- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:16:43+12:00
- Desc:
- committing version01 of aon_cortassa_2002
- Permanent Source URI:
- http://models.cellml.org/workspace/aon_cortassa_2002/rawfile/ba3d4b6d9fbe2b0c3f0fadb3a0d90b2c1688c410/aon_cortassa_2002.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : aon_model_2002.xml
CREATED : 14th August 2003
LAST MODIFIED : 21st April 2005
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 Aon and Cortassa's 2002 mathematical model of a metabolic network.
CHANGES:
21/04/2005 - PJV - Removed unnecessary type
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="aon_cortassa_2002_version01" name="aon_cortassa_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modulation of a Metabolic Network by Cytoskeletal Organisation and Dynamics</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The spatio-temporal coordination of cellular processes is a challenge which is faced by many biological systems, including cell growth, proliferation, differentiation, and functional adaptation. Such coordination is apparent in processes such as signal transduction, gene expression, and metabolism. Over the past few decades, two main theories concerning the organisation of metabolism have evolved:
</para>
<orderedlist continuation="restarts" inheritnum="ignore">
<listitem>
<para>The concept of metabolic channelling, where reactions are facilitated by substrate transfer between closely associated enzymes; and</para>
</listitem>
<listitem>
<para>The idea of cytoskeletal driven control of enzyme fluxes.</para>
</listitem>
</orderedlist>
<para>
Although these two theories are not mutually exclusive, there are cases where one mechanism will be favoured over the other, for example, channelling would not be favoured on the surface of a supramolecular structure.
</para>
<para>
The microtubular protein enhancement of metabolic flux depends on several factors, including:
</para>
<itemizedlist>
<listitem>
<para>The concentration of the microtubular protein;</para>
</listitem>
<listitem>
<para>The presence of microtubule associated proteins (MAPs);</para>
</listitem>
<listitem>
<para>The polymerisation state of the cytoskeletal proteins; and</para>
</listitem>
<listitem>
<para>The type of cytoskeletal protein present.</para>
</listitem>
</itemizedlist>
<para>
The cellular metabolic response to hormones such as insulin and glucagon depends on cell volume: turgid cells synthesise protein and glycogen, whereas flaccid cells break down these substances. Cytoskeletal dynamics play an essential role in sensing and responding to osmotic stress. It is likely that the spatial organisation and orientation of cytoskeletal proteins are modulating gene expression, signal transduction, and metabolic fluxes. Microtubules, actin microfilaments, and intermediate filaments represent a large surface area in the cell (estimated to be 3000 micrometres square per mammalian cell). This large surface area provides an interface for enzyme and other protein binding.
</para>
<para>
Although much is known about the interactions between glycolytic enzymes and cytoskeletal proteins, much less is understood about the consequences of these interactions. In their 2002 mathematical model of cytoskeletal modulation of a metabolic network, Miguel Aon and Sonia Cortassa look to determine the influence of cytoskeletal organisation and dynamics on cellular biochemistry. Specifically, they address the question of whether the degree of microtubule polymerisation affects the metabolic flux through the glycolytic pathway and/or it branches towards the pentose phosphate cycle, the tricarboxylic acid (TCA) cycle, and ethanol fermentation. Their model (see <xref linkend="fig_reaction_diagram"/> below) is based on experimental data from yeast.
</para>
<para>
The main observation taken from the model simulations was that the cytoskeleton provides the modulation of metabolism with coherence (the integration of diverse elements and activities to produce a consistent response) and robustness (enhanced stability in the steady state dynamic behaviour of the metabolic network when parameters are varied).
</para>
<para>
The model has been described here in CellML (the raw CellML description of the Aon and Cortassa model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TFB-45R7WBF-3&_user=140507&_coverDate=06%2F19%2F2002&_alid=108052762&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=5222&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=f721a3270481db2b2560eb6f3781f295">Coherent and robust modulation of a metabolic network by cytoskeletal organization and dynamics</ulink>, Miguel A. Aon and Sonia Cortassa, 2002, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5222&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=7d06a1ef3b4293bc0633b8269aa54192">
<emphasis>Biophysical Chemistry</emphasis>
</ulink>, 97, 213-231. (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TFB-45R7WBF-3&_coverDate=06%2F19%2F2002&_alid=108052762&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5222&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=1c7c67cd16a36773e5073a16450ae963">Full text (HTML)</ulink> and PDF versions of the article are available on the <emphasis>Biophysical Chemistry</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12050011&dopt=Abstract">PubMed ID: 12050011</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="reaction_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the metabolic network, the cycle of assembly-disassembly of microtubular proteins, and their interactions, upon which the Aon-Cortassa model is based.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
mitochondrial_membrane within the model.
