- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-07-08 02:05:47+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:
- https://models.physiomeproject.org/workspace/leloup_goldbeter_2004/rawfile/84dffe653970526bde3c4adbdfed59213b80b65f/leloup_goldbeter_2004.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : leloup_2004.xml
CREATED : 14th August 2007
LAST MODIFIED : 14th August 2007
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Leloup and Goldbeter's 2004 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_2004" cmeta:id="leloup_2004">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms</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 2C from the published paper). 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. Also please note that in the version of the model presented here, parameter set 4 from the original paper has been used. The units have been checked and they are consistent.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="leloup_2004.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model for circadian oscillations in mammals including positive and negative feedback on the transcription of the Per, Cry and Bmal1 genes by their protein products. Per, Cry and Bmal1 are transcribed in the nucleus and are then transferred to the cytosol where their proteins are translated and the mRNAs are degraded. Light increases the rate of Per transcription.</caption>
</informalfigure>
<para>
The original paper reference is cited below:
</para>
<para>
Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms, Jean-Christophe Leloup and Albert Goldbeter, 2004,
<emphasis>Journal of Theoretical Biology</emphasis>, 230, 541-562. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/15363675">PubMed ID: 15363675</ulink>
</para>
</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="0.5"/>
<variable units="flux" name="vsP"/>
<variable units="flux" name="vmP" initial_value="1.1"/>
<variable units="first_order_rate_constant" name="kdmp" initial_value="0.01"/>
<variable units="nanomolar" name="KAP" initial_value="0.7"/>
<variable units="nanomolar" name="KmP" initial_value="0.3"/>
<variable units="flux" public_interface="in" name="vstot"/>
<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>
<apply>
<eq/>
<ci> vsP </ci>
<ci> vstot </ci>
</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="0.3"/>
<variable units="flux" name="vsC"/>
<variable units="flux" name="vmC" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="kdmc" initial_value="0.01"/>
<variable units="nanomolar" name="KAC" initial_value="1.0"/>
<variable units="nanomolar" name="KmC" initial_value="0.4"/>
<variable units="flux" public_interface="in" name="vstot"/>
<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>
<apply>
<eq/>
<ci> vsC </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.8 </cn>
<ci> vstot </ci>
</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="3.1"/>
<variable units="flux" name="vsB"/>
<variable units="flux" name="vmB" initial_value="0.2"/>
<variable units="first_order_rate_constant" name="kdmb" initial_value="0.01"/>
<variable units="nanomolar" name="KIB" initial_value="0.8"/>
<variable units="nanomolar" name="KmB" initial_value="0.4"/>
<variable units="flux" public_interface="in" name="vstot"/>
<variable units="dimensionless" public_interface="in" name="m"/>
<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> 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> BN </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>
<apply>
<eq/>
<ci> vsB </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.7 </cn>
<ci> vstot </ci>
</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" 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>
</apply>
<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" 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>
</apply>
<apply>
<minus/>
<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>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k4 </ci>
<ci> PCC </ci>
</apply>
</apply>
<apply>
<plus/>
<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="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" 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" 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" 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" 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="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" 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" 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" 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" 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" 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" 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" 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="0.2"/>
<variable units="second_order_rate_constant" public_interface="out" name="k3" initial_value="0.8"/>
<variable units="first_order_rate_constant" public_interface="out" name="k4" initial_value="0.2"/>
<variable units="first_order_rate_constant" public_interface="out" name="k5" initial_value="0.4"/>
<variable units="first_order_rate_constant" public_interface="out" name="k6" initial_value="0.2"/>
