- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-07-08 02:05:08+12:00
- Desc:
- Added initial conditions, fixed annotations and added a model status comment. Model is fine in OpenCell but there's an odd error message in COR which I can't see in the model itself.
- Permanent Source URI:
- http://models.cellml.org/workspace/leloup_goldbeter_2003/rawfile/886d956f914ddc1a1e1cde5e4aee5b41e9c310f6/leloup_goldbeter_2003.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : leloup_model_2003.xml
CREATED : 22nd September 2003
LAST MODIFIED : 14th August 2007
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 Leloup and Goldbeter's 2003 mathematical model of the mammalian circadian clock.
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#" name="leloup_2003" cmeta:id="leloup_2003">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Detailed Computational Model for the Mammalian Circadian Clock</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 runs in OpenCell to recreate the published results (figure 2A from the published paper, where KAC = 0.6nM). The model needs to be run for 160 hours with a step size of 0.1 hours, and MP, MB and MC are plotted. Ignore the first couple of oscillations as the model needs to stabilise. Please note that the model presented here is the extended version of the model which includes equations to define the role of REV-ERB-alpha in inhibiting the transcription of Bmal1. There are 19 equations and the parameters are listed as part of the Supplementary data set under Figure 8.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Toward a detailed computational model for the mammalian circadian clock, Jean-Christophe Leloup and Albert Goldbeter, 2003,<emphasis>PNAS</emphasis>, 100, 7051-7056. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12775757&dopt=Abstract">PubMed ID: 12775757</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="leloup_2003.png"/>
</imageobject>
</mediaobject>
<caption>Model for circadian oscillations in mammals involving interlocked negative and positive regulations of <emphasis>Per</emphasis>, <emphasis>Cry</emphasis>, <emphasis>Bmal1</emphasis>, and <emphasis>Rev-Erb</emphasis> genes by their protein products.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="hour">
<unit units="second" multiplier="3600.0"/>
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</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>
<component name="environment">
<variable units="hour" public_interface="out" name="time" cmeta:id="environment_time"/>
</component>
<component name="MP" cmeta:id="MP">
<rdf:RDF>
<rdf:Description rdf:about="#MP">
<dc:title>MP</dc:title>
<dcterms:alternative>Per mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="MP" cmeta:id="MP_MP" initial_value="0.1"/>
<variable units="flux" name="vsP" initial_value="2.4"/>
<variable units="flux" name="vmP" initial_value="2.2"/>
<variable units="first_order_rate_constant" name="kdmp" initial_value="0.02"/>
<variable units="nanomolar" name="KAP" initial_value="0.6"/>
<variable units="nanomolar" name="KmP" initial_value="0.3"/>
<variable units="dimensionless" public_interface="in" name="n"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> vsP </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KAP </ci>
<ci> n </ci>
</apply>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmP </ci>
<apply>
<divide/>
<ci> MP </ci>
<apply>
<plus/>
<ci> KmP </ci>
<ci> MP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmp </ci>
<ci> MP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MC" cmeta:id="MC">
<rdf:RDF>
<rdf:Description rdf:about="#MC">
<dc:title>MC</dc:title>
<dcterms:alternative>Cry mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="MC" cmeta:id="MC_MC" initial_value="1.2"/>
<variable units="flux" name="vsC" initial_value="2.2"/>
<variable units="flux" name="vmC" initial_value="2.0"/>
<variable units="first_order_rate_constant" name="kdmc" initial_value="0.02"/>
<variable units="nanomolar" name="KAC" initial_value="0.6"/>
<variable units="nanomolar" name="KmC" initial_value="0.4"/>
<variable units="dimensionless" public_interface="in" name="n"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MC </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> vsC </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KAC </ci>
<ci> n </ci>
</apply>
<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmC </ci>
<apply>
<divide/>
<ci> MC </ci>
<apply>
<plus/>
<ci> KmC </ci>
<ci> MC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmc </ci>
<ci> MC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MB" cmeta:id="MB">
<rdf:RDF>
<rdf:Description rdf:about="#MB">
<dc:title>MB</dc:title>
<dcterms:alternative>Bmal1 mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="MB" cmeta:id="MB_MB" initial_value="9"/>
<variable units="flux" name="vsB" initial_value="1.8"/>
<variable units="flux" name="vmB" initial_value="1.3"/>
