<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : kongas_model_2001.xml
CREATED : 5th February 2004
LAST MODIFIED : 5th February 2004
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 Kongas and van Beek's mathematical model of creatine kinase in energy metabolic signalling in muscle.
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://www.cellml.org/metadata/simulation/1.0#" 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/bqs/1.0#" xmlns:NS1="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:NS2="http://purl.org/dc/elements/1.1/" xmlns:NS3="http://imc.org/vCard/3.0#" xmlns:NS4="http://www.w3.org/2001/vcard-rdf/3.0#" 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="kongas_model_2001" name="kongas_model_2001">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Creatine Kinase in Energy Metabolic Signalling in Muscle</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 is known to run on both OpenCell and COR. The units have been checked and they are balanced. The figures in the original publication display slightly unusual variables, hence we are unsure as to whether or not the CellML model is recreating the published results. To address this we are working with the original model authors to complete the curation of the CellML model. Please also note there are some typographical errors in the original publication, and that in equations 6-10 in the appendix, the metabolites should have an "i" subscript(to denote IMS concentrations), and also the "Vhyd"s in these equations should be "Vsyn"s.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ATP is the major energy currency in cells. It is synthesised during aerobic respiration in the mitochondria and it's main use in muscle is in myofibrillar contraction an ion pumping. Phosphocreatine (PCr) is another major energy carrier in muscle cells, in fact the majority of the energy-carrying phosphate groups leave the mitochondria in the form of PCr, not ATP. This is possible due to the creatine kinase (CK) reaction, see Figure 1 below, where Cr is creatine:
</para>
<informalfigure float="0">
<mediaobject>
<imageobject>
<imagedata fileref="kongas_2001a.png"/>
</imageobject>
</mediaobject>
<caption>Figure 1. The creatine kinase reaction.</caption>
</informalfigure>
<para>
The mitochondrial isoform of the CK enzyme (MiCK) produces PCr, while the main myofibrillar isoform (MMCK) converts it back into ATP. This energy transfer is also referred to as the phosphocreatine shuttle, and it facilitates energy transfer by providing a parallel pathway to ATP diffusion. In muscle cells, the CK system also acts as an energy buffer, allowing ATP levels to remain fairly constant during muscle contraction as PCr levels fluctuate to closely follow force generation.
</para>
<para>
In the Kongas and van Beek 2001 publication described here, the authors aim to determine the mode of functioning of the CK system in the heart. To this end they devloped a mathematical model of energy production, transfer, and consumption (see Figure 2 below) and analysed the roles of different CK isoenzymes in the dynamic response to workload transitions.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Creatine kinase in energy metabolic signaling in muscle, Olav Kongas and Johannes H. G. M. van Beek, 2001, <emphasis>ICSB2001: The 2nd International Conference on Systems Biology</emphasis>
</para>
<informalfigure float="0">
<mediaobject>
<imageobject>
<imagedata fileref="kongas_2001b.png"/>
</imageobject>
</mediaobject>
<caption>Figure 2. Schematic diagram of the mathematical model. The model contains two compartments: the cytosol and the intermembrane space, and these are separated by a partialy permeable membrane (dashed line). Vertical arrows across this membrane represent diffusional fluxes. The horizontal arrows represent reactions, namely ATP synthesis (OxPhos), ATP hydrolysis (ATPase), mitochondrial and myofibrillar kinases (MiCK and MMCK).</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<component name="ATP" cmeta:id="ATP">
