/Users/Brian/Desktop/tran_smith_loiselle_crampin_2009/tran_smith_loiselle_crampin_2009.cellml
<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status 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 three-state cooperative SERCA model and recreates figure 13. In order to recreate this figure we have had to add an additional equation to the model to define the rate of change in Casr. 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. <sect1 id="sec_structure"> Model Structure 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. The complete original paper reference is cited below: 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, Biophysical Journal , 96 (5) 2029-2042. PubMed ID: 19254563 <informalfigure float="0"> <mediaobject> <imageobject> <imagedata fileref="tran_2009.png" /> </imageobject> </mediaobject> Schematic of the simplified three-state model. Application of the rapid equilibrium assumption to the ion-binding partial reactions (states within the two dotted boxes in Fig. 1) results in a simplified three-state model. The apparent rate constants (alphai + or -, i = 1, 2, 3) replace the forward and backward rate constants and are a function of ion concentrations and dissociation constants. </informalfigure> </sect1> </documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:j.0="http://imc.org/vCard/3.0#"> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#tran_model_2009"> <cmeta:comment> <rdf:Description rdf:about="rdf:#594c54e4-2368-4aba-8dee-bd2175490d26"> <rdf:value></rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#6b548755-48ec-4433-8329-94c1c0c1c7c3"> <vCard:FN></vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <bqs:reference rdf:parseType="Resource"> <dc:subject rdf:parseType="Resource"> <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> <bqs:subject_type>keyword</bqs:subject_type> </dc:subject> </bqs:reference> <bqs:reference> <rdf:Description rdf:about="rdf:#dde09b5f-2570-44e4-b7af-2782b3f4dc03"> <bqs:JournalArticle> <rdf:Description rdf:about="rdf:#1aa7136e-0363-4f6f-8e67-d823ba86d1ab"> <bqs:last_page>2042</bqs:last_page> <dcterms:issued> <rdf:Description rdf:about="rdf:#80797212-992e-4436-9c29-95f80d6ea1d5"> <dcterms:W3CDTF>2009-03-00 00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:issued> <bqs:Journal> <rdf:Description rdf:about="rdf:#dbd53168-2407-4b79-a3da-77beb4f217ab"> <dc:title>Biophysical Journal</dc:title> </rdf:Description> </bqs:Journal> <bqs:first_page>2029</bqs:first_page> <bqs:volume>96</bqs:volume> <dc:title>A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#277d3fce-1e82-45ea-884f-2e76a89f4a54"> <rdf:li> <bqs:Person rdf:about="rdf:#5a8af88e-79ba-4e3a-a593-38f0298d25aa"> <vCard:N> <rdf:Description rdf:about="rdf:#62cab138-9811-478d-9183-2d5af616ef1e"> <vCard:Family>Tran</vCard:Family> <vCard:Given>Kenneth</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#3e2e26bb-0f27-47bd-bd91-6953b7b7b874"> <vCard:N> <rdf:Description rdf:about="rdf:#01fe663c-eefc-4a1e-8d24-f6891a804dc2"> <vCard:Other>P</vCard:Other> <vCard:Family>Smith</vCard:Family> <vCard:Given>Nicolas</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#7eff5bdd-8d4f-40df-8629-2acc3d9f4733"> <vCard:N> <rdf:Description rdf:about="rdf:#6c88af07-dec5-4659-aa5c-908846a4c4ad"> <vCard:Other>S</vCard:Other> <vCard:Family>Loiselle</vCard:Family> <vCard:Given>Denis</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#a2f05790-5ec5-42ca-a8d9-6db94a7a06eb"> <vCard:N> <rdf:Description rdf:about="rdf:#b06c7bb6-6563-4d49-b6d0-be2036ec2c30"> <vCard:Other>J</vCard:Other> <vCard:Family>Crampin</vCard:Family> <vCard:Given>Edmund</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </bqs:JournalArticle> <bqs:Pubmed_id>19254563</bqs:Pubmed_id> </rdf:Description> </bqs:reference> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <dc:creator> <rdf:Description rdf:about="rdf:#56464cca-dd1f-4ca3-adbb-ebdb90f265be"> <vCard:N> <rdf:Description rdf:about="rdf:#a3800ea1-7856-4edb-9cf1-0579364ed799"> <vCard:Other></vCard:Other> <vCard:Family>Tran</vCard:Family> <vCard:Given>Kenneth</vCard:Given> </rdf:Description> </vCard:N> <vCard:EMAIL> <j.0:internet rdf:about="rdf:#b59fbe3f-3a81-46d3-a98c-90bb39108878"> <rdf:value>k.tran@auckland.ac.nz</rdf:value> </j.0:internet> </vCard:EMAIL> <vCard:ORG> <rdf:Description rdf:about="rdf:#05a40c92-02a0-4779-941b-2267d63e9f20"> <vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit> <vCard:Orgname>The University of Auckland</vCard:Orgname> </rdf:Description> </vCard:ORG> </rdf:Description> </dc:creator> <dcterms:created> <rdf:Description rdf:about="rdf:#f4cfda0d-7868-4c07-b67f-c405e97eee3e"> <dcterms:W3CDTF>2009-03-05T00:00:00+00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:created> <cmeta:comment> <rdf:Description rdf:about="rdf:#59ac1836-2f1d-4123-9e4d-279bd99d90be"> <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 three-state cooperative SERCA model and recreates figure 13. In order to recreate this figure we have had to add an additional equation to the model to define the rate of change in Casr.