<variable units="first_order_rate_constant" name="kdmb" initial_value="0.02"/>
<variable units="nanomolar" name="KIB" initial_value="2.2"/>
<variable units="nanomolar" name="KmB" initial_value="0.4"/>
<variable units="dimensionless" public_interface="in" name="m"/>
<variable units="nanomolar" public_interface="in" name="RN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MB </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> vsB </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KIB </ci>
<ci> m </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KIB </ci>
<ci> m </ci>
</apply>
<apply>
<power/>
<ci> RN </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmB </ci>
<apply>
<divide/>
<ci> MB </ci>
<apply>
<plus/>
<ci> KmB </ci>
<ci> MB </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmb </ci>
<ci> MB </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MR" cmeta:id="MR">
<rdf:RDF>
<rdf:Description rdf:about="#MR">
<dc:title>MR</dc:title>
<dcterms:alternative>Rev-Erb</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="MR" cmeta:id="MR_MR" initial_value="1.5"/>
<variable units="flux" name="vsR" initial_value="1.6"/>
<variable units="flux" name="vmR" initial_value="1.6"/>
<variable units="first_order_rate_constant" name="kdmr" initial_value="0.02"/>
<variable units="nanomolar" name="KAR" initial_value="0.6"/>
<variable units="nanomolar" name="KmR" initial_value="0.4"/>
<variable units="dimensionless" public_interface="in" name="h"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> MR </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> vsR </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> BN </ci>
<ci> h </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KAR </ci>
<ci> h </ci>
</apply>
<apply>
<power/>
<ci> BN </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> vmR </ci>
<apply>
<divide/>
<ci> MR </ci>
<apply>
<plus/>
<ci> KmR </ci>
<ci> MR </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdmr </ci>
<ci> MR </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PC" cmeta:id="PC">
<rdf:RDF>
<rdf:Description rdf:about="#PC">
<dc:title>PC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated PER protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="PC" cmeta:id="PC_PC" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksP"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="second_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k4"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1P"/>
<variable units="flux" public_interface="in" name="V2P"/>
<variable units="nanomolar" public_interface="in" name="PCP"/>
<variable units="nanomolar" public_interface="in" name="PCC"/>
<variable units="nanomolar" public_interface="in" name="CC"/>
<variable units="nanomolar" public_interface="in" name="MP"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> ksP </ci>
<ci> MP </ci>
</apply>
<apply>
<times/>
<ci> V2P </ci>
<apply>
<divide/>
<ci> PCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k4 </ci>
<ci> PCC </ci>
</apply>
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<apply>
<plus/>
<apply>
<times/>
<ci> V1P </ci>
<apply>
<divide/>
<ci> PC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> PC </ci>
<ci> CC </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CC" cmeta:id="CC">
<rdf:RDF>
<rdf:Description rdf:about="#CC">
<dc:title>CC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated CRY protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="CC" cmeta:id="CC_CC" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksC"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="second_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k4"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdnc"/>
<variable units="flux" public_interface="in" name="V1C"/>
<variable units="flux" public_interface="in" name="V2C"/>
<variable units="nanomolar" public_interface="in" name="CCP"/>
<variable units="nanomolar" public_interface="in" name="PC"/>
<variable units="nanomolar" public_interface="in" name="PCC"/>
<variable units="nanomolar" public_interface="in" name="MC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> CC </ci>
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<apply>
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<apply>
<plus/>
<apply>
<times/>
<ci> ksC </ci>
<ci> MC </ci>
</apply>
<apply>
<times/>
<ci> V2C </ci>
<apply>
<divide/>
<ci> CCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> CCP </ci>
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</apply>
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<apply>
<times/>
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<ci> PCC </ci>
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<apply>
<times/>
<ci> V1C </ci>
<apply>
<divide/>
<ci> CC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> CC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> PC </ci>
<ci> CC </ci>
</apply>
<apply>