<rdf:RDF>
<rdf:Description rdf:about="#ATP">
<dc:title>ATP</dc:title>
<dcterms:alternative>cytosolic adenosine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="ATP" initial_value="9644.425"/>
<variable units="flux" public_interface="in" name="V_hyd"/>
<variable units="flux" public_interface="in" name="V_MMCK"/>
<variable units="flux" public_interface="in" name="J_ATP"/>
<variable units="dimensionless" public_interface="in" name="V_cyt"/>
<variable units="second" 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>
<divide/>
<apply>
<minus/>
<ci>J_ATP</ci>
<apply>
<plus/>
<ci>V_hyd</ci>
<ci>V_MMCK</ci>
</apply>
</apply>
<ci>V_cyt</ci>
</apply>
</apply>
</math>
</component>
<component name="ADP" cmeta:id="ADP">
<rdf:RDF>
<rdf:Description rdf:about="#ADP">
<dc:title>ADP</dc:title>
<dcterms:alternative>cytosolic adenosine diphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="ADP" initial_value="60.0"/>
<variable units="flux" public_interface="in" name="V_hyd"/>
<variable units="flux" public_interface="in" name="V_MMCK"/>
<variable units="flux" public_interface="in" name="J_ADP"/>
<variable units="dimensionless" public_interface="in" name="V_cyt"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ADP</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>J_ADP</ci>
<ci>V_hyd</ci>
<ci>V_MMCK</ci>
</apply>
<ci>V_cyt</ci>
</apply>
</apply>
</math>
</component>
<component name="PCr" cmeta:id="PCr">
<rdf:RDF>
<rdf:Description rdf:about="#PCr">
<dc:title>PCr</dc:title>
<dcterms:alternative>cytosolic phosphocreatine</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="PCr" initial_value="12500.0"/>
<variable units="flux" public_interface="in" name="V_MMCK"/>
<variable units="flux" public_interface="in" name="J_PCr"/>
<variable units="dimensionless" public_interface="in" name="V_cyt"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PCr</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>J_PCr</ci>
<ci>V_MMCK</ci>
</apply>
<ci>V_cyt</ci>
</apply>
</apply>
</math>
</component>
<component name="Cr" cmeta:id="Cr">
<rdf:RDF>
<rdf:Description rdf:about="#Cr">
<dc:title>Cr</dc:title>
<dcterms:alternative>cytosolic creatine</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Cr" initial_value="13500.0"/>
<variable units="flux" public_interface="in" name="V_MMCK"/>
<variable units="flux" public_interface="in" name="J_Cr"/>
<variable units="dimensionless" public_interface="in" name="V_cyt"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cr</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>J_Cr</ci>
<ci>V_MMCK</ci>
</apply>
<ci>V_cyt</ci>
</apply>
</apply>
</math>
</component>
<component name="Pi" cmeta:id="Pi">
<rdf:RDF>
<rdf:Description rdf:about="#Pi">
<dc:title>Pi</dc:title>
<dcterms:alternative>cytosolic inorganic phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Pi" initial_value="8000.0"/>
<variable units="flux" public_interface="in" name="V_hyd"/>
<variable units="flux" public_interface="in" name="J_Pi"/>
<variable units="dimensionless" public_interface="in" name="V_cyt"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Pi</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>J_Pi</ci>
<ci>V_hyd</ci>
</apply>
<ci>V_cyt</ci>
</apply>
</apply>
</math>
</component>
<component name="ATP_i" cmeta:id="ATP_i">
<rdf:RDF>
<rdf:Description rdf:about="#ATP_i">
<dc:title>ATP_i</dc:title>
<dcterms:alternative>IMS adenosine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="ATP_i" initial_value="9644.425"/>
<variable units="flux" public_interface="in" name="V_MiCK"/>
<variable units="flux" public_interface="in" name="V_syn"/>
<variable units="flux" public_interface="in" name="J_ATP"/>
<variable units="dimensionless" public_interface="in" name="V_ims"/>
