- Author:
- Tommy Yu <tommy.yu@auckland.ac.nz>
- Date:
- 2010-08-26 12:17:27+12:00
- Desc:
- xml:base fix
- Permanent Source URI:
- http://models.cellml.org/workspace/jelic_cupic_kolaranic_2005/rawfile/f87590c7d7dc16a2289c32be28f8b5fa3bf80934/jelic_cupic_kolaranic_2005.session.xml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 12/04/2010 at 11:25:31 at a.m. using:
COR (0.9.31.1371)
Copyright 2002-2010 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="jelic_cupic_kolaranic_2005" name="jelic_cupic_kolaranic_2005">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical modeling of the hypothalamic-pituitary-adrenal system activity</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 PCEnv and OpenCell, but not in COR because the free variable (time) is dimensionless. The units are consistent throughout, but it does not reproduce the published results. It is a faithful reproduction of the paper equations (eqns 5-8), where all reaction constants are defined by equations, but the CellML model does not precisely reproduce the figures in the paper because to do this the reaction constants have to be defined explicitly (the parameter values are listed in the figure legends). Such CellML models have been created (called Fig4 and Fig5) and they exist in this workspace.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Mathematical modeling of the hypothalamic-pituitary-adrenal system activity, Smiljana Jelic, Zeljko Cupic, and Ljiljana Kolar-Anic, 2005, <emphasis>Mathematical Biosciences</emphasis>, 197, pp173-187. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/16112688">PubMed ID: 16112688</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="jelic_2005.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the hypothalamic-pituitary-adrenal system. Corticotrophin-releasing hormone (CRH) and arginin-vasopressin (AVP) stimulate adrenocorticotropin (ACTH) secretion from the pituitary, followed by cortisol secretion from the adrenal cortex. GR represents a glucocorticoid receptor and MR denotes a mineralocorticoid receptor. + represents a postive feedback loop while - represents a negative feedback loop.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Bag rdf:about="rdf:#2e4d4ce4-6ae2-4061-bcf5-b2ef34531aff">
<rdf:li>endocrine</rdf:li>
<rdf:li>hpa axis</rdf:li>
<rdf:li>HPA axis</rdf:li>
<rdf:li>hypothalamus</rdf:li>
<rdf:li>cortisol</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#b1112dc7-e29b-46eb-a7df-f53c39f74743">
<rdf:li rdf:resource="rdf:#bd414160-67ab-46a4-8758-ca5babf67bc6"/>
<rdf:li rdf:resource="rdf:#8543587a-38f3-4d4c-a6ad-1ae3953632c2"/>
<rdf:li rdf:resource="rdf:#4d396b19-197d-4bb5-886f-e5448827352e"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#f58e6aa6-2b7b-4ac6-a009-77ada78baa68">
<vCard:Orgname xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The University of Auckland</vCard:Orgname>
<vCard:Orgunit xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">A Hypothalamic-Pituitary-Adrenal System Model: Full Model</dc:title>
<dc:publisher xmlns:dc="http://purl.org/dc/elements/1.1/">The University of Auckland, Auckland Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#67b53216-9e4e-4ed6-96a1-c124f83b1702"/>
<dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#8e59f600-e339-4e25-b182-2329b0eed66a"/>
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#09b1e34e-4b56-4f51-8ac1-d37b6bef445a"/>
<cmeta:modification rdf:resource="rdf:#dd414d54-bb0c-41bc-a297-f9151606fb95"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#43c6d79f-c4d2-459a-8cd6-8f86280ab104">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#da1eb32e-2dc8-48f7-b748-8c9a5f240b35">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2005-00-00 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ca677a9f-3125-4f4a-b992-99d9851754db">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lloyd</vCard:Family>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#67b53216-9e4e-4ed6-96a1-c124f83b1702">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#43c6d79f-c4d2-459a-8cd6-8f86280ab104"/>
<rdf:value>The model has now been checked in COR too. I've added a complicated pulse stimulus equation to the model - but I'm not sure it's working properly! Can PCEnv handle "sin"?