<times/>
<ci> kdnc </ci>
<ci> CC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="RC" cmeta:id="RC">
<rdf:RDF>
<rdf:Description rdf:about="#RC">
<dc:title>RC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated REV-ERB</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="RC" cmeta:id="RC_RC" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksR"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="k9"/>
<variable units="first_order_rate_constant" public_interface="in" name="k10"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="vdRC"/>
<variable units="nanomolar" public_interface="in" name="RN"/>
<variable units="nanomolar" public_interface="in" name="MR"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> RC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> ksR </ci>
<ci> MR </ci>
</apply>
<apply>
<times/>
<ci> k10 </ci>
<ci> RN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k9 </ci>
<ci> RC </ci>
</apply>
<apply>
<times/>
<ci> vdRC </ci>
<apply>
<divide/>
<ci> RC </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> RC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> RC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCP" cmeta:id="PCP">
<rdf:RDF>
<rdf:Description rdf:about="#PCP">
<dc:title>PCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated PER protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="PCP" cmeta:id="PCP_PCP" initial_value="0.1"/>
<variable units="flux" public_interface="in" name="vdPC"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1P"/>
<variable units="flux" public_interface="in" name="V2P"/>
<variable units="nanomolar" public_interface="in" name="PC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1P </ci>
<apply>
<divide/>
<ci> PC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2P </ci>
<apply>
<divide/>
<ci> PCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdPC </ci>
<apply>
<divide/>
<ci> PCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CCP" cmeta:id="CCP">
<rdf:RDF>
<rdf:Description rdf:about="#CCP">
<dc:title>CCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated CRY protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="CCP" cmeta:id="CCP_CCP" initial_value="0.1"/>
<variable units="flux" public_interface="in" name="vdCC"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1C"/>
<variable units="flux" public_interface="in" name="V2C"/>
<variable units="nanomolar" public_interface="in" name="CC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> CCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1C </ci>
<apply>
<divide/>
<ci> CC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> CC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2C </ci>
<apply>
<divide/>
<ci> CCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdCC </ci>
<apply>
<divide/>
<ci> CCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> CCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCC" cmeta:id="PCC">
<rdf:RDF>
<rdf:Description rdf:about="#PCC">
<dc:title>PCC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="PCC" cmeta:id="PCC_PCC" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="k1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k4"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1PC"/>
<variable units="flux" public_interface="in" name="V2PC"/>
<variable units="nanomolar" public_interface="in" name="PCCP"/>
<variable units="nanomolar" public_interface="in" name="PCN"/>
<variable units="nanomolar" public_interface="in" name="PC"/>
<variable units="nanomolar" public_interface="in" name="CC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V2PC </ci>
<apply>
<divide/>
<ci> PCCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> PC </ci>
<ci> CC </ci>
</apply>
<apply>
<times/>
<ci> k2 </ci>
<ci> PCN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1PC </ci>
<apply>
<divide/>
<ci> PCC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k4 </ci>
<ci> PCC </ci>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> PCC </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCN" cmeta:id="PCN">
<rdf:RDF>
<rdf:Description rdf:about="#PCN">
<dc:title>PCN</dc:title>
<dcterms:alternative>nuclear non-phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="PCN" cmeta:id="PCN_PCN" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="k1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k7"/>
<variable units="first_order_rate_constant" public_interface="in" name="k8"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3PC"/>
<variable units="flux" public_interface="in" name="V4PC"/>
<variable units="nanomolar" public_interface="in" name="PCNP"/>
<variable units="nanomolar" public_interface="in" name="PCC"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="nanomolar" public_interface="in" name="IN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCN </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V4PC </ci>
<apply>