-->
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</units>
<units name="flux">
<unit units="millimolar"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="minute" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="millimolar" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="third_order_rate_constant">
<unit units="millimolar" exponent="-2"/>
<unit units="minute" exponent="-1"/>
</units>
<component name="environment">
<variable units="minute" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component name="G_o" cmeta:id="G_o">
<rdf:RDF>
<rdf:Description rdf:about="G_o">
<dc:title>G_o</dc:title>
<dcterms:alternative>external glucose</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="G_o" initial_value="1.0"/>
</component>
<component name="G" cmeta:id="G">
<rdf:RDF>
<rdf:Description rdf:about="G">
<dc:title>G</dc:title>
<dcterms:alternative>cytosolic glucose</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="G"/>
<variable units="flux" public_interface="in" name="V_IN"/>
<variable units="flux" public_interface="in" name="V_HK"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G</ci>
</apply>
<apply>
<minus/>
<ci>V_IN</ci>
<ci>V_HK</ci>
</apply>
</apply>
</math>
</component>
<component name="G6P" cmeta:id="G6P">
<rdf:RDF>
<rdf:Description rdf:about="G6P">
<dc:title>G6P</dc:title>
<dcterms:alternative>glucose-6-phopshate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="G6P"/>
<variable units="flux" public_interface="in" name="V_PFK"/>
<variable units="flux" public_interface="in" name="V_HK"/>
<variable units="flux" public_interface="in" name="V_G6PDH"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G6P</ci>
</apply>
<apply>
<minus/>
<ci>V_HK</ci>
<apply>
<plus/>
<ci>V_PFK</ci>
<ci>V_G6PDH</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="FDP" cmeta:id="FDP">
<rdf:RDF>
<rdf:Description rdf:about="FDP">
<dc:title>FDP</dc:title>
<dcterms:alternative>fructose-1,6 bisphopshate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="FDP"/>
<variable units="flux" public_interface="in" name="V_PFK"/>
<variable units="flux" public_interface="in" name="V_ALD"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>FDP</ci>
</apply>
<apply>
<minus/>
<ci>V_PFK</ci>
<ci>V_ALD</ci>
</apply>
</apply>
</math>
</component>
<component name="G3P" cmeta:id="G3P">
<rdf:RDF>
<rdf:Description rdf:about="G3P">
<dc:title>G3P</dc:title>
<dcterms:alternative>glyceraldehyde-3-phopshate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="G3P"/>
<variable units="flux" public_interface="in" name="V_GAPDH"/>
<variable units="flux" public_interface="in" name="V_ALD"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G3P</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci>V_ALD</ci>
</apply>
<ci>V_GAPDH</ci>
</apply>
</apply>
</math>
</component>
<component name="DPG" cmeta:id="DPG">
<rdf:RDF>
<rdf:Description rdf:about="DPG">
<dc:title>DPG</dc:title>
<dcterms:alternative>1,3-diphosphoglycerate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="DPG"/>
<variable units="flux" public_interface="in" name="V_PGK"/>
<variable units="flux" public_interface="in" name="V_GAPDH"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>DPG</ci>
</apply>
<apply>
<minus/>
<ci>V_GAPDH</ci>
<ci>V_PGK</ci>
</apply>
</apply>
</math>
</component>
<component name="PEP" cmeta:id="PEP">
<rdf:RDF>
<rdf:Description rdf:about="PEP">
<dc:title>PEP</dc:title>
<dcterms:alternative>phosphoenolpyruvate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="PEP"/>
<variable units="flux" public_interface="in" name="V_PGK"/>
<variable units="flux" public_interface="in" name="V_PK"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PEP</ci>
</apply>
<apply>
<minus/>
<ci>V_PGK</ci>
<ci>V_PK</ci>
</apply>
</apply>
</math>
</component>
<component name="Py" cmeta:id="Py">
<rdf:RDF>
<rdf:Description rdf:about="Py">
<dc:title>Py</dc:title>
<dcterms:alternative>pyruvate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="Py"/>
<variable units="flux" public_interface="in" name="V_PK"/>
<variable units="flux" public_interface="in" name="V_TCA"/>
