- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-08-13 23:36:06+12:00
- Desc:
- committing version01 of leloup_goldbeter_2004
- Permanent Source URI:
- http://models.cellml.org/workspace/leloup_goldbeter_2004/rawfile/67dbf1ed4fcfb04801f6826edf6302c422737bf3/leloup_goldbeter_2004.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : leloup_model_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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:NS5="http://purl.org/dc/terms/" xmlns:RDF="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:NS7="http://www.cellml.org/metadata/simulation/1.0#" xmlns:NS1="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:NS2="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:NS3="http://imc.org/vCard/3.0#" xmlns:NS4="http://purl.org/dc/elements/1.1/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:NS6="http://www.cellml.org/metadata/1.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="leloup_model_2004" name="leloup_model_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>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Circadian rhythms are sustained oscillations which arise spontaneously with a period of about 24 hours. They occurs in a wide range of living organisms, including cyanobacteria, plants, insects and mammals. Interestingly, these rhythms have been shown to be independent of environmental cues - for example they continue to occur even when an organism is maintained under conditions of continuous light or dark. During the past decade the molecular mechanisms underlying circadian rhythms have been intensely studied, across a range of organisms, including <emphasis>Drosophila</emphasis>, <emphasis>Neurospora</emphasis>, cyanobacteria, plants and mammals. Common to all these organisms, the molecular mechanisms underlying the circadian oscillations rely on negative feedback regulation of gene expression.
</para>
<para>
The mechanism of circadian rhythms relies on interactions between negative and positive feedback loops (as shown in the figure below). The primary function of circadian rhythms is to allow organisms to adapt to their ever changing environment, which changes periodically on a 24 hour cycle. Although circadian rhythms are endogenous and can continue in the absence of environmental cues, light can entrain the cycle and in mammals it acts by enhancing the expression of the Per gene.
</para>
<para>
In the paper described here, Leloup and Goldbeter present a deterministic mathematical model for the mammalian circadian clock. This model incorporates the regulatory effects exerted on gene expression by the PER, CRY, BMAL1, and CLOCK proteins. It also describes how the activity of these proteins is regulated post-translationally by their reversible phosphorylation and and the afore mentioned light-induced Per expression. In particular they use this model to investigate disorders of the sleep-wake cycle in humans, such as those seen in shift workers.
</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 complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-4D0Y3RC-1&_user=140507&_coverDate=10%2F21%2F2004&_rdoc=12&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%236932%232004%23997699995%23519357%23FLA%23display%23Volume)&_cdi=6932&_sort=d&_docanchor=&_ct=17&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=b2843b3fee90f5ce16d4880536264c81">Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms</ulink>, Jean-Christophe Leloup and Albert Goldbeter, 2004, <ulink url="http://www.elsevier.com/wps/find/journaldescription.cws_home/622904/description#description">
<emphasis>Journal of Theoretical Biology</emphasis>
</ulink>, 230, 541-562. (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-4D0Y3RC-1&_user=140507&_coverDate=10%2F21%2F2004&_rdoc=12&_fmt=full&_orig=browse&_srch=doc-info(%23toc%236932%232004%23997699995%23519357%23FLA%23display%23Volume)&_cdi=6932&_sort=d&_docanchor=&_ct=17&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=3eb9f0afd81ebfaf16bf264648c4eead">Full text</ulink> and PDF versions of the article are available to subscribers on the <emphasis>Journal of Theoretical Biology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=15363675&query_hl=1&itool=pubmed_docsum">PubMed ID: 15363675</ulink>
</para>
<para>
Please note that the model is parameter senstitive. In the version of the model presented here, parameter set 1 from the original paper has been used. Oscillations disappear when PER is absent or when negative autoregulation by BMAL1 is not operative.
</para>
</sect1>
</article>
</documentation>
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<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 cmeta:id="PCN" name="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"/>
<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 cmeta:id="PCCP" name="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"/>
<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 cmeta:id="PCNP" name="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"/>
<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 cmeta:id="BC" name="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"/>
<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 cmeta:id="BCP" name="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"/>
<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 cmeta:id="BN" name="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"/>
<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 cmeta:id="BNP" name="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"/>
<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 cmeta:id="IN" name="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"/>
<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="0.4"/>
<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="0.4"/>
<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="0.12"/>
<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="2.0"/>
<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="0.1"/>
<variable units="nanomolar" public_interface="out" name="Kp" initial_value="0.1"/>
<variable units="flux" name="Vphos" initial_value="0.4"/>
<variable units="flux" public_interface="out" name="V1B" initial_value="0.5"/>
<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="0.5"/>
<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="0.5"/>
<variable units="flux" public_interface="out" name="vdBN" initial_value="0.6"/>
<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="0.7"/>
<variable units="flux" public_interface="out" name="vdPCN" initial_value="0.7"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> ksB </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> kstot </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> ksC </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.6 </cn>
<ci> kstot </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> ksP </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.6 </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"/>
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