<divide/>
<ci> PCNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> PCC </ci>
</apply>
<apply>
<times/>
<ci> k8 </ci>
<ci> IN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V3PC </ci>
<apply>
<divide/>
<ci> PCN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k2 </ci>
<ci> PCN </ci>
</apply>
<apply>
<times/>
<ci> k7 </ci>
<ci> BN </ci>
<ci> PCN </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="RN" cmeta:id="RN">
<rdf:RDF>
<rdf:Description rdf:about="#RN">
<dc:title>RN</dc:title>
<dcterms:alternative>nuclear non-phosphorylated REV-ERB</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="RN" cmeta:id="RN_RN" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="k9"/>
<variable units="first_order_rate_constant" public_interface="in" name="k10"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="vdRN"/>
<variable units="nanomolar" public_interface="in" name="RC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> RN </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k9 </ci>
<ci> RC </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k10 </ci>
<ci> RN </ci>
</apply>
<apply>
<times/>
<ci> vdRN</ci>
<apply>
<divide/>
<ci> RN </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> RN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> RN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCCP" cmeta:id="PCCP">
<rdf:RDF>
<rdf:Description rdf:about="#PCCP">
<dc:title>PCCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="PCCP" cmeta:id="PCCP_PCCP" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1PC"/>
<variable units="flux" public_interface="in" name="V2PC"/>
<variable units="flux" public_interface="in" name="vdPCC"/>
<variable units="nanomolar" public_interface="in" name="PCC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1PC </ci>
<apply>
<divide/>
<ci> PCC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2PC </ci>
<apply>
<divide/>
<ci> PCCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdPCC </ci>
<apply>
<divide/>
<ci> PCCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PCNP" cmeta:id="PCNP">
<rdf:RDF>
<rdf:Description rdf:about="#PCNP">
<dc:title>PCNP</dc:title>
<dcterms:alternative>nuclear phosphorylated PER-CRY protein complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="PCNP" cmeta:id="PCNP_PCNP" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3PC"/>
<variable units="flux" public_interface="in" name="V4PC"/>
<variable units="flux" public_interface="in" name="vdPCN"/>
<variable units="nanomolar" public_interface="in" name="PCN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> PCNP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V3PC </ci>
<apply>
<divide/>
<ci> PCN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> PCN </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V4PC </ci>
<apply>
<divide/>
<ci> PCNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdPCN </ci>
<apply>
<divide/>
<ci> PCNP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> PCNP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BC" cmeta:id="BC">
<rdf:RDF>
<rdf:Description rdf:about="#BC">
<dc:title>BC</dc:title>
<dcterms:alternative>cytosolic non-phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="BC" cmeta:id="BC_BC" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="ksB"/>
<variable units="first_order_rate_constant" public_interface="in" name="k5"/>
<variable units="first_order_rate_constant" public_interface="in" name="k6"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1B"/>
<variable units="flux" public_interface="in" name="V2B"/>
<variable units="nanomolar" public_interface="in" name="MB"/>
<variable units="nanomolar" public_interface="in" name="BCP"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BC </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V2B </ci>
<apply>
<divide/>
<ci> BCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k6 </ci>
<ci> BN </ci>
</apply>
<apply>
<times/>
<ci> ksB </ci>
<ci> MB </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V1B </ci>
<apply>
<divide/>
<ci> BC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BC </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k5 </ci>
<ci> BC </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BCP" cmeta:id="BCP">
<rdf:RDF>
<rdf:Description rdf:about="#BCP">
<dc:title>BCP</dc:title>
<dcterms:alternative>cytosolic phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="BCP" cmeta:id="BCP_BCP" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V1B"/>
<variable units="flux" public_interface="in" name="V2B"/>
<variable units="flux" public_interface="in" name="vdBC"/>
<variable units="nanomolar" public_interface="in" name="BC"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BCP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V1B </ci>
<apply>
<divide/>
<ci> BC </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BC </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V2B </ci>