<variable units="flux" public_interface="in" name="V_ADH"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Py</ci>
</apply>
<apply>
<minus/>
<ci>V_PK</ci>
<apply>
<plus/>
<ci>V_TCA</ci>
<ci>V_ADH</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP" cmeta:id="ATP">
<rdf:RDF>
<rdf:Description rdf:about="ATP">
<dc:title>ATP</dc:title>
<dcterms:alternative>adenosine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ATP"/>
<variable units="dimensionless" name="PO" initial_value="4.0"/>
<variable units="flux" public_interface="in" name="V_HK"/>
<variable units="flux" public_interface="in" name="V_PFK"/>
<variable units="flux" public_interface="in" name="V_PGK"/>
<variable units="flux" public_interface="in" name="V_PK"/>
<variable units="flux" public_interface="in" name="V_TCA"/>
<variable units="flux" public_interface="in" name="V_ATPase"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ATP</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_PGK</ci>
<ci>V_PK</ci>
<apply>
<times/>
<ci>PO</ci>
<ci>V_TCA</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>V_HK</ci>
<ci>V_PFK</ci>
<ci>V_ATPase</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ADP" cmeta:id="ADP">
<rdf:RDF>
<rdf:Description rdf:about="ADP">
<dc:title>ADP</dc:title>
<dcterms:alternative>adenosine diphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ADP"/>
</component>
<component name="AMP" cmeta:id="AMP">
<rdf:RDF>
<rdf:Description rdf:about="AMP">
<dc:title>AMP</dc:title>
<dcterms:alternative>adenosine monophosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="AMP" initial_value="0.5"/>
</component>
<component name="Cn" cmeta:id="Cn">
<rdf:RDF>
<rdf:Description rdf:about="Cn">
<dc:title>Cn</dc:title>
<dcterms:alternative>total concentration of adenosine phosphates</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="Cn" initial_value="9.0"/>
<variable units="millimolar" public_interface="in" name="AMP"/>
<variable units="millimolar" public_interface="in" name="ADP"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cn_calculation">
<eq/>
<ci> Cn </ci>
<apply>
<plus/>
<ci> ATP </ci>
<ci> ADP </ci>
<ci> AMP </ci>
</apply>
</apply>
</math>
</component>
<component name="GTP" cmeta:id="GTP">
<rdf:RDF>
<rdf:Description rdf:about="GTP">
<dc:title>GTP</dc:title>
<dcterms:alternative>guanine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="GTP" initial_value="0.95"/>
</component>
<component name="GDP" cmeta:id="GDP">
<rdf:RDF>
<rdf:Description rdf:about="GDP">
<dc:title>GDP</dc:title>
<dcterms:alternative>guanine diphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="GDP" initial_value="0.05"/>
</component>
<component name="H" cmeta:id="H">
<rdf:RDF>
<rdf:Description rdf:about="H">
<dc:title>H</dc:title>
<dcterms:alternative>proton</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="H" initial_value="3.2E-8"/>
</component>
<component name="NADP">
<variable units="millimolar" public_interface="out" name="NADP" initial_value="1.0"/>
</component>
<component name="NADH" cmeta:id="NADH">
<rdf:RDF>
<rdf:Description rdf:about="NADH">
<dc:title>NADH</dc:title>
<dcterms:alternative>nicotinamide adenine dinucleotide</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="NADH" initial_value="0.01"/>
</component>
<component name="NAD" cmeta:id="NAD">
<rdf:RDF>
<rdf:Description rdf:about="NAD">
<dc:title>NAD</dc:title>
<dcterms:alternative>nicotinamide adenine dinucleotide positive</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="NAD" initial_value="1.0"/>
</component>
<component name="CD" cmeta:id="CD">
<rdf:RDF>
<rdf:Description rdf:about="CD">
<dc:title>CD</dc:title>
<dcterms:alternative>dimeric microtubular protein bound to GDP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="CD"/>
</component>
<component name="CT" cmeta:id="CT">
<rdf:RDF>
<rdf:Description rdf:about="CT">
<dc:title>CT</dc:title>
<dcterms:alternative>dimeric microtubular protein bound to GTP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="CT"/>
<variable units="third_order_rate_constant" public_interface="out" name="kpol" initial_value="10.0"/>
<variable units="first_order_rate_constant" name="kf" initial_value="3.0"/>
