<?xml version="1.0"?>
<!-- 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#" cmeta:id="leloup_2003" name="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>
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<times/>
<ci> kdn </ci>
<ci> PCC </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="PCN" name="PCN">
<variable cmeta:id="PCN_PCN" initial_value="0.1" name="PCN" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="k1" public_interface="in" units="first_order_rate_constant"/>
<variable name="k2" public_interface="in" units="first_order_rate_constant"/>
<variable name="k7" public_interface="in" units="second_order_rate_constant"/>
<variable name="k8" public_interface="in" units="first_order_rate_constant"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V3PC" public_interface="in" units="flux"/>
<variable name="V4PC" public_interface="in" units="flux"/>
<variable name="PCNP" public_interface="in" units="nanomolar"/>
<variable name="PCC" public_interface="in" units="nanomolar"/>
<variable name="BN" public_interface="in" units="nanomolar"/>
<variable name="IN" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="RN" name="RN">
<variable cmeta:id="RN_RN" initial_value="0.1" name="RN" public_interface="out" units="nanomolar"/>
<variable name="Kd" public_interface="in" units="nanomolar"/>
<variable name="k9" public_interface="in" units="first_order_rate_constant"/>
<variable name="k10" public_interface="in" units="first_order_rate_constant"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="vdRN" public_interface="in" units="flux"/>
<variable name="RC" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="PCCP" name="PCCP">
<variable cmeta:id="PCCP_PCCP" initial_value="0.1" name="PCCP" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="Kd" public_interface="in" units="nanomolar"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V1PC" public_interface="in" units="flux"/>
<variable name="V2PC" public_interface="in" units="flux"/>
<variable name="vdPCC" public_interface="in" units="flux"/>
<variable name="PCC" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="PCNP" name="PCNP">
<variable cmeta:id="PCNP_PCNP" initial_value="0.1" name="PCNP" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="Kd" public_interface="in" units="nanomolar"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V3PC" public_interface="in" units="flux"/>
<variable name="V4PC" public_interface="in" units="flux"/>
<variable name="vdPCN" public_interface="in" units="flux"/>
<variable name="PCN" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="BC" name="BC">
<variable cmeta:id="BC_BC" initial_value="0.1" name="BC" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="ksB" public_interface="in" units="first_order_rate_constant"/>
<variable name="k5" public_interface="in" units="first_order_rate_constant"/>
<variable name="k6" public_interface="in" units="first_order_rate_constant"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V1B" public_interface="in" units="flux"/>
<variable name="V2B" public_interface="in" units="flux"/>
<variable name="MB" public_interface="in" units="nanomolar"/>
<variable name="BCP" public_interface="in" units="nanomolar"/>
<variable name="BN" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="BCP" name="BCP">
<variable cmeta:id="BCP_BCP" initial_value="0.1" name="BCP" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="Kd" public_interface="in" units="nanomolar"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V1B" public_interface="in" units="flux"/>
<variable name="V2B" public_interface="in" units="flux"/>
<variable name="vdBC" public_interface="in" units="flux"/>
<variable name="BC" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="BN" name="BN">
<variable cmeta:id="BN_BN" initial_value="0.1" name="BN" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="k5" public_interface="in" units="first_order_rate_constant"/>
<variable name="k6" public_interface="in" units="first_order_rate_constant"/>
<variable name="k7" public_interface="in" units="second_order_rate_constant"/>
<variable name="k8" public_interface="in" units="first_order_rate_constant"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V3B" public_interface="in" units="flux"/>
<variable name="V4B" public_interface="in" units="flux"/>
<variable name="BNP" public_interface="in" units="nanomolar"/>
<variable name="BC" public_interface="in" units="nanomolar"/>
<variable name="PCN" public_interface="in" units="nanomolar"/>
<variable name="IN" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="BNP" name="BNP">
<variable cmeta:id="BNP_BNP" initial_value="0.1" name="BNP" public_interface="out" units="nanomolar"/>
<variable name="Kp" public_interface="in" units="nanomolar"/>
<variable name="Kdp" public_interface="in" units="nanomolar"/>
