- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 14:51:36+12:00
- Desc:
- committing version03 of leloup_goldbeter_2003
- Permanent Source URI:
- https://models.cellml.org/workspace/leloup_goldbeter_2003/rawfile/f7afb9c5cf2a5db07af8b8a431a59668230a80c4/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:
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<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>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Many living organisms, from bacteria to plants, insects to mammals, display circadian rhythms. These are spontaneously sustained oscillations with a period close to 24 hours. Even in the absence of environment cues such as the light changes associated with day and night, organisms have been shown to retain their circadian behaviour, therefore suggesting that the rhythms are endogenous. Experiments with <emphasis>Drosophila</emphasis> (fruit fly), <emphasis>Neurospora</emphasis> (fungus), cyanobacteria, plants and mammals have improved our understanding of the molecular mechanisms underlying circadian rhythms. It seems that they rely on negative feedback on gene expression. A number of genes involved in circadian rhythms have been identified. These include: <emphasis>Per</emphasis> (period) and <emphasis>Tim</emphasis> (timeless); <emphasis>Cyc</emphasis> (cycle) and <emphasis>Clock</emphasis>; and <emphasis>Cry</emphasis> (cryptochrome).
</para>
<para>
To date, mathematical models for circadian rhythms have been developed for <emphasis>Drosophila</emphasis> and <emphasis>Neurospora</emphasis>. These models, which are based on experimental data, predict that within a certain parameter range the genetic regulatory network undergoes sustained oscillatory cycles corresponding to circadian rhythmic behaviour. In this 2003 publication, Leloup and Goldbeter develop a deterministic model for the mammalian circadian clock. Their model includes the regulatory effects exerted on gene expression by the proteins PER, CRY, BMAL1, CLOCK and REV-ERB, as well as posttranslational regulation of these proteins by reversible phosphorylation (see the figure below).
</para>
<para>
Model simulations reveal that their model can account for the autonomous, sustained circadian oscillations in conditions which correspond to continuous darkness (no environmental cues), and also for light-dark cycle entrainment of circadian rhythms - light can entrain circadian rhythms in mammals by inducing the expression of the <emphasis>Per</emphasis> gene. Model simulations also showed that the phase of the oscillations could vary by several hours with relatively small changes in parameter values. This may account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of light-dark entrainment can be related to the non-24 hour sleep-wake syndrome. Further, detailed model analysis suggests that there could be several sources of periodic behaviour in the genetic regulatory network that controls circadian oscillations.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.pnas.org/cgi/content/abstract/100/12/7051">Toward a detailed computational model for the mammalian circadian clock</ulink>, Jean-Christophe Leloup and Albert Goldbeter, 2003, <ulink url="http://www.pnas.org/">
<emphasis>PNAS</emphasis>
</ulink>, 100, 7051-7056. (<ulink url="http://www.pnas.org/cgi/content/full/100/12/7051">Full text (HTML)</ulink> and <ulink url="http://www.pnas.org/cgi/reprint/100/12/7051.pdf">PDF</ulink> versions of the article are available on the <emphasis>PNAS</emphasis> website.) <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>
<para>
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>
</sect1>
</article>
</documentation>
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<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"/>
<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"/>
<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"/>
<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"/>
<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"/>
<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"/>
<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"/>
<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"/>
<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"/>
<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"/>
<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>
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<vCard:Given>James</vCard:Given>
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