<variable units="second_order_rate_constant" name="kb" initial_value="2.5"/>
<variable units="millimolar" public_interface="in" name="GDP"/>
<variable units="millimolar" public_interface="in" name="CP"/>
<variable units="millimolar" public_interface="in" name="CD"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CT</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>kpol</ci>
<ci>CT</ci>
<apply>
<power/>
<ci>CP</ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci>kf</ci>
<ci>CD</ci>
</apply>
<apply>
<times/>
<ci>kb</ci>
<ci>CT</ci>
<ci>GDP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CP" cmeta:id="CP">
<rdf:RDF>
<rdf:Description rdf:about="CP">
<dc:title>CP</dc:title>
<dcterms:alternative>microtubular protein integrating the microtubular structure</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="CP"/>
<variable units="third_order_rate_constant" public_interface="in" name="kpol"/>
<variable units="first_order_rate_constant" name="kdp" initial_value="0.0025"/>
<variable units="millimolar" public_interface="in" name="CT"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CP</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kpol</ci>
<ci>CT</ci>
<apply>
<power/>
<ci>CP</ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci>kdp</ci>
<ci>CP</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CMTP" cmeta:id="CMTP">
<rdf:RDF>
<rdf:Description rdf:about="CMTP">
<dc:title>CMTP</dc:title>
<dcterms:alternative>total concentration of microtubular protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="CMTP" initial_value="0.9"/>
<variable units="millimolar" public_interface="in" name="CD"/>
<variable units="millimolar" public_interface="in" name="CT"/>
<variable units="millimolar" public_interface="in" name="CP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CMTP_calculation">
<eq/>
<ci> CMTP </ci>
<apply>
<plus/>
<ci> CD </ci>
<ci> CT </ci>
<ci> CP </ci>
</apply>
</apply>
</math>
</component>
<component name="PKp" cmeta:id="PKp">
<rdf:RDF>
<rdf:Description rdf:about="PKp">
<dc:title>PKp</dc:title>
<dcterms:alternative>pentameric form of pyruvate kinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="PKp"/>
<variable units="second_order_rate_constant" name="kp2" initial_value="10.0"/>
<variable units="first_order_rate_constant" name="kp3" initial_value="0.05"/>
<variable units="second_order_rate_constant" name="k4" initial_value="0.02"/>
<variable units="millimolar" public_interface="in" name="GTP"/>
<variable units="millimolar" public_interface="in" name="PKt"/>
<variable units="millimolar" public_interface="in" name="CP"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PKp</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1 </cn>
<ci>kp2</ci>
<ci>PKt</ci>
<ci>CP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>kp3</ci>
<ci>PKp</ci>
</apply>
<apply>
<times/>
<ci>k4</ci>
<ci>PKp</ci>
<ci>GTP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="PKt" cmeta:id="PKt">
<rdf:RDF>
<rdf:Description rdf:about="PKt">
<dc:title>PKt</dc:title>
<dcterms:alternative>tetrameric form of pyruvate kinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="PKt"/>
</component>
<component name="C_PK" cmeta:id="C_PK">
<rdf:RDF>
<rdf:Description rdf:about="C_PK">
<dc:title>C_PK</dc:title>
<dcterms:alternative>total concentration of pyruvate kinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="C_PK" initial_value="0.1"/>
<variable units="millimolar" public_interface="in" name="PKt"/>
<variable units="millimolar" public_interface="in" name="PKp"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="C_PK_calculation">
<eq/>
<ci> C_PK </ci>
<apply>
<plus/>
<ci> PKt </ci>
<ci> PKp </ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="V_IN">
<variable units="flux" public_interface="out" name="V_IN"/>
<variable units="millimolar" public_interface="in" name="G_o"/>
<variable units="millimolar" public_interface="in" name="G"/>
<variable units="millimolar" public_interface="in" name="G6P"/>
<variable units="millimolar" name="Ke_in" initial_value="12.0"/>
<variable units="millimolar" name="KG_in" initial_value="0.001"/>