<variable name="Kd" public_interface="in" units="nanomolar"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="V3B" public_interface="in" units="flux"/>
<variable name="V4B" public_interface="in" units="flux"/>
<variable name="vdBN" public_interface="in" units="flux"/>
<variable name="BN" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 cmeta:id="IN" name="IN">
<variable cmeta:id="IN_IN" initial_value="0.1" name="IN" public_interface="out" units="nanomolar"/>
<variable name="Kd" public_interface="in" units="nanomolar"/>
<variable name="kdn" public_interface="in" units="first_order_rate_constant"/>
<variable name="k7" public_interface="in" units="second_order_rate_constant"/>
<variable name="k8" public_interface="in" units="first_order_rate_constant"/>
<variable name="vdIN" public_interface="in" units="flux"/>
<variable name="PCN" public_interface="in" units="nanomolar"/>
<variable name="BN" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="hour"/>
<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 initial_value="0.8" name="k1" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.4" name="k2" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.8" name="k3" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="0.4" name="k4" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.8" name="k5" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.4" name="k6" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="1.0" name="k7" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="0.2" name="k8" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.8" name="k9" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.4" name="k10" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.02" name="kdnc" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.02" name="kdn" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.32" name="ksB" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="3.2" name="ksC" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="1.2" name="ksP" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="1.7" name="ksR" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="2.0" name="m" public_interface="out" units="dimensionless"/>
<variable initial_value="2.0" name="n" public_interface="out" units="dimensionless"/>
<variable initial_value="2.0" name="h" public_interface="out" units="dimensionless"/>
<variable initial_value="0.3" name="Kd" public_interface="out" units="nanomolar"/>
<variable initial_value="0.1" name="Kdp" public_interface="out" units="nanomolar"/>
<variable initial_value="1.006" name="Kp" public_interface="out" units="nanomolar"/>
<variable initial_value="1.4" name="V1B" public_interface="out" units="flux"/>
<variable initial_value="1.2" name="V1C" public_interface="out" units="flux"/>
<variable initial_value="9.6" name="V1P" public_interface="out" units="flux"/>
<variable initial_value="2.4" name="V1PC" public_interface="out" units="flux"/>
<variable initial_value="0.2" name="V2B" public_interface="out" units="flux"/>
<variable initial_value="0.2" name="V2C" public_interface="out" units="flux"/>
<variable initial_value="0.6" name="V2P" public_interface="out" units="flux"/>
<variable initial_value="0.2" name="V2PC" public_interface="out" units="flux"/>
<variable initial_value="1.4" name="V3B" public_interface="out" units="flux"/>
<variable initial_value="2.4" name="V3PC" public_interface="out" units="flux"/>
<variable initial_value="0.4" name="V4B" public_interface="out" units="flux"/>
<variable initial_value="0.2" name="V4PC" public_interface="out" units="flux"/>
<variable initial_value="3.0" name="vdBC" public_interface="out" units="flux"/>
<variable initial_value="3.0" name="vdBN" public_interface="out" units="flux"/>
<variable initial_value="1.4" name="vdCC" public_interface="out" units="flux"/>
<variable initial_value="1.6" name="vdIN" public_interface="out" units="flux"/>
<variable initial_value="3.4" name="vdPC" public_interface="out" units="flux"/>
<variable initial_value="1.4" name="vdPCC" public_interface="out" units="flux"/>
<variable initial_value="1.4" name="vdPCN" public_interface="out" units="flux"/>
<variable initial_value="4.4" name="vdRC" public_interface="out" units="flux"/>
<variable initial_value="0.8" name="vdRN" public_interface="out" units="flux"/>
</component>
<connection>
<map_components component_1="MP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MC" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MB" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MR" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="RC" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PC" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="CC" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PCP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="CCP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PCC" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PCN" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="RN" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PCCP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="PCNP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
