<?xml version='1.0' encoding='utf-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/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:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" 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:NS1="http://purl.org/dc/terms/" 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:NS5="http://www.cellml.org/metadata/simulation/1.0#" xmlns:NS6="http://www.cellml.org/metadata/1.0#" xmlns:NS7="http://www.cellml.org/bqs/1.0#" cmeta:id="tran_model_2009" name="tran_model_2009">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump</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 has been unit checked and is known to run in both OpenCell and COR. This particular version of the CellML model describes the two-state SERCA model and recreates figure 12. In order to recreate this figure we have had to add an additional equation to the model to define the rate of change in ATP. Please also note there are typographical errors in the original paper and [H+] should be raised to the power of n (n=2) for T_Hi and T_Hsr. Also in figure 12 the concentrations of ADP should be 8uM and 20uM rather than 20uM and 40uM.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We present a biophysically based kinetic model of the cardiac SERCA pump that consolidates a range of experimental data into a consistent and thermodynamically constrained framework. The SERCA model consists of a number of sub-states with partial reactions that are sensitive to Ca(2+) and pH, and to the metabolites MgATP, MgADP, and Pi. Optimization of model parameters to fit experimental data favors a fully cooperative Ca(2+)-binding mechanism and predicts a Ca(2+)/H(+) counter-transport stoichiometry of 2. Moreover, the order of binding of the partial reactions, particularly the binding of MgATP, proves to be a strong determinant of the ability of the model to fit the data. A thermodynamic investigation of the model indicates that the binding of MgATP has a large inhibitory effect on the maximal reverse rate of the pump. The model is suitable for integrating into whole-cell models of cardiac electrophysiology and Ca(2+) dynamics to simulate the effects on the cell of compromised metabolism arising in ischemia and hypoxia.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump, Kenneth Tran, Nicolas P. Smith, Denis S. Loiselle, and Edmund J. Crampin, 2009, <emphasis>Biophysical Journal</emphasis>, 96 (5) 2029-2042. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=19254563&query_hl=1&itool=pubmed_docsum">PubMed ID: 19254563</ulink>
</para>
<informalfigure float="0">
<mediaobject>
<imageobject>
<imagedata fileref="tran_2009b.png"/>
</imageobject>
</mediaobject>
<caption> Application of the rapid equilibrium assumption to the ATP binding step reduces the three-state model further to a two-state model. The releases of ADP and Pi are assumed to be concomitant with the conformational change of the SERCA enzyme from the E1 to E2 state and are therefore modeled as relatively slower reactions.
</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="per_second_squared">
<unit units="second" exponent="-2"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="millimolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="millimolar_squared">
<unit units="millimolar" exponent="2"/>
</units>
<units name="second_order_rate_constant">
<unit units="millimolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<component name="SERCA">
<variable units="second_order_rate_constant" name="k_p1" initial_value="25900"/>
<variable units="first_order_rate_constant" name="k_p2" initial_value="2540"/>
<variable units="first_order_rate_constant" name="k_p3" initial_value="20.5"/>
<variable units="first_order_rate_constant" name="k_m1" initial_value="2"/>
<variable units="second_order_rate_constant" name="k_m2" initial_value="67200"/>
<variable units="second_order_rate_constant" name="k_m3" initial_value="149"/>
<variable units="millimolar" name="kdatp"/>
<variable units="millimolar" name="kdcai" initial_value="0.9"/>
<variable units="millimolar" name="kdcasr" initial_value="2.24"/>
<variable units="millimolar" name="kdh1" initial_value="1.09e-5"/>
<variable units="millimolar_squared" name="kdhi" initial_value="3.54e-3"/>
<variable units="millimolar_squared" name="kdhsr" initial_value="1.05e-8"/>
<variable units="millimolar" name="kdh" initial_value="7.24e-5"/>
<variable units="dimensionless" name="n" initial_value="2"/>
<variable units="millimolar" name="Ca_i" initial_value="1e-3"/>
<variable units="millimolar" name="Ca_sr" initial_value="1"/>
<variable units="millimolar" name="H_i" initial_value="1e-4"/>