<variable units="flux" name="V_IN_max" initial_value="10.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_IN_calculation">
<eq/>
<ci> V_IN </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> V_IN_max </ci>
<apply>
<divide/>
<ci> G_o </ci>
<apply>
<times/>
<apply>
<plus/>
<ci> KG_in </ci>
<ci> G_o </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> G6P </ci>
<ci> Ke_in </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> G </ci>
<apply>
<times/>
<apply>
<plus/>
<ci> KG_in </ci>
<ci> G </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> G6P </ci>
<ci> Ke_in </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_HK">
<variable units="flux" public_interface="out" name="V_HK"/>
<variable units="millimolar" public_interface="in" name="G"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="millimolar" name="KG_m" initial_value="0.11"/>
<variable units="millimolar" name="KG_s" initial_value="0.0062"/>
<variable units="millimolar" name="KATP_m" initial_value="0.1"/>
<variable units="flux" name="V_HK_max" initial_value="13.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_HK_calculation">
<eq/>
<ci> V_HK </ci>
<apply>
<times/>
<ci> V_HK_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> KG_s </ci>
<ci> KATP_m </ci>
</apply>
<apply>
<times/>
<ci> G </ci>
<ci> ATP </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> KG_m </ci>
<ci> G </ci>
</apply>
<apply>
<divide/>
<ci> KATP_m </ci>
<ci> ATP </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_PFK">
<variable units="flux" public_interface="out" name="V_PFK"/>
<variable units="millimolar" public_interface="in" name="G6P"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="millimolar" public_interface="in" name="AMP"/>
<variable units="millimolar" name="KG6P_r" initial_value="1.0"/>
<variable units="millimolar" name="KATP_r" initial_value="0.06"/>
<variable units="millimolar" name="KAMP_r" initial_value="0.025"/>
<variable units="dimensionless" name="cATP" initial_value="1.0"/>
<variable units="dimensionless" name="cAMP" initial_value="0.019"/>
<variable units="dimensionless" name="cG6P" initial_value="0.0005"/>
<variable units="dimensionless" name="Lo" initial_value="25000.0"/>
<variable units="dimensionless" name="gr" initial_value="10.0"/>
<variable units="dimensionless" name="n1" initial_value="2.0"/>
<variable units="flux" name="V_PFK_max" initial_value="30.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_PFK_calculation">
<eq/>
<ci> V_PFK </ci>
<apply>
<times/>
<ci> V_PFK_max </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> gr </ci>
<apply>
<divide/>
<ci> G6P </ci>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> KATP_r </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> G6P </ci>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> KATP_r </ci>
</apply>
<apply>
<times/>
<ci> gr </ci>
<apply>
<divide/>
<ci> G6P </ci>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> KATP_r </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci> n1 </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> G6P </ci>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> KATP_r </ci>
</apply>
<apply>
<times/>
<ci> gr </ci>
<apply>
<divide/>
<ci> G6P </ci>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> KATP_r </ci>
</apply>
</apply>
</apply>
<ci> n1 </ci>
</apply>
<apply>
<times/>
<ci> Lo </ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> cAMP </ci>
<ci> AMP </ci>
</apply>
<ci> KAMP_r </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> AMP </ci>
<ci> KAMP_r </ci>
</apply>
</apply>
</apply>
<ci> n1 </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> cG6P </ci>
<ci> G6P </ci>
</apply>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> cATP </ci>
<ci> ATP </ci>
</apply>
<ci> KATP_r </ci>
</apply>
<apply>
<times/>
<ci> gr </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> cG6P </ci>
<ci> G6P </ci>
</apply>
<ci> KG6P_r </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> cATP </ci>
<ci> ATP </ci>
</apply>
<ci> KATP_r </ci>
</apply>
</apply>
</apply>
<ci> n1 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_G6PDH">
<variable units="flux" public_interface="out" name="V_G6PDH"/>