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rdf:about="rdf:#11156794-1c33-4be2-a242-abb8992adcd0"/></N></rdf:Description><rdf:Description rdf:about="#BNP"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">nuclear phosphorylated BMAL1 protein</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">BNP</title></rdf:Description><rdf:Description rdf:about="rdf:#11156794-1c33-4be2-a242-abb8992adcd0"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Richard</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">James</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lawson</Family></rdf:Description><rdf:Description rdf:about="#MR"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">Rev-Erb</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">MR</title></rdf:Description><rdf:Description rdf:about="rdf:#0083d49b-c94d-4623-9cdb-67baef800be6"><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Auckland Bioengineering Institute</Orgunit><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname></rdf:Description><rdf:Description rdf:about="rdf:#7f865008-3b3b-4afe-bdd6-5e5bd2023d03"><rdf:_1 xml:lang="en">circadian rhythms</rdf:_1><rdf:_3 xml:lang="en">signal transduction</rdf:_3><rdf:_2 xml:lang="en">CLOCK</rdf:_2><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#9ec8db97-cfef-408a-8fd1-fb25424c7901"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">PNAS</title></rdf:Description><rdf:Description rdf:about="rdf:#e5bbe9cf-03c3-48ec-bfc1-9cac27b2fde4"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-08-14T00:00:00+00:00</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#ee9c890e-69a9-4b9a-94fc-ff891c14c604"><rdf:value xml:lang="en">Added cmeta:id's to variables for PCEnv session</rdf:value><modified xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#55fea3ca-18dc-47f2-86cd-cea441e47d9b"/></modified><cmeta:modifier><rdf:Description rdf:about="rdf:#3c47e455-2429-40a9-8087-a0bc853845ab"/></cmeta:modifier></rdf:Description><rdf:Description rdf:about="#RN"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">nuclear non-phosphorylated REV-ERB</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">RN</title></rdf:Description><rdf:Description rdf:about="#PCNP"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">nuclear phosphorylated PER-CRY protein complex</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">PCNP</title></rdf:Description><rdf:Description rdf:about="rdf:#494945b1-33de-4c74-9c3c-1ddfdd4c80ee"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">12775757</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#8a1dcf67-d17e-4c74-b764-b8afe6561cca"/></JournalArticle></rdf:Description><rdf:Description rdf:about="#leloup_2003"><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#911cc113-48ca-43b1-a1c1-d546bc1a8c77"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#494945b1-33de-4c74-9c3c-1ddfdd4c80ee"/></reference><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n2"/></simulation><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Leloup and Goldbeter's 2004 mathematical model of the mammalian circadian clock.</title><cmeta:comment><rdf:Description rdf:about="rdf:#3daba50a-f7dd-448b-af53-1fdc611127b6"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="#PCCP"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">cytosolic phosphorylated PER-CRY protein complex</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">PCCP</title></rdf:Description><rdf:Description rdf:about="#PCP"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">cytosolic phosphorylated PER protein</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">PCP</title></rdf:Description><rdf:Description rdf:about="#CC"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">cytosolic non-phosphorylated CRY protein</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">CC</title></rdf:Description><rdf:Description rdf:about="rdf:#$U+rBq1"><rdf:first><rdf:Description rdf:about="rdf:#$V+rBq1"/></rdf:first><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest></rdf:Description><rdf:Description rdf:about="#IN"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">nuclear inactive complex between PER-CRY and CLOCK-BMAL1</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">IN</title></rdf:Description><rdf:Description rdf:about="#CCP"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">cytosolic phosphorylated CRY protein</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">CCP</title></rdf:Description><rdf:Description rdf:about="rdf:#d8aafbd7-de2f-4f68-979c-51febd133301"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family></rdf:Description></rdf:RDF></model>