<variable units="second" 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_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>J_ATP</ci>
<ci>V_syn</ci>
<ci>V_MiCK</ci>
</apply>
</apply>
<ci>V_ims</ci>
</apply>
</apply>
</math>
</component>
<component name="ADP_i" cmeta:id="ADP_i">
<rdf:RDF>
<rdf:Description rdf:about="#ADP_i">
<dc:title>ADP_i</dc:title>
<dcterms:alternative>IMS adenosine diphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="ADP_i" initial_value="2.5"/>
<variable units="flux" public_interface="in" name="V_MiCK"/>
<variable units="flux" public_interface="in" name="V_syn"/>
<variable units="flux" public_interface="in" name="J_ADP"/>
<variable units="dimensionless" public_interface="in" name="V_ims"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ADP_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_syn</ci>
<ci>V_MiCK</ci>
</apply>
<ci>J_ADP</ci>
</apply>
<ci>V_ims</ci>
</apply>
</apply>
</math>
</component>
<component name="PCr_i" cmeta:id="PCr_i">
<rdf:RDF>
<rdf:Description rdf:about="#PCr_i">
<dc:title>PCr_i</dc:title>
<dcterms:alternative>IMS phosphocreatine</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="PCr_i" initial_value="12500.0"/>
<variable units="flux" public_interface="in" name="V_MiCK"/>
<variable units="flux" public_interface="in" name="J_PCr"/>
<variable units="dimensionless" public_interface="in" name="V_ims"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PCr_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>V_MiCK</ci>
<ci>J_PCr</ci>
</apply>
<ci>V_ims</ci>
</apply>
</apply>
</math>
</component>
<component name="Cr_i" cmeta:id="Cr_i">
<rdf:RDF>
<rdf:Description rdf:about="#Cr_i">
<dc:title>Cr_i</dc:title>
<dcterms:alternative>IMS creatine</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Cr_i" initial_value="13500.0"/>
<variable units="flux" public_interface="in" name="V_MiCK"/>
<variable units="flux" public_interface="in" name="J_Cr"/>
<variable units="dimensionless" public_interface="in" name="V_ims"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cr_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_MiCK</ci>
<ci>J_Cr</ci>
</apply>
</apply>
<ci>V_ims</ci>
</apply>
</apply>
</math>
</component>
<component name="Pi_i" cmeta:id="Pi_i">
<rdf:RDF>
<rdf:Description rdf:about="#Pi_i">
<dc:title>Pi_i</dc:title>
<dcterms:alternative>IMS inorganic phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Pi_i" initial_value="8000.0"/>
<variable units="flux" public_interface="in" name="V_syn"/>
<variable units="flux" public_interface="in" name="J_Pi"/>
<variable units="dimensionless" public_interface="in" name="V_ims"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Pi_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>V_syn</ci>
<ci>J_Pi</ci>
</apply>
<ci>V_ims</ci>
</apply>
</apply>
</math>
</component>
<component name="V_MMCK">
<variable units="flux" public_interface="out" name="V_MMCK"/>
<variable units="micromolar" public_interface="in" name="ATP"/>
<variable units="micromolar" public_interface="in" name="ADP"/>
<variable units="micromolar" public_interface="in" name="PCr"/>
<variable units="micromolar" public_interface="in" name="Cr"/>
<variable units="dimensionless" name="Den_MMCK"/>
<variable units="micromolar" name="Kia" initial_value="9.0E2"/>
<variable units="micromolar" name="Kb" initial_value="1.55E4"/>
<variable units="micromolar" name="Kib" initial_value="3.49E4"/>
<variable units="micromolar" name="KIb"/>
<variable units="micromolar" name="Kc"/>
<variable units="micromolar" name="Kic" initial_value="2.224E2"/>
<variable units="micromolar" name="Kd" initial_value="1.67E3"/>
<variable units="micromolar" name="Kid" initial_value="4.73E3"/>
<variable units="flux" name="Vf" initial_value="6.966E3"/>
<variable units="flux" name="Vb" initial_value="2.925E4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_MMCK_calculation">