<variable units="second_order_rate_constant" public_interface="out" name="k7" initial_value="0.5"/>
<variable units="first_order_rate_constant" public_interface="out" name="k8" initial_value="0.1"/>
<variable units="first_order_rate_constant" public_interface="out" name="kdnc" initial_value="0.01"/>
<variable units="first_order_rate_constant" public_interface="out" name="kdn" initial_value="0.01"/>
<variable units="first_order_rate_constant" name="kstot" initial_value="1.0"/>
<variable units="first_order_rate_constant" public_interface="out" name="ksB"/>
<variable units="first_order_rate_constant" public_interface="out" name="ksC"/>
<variable units="first_order_rate_constant" public_interface="out" name="ksP"/>
<variable units="dimensionless" public_interface="out" name="m" initial_value="4.0"/>
<variable units="dimensionless" public_interface="out" name="n" initial_value="4.0"/>
<variable units="flux" public_interface="out" name="vstot" initial_value="1.0"/>
<variable units="nanomolar" public_interface="out" name="Kd" initial_value="0.3"/>
<variable units="nanomolar" public_interface="out" name="Kdp" initial_value="0.3"/>
<variable units="nanomolar" public_interface="out" name="Kp" initial_value="0.1"/>
<variable units="flux" name="Vphos" initial_value="0.6"/>
<variable units="flux" public_interface="out" name="V1B" initial_value="1.0"/>
<variable units="flux" public_interface="out" name="V1C" initial_value="0.6"/>
<variable units="flux" public_interface="out" name="V1P"/>
<variable units="flux" public_interface="out" name="V1PC"/>
<variable units="flux" public_interface="out" name="V2B" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V2C" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V2P" initial_value="0.3"/>
<variable units="flux" public_interface="out" name="V2PC" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="V3B" initial_value="1.0"/>
<variable units="flux" public_interface="out" name="V3PC"/>
<variable units="flux" public_interface="out" name="V4B" initial_value="0.2"/>
<variable units="flux" public_interface="out" name="V4PC" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="vdBC" initial_value="1.0"/>
<variable units="flux" public_interface="out" name="vdBN" initial_value="0.5"/>
<variable units="flux" public_interface="out" name="vdCC" initial_value="0.7"/>
<variable units="flux" public_interface="out" name="vdIN" initial_value="0.8"/>
<variable units="flux" public_interface="out" name="vdPC" initial_value="0.7"/>
<variable units="flux" public_interface="out" name="vdPCC" initial_value="1.0"/>
<variable units="flux" public_interface="out" name="vdPCN" initial_value="1.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> ksB </ci>
<ci> kstot </ci>
</apply>
<apply>
<eq/>
<ci> ksC </ci>
<ci> kstot </ci>
</apply>
<apply>
<eq/>
<ci> ksP </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.5 </cn>
<ci> kstot </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> V1P </ci>
<ci> Vphos </ci>
</apply>
<apply>
<eq/>
<ci> V1PC </ci>
<ci> Vphos </ci>
</apply>
<apply>
<eq/>
<ci> V3PC </ci>
<ci> Vphos </ci>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="MP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MB"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="CC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="CCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCNP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BCP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BNP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="IN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="BN" component_1="MP"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="MP"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="vstot" variable_1="vstot"/>
</connection>
<connection>
<map_components component_2="BN" component_1="MC"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="MC"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="vstot" variable_1="vstot"/>
</connection>
<connection>
<map_components component_2="BN" component_1="MB"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="MB"/>
<map_variables variable_2="m" variable_1="m"/>
<map_variables variable_2="vstot" variable_1="vstot"/>
</connection>
<connection>
<map_components component_2="MP" component_1="PC"/>
<map_variables variable_2="MP" variable_1="MP"/>
</connection>
<connection>
<map_components component_2="PCP" component_1="PC"/>
<map_variables variable_2="PC" variable_1="PC"/>
<map_variables variable_2="PCP" variable_1="PCP"/>
</connection>
<connection>
<map_components component_2="PCC" component_1="PC"/>
<map_variables variable_2="PC" variable_1="PC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
</connection>
<connection>
<map_components component_2="CC" component_1="PC"/>
<map_variables variable_2="PC" variable_1="PC"/>
<map_variables variable_2="CC" variable_1="CC"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PC"/>
<map_variables variable_2="ksP" variable_1="ksP"/>
<map_variables variable_2="V1P" variable_1="V1P"/>
<map_variables variable_2="V2P" variable_1="V2P"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k4" variable_1="k4"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="MC" component_1="CC"/>
