variable initial_value="1.0" name="Dbt_c" units="nanomolar"/>
<variable name="V1" public_interface="in" units="second_order_rate_constant"/>
<variable name="V2" public_interface="in" units="first_order_rate_constant"/>
<variable name="Per_m" public_interface="in" units="nanomolar"/>
<variable name="Tim_c" public_interface="in" units="nanomolar"/>
<variable name="PT_c" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<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/>
<apply>
<plus/>
<apply>
<times/>
<ci> S2 </ci>
<ci> Per_m </ci>
</apply>
<apply>
<times/>
<ci> V2 </ci>
<ci> PT_c </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1 </ci>
<ci> Per_c </ci>
<ci> Tim_c </ci>
</apply>
<apply>
<times/>
<ci> D2 </ci>
<ci> Dbt_c </ci>
<apply>
<divide/>
<ci> Per_c </ci>
<apply>
<plus/>
<ci> L2 </ci>
<ci> Per_c </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> Per_c </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Tim_m" name="Tim_m">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Tim_m">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Tim_m</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Tim mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Tim_m_Tim_m" initial_value="0.7" name="Tim_m" public_interface="out" units="nanomolar"/>
<variable initial_value="0.0" name="B2" units="dimensionless"/>
<variable initial_value="0.0" name="C2" units="flux"/>
<variable initial_value="1.45" name="S3" units="flux"/>
<variable initial_value="0.94" name="D3" units="flux"/>
<variable initial_value="0.3" name="L3" units="nanomolar"/>
<variable initial_value="1.02" name="R2" units="nanomolar"/>
<variable initial_value="0.45" name="A2" units="nanomolar"/>
<variable name="PT_n" public_interface="in" units="nanomolar"/>
<variable name="CC_n" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<variable name="a" public_interface="in" units="dimensionless"/>
<variable name="r" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Tim_m</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> C2 </ci>
<apply>
<times/>
<ci> S3 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci> CC_n </ci>
<ci> A2 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B2 </ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> D3 </ci>
<apply>
<divide/>
<ci> Tim_m </ci>
<apply>
<plus/>
<ci> L3 </ci>
<ci> Tim_m </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> Tim_m </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Tim_c" name="Tim_c">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Tim_c">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Tim_c</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">cytosolic Tim protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Tim_c_Tim_c" initial_value="0.8" name="Tim_c" public_interface="out" units="nanomolar"/>
<variable initial_value="0.48" name="S4" units="first_order_rate_constant"/>
<variable initial_value="0.44" name="D4" units="flux"/>
<variable initial_value="0.2" name="L4" units="nanomolar"/>
<variable name="V1" public_interface="in" units="second_order_rate_constant"/>
<variable name="V2" public_interface="in" units="first_order_rate_constant"/>
<variable name="Tim_m" public_interface="in" units="nanomolar"/>
<variable name="Per_c" public_interface="in" units="nanomolar"/>
<variable name="PT_c" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<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/>
<ci> V1 </ci>
<ci> Per_c </ci>
<ci> Tim_c </ci>
</apply>
<apply>
<times/>
<ci> D4 </ci>
<apply>
<divide/>
<ci> Tim_c </ci>
<apply>
<plus/>
<ci> L4 </ci>
<ci> Tim_c </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> Tim_c </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="PT_c" name="PT_c">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#PT_c">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">PT_c</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">cytosolic Per-Tim protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="PT_c_PT_c" initial_value="0.9" name="PT_c" public_interface="out" units="nanomolar"/>
<variable initial_value="0.44" name="D5" units="flux"/>
<variable initial_value="0.2" name="L5" units="nanomolar"/>
<variable name="K1" public_interface="in" units="nanomolar"/>
<variable name="K2" public_interface="in" units="nanomolar"/>
<variable name="T1" public_interface="in" units="flux"/>
<variable name="T2" public_interface="in" units="flux"/>
<variable name="V1" public_interface="in" units="second_order_rate_constant"/>