<eq/>
<ci> V_MMCK </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Vf </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> ATP </ci>
<ci> Cr </ci>
</apply>
<apply>
<times/>
<ci> Kia </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Vb </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> ADP </ci>
<ci> PCr </ci>
</apply>
<apply>
<times/>
<ci> Kic </ci>
<ci> Kd </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Den_MMCK </ci>
</apply>
</apply>
<apply id="Den_MMCK_calculation">
<eq/>
<ci> Den_MMCK </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Cr </ci>
<ci> Kib </ci>
</apply>
<apply>
<divide/>
<ci> PCr </ci>
<ci> Kid </ci>
</apply>
<apply>
<times/>
<ci> ATP </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Kia </ci>
</apply>
<apply>
<divide/>
<ci> Cr </ci>
<apply>
<times/>
<ci> Kia </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> ADP </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Kic </ci>
</apply>
<apply>
<divide/>
<ci> PCr </ci>
<apply>
<times/>
<ci> Kid </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Cr </ci>
<apply>
<times/>
<ci> Kic </ci>
<ci> KIb </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Kc_calculation">
<eq/>
<ci> Kc </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Kic </ci>
<ci> Kd </ci>
</apply>
<ci> Kid </ci>
</apply>
</apply>
<apply id="KIb_calculation">
<eq/>
<ci> KIb </ci>
<ci> Kib </ci>
</apply>
</math>
</component>
<component name="V_MiCK">
<variable units="flux" public_interface="out" name="V_MiCK"/>
<variable units="micromolar" public_interface="in" name="ATP_i"/>
<variable units="micromolar" public_interface="in" name="ADP_i"/>
<variable units="micromolar" public_interface="in" name="PCr_i"/>
<variable units="micromolar" public_interface="in" name="Cr_i"/>
<variable units="dimensionless" name="Den_MiCK"/>
<variable units="micromolar" name="Kia" initial_value="7.5E2"/>
<variable units="micromolar" name="Kb" initial_value="5.2E3"/>
<variable units="micromolar" name="Kib" initial_value="2.88E4"/>
<variable units="micromolar" name="KIb"/>
<variable units="micromolar" name="Kc"/>
<variable units="micromolar" name="Kic" initial_value="2.048E2"/>
<variable units="micromolar" name="Kd" initial_value="5.0E2"/>
<variable units="micromolar" name="Kid" initial_value="1.6E3"/>
<variable units="flux" name="Vf" initial_value="2.658E3"/>
<variable units="flux" name="Vb" initial_value="1.116E4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_MiCK_calculation">
<eq/>
<ci> V_MiCK </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Vf </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> ATP_i </ci>
<ci> Cr_i </ci>
</apply>
<apply>
<times/>
<ci> Kia </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Vb </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> ADP_i </ci>
<ci> PCr_i </ci>
</apply>
<apply>
<times/>
<ci> Kic </ci>
<ci> Kd </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Den_MiCK </ci>
</apply>
</apply>
<apply id="Den_MiCK_calculation">
<eq/>
<ci> Den_MiCK </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Cr_i </ci>
<ci> Kib </ci>
</apply>
<apply>
<divide/>
<ci> PCr_i </ci>
<ci> Kid </ci>
</apply>
<apply>
<times/>
<ci> ATP_i </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Kia </ci>
</apply>
<apply>
<divide/>
<ci> Cr_i </ci>
<apply>
<times/>
<ci> Kia </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> ADP_i </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Kic </ci>
</apply>
<apply>
<divide/>
<ci> PCr_i </ci>
<apply>
<times/>
<ci> Kid </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Cr_i </ci>
<apply>
<times/>
<ci> Kic </ci>
<ci> KIb </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Kc_calculation">
<eq/>
<ci> Kc </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Kic </ci>
<ci> Kd </ci>
</apply>
<ci> Kid </ci>
</apply>
</apply>