<map_variables variable_2="MC" variable_1="MC"/>
</connection>
<connection>
<map_components component_2="CCP" component_1="CC"/>
<map_variables variable_2="CC" variable_1="CC"/>
<map_variables variable_2="CCP" variable_1="CCP"/>
</connection>
<connection>
<map_components component_2="PCC" component_1="CC"/>
<map_variables variable_2="CC" variable_1="CC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="CC"/>
<map_variables variable_2="ksC" variable_1="ksC"/>
<map_variables variable_2="V1C" variable_1="V1C"/>
<map_variables variable_2="V2C" variable_1="V2C"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k4" variable_1="k4"/>
<map_variables variable_2="kdnc" variable_1="kdnc"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V1P" variable_1="V1P"/>
<map_variables variable_2="V2P" variable_1="V2P"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdPC" variable_1="vdPC"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="CCP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V1C" variable_1="V1C"/>
<map_variables variable_2="V2C" variable_1="V2C"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdCC" variable_1="vdCC"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="PCCP" component_1="PCC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
<map_variables variable_2="PCCP" variable_1="PCCP"/>
</connection>
<connection>
<map_components component_2="PCN" component_1="PCC"/>
<map_variables variable_2="PCC" variable_1="PCC"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCC"/>
<map_variables variable_2="k1" variable_1="k1"/>
<map_variables variable_2="k2" variable_1="k2"/>
<map_variables variable_2="V1PC" variable_1="V1PC"/>
<map_variables variable_2="V2PC" variable_1="V2PC"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k4" variable_1="k4"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="BN" component_1="PCN"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="IN" component_1="PCN"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
<map_variables variable_2="IN" variable_1="IN"/>
</connection>
<connection>
<map_components component_2="PCN" component_1="PCNP"/>
<map_variables variable_2="PCNP" variable_1="PCNP"/>
<map_variables variable_2="PCN" variable_1="PCN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCN"/>
<map_variables variable_2="k1" variable_1="k1"/>
<map_variables variable_2="k2" variable_1="k2"/>
<map_variables variable_2="V3PC" variable_1="V3PC"/>
<map_variables variable_2="V4PC" variable_1="V4PC"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k7" variable_1="k7"/>
<map_variables variable_2="k8" variable_1="k8"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCCP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V1PC" variable_1="V1PC"/>
<map_variables variable_2="V2PC" variable_1="V2PC"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdPCC" variable_1="vdPCC"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="PCNP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V3PC" variable_1="V3PC"/>
<map_variables variable_2="V4PC" variable_1="V4PC"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdPCN" variable_1="vdPCN"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="MB" component_1="BC"/>
<map_variables variable_2="MB" variable_1="MB"/>
</connection>
<connection>
<map_components component_2="BCP" component_1="BC"/>
<map_variables variable_2="BC" variable_1="BC"/>
<map_variables variable_2="BCP" variable_1="BCP"/>
</connection>
<connection>
<map_components component_2="BN" component_1="BC"/>
<map_variables variable_2="BC" variable_1="BC"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="BC"/>
<map_variables variable_2="ksB" variable_1="ksB"/>
<map_variables variable_2="V1B" variable_1="V1B"/>
<map_variables variable_2="V2B" variable_1="V2B"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k5" variable_1="k5"/>
<map_variables variable_2="k6" variable_1="k6"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="BCP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V1B" variable_1="V1B"/>
<map_variables variable_2="V2B" variable_1="V2B"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdBC" variable_1="vdBC"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="BNP" component_1="BN"/>
<map_variables variable_2="BN" variable_1="BN"/>
<map_variables variable_2="BNP" variable_1="BNP"/>
</connection>
<connection>
<map_components component_2="BN" component_1="IN"/>
<map_variables variable_2="IN" variable_1="IN"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="BN"/>
<map_variables variable_2="k7" variable_1="k7"/>
<map_variables variable_2="k8" variable_1="k8"/>
<map_variables variable_2="V3B" variable_1="V3B"/>
<map_variables variable_2="V4B" variable_1="V4B"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="k5" variable_1="k5"/>
<map_variables variable_2="k6" variable_1="k6"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="BNP"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="V3B" variable_1="V3B"/>
<map_variables variable_2="V4B" variable_1="V4B"/>
<map_variables variable_2="Kp" variable_1="Kp"/>