<variable name="V2" public_interface="in" units="first_order_rate_constant"/>
<variable name="Tim_c" public_interface="in" units="nanomolar"/>
<variable name="Per_c" public_interface="in" units="nanomolar"/>
<variable name="PT_n" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PT_c</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V1 </ci>
<ci> Per_c </ci>
<ci> Tim_c </ci>
</apply>
<apply>
<times/>
<ci> T2 </ci>
<apply>
<divide/>
<ci> PT_n </ci>
<apply>
<plus/>
<ci> K2 </ci>
<ci> PT_n </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2 </ci>
<ci> PT_c </ci>
</apply>
<apply>
<times/>
<ci> T1 </ci>
<apply>
<divide/>
<ci> PT_c </ci>
<apply>
<plus/>
<ci> K1 </ci>
<ci> PT_c </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D5 </ci>
<apply>
<divide/>
<ci> PT_c </ci>
<apply>
<plus/>
<ci> L5 </ci>
<ci> PT_c </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> PT_c </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="PT_n" name="PT_n">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#PT_n">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">PT_n</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">nuclear Per-Tim protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="PT_n_PT_n" initial_value="1.0" name="PT_n" public_interface="out" units="nanomolar"/>
<variable initial_value="0.29" name="D6" units="flux"/>
<variable initial_value="0.2" name="L6" units="nanomolar"/>
<variable name="K1" public_interface="in" units="nanomolar"/>
<variable name="K2" public_interface="in" units="nanomolar"/>
<variable name="T1" public_interface="in" units="flux"/>
<variable name="T2" public_interface="in" units="flux"/>
<variable name="PT_c" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PT_n</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> T1 </ci>
<apply>
<divide/>
<ci> PT_c </ci>
<apply>
<plus/>
<ci> K1 </ci>
<ci> PT_c </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> T2 </ci>
<apply>
<divide/>
<ci> PT_n </ci>
<apply>
<plus/>
<ci> K2 </ci>
<ci> PT_n </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D6 </ci>
<apply>
<divide/>
<ci> PT_n </ci>
<apply>
<plus/>
<ci> L6 </ci>
<ci> PT_n </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> PT_n </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Clk_m" name="Clk_m">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Clk_m">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Clk_m</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Clk mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Clk_m_Clk_m" initial_value="0.1" name="Clk_m" public_interface="out" units="nanomolar"/>
<variable initial_value="0.6" name="B3" units="dimensionless"/>
<variable initial_value="0.0" name="C3" units="flux"/>
<variable initial_value="1.63" name="S5" units="flux"/>
<variable initial_value="0.54" name="D7" units="flux"/>
<variable initial_value="0.13" name="L7" units="nanomolar"/>
<variable initial_value="0.89" name="R3" units="nanomolar"/>
<variable initial_value="0.8" name="A3" units="nanomolar"/>
<variable name="CC_n" public_interface="in" units="nanomolar"/>
<variable name="PT_n" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<variable name="D0" public_interface="in" units="first_order_rate_constant"/>
<variable name="a" public_interface="in" units="dimensionless"/>
<variable name="r" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Clk_m</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> C3 </ci>
<apply>
<times/>
<ci> S5 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci> PT_n </ci>
<ci> A3 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B3 </ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> CC_n </ci>
<ci> R3 </ci>
</apply>
<ci> r </ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> PT_n </ci>
<ci> A3 </ci>
</apply>
<ci> a </ci>
</apply>
<ci> B3 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> D7 </ci>
<apply>
<divide/>
<ci> Clk_m </ci>
<apply>
<plus/>
<ci> L7 </ci>
<ci> Clk_m </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> D0 </ci>
<ci> Clk_m </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Clk_c" name="Clk_c">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Clk_c">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Clk_c</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">cytosolic Clk protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Journal of Theoretical Biology</dc:title>
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