I've added initially values from the paper and have also made every varible (except time) dimensionless.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#a">
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">ACTH</dcterms:alternative>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">adrenocorticotropic hormone</dcterms:alternative>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">a</dc:title>
</rdf:Description>
<rdf:Description rdf:about="#g">
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">cortisol</dcterms:alternative>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">g</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8e59f600-e339-4e25-b182-2329b0eed66a">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2007-06-15T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#633f05ae-1918-4673-842b-9016079fba7f">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#b1112dc7-e29b-46eb-a7df-f53c39f74743"/>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Mathematical modeling of the hypothalamic-pituitary-adrenal system activity</dc:title>
<bqs:volume xmlns:bqs="http://www.cellml.org/bqs/1.0#">197</bqs:volume>
<bqs:first_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">173</bqs:first_page>
<bqs:Journal xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#1b108538-9188-49c6-874a-f4198660c7ae"/>
<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#da1eb32e-2dc8-48f7-b748-8c9a5f240b35"/>
<bqs:last_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">187</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#09b1e34e-4b56-4f51-8ac1-d37b6bef445a">
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#f58e6aa6-2b7b-4ac6-a009-77ada78baa68"/>
<vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#8f48c3b2-a7ae-468a-bdaa-25bbae42e8b1"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#fd43087c-75d5-413e-b592-15972c11a718"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fd43087c-75d5-413e-b592-15972c11a718">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lloyd</vCard:Family>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bd414160-67ab-46a4-8758-ca5babf67bc6">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#e563758e-7d71-4220-a5d3-20403e3a7213"/>
</rdf:Description>
<rdf:Description rdf:about="#jelic_cupic_kolaranic_2005">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">
Jelic et al's 2005 hypothalamic pituitary adrenal axis model.
</dc:title>
<cmeta:bio_entity>hypothalamic pituitary adrenal axis</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#09ad4983-41f9-45bf-a05d-70646bd83cd2"/>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#9848fe8c-27fc-4472-9b78-cce4ecfe58ee"/>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#d100751a-fd7a-4d33-94a5-0bceba99b70a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a40f38cd-1dd5-4029-80a1-bb8ed596e7cc">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Ljiljana</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Kolar-Anic</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c8d32cc3-51fb-418f-952d-bbc98c024d88">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Zeljko</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Cupic</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8543587a-38f3-4d4c-a6ad-1ae3953632c2">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#c8d32cc3-51fb-418f-952d-bbc98c024d88"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d100751a-fd7a-4d33-94a5-0bceba99b70a">
<bqs:Pubmed_id xmlns:bqs="http://www.cellml.org/bqs/1.0#">16112688</bqs:Pubmed_id>
<bqs:JournalArticle xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#633f05ae-1918-4673-842b-9016079fba7f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#09ad4983-41f9-45bf-a05d-70646bd83cd2">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#761e2d67-2343-4106-9fbe-0f6427f13163"/>
<rdf:value>This is the CellML description of Jelic et al's 2005 hypothalamic pituitary adrenal axis model.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d95174cd-f8f8-445c-939f-784969bdc067">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2007-09-03T07:48:26+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3fc83b18-f1a0-456a-a674-0203e2571610">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#ca677a9f-3125-4f4a-b992-99d9851754db"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4d396b19-197d-4bb5-886f-e5448827352e">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#a40f38cd-1dd5-4029-80a1-bb8ed596e7cc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dd414d54-bb0c-41bc-a297-f9151606fb95">
<dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#d95174cd-f8f8-445c-939f-784969bdc067"/>
<rdf:value>The model has now been checked in COR too. I've added a complicated pulse stimulus equation to the model - but I'm not sure it's working properly! Can PCEnv handle "sin"?
I've added initially values from the paper and have also made every varible (except time) dimensionless.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#3fc83b18-f1a0-456a-a674-0203e2571610"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8f48c3b2-a7ae-468a-bdaa-25bbae42e8b1">
<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:#e563758e-7d71-4220-a5d3-20403e3a7213">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Smiljana</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Jelic</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b963de07-ee98-4d4a-a54c-2ce4b25a212a">
<bqs:subject_type xmlns:bqs="http://www.cellml.org/bqs/1.0#">keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#2e4d4ce4-6ae2-4061-bcf5-b2ef34531aff"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1b108538-9188-49c6-874a-f4198660c7ae">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Mathematical Biosciences</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#761e2d67-2343-4106-9fbe-0f6427f13163">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9848fe8c-27fc-4472-9b78-cce4ecfe58ee">
<dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#b963de07-ee98-4d4a-a54c-2ce4b25a212a"/>
</rdf:Description>
</rdf:RDF>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="molar">
<unit units="mole"/>
<unit exponent="-1" units="liter"/>
</units>
<units name="molar_per_second">
<unit units="molar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="second_per_molar">
<unit units="second"/>
<unit exponent="-1" units="molar"/>
</units>
<units name="per_molar2_per_second">
<unit exponent="-2" units="molar"/>
<unit exponent="-1" units="second"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
<variable name="tau" public_interface="out" units="dimensionless"/>
<variable name="C_0" public_interface="in" units="per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>time</ci>
<apply>
<divide/>
<ci>tau</ci>
<ci>C_0</ci>
</apply>
</apply>
</math>
</component>
<component name="a">
<variable name="A" units="molar"/>
<variable cmeta:id="a_a" initial_value="7.68e-8" name="a" public_interface="out" units="dimensionless"/>
<variable name="alpha" public_interface="in" units="dimensionless"/>
<variable name="beta" public_interface="in" units="dimensionless"/>
<variable name="K" public_interface="in" units="dimensionless"/>
<variable name="g" public_interface="in" units="dimensionless"/>
<variable name="tau" public_interface="in" units="dimensionless"/>
<variable name="C_1" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>A</ci>
<apply>
<times/>
<ci>C_1</ci>
<ci>a</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>tau</ci>
</bvar>
<ci>a</ci>
</apply>
<apply>
<minus/>
<ci>K</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>alpha</ci>
<ci>beta</ci>
</apply>
<ci>a</ci>
</apply>
<apply>
<times/>
<ci>a</ci>
<apply>
<power/>
<ci>g</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="g">
<variable name="G" units="molar"/>
<variable cmeta:id="g_g" initial_value="3.43e-8" name="g" public_interface="out" units="dimensionless"/>
<variable name="alpha" public_interface="in" units="dimensionless"/>
<variable name="gamma" public_interface="in" units="dimensionless"/>
<variable name="L" public_interface="in" units="dimensionless"/>
<variable name="a" public_interface="in" units="dimensionless"/>
<variable name="tau" public_interface="in" units="dimensionless"/>
<variable name="C_2" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>G</ci>
<apply>
<times/>
<ci>C_2</ci>
<ci>g</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>tau</ci>
</bvar>
<ci>g</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>alpha</ci>
</apply>
<ci>a</ci>
</apply>
<apply>
<times/>
<ci>a</ci>
<apply>
<power/>
<ci>g</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>L</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>g</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="reaction_constants">
<variable name="alpha" public_interface="out" units="dimensionless"/>
<variable name="beta" public_interface="out" units="dimensionless"/>
<variable name="gamma" public_interface="out" units="dimensionless"/>
<variable name="L" public_interface="out" units="dimensionless"/>
<variable initial_value="6e-4" name="k2" units="per_second"/>
<variable initial_value="0.0000048" name="k3" units="per_second"/>
<variable initial_value="0.000891" name="k6" units="per_second"/>
<variable initial_value="0.006831" name="k7" units="per_second"/>
<variable initial_value="8.7831e-11" name="k0" units="molar_per_second"/>
<variable initial_value="2.1e12" name="k4" units="per_molar2_per_second"/>
<variable initial_value="6.9001e-14" name="km" units="molar_per_second"/>
<variable name="K" public_interface="out" units="dimensionless"/>
<variable name="C_0" public_interface="out" units="per_second"/>
<variable name="C_1" public_interface="out" units="molar"/>
<variable name="C_2" public_interface="out" units="molar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_0</ci>
<ci>k2</ci>
</apply>
<apply>
<eq/>
<ci>C_1</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>k2</ci>
<ci>k4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C_2</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>k2</ci>
<ci>k4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha</ci>
<apply>
<divide/>
<ci>k3</ci>
<ci>k2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<divide/>
<ci>k6</ci>
<ci>k2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma</ci>
<apply>
<divide/>
<ci>k7</ci>
<ci>k2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K</ci>
<apply>
<root/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k0</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<ci>k4</ci>
</apply>
<apply>
<power/>
<ci>k2</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>L</ci>
<apply>
<root/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>km</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<ci>k4</ci>
</apply>
<apply>
<power/>
<ci>k2</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="a" component_2="environment"/>
<map_variables variable_1="tau" variable_2="tau"/>
</connection>
<connection>
<map_components component_1="g" component_2="environment"/>
<map_variables variable_1="tau" variable_2="tau"/>
</connection>
<connection>
<map_components component_1="reaction_constants" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="C_0" variable_2="C_0"/>
</connection>
<connection>
<map_components component_1="a" component_2="g"/>
<map_variables variable_1="g" variable_2="g"/>
<map_variables variable_1="a" variable_2="a"/>
</connection>
<connection>
<map_components component_1="a" component_2="reaction_constants"/>
<map_variables variable_1="alpha" variable_2="alpha"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="K" variable_2="K"/>
<map_variables variable_1="C_1" variable_2="C_1"/>
</connection>
<connection>
<map_components component_1="g" component_2="reaction_constants"/>
<map_variables variable_1="alpha" variable_2="alpha"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
<map_variables variable_1="L" variable_2="L"/>
<map_variables variable_1="C_2" variable_2="C_2"/>
</connection>
</model>