<variable units="millimolar" name="ATP" initial_value="0.01"/>
<variable units="millimolar" name="ADP" initial_value="20e-3"/>
<variable units="millimolar" name="P_i" initial_value="1"/>
<variable units="dimensionless" name="T_ATP"/>
<variable units="dimensionless" name="T_Cai"/>
<variable units="dimensionless" name="T_Casr"/>
<variable units="dimensionless" name="T_H1"/>
<variable units="dimensionless" name="T_Hi"/>
<variable units="dimensionless" name="T_Hsr"/>
<variable units="dimensionless" name="T_H"/>
<variable units="first_order_rate_constant" name="a_p1"/>
<variable units="first_order_rate_constant" name="a_p2"/>
<variable units="first_order_rate_constant" name="a_m1"/>
<variable units="first_order_rate_constant" name="a_m2"/>
<variable units="first_order_rate_constant" name="s2"/>
<variable units="first_order_rate_constant" name="v_cycle"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>T_Cai</ci>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>kdcai</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_Casr</ci>
<apply>
<divide/>
<ci>Ca_sr</ci>
<ci>kdcasr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_H1</ci>
<apply>
<divide/>
<ci>H_i</ci>
<ci>kdh1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_Hi</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>H_i</ci>
<ci>n</ci>
</apply>
<ci>kdhi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_Hsr</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>H_i</ci>
<ci>n</ci>
</apply>
<ci>kdhsr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_H</ci>
<apply>
<divide/>
<ci>H_i</ci>
<ci>kdh</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>T_ATP</ci>
<apply>
<divide/>
<ci>ATP</ci>
<ci>kdatp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>kdatp</ci>
<apply>
<divide/>
<ci>k_m1</ci>
<ci>k_p1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>a_p1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_p2</ci>
<ci>T_ATP</ci>
<apply>
<power/>
<ci>T_Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>T_ATP</ci>
<apply>
<power/>
<ci>T_Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>T_Hi</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>T_ATP</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>T_H1</ci>
<apply>
<power/>
<ci>T_Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a_p2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_p3</ci>
<ci>T_Hsr</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>T_Hsr</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>T_H</ci>
</apply>
</apply>
<apply>
<times/>
<ci>T_H</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<ci>T_Casr</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a_m1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_m2</ci>
<ci>ADP</ci>
<apply>
<power/>
<ci>T_Casr</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>T_H</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>T_Hsr</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>T_H</ci>
</apply>
</apply>
<apply>
<times/>
<ci>T_H</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<ci>T_Casr</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a_m2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_m3</ci>
<ci>P_i</ci>
<ci>T_Hi</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>T_ATP</ci>
<apply>
<power/>
<ci>T_Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>T_Hi</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>T_ATP</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>T_H1</ci>
<apply>
<power/>
<ci>T_Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>s2</ci>
<apply>
<plus/>
<ci>a_p1</ci>
<ci>a_p2</ci>
<ci>a_m1</ci>
<ci>a_m2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_cycle</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>a_p1</ci>
<ci>a_p2</ci>
</apply>
<apply>
<times/>
<ci>a_m1</ci>
<ci>a_m2</ci>
</apply>
</apply>
<ci>s2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> ATP </ci>
</apply>
<cn cellml:units="flux"> 0.1 </cn>
</apply>
</math>
</component>
<connection>
<map_components component_2="SERCA" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Seq rdf:about="rdf:#6cedf02e-4ccb-40f7-97b2-d842cebfd9e7">
<rdf:li rdf:resource="rdf:#a662f33b-9647-4284-8474-6fe21a549915"/>
<rdf:li rdf:resource="rdf:#896e835a-ed3f-44a8-a7bc-f3a2f978276c"/>
<rdf:li rdf:resource="rdf:#1eac9a8c-71da-4593-aa2c-a1c1f61947db"/>
<rdf:li rdf:resource="rdf:#8a8c85a7-e1aa-4035-9622-bbb0860bf9db"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#4ad70129-50dd-4054-88b4-8df14479f6b7">
<vCard:ORG rdf:resource="rdf:#e83aca73-df9a-4f9a-b6e8-f89718a3b12a"/>
<vCard:EMAIL rdf:resource="rdf:#13740c38-86ed-48e9-9a27-b01b8acfed85"/>