<apply>
<divide/>
<ci> BCP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdBC </ci>
<apply>
<divide/>
<ci> BCP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BCP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BN" cmeta:id="BN">
<rdf:RDF>
<rdf:Description rdf:about="#PCN">
<dc:title>BN</dc:title>
<dcterms:alternative>nuclear non-phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="BN" cmeta:id="BN_BN" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="first_order_rate_constant" public_interface="in" name="k5"/>
<variable units="first_order_rate_constant" public_interface="in" name="k6"/>
<variable units="second_order_rate_constant" public_interface="in" name="k7"/>
<variable units="first_order_rate_constant" public_interface="in" name="k8"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3B"/>
<variable units="flux" public_interface="in" name="V4B"/>
<variable units="nanomolar" public_interface="in" name="BNP"/>
<variable units="nanomolar" public_interface="in" name="BC"/>
<variable units="nanomolar" public_interface="in" name="PCN"/>
<variable units="nanomolar" public_interface="in" name="IN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BN </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> V4B </ci>
<apply>
<divide/>
<ci> BNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k5 </ci>
<ci> BC </ci>
</apply>
<apply>
<times/>
<ci> k8 </ci>
<ci> IN </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V3B </ci>
<apply>
<divide/>
<ci> BN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k6 </ci>
<ci> BN </ci>
</apply>
<apply>
<times/>
<ci> k7 </ci>
<ci> BN </ci>
<ci> PCN </ci>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="BNP" cmeta:id="BNP">
<rdf:RDF>
<rdf:Description rdf:about="#BNP">
<dc:title>BNP</dc:title>
<dcterms:alternative>nuclear phosphorylated BMAL1 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="BNP" cmeta:id="BNP_BNP" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kp"/>
<variable units="nanomolar" public_interface="in" name="Kdp"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="flux" public_interface="in" name="V3B"/>
<variable units="flux" public_interface="in" name="V4B"/>
<variable units="flux" public_interface="in" name="vdBN"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> BNP </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> V3B </ci>
<apply>
<divide/>
<ci> BN </ci>
<apply>
<plus/>
<ci> Kp </ci>
<ci> BN </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> V4B </ci>
<apply>
<divide/>
<ci> BNP </ci>
<apply>
<plus/>
<ci> Kdp </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vdBN </ci>
<apply>
<divide/>
<ci> BNP </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> BNP </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="IN" cmeta:id="IN">
<rdf:RDF>
<rdf:Description rdf:about="#IN">
<dc:title>IN</dc:title>
<dcterms:alternative>nuclear inactive complex between PER-CRY and CLOCK-BMAL1</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="IN" cmeta:id="IN_IN" initial_value="0.1"/>
<variable units="nanomolar" public_interface="in" name="Kd"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdn"/>
<variable units="second_order_rate_constant" public_interface="in" name="k7"/>
<variable units="first_order_rate_constant" public_interface="in" name="k8"/>
<variable units="flux" public_interface="in" name="vdIN"/>
<variable units="nanomolar" public_interface="in" name="PCN"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> IN </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k7 </ci>
<ci> BN </ci>
<ci> PCN </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k8 </ci>
<ci> IN </ci>
</apply>
<apply>
<times/>
<ci> vdIN </ci>
<apply>
<divide/>
<ci> IN </ci>
<apply>
<plus/>
<ci> Kd </ci>
<ci> IN </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdn </ci>
<ci> IN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="first_order_rate_constant" public_interface="out" name="k1" initial_value="0.8"/>
<variable units="first_order_rate_constant" public_interface="out" name="k2" initial_value="0.4"/>
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<dcterms:W3CDTF>2007-08-14T00:00:00+00:00</dcterms:W3CDTF>
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<dcterms:W3CDTF>2008-08-20T18:38:00+12:00</dcterms:W3CDTF>
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<vCard:Given>James</vCard:Given>
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<dcterms:W3CDTF>2003-06-10</dcterms:W3CDTF>
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<vCard:Given>Jean-Christophe</vCard:Given>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
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<dc:title>Toward a detailed computational model for the mammalian circadian clock</dc:title>
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<vCard:Given>Catherine</vCard:Given>
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