<variable units="millimolar" public_interface="in" name="G6P"/>
<variable units="millimolar" public_interface="in" name="NADP"/>
<variable units="millimolar" public_interface="in" name="CT"/>
<variable units="millimolar" public_interface="in" name="CD"/>
<variable units="millimolar" name="TUB"/>
<variable units="millimolar" name="KG6P" initial_value="0.05"/>
<variable units="millimolar" name="KNADP" initial_value="0.05"/>
<variable units="millimolar" name="KNADP_" initial_value="0.05"/>
<variable units="millimolar" name="KTUB" initial_value="0.4"/>
<variable units="flux" name="V_G6PDH_max" initial_value="1.6"/>
<variable units="flux" name="V_G6PDH_max_II" initial_value="1.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_G6PDH_calculation">
<eq/>
<ci> V_G6PDH </ci>
<apply>
<plus/>
<apply>
<divide/>
<ci> V_G6PDH_max </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci> KG6P </ci>
<ci> KNADP </ci>
</apply>
<apply>
<times/>
<ci> G6P </ci>
<ci> NADP </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> KG6P </ci>
<ci> G6P </ci>
</apply>
<apply>
<divide/>
<ci> KNADP </ci>
<ci> NADP </ci>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
<apply>
<divide/>
<ci> V_G6PDH_max_II </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci> KG6P </ci>
<ci> KNADP_ </ci>
<ci> KTUB </ci>
</apply>
<apply>
<times/>
<ci> G6P </ci>
<ci> NADP </ci>
<ci> TUB </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> KG6P </ci>
<ci> KNADP_ </ci>
</apply>
<apply>
<times/>
<ci> G6P </ci>
<ci> NADP </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> KNADP_ </ci>
<ci> KTUB </ci>
</apply>
<apply>
<times/>
<ci> NADP </ci>
<ci> TUB </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> KG6P </ci>
<ci> KTUB </ci>
</apply>
<apply>
<times/>
<ci> G6P </ci>
<ci> TUB </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> KTUB </ci>
<ci> TUB </ci>
</apply>
<apply>
<divide/>
<ci> KG6P </ci>
<ci> G6P </ci>
</apply>
<apply>
<divide/>
<ci> KNADP_ </ci>
<ci> NADP </ci>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="TUB_calculation">
<eq/>
<ci> TUB </ci>
<apply>
<plus/>
<ci> CT </ci>
<ci> CD </ci>
</apply>
</apply>
</math>
</component>
<component name="V_ALD">
<variable units="flux" public_interface="out" name="V_ALD"/>
<variable units="millimolar" public_interface="in" name="G3P"/>
<variable units="millimolar" public_interface="in" name="FDP"/>
<variable units="millimolar" name="KG3P_m" initial_value="20.0"/>
<variable units="millimolar" name="KFDP_m" initial_value="0.5"/>
<variable units="flux" name="V_ALD_max" initial_value="2.5"/>
<variable units="flux" name="V_ALD_max_r" initial_value="1.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ALD_calculation">
<eq/>
<ci> V_ALD </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> V_ALD_max </ci>
<apply>
<divide/>
<ci> FDP </ci>
<ci> KFDP_m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> V_ALD_max_r </ci>
<apply>
<divide/>
<ci> G3P </ci>
<ci> KG3P_m </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> FDP </ci>
<ci> KFDP_m </ci>
</apply>
<apply>
<divide/>
<ci> G3P </ci>
<ci> KG3P_m </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_GAPDH">
<variable units="flux" public_interface="out" name="V_GAPDH"/>
<variable units="millimolar" public_interface="in" name="G3P"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="millimolar" public_interface="in" name="AMP"/>
<variable units="millimolar" public_interface="in" name="ADP"/>
<variable units="millimolar" name="K1" initial_value="1.1"/>
<variable units="millimolar" name="K2" initial_value="1.5"/>
<variable units="millimolar" name="K3" initial_value="2.5"/>
<variable units="millimolar" name="KG3P" initial_value="0.0025"/>
<variable units="millimolar" name="KNAD" initial_value="0.18"/>
<variable units="millimolar" name="KNADH_i" initial_value="0.0003"/>
<variable units="flux" name="V_GAPDH_max" initial_value="10.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_GAPDH_calculation">
<eq/>
<ci> V_GAPDH </ci>
<apply>
<divide/>
<ci> V_GAPDH_max </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> KG3P </ci>
<ci> G3P </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> KNAD </ci>