<vCard:N rdf:resource="rdf:#3e46e900-d53e-4ee9-a6bb-6c355e40c9ab"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d8d09de4-406b-4f71-9665-8b56638ba304">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1eac9a8c-71da-4593-aa2c-a1c1f61947db">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#2d5fcb70-2968-4f24-8721-cffc8d3cbd65"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f62649a6-9873-459f-bf05-4da22e7b14d6">
<dcterms:W3CDTF>2009-03-00 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#tran_model_2009">
<bqs:reference rdf:resource="rdf:#463f4cfe-9a27-4cd1-9f1c-ca2d3a8fb2af"/>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>SERCA</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<cmeta:comment rdf:resource="rdf:#51c1d391-938e-427d-9348-507dfddf560b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3e46e900-d53e-4ee9-a6bb-6c355e40c9ab">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e83aca73-df9a-4f9a-b6e8-f89718a3b12a">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#13740c38-86ed-48e9-9a27-b01b8acfed85">
<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:title>A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump: the two-state SERCA model</dc:title>
<dc:publisher/>
<cmeta:comment rdf:resource="rdf:#b1131b1d-2f13-4858-aec3-902480e9cbfc"/>
<dcterms:created rdf:resource="rdf:#cbe0d409-c991-4960-96d4-1b321da04cf2"/>
<dc:creator rdf:resource="rdf:#4ad70129-50dd-4054-88b4-8df14479f6b7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b1131b1d-2f13-4858-aec3-902480e9cbfc">
<dc:creator rdf:resource="rdf:#d8d09de4-406b-4f71-9665-8b56638ba304"/>
<rdf:value>This CellML model has been unit checked and is known to run in both PCEnv and COR. This particular version of the CellML model describes the two-state SERCA model and recreates figure 12. In order to recreate this figure we have had to add an additional equation to the model to define the rate of change in ATP. Please also note there are typographical errors in the original paper and [H+] should be raised to the power of n (n=2) for T_Hi and T_Hsr. The value of K-1 should be 2, not 16 as it states in Table 2. And finally, in figure 12 the concetrations of ADP should be 8uM and 20uM rather than 20uM and 40uM.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ae913be1-e235-40b9-b5c0-765dbbd1ddae">
<dc:creator rdf:resource="rdf:#6cedf02e-4ccb-40f7-97b2-d842cebfd9e7"/>
<dc:title>A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump</dc:title>
<bqs:volume>96</bqs:volume>
<bqs:first_page>2029</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#b9b3fd4e-6b76-4060-a887-35e574813005"/>
<dcterms:issued rdf:resource="rdf:#f62649a6-9873-459f-bf05-4da22e7b14d6"/>
<bqs:last_page>2042</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8a8c85a7-e1aa-4035-9622-bbb0860bf9db">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#6686405f-4440-4f18-9ccb-62ae7d33c7f1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cbe0d409-c991-4960-96d4-1b321da04cf2">
<dcterms:W3CDTF>2009-03-05T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51c1d391-938e-427d-9348-507dfddf560b">
<dc:creator rdf:resource="rdf:#dd49e40b-377e-42f0-a57d-10907b400507"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a662f33b-9647-4284-8474-6fe21a549915">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#378b1409-b189-4919-b417-839e6ebff969"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4d7db92b-1066-4116-8376-6c6a5369a1d9">
<vCard:Given>Nicolas</vCard:Given>
<vCard:Family>Smith</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2d5fcb70-2968-4f24-8721-cffc8d3cbd65">
<vCard:Given>Denis</vCard:Given>
<vCard:Family>Loiselle</vCard:Family>
<vCard:Other>S</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6686405f-4440-4f18-9ccb-62ae7d33c7f1">
<vCard:Given>Edmund</vCard:Given>
<vCard:Family>Crampin</vCard:Family>
<vCard:Other>J</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#463f4cfe-9a27-4cd1-9f1c-ca2d3a8fb2af">
<bqs:Pubmed_id>19254563</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#ae913be1-e235-40b9-b5c0-765dbbd1ddae"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#378b1409-b189-4919-b417-839e6ebff969">
<vCard:Given>Kenneth</vCard:Given>
<vCard:Family>Tran</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dd49e40b-377e-42f0-a57d-10907b400507">
<vCard:FN/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b9b3fd4e-6b76-4060-a887-35e574813005">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#896e835a-ed3f-44a8-a7bc-f3a2f978276c">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#4d7db92b-1066-4116-8376-6c6a5369a1d9"/>
</rdf:Description>
</rdf:RDF>
</model>