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#f89919f3-1b06-4a91-b591-952b37d6146d"> <vCard:FN>Catherine Lloyd</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:publisher></dc:publisher> <dc:title>A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump: the three-state SERCA model</dc:title> </rdf:Description> </rdf:RDF>
Brian Carlson
Model of the cardiac SERCA pump
Chemical concentration
ATP
ADP
phosphate
calcium(2+)
Cardiac myocyte
Cytoplasmic organelle matrix
Portion of cytosol
Sarcoplasmic reticulum
A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
Concentration of adenosine diphosphate in the cytosol
Concentration of adenosine triphosphate in the cytosol
Concentration of calcium in the cytosol
Concentration of calcium in the sarcoplasmic reticulum
Concentration of hydrogen in the cytosol
Concentration of phosphate in the cytosol
Time
Simulation time domain
<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>a_p1</ci> <apply> <times /> <ci>k_p1</ci> <ci>ATP</ci> </apply> </apply> <apply> <eq /> <ci>a_p2</ci> <apply> <divide /> <apply> <times /> <ci>k_p2</ci> <apply> <power /> <ci>T_Cai</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>T_Cai</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <apply> <times /> <apply> <power /> <ci>T_Cai</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>T_Hi</ci> </apply> <apply> <times /> <ci>T_Hi</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>T_H1</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>a_p3</ci> <apply> <divide /> <apply> <times /> <ci>k_p3</ci> <ci>T_Hsr</ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci>T_Casr</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>T_H</ci> </apply> <ci>T_H</ci> <apply> <times /> <ci>T_Hsr</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>T_H</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>a_m1</ci> <apply> <divide /> <apply> <times /> <ci>k_m1</ci> <ci>T_Hi</ci> </apply> <apply> <plus /> <apply> <power /> <ci>T_Cai</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <apply> <times /> <apply> <power /> <ci>T_Cai</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>T_Hi</ci> </apply> <apply> <times /> <ci>T_Hi</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>T_H1</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>a_m2</ci> <apply> <divide /> <apply> <times /> <ci>k_m2</ci> <ci>ADP</ci> <apply> <power /> <ci>T_Casr</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>T_H</ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci>T_Casr</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>T_H</ci> </apply> <ci>T_H</ci> <apply> <times /> <ci>T_Hsr</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>T_H</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>a_m3</ci> <apply> <times /> <ci>k_m3</ci> <ci>P_i</ci> </apply> </apply> <apply> <eq /> <ci>s1</ci> <apply> <plus /> <apply> <times /> <ci>a_p2</ci> <ci>a_p3</ci> </apply> <apply> <times /> <ci>a_m1</ci> <ci>a_p3</ci> </apply> <apply> <times /> <ci>a_m1</ci> <ci>a_m2</ci> </apply> </apply> </apply> <apply> <eq /> <ci>s2</ci> <apply> <plus /> <apply> <times /> <ci>a_p1</ci> <ci>a_p3</ci> </apply> <apply> <times /> <ci>a_m2</ci> <ci>a_p1</ci> </apply> <apply> <times /> <ci>a_m2</ci> <ci>a_m3</ci> </apply> </apply> </apply> <apply> <eq /> <ci>s3</ci> <apply> <plus /> <apply> <times /> <ci>a_p1</ci> <ci>a_p2</ci> </apply> <apply> <times /> <ci>a_m3</ci> <ci>a_m1</ci> </apply> <apply> <times /> <ci>a_m3</ci> <ci>a_p2</ci> </apply> </apply> </apply> <apply> <eq /> <ci>v_cycle</ci> <apply> <divide /> <apply> <minus /> <apply> <times /> <ci>a_p1</ci> <ci>a_p2</ci> <ci>a_p3</ci> </apply> <apply> <times /> <ci>a_m1</ci> <ci>a_m2</ci> <ci>a_m3</ci> </apply> </apply> <apply> <plus /> <ci>s1</ci> <ci>s2</ci> <ci>s3</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_sr</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="flux">1.0</cn> </apply>
hydrogen(1+)