<ci> NAD </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> AMP </ci>
<ci> K1 </ci>
</apply>
<apply>
<divide/>
<ci> ADP </ci>
<ci> K2 </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> K3 </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> KG3P </ci>
<ci> KNAD </ci>
</apply>
<apply>
<times/>
<ci> G3P </ci>
<ci> NAD </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NADH </ci>
<ci> KNADH_i </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> AMP </ci>
<ci> K1 </ci>
</apply>
<apply>
<divide/>
<ci> ADP </ci>
<ci> K2 </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> K3 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_PGK">
<variable units="flux" public_interface="out" name="V_PGK"/>
<variable units="millimolar" public_interface="in" name="DPG"/>
<variable units="millimolar" name="KDPG_m" initial_value="0.002"/>
<variable units="flux" name="V_PGK_max" initial_value="3.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_PGK_calculation">
<eq/>
<ci> V_PGK </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_PGK_max </ci>
<ci> DPG </ci>
</apply>
<apply>
<plus/>
<ci> KDPG_m </ci>
<ci> DPG </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_PK">
<variable units="flux" public_interface="out" name="V_PK"/>
<variable units="millimolar" public_interface="in" name="PEP"/>
<variable units="millimolar" public_interface="in" name="ADP"/>
<variable units="millimolar" public_interface="in" name="FDP"/>
<variable units="millimolar" public_interface="in" name="H"/>
<variable units="millimolar" public_interface="in" name="C_PK"/>
<variable units="millimolar" public_interface="in" name="PKp"/>
<variable units="millimolar" name="R"/>
<variable units="millimolar" name="T"/>
<variable units="dimensionless" name="KpH" initial_value="9.5E-9"/>
<variable units="millimolar" name="KPEP_r" initial_value="1.0"/>
<variable units="millimolar" name="KADP_r" initial_value="0.06"/>
<variable units="millimolar" name="KFDP_r" initial_value="0.025"/>
<variable units="dimensionless" name="cADP" initial_value="1.0"/>
<variable units="dimensionless" name="cFDP" initial_value="0.01"/>
<variable units="dimensionless" name="cPEP" initial_value="0.02"/>
<variable units="dimensionless" name="Lo_PK" initial_value="1000.0"/>
<variable units="dimensionless" name="gr_PK" initial_value="0.1"/>
<variable units="dimensionless" name="gt_PK" initial_value="1.0"/>
<variable units="dimensionless" name="n" initial_value="4.0"/>
<variable units="flux" name="V_PK_max"/>
<variable units="flux" name="V_PKt_max" initial_value="25.0"/>
<variable units="flux" name="V_PKp_max" initial_value="50.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_PK_calculation">
<eq/>
<ci> V_PK </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> V_PK_max </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> KpH </ci>
<ci> H </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci> gr_PK </ci>
<apply>
<divide/>
<ci> PEP </ci>
<ci> KPEP_r </ci>
</apply>
<apply>
<divide/>
<ci> ADP </ci>
<ci> KADP_r </ci>
</apply>
<apply>
<power/>
<ci> R </ci>
<ci> n </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Lo_PK </ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> cFDP </ci>
<ci> FDP </ci>
</apply>
<ci> KFDP_r </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> FDP </ci>
<ci> KFDP_r </ci>
</apply>
</apply>
</apply>
<ci> n </ci>
</apply>
<apply>
<divide/>
<ci> FDP </ci>
<ci> KFDP_r </ci>
</apply>
<ci> gt_PK </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> cPEP </ci>
<ci> PEP </ci>
</apply>
<ci> KPEP_r </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> cADP </ci>
<ci> ADP </ci>
</apply>
<ci> KADP_r </ci>
</apply>
<apply>
<power/>
<ci> T </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> R </ci>
<ci> n </ci>
</apply>
<apply>
<times/>
<ci> Lo_PK </ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> cFDP </ci>
<ci> FDP </ci>
</apply>
<ci> KFDP_r </ci>
</apply>
</apply>
<apply>
<plus/>
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Aon and Cortassa's 2002 mathematical model of a metabolic network.
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