<apply id="KIb_calculation">
<eq/>
<ci> KIb </ci>
<ci> Kib </ci>
</apply>
</math>
</component>
<component name="V_hyd">
<variable units="flux" public_interface="out" name="V_hyd" initial_value="4.6E3"/>
</component>
<component name="V_syn">
<variable units="flux" public_interface="out" name="V_syn"/>
<variable units="micromolar" public_interface="in" name="Pi_i"/>
<variable units="micromolar" public_interface="in" name="ADP_i"/>
<variable units="dimensionless" name="Den_syn"/>
<variable units="micromolar" name="KPi" initial_value="20.0"/>
<variable units="micromolar" name="KADP" initial_value="8.0E2"/>
<variable units="flux" name="V_syn_max" initial_value="4.6E3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_syn_calculation">
<eq/>
<ci> V_syn </ci>
<apply>
<times/>
<ci> V_syn_max </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> ADP_i </ci>
<ci> Pi_i </ci>
</apply>
<apply>
<times/>
<ci> KPi </ci>
<ci> KADP </ci>
<ci> Den_syn </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Den_syn_calculation">
<eq/>
<ci> Den_syn </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ADP_i </ci>
<ci> KADP </ci>
</apply>
<apply>
<divide/>
<ci> Pi_i </ci>
<ci> KPi </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> ADP_i </ci>
<ci> Pi_i </ci>
</apply>
<apply>
<times/>
<ci> KADP </ci>
<ci> KPi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_ATP">
<variable units="flux" public_interface="out" name="J_ATP"/>
<variable units="micromolar" public_interface="in" name="ATP_i"/>
<variable units="micromolar" public_interface="in" name="ATP"/>
<variable units="first_order_rate_constant" name="R_ATP" initial_value="8.16"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ATP_calculation">
<eq/>
<ci> J_ATP </ci>
<apply>
<times/>
<ci> R_ATP </ci>
<apply>
<minus/>
<ci> ATP_i </ci>
<ci> ATP </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_ADP">
<variable units="flux" public_interface="out" name="J_ADP"/>
<variable units="micromolar" public_interface="in" name="ADP_i"/>
<variable units="micromolar" public_interface="in" name="ADP"/>
<variable units="first_order_rate_constant" name="R_ADP" initial_value="8.16"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ADP_calculation">
<eq/>
<ci> J_ADP </ci>
<apply>
<times/>
<ci> R_ADP </ci>
<apply>
<minus/>
<ci> ADP_i </ci>
<ci> ADP </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_PCr">
<variable units="flux" public_interface="out" name="J_PCr"/>
<variable units="micromolar" public_interface="in" name="PCr_i"/>
<variable units="micromolar" public_interface="in" name="PCr"/>
<variable units="first_order_rate_constant" name="R_PCr" initial_value="14.6"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_PCr_calculation">
<eq/>
<ci> J_PCr </ci>
<apply>
<times/>
<ci> R_PCr </ci>
<apply>
<minus/>
<ci> PCr_i </ci>
<ci> PCr </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_Cr">
<variable units="flux" public_interface="out" name="J_Cr"/>
<variable units="micromolar" public_interface="in" name="Cr_i"/>
<variable units="micromolar" public_interface="in" name="Cr"/>
<variable units="first_order_rate_constant" name="R_Cr" initial_value="14.6"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_Cr_calculation">
<eq/>
<ci> J_Cr </ci>
<apply>
<times/>
<ci> R_Cr </ci>
<apply>
<minus/>
<ci> Cr_i </ci>
<ci> Cr </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_Pi">
<variable units="flux" public_interface="out" name="J_Pi"/>
<variable units="micromolar" public_interface="in" name="Pi_i"/>
<variable units="micromolar" public_interface="in" name="Pi"/>
<variable units="first_order_rate_constant" name="R_Pi" initial_value="18.4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_Pi_calculation">
<eq/>
<ci> J_Pi </ci>
<apply>
<times/>
<ci> R_Pi </ci>
<apply>
<minus/>
<ci> Pi_i </ci>
<ci> Pi </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fractional_volumes">