<map_variables variable_2="Kdp" variable_1="Kdp"/>
<map_variables variable_2="vdBN" variable_1="vdBN"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="IN"/>
<map_variables variable_2="k7" variable_1="k7"/>
<map_variables variable_2="k8" variable_1="k8"/>
<map_variables variable_2="Kd" variable_1="Kd"/>
<map_variables variable_2="vdIN" variable_1="vdIN"/>
<map_variables variable_2="kdn" variable_1="kdn"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Bag rdf:about="rdf:#83e5ada9-bb95-4648-a6fa-6dcc1ab69ff5">
<rdf:li>circadian rhythms</rdf:li>
<rdf:li>clock</rdf:li>
<rdf:li>signal transduction</rdf:li>
</rdf:Bag>
<rdf:Description rdf:about="rdf:#83e5ada9-bb95-4648-a6fa-6dcc1ab69ff5"/>
<rdf:Seq rdf:about="rdf:#4f2642b3-4111-4ed1-aba2-b5b44e51f389">
<rdf:li rdf:resource="rdf:#1e842903-74ae-4e10-b0f6-3adbbdec10ce"/>
<rdf:li rdf:resource="rdf:#a0a9fcc7-18e3-4f9a-b305-ffaf452f018a"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#4f2642b3-4111-4ed1-aba2-b5b44e51f389"/>
<rdf:Description rdf:about="rdf:#0f64b497-f93e-4617-abfe-b0336720bf77">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1e842903-74ae-4e10-b0f6-3adbbdec10ce">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#9fec0c66-7271-4c04-b909-42c3d09e7911"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#83d99a85-727f-4bfe-9afa-393af1c8b0e3">
<vCard:Given>Albert</vCard:Given>
<vCard:Family>Goldbeter</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d7eb62b2-cb09-4ce8-8984-8879206b0f4b">
<vCard:ORG rdf:resource="rdf:#daccc722-a49f-43fd-8c86-0ce6ec19bf4d"/>
<vCard:EMAIL rdf:resource="rdf:#0f64b497-f93e-4617-abfe-b0336720bf77"/>
<vCard:N rdf:resource="rdf:#0fee36ab-4a8d-4fb6-b1ae-009bbe074e14"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a0a9fcc7-18e3-4f9a-b305-ffaf452f018a">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#83d99a85-727f-4bfe-9afa-393af1c8b0e3"/>
</rdf:Description>
<rdf:Description rdf:about="#leloup_2004">
<dc:title>Leloup and Goldbeter's 2004 mathematical model of the mammalian circadian clock.</dc:title>
<cmeta:comment rdf:resource="rdf:#7c60384a-188c-46ed-8d88-851b1fe9bafa"/>
<bqs:reference rdf:resource="rdf:#03db62d8-1230-4082-8b85-d1e9703236e8"/>
<bqs:reference rdf:resource="rdf:#cb857320-723e-46c5-9e32-d833a9b32817"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9fec0c66-7271-4c04-b909-42c3d09e7911">
<vCard:Given>Jean-Christophe</vCard:Given>
<vCard:Family>Leloup</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7c60384a-188c-46ed-8d88-851b1fe9bafa">
<dc:creator rdf:resource="rdf:#d45568b4-aa15-4caf-92f2-6e926c2db09d"/>
<rdf:value>This is a CellML description of Leloup and Goldbeter's 2004 mathematical model of the mammalian circadian clock.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#daccc722-a49f-43fd-8c86-0ce6ec19bf4d">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0fee36ab-4a8d-4fb6-b1ae-009bbe074e14">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#159a942b-3ca5-4824-972b-7e71055a5836">
<dcterms:W3CDTF>2007-08-14T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d45568b4-aa15-4caf-92f2-6e926c2db09d">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#76232b07-ac25-44af-b4cf-34e418555ad9">
<dc:creator rdf:resource="rdf:#4f2642b3-4111-4ed1-aba2-b5b44e51f389"/>
<dc:title>Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms</dc:title>
<bqs:volume>230</bqs:volume>
<bqs:first_page>541</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#bb67a50e-31f7-40a5-b350-e513678c2c84"/>
<dcterms:issued rdf:resource="rdf:#2ab1c081-0d1c-4f78-a9df-969eeb9544e9"/>
<bqs:last_page>562</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fca2df73-ec55-4a88-a802-fc4bda7937ad">
<vCard:FN/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bb67a50e-31f7-40a5-b350-e513678c2c84">
<dc:title>Journal of Thoretical Biology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3531c524-aefc-4bf7-86e5-ebe71fc32999">
<dc:creator rdf:resource="rdf:#fca2df73-ec55-4a88-a802-fc4bda7937ad"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2ab1c081-0d1c-4f78-a9df-969eeb9544e9">
<dcterms:W3CDTF>2004-10-21</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$u2tBq1">
<rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
<rdf:first rdf:resource="rdf:#$v2tBq1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#50edd79a-c4b7-4575-8fde-821aa85e5792">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#83e5ada9-bb95-4648-a6fa-6dcc1ab69ff5"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>The University of Auckland, Auckland Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#3531c524-aefc-4bf7-86e5-ebe71fc32999"/>
<dcterms:created rdf:resource="rdf:#159a942b-3ca5-4824-972b-7e71055a5836"/>
<dc:creator rdf:resource="rdf:#d7eb62b2-cb09-4ce8-8984-8879206b0f4b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03db62d8-1230-4082-8b85-d1e9703236e8">
<dc:subject rdf:resource="rdf:#50edd79a-c4b7-4575-8fde-821aa85e5792"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cb857320-723e-46c5-9e32-d833a9b32817">
<bqs:Pubmed_id>15363675</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#76232b07-ac25-44af-b4cf-34e418555ad9"/>
</rdf:Description>
</rdf:RDF>
</model>