<variable units="dimensionless" public_interface="out" name="V_cyt" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="V_ims" initial_value="0.0625"/>
</component>
<connection>
<map_components component_2="environment" component_1="ATP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ADP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCr"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Cr"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Pi"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ATP_i"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ADP_i"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="PCr_i"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Cr_i"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Pi_i"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="V_MMCK" component_1="ATP"/>
<map_variables variable_2="ATP" variable_1="ATP"/>
<map_variables variable_2="V_MMCK" variable_1="V_MMCK"/>
</connection>
<connection>
<map_components component_2="V_hyd" component_1="ATP"/>
<map_variables variable_2="V_hyd" variable_1="V_hyd"/>
</connection>
<connection>
<map_components component_2="J_ATP" component_1="ATP"/>
<map_variables variable_2="ATP" variable_1="ATP"/>
<map_variables variable_2="J_ATP" variable_1="J_ATP"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="ATP"/>
<map_variables variable_2="V_cyt" variable_1="V_cyt"/>
</connection>
<connection>
<map_components component_2="V_MMCK" component_1="ADP"/>
<map_variables variable_2="ADP" variable_1="ADP"/>
<map_variables variable_2="V_MMCK" variable_1="V_MMCK"/>
</connection>
<connection>
<map_components component_2="V_hyd" component_1="ADP"/>
<map_variables variable_2="V_hyd" variable_1="V_hyd"/>
</connection>
<connection>
<map_components component_2="J_ADP" component_1="ADP"/>
<map_variables variable_2="ADP" variable_1="ADP"/>
<map_variables variable_2="J_ADP" variable_1="J_ADP"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="ADP"/>
<map_variables variable_2="V_cyt" variable_1="V_cyt"/>
</connection>
<connection>
<map_components component_2="V_MMCK" component_1="PCr"/>
<map_variables variable_2="PCr" variable_1="PCr"/>
<map_variables variable_2="V_MMCK" variable_1="V_MMCK"/>
</connection>
<connection>
<map_components component_2="J_PCr" component_1="PCr"/>
<map_variables variable_2="PCr" variable_1="PCr"/>
<map_variables variable_2="J_PCr" variable_1="J_PCr"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="PCr"/>
<map_variables variable_2="V_cyt" variable_1="V_cyt"/>
</connection>
<connection>
<map_components component_2="V_MMCK" component_1="Cr"/>
<map_variables variable_2="Cr" variable_1="Cr"/>
<map_variables variable_2="V_MMCK" variable_1="V_MMCK"/>
</connection>
<connection>
<map_components component_2="J_Cr" component_1="Cr"/>
<map_variables variable_2="Cr" variable_1="Cr"/>
<map_variables variable_2="J_Cr" variable_1="J_Cr"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="Cr"/>
<map_variables variable_2="V_cyt" variable_1="V_cyt"/>
</connection>
<connection>
<map_components component_2="V_hyd" component_1="Pi"/>
<map_variables variable_2="V_hyd" variable_1="V_hyd"/>
</connection>
<connection>
<map_components component_2="J_Pi" component_1="Pi"/>
<map_variables variable_2="Pi" variable_1="Pi"/>
<map_variables variable_2="J_Pi" variable_1="J_Pi"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="Pi"/>
<map_variables variable_2="V_cyt" variable_1="V_cyt"/>
</connection>
<connection>
<map_components component_2="V_MiCK" component_1="ATP_i"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
<map_variables variable_2="V_MiCK" variable_1="V_MiCK"/>
</connection>
<connection>
<map_components component_2="V_syn" component_1="ATP_i"/>
<map_variables variable_2="V_syn" variable_1="V_syn"/>
</connection>
<connection>
<map_components component_2="J_ATP" component_1="ATP_i"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
<map_variables variable_2="J_ATP" variable_1="J_ATP"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="ATP_i"/>
<map_variables variable_2="V_ims" variable_1="V_ims"/>
</connection>
<connection>
<map_components component_2="V_MiCK" component_1="ADP_i"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
<map_variables variable_2="V_MiCK" variable_1="V_MiCK"/>
</connection>
<connection>
<map_components component_2="V_syn" component_1="ADP_i"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
<map_variables variable_2="V_syn" variable_1="V_syn"/>
</connection>
<connection>
<map_components component_2="J_ADP" component_1="ADP_i"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
<map_variables variable_2="J_ADP" variable_1="J_ADP"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="ADP_i"/>
<map_variables variable_2="V_ims" variable_1="V_ims"/>
</connection>
<connection>
<map_components component_2="V_MiCK" component_1="PCr_i"/>
<map_variables variable_2="PCr_i" variable_1="PCr_i"/>
<map_variables variable_2="V_MiCK" variable_1="V_MiCK"/>
</connection>
<connection>
<map_components component_2="J_PCr" component_1="PCr_i"/>
<map_variables variable_2="PCr_i" variable_1="PCr_i"/>
<map_variables variable_2="J_PCr" variable_1="J_PCr"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="PCr_i"/>
<map_variables variable_2="V_ims" variable_1="V_ims"/>
</connection>
<connection>
<map_components component_2="V_MiCK" component_1="Cr_i"/>
<map_variables variable_2="Cr_i" variable_1="Cr_i"/>
<map_variables variable_2="V_MiCK" variable_1="V_MiCK"/>
</connection>
<connection>
<map_components component_2="J_Cr" component_1="Cr_i"/>
<map_variables variable_2="Cr_i" variable_1="Cr_i"/>
<map_variables variable_2="J_Cr" variable_1="J_Cr"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="Cr_i"/>
<map_variables variable_2="V_ims" variable_1="V_ims"/>
</connection>
<connection>
<map_components component_2="V_syn" component_1="Pi_i"/>
<map_variables variable_2="Pi_i" variable_1="Pi_i"/>
<map_variables variable_2="V_syn" variable_1="V_syn"/>
</connection>
<connection>
<map_components component_2="J_Pi" component_1="Pi_i"/>
<map_variables variable_2="Pi_i" variable_1="Pi_i"/>
<map_variables variable_2="J_Pi" variable_1="J_Pi"/>
</connection>
<connection>
<map_components component_2="fractional_volumes" component_1="Pi_i"/>
<map_variables variable_2="V_ims" variable_1="V_ims"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Seq rdf:about="rdf:#4b3b9f01-4f64-4a76-b2b5-5835c62eb829">
<rdf:li rdf:resource="rdf:#203663c8-91a1-49f1-9cea-739458a3102e"/>
<rdf:li rdf:resource="rdf:#3031d17d-554b-441f-9df3-95bcb473ea3d"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#0691b60a-998c-4f6e-9dc1-8e188de5b16f">
<vCard:ORG rdf:resource="rdf:#3a67967c-502f-4479-a22d-dae194cd7eee"/>
<vCard:EMAIL rdf:resource="rdf:#74524153-d5cc-4e69-9b0c-2615ad5432a0"/>
<vCard:N rdf:resource="rdf:#f5ed4e7b-f9f8-44b9-960e-ba94d43444fc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f5ed4e7b-f9f8-44b9-960e-ba94d43444fc">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#437dcc78-c1bc-4a65-a12d-28de24db5c7a">
<dcterms:W3CDTF>2009-04-28T10:35:01+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f4592fc-c6dc-4a68-a7fa-1e8d5ef4b65e">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9e492277-baae-42e8-8845-d668c9a84693">
<vCard:Given>Olav</vCard:Given>
<vCard:Family>Kongas</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#203663c8-91a1-49f1-9cea-739458a3102e">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#9e492277-baae-42e8-8845-d668c9a84693"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4ab5a9a3-478e-4fb9-bf0d-c004358c9ade">
<bqs:Pubmed_id/>
<bqs:JournalArticle rdf:resource="rdf:#017f3f02-4f59-4d8e-9599-be5757824888"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c11b4b9f-ef19-49ce-b35c-3abcefd07602">
<dc:creator rdf:resource="rdf:#73947938-e3ff-46a9-90f2-5dd344402098"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d8a6bb7b-a8f7-4d87-b924-b52b72a537c2">
<dcterms:W3CDTF>2004-02-04T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ce7a6a8b-c5c4-4183-ba33-1bce648c2ece">
<dcterms:W3CDTF>2001-00-00 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3a67967c-502f-4479-a22d-dae194cd7eee">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#74524153-d5cc-4e69-9b0c-2615ad5432a0">
<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="">
<dc:publisher/>
<cmeta:comment rdf:resource="rdf:#10547ec9-e84b-4d06-baba-4bbe64004787"/>
<dcterms:created rdf:resource="rdf:#d8a6bb7b-a8f7-4d87-b924-b52b72a537c2"/>
<dc:creator rdf:resource="rdf:#0691b60a-998c-4f6e-9dc1-8e188de5b16f"/>
<cmeta:modification rdf:resource="rdf:#a2c99c47-e98a-4f9a-aeeb-969c66779924"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#004d778e-7137-4034-b26e-8e9f37337bfe">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#10547ec9-e84b-4d06-baba-4bbe64004787">
<dc:creator rdf:resource="rdf:#004d778e-7137-4034-b26e-8e9f37337bfe"/>
<rdf:value>This CellML model is known to run on both OpenCell and COR. The units have been checked and they are balanced. The figures in the original publication display slightly unusual variables, hence we are unsure as to whether or not the CellML model is recreating the published results. To address this we are working with the original model authors to complete the curation of the CellML model. Please also note there are some typographical errors in the original publication, and that in equations 6-10 in the appendix, the metabolites should have an "i" subscript(to denote IMS concentrations), and also the "Vhyd"s in these equations should be "Vsyn"s.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#73947938-e3ff-46a9-90f2-5dd344402098">
<vCard:FN/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#017f3f02-4f59-4d8e-9599-be5757824888">
<dc:creator rdf:resource="rdf:#4b3b9f01-4f64-4a76-b2b5-5835c62eb829"/>
<dc:title>Creatine kinase in energy metabolic signaling in muscle</dc:title>
<bqs:volume/>
<bqs:first_page/>
<bqs:Journal rdf:resource="rdf:#d484f968-9b92-49e4-9f7f-d1d3b374dfea"/>
<dcterms:issued rdf:resource="rdf:#ce7a6a8b-c5c4-4183-ba33-1bce648c2ece"/>
<bqs:last_page/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5893d25e-4fc1-42de-b3cb-d4e5a5b617fc">
<vCard:Given>Johannes</vCard:Given>
<vCard:Family>van Beek</vCard:Family>
<vCard:Other>G</vCard:Other>
<vCard:Other>H</vCard:Other>
<vCard:Other>M</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a2c99c47-e98a-4f9a-aeeb-969c66779924">
<dcterms:modified rdf:resource="rdf:#437dcc78-c1bc-4a65-a12d-28de24db5c7a"/>
<rdf:value>Balanced units
Added initial conditions
Removed the conservation equations as these made the CellML model overconstrained</rdf:value>
<cmeta:modifier rdf:resource="rdf:#9da4b94f-d300-4c22-acf5-275a89c40c40"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9da4b94f-d300-4c22-acf5-275a89c40c40">
<vCard:N rdf:resource="rdf:#4f4592fc-c6dc-4a68-a7fa-1e8d5ef4b65e"/>
</rdf:Description>
<rdf:Description rdf:about="#kongas_model_2001">
<bqs:reference rdf:resource="rdf:#4ab5a9a3-478e-4fb9-bf0d-c004358c9ade"/>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>cardiac</rdf:li>
<rdf:li>metabolism</rdf:li>
<rdf:li>ATP</rdf:li>
<rdf:li>mitochondria</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<cmeta:comment rdf:resource="rdf:#c11b4b9f-ef19-49ce-b35c-3abcefd07602"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d484f968-9b92-49e4-9f7f-d1d3b374dfea">
<dc:title>ICSB 2001 Conference Proceedings</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3031d17d-554b-441f-9df3-95bcb473ea3d">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#5893d25e-4fc1-42de-b3cb-d4e5a5b617fc"/>
</rdf:Description>
</rdf:RDF>
</model>
