- Author:
- Dewan Sarwar <sarwarcse@gmail.com>
- Date:
- 2019-01-22 15:53:48+13:00
- Desc:
- adding the removed namepsaces
- Permanent Source URI:
- http://models.cellml.org/workspace/584/rawfile/f42c82f77870f412e1964b9b0701fec331344c8d/smith_crampin_2004.cellml
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<title>Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study</title>
<author>
<firstname>Alice</firstname>
<surname>Boit</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: This study presents a method for the reduction of biophysically-based kinetic models for the active transport of ions. A lumping scheme is presented which exploits the differences in timescales associated with fast and slow transitions between model states, while maintaining the thermodynamic properties of the model. The goal of this approach is to contribute to modelling of the effects of disturbances to metabolism, associated with ischaemic heart disease, on cardiac cell function. The approach is illustrated for the sodium-potassium pump in the myocyte. The lumping scheme is applied to produce a 4-state representation from the detailed 15-state model of Lauger and Apell, Eur. Biophys. J. 13 (1986) 309, for which the principles of free energy transduction are used to link the free energy released from ATP hydrolysis (deltaGATP) to the transition rates between states of the model. An iterative minimisation algorithm is implemented to determine the transition rate parameters based on the model fit to experimental data. Finally, the relationship between deltaGATP and pump cycling direction is investigated and compared with recent experimental findings.</para>
<para>The original paper reference is cited below:</para>
<para>
Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study, N. P. Smith and E. J. Crampin, 2004,
<emphasis>Progress in Biophysics and Molecular Biology</emphasis>
<ulink url="http://www.ncbi.nlm.nih.gov/pubmed/15142754">PubMed ID: 15142754</ulink>
</para>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
<ci>dimless_MgATP</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="minus_alpha4_calc">
<eq />
<ci>minus_alpha4</ci>
<apply>
<divide />
<apply>
<times />
<ci>minus_k4</ci>
<apply>
<power />
<ci>dimless_K_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<minus />
<apply>
<plus />
<apply>
<power />
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
<ci>dimless_Na_i</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power />
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
<ci>dimless_K_i</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="diagram_sum">
<eq />
<ci>diagram_sum</ci>
<apply>
<plus />
<apply>
<times />
<ci>minus_alpha3</ci>
<ci>minus_alpha2</ci>
<ci>minus_alpha1</ci>
</apply>
<apply>
<times />
<ci>alpha4</ci>
<ci>minus_alpha2</ci>
<ci>minus_alpha1</ci>
</apply>
<apply>
<times />
<ci>alpha4</ci>
<ci>alpha2</ci>
<ci>alpha3</ci>
</apply>
<apply>
<times />
<ci>alpha4</ci>
<ci>minus_alpha1</ci>
<ci>alpha3</ci>
</apply>
<apply>
<times />
<ci>minus_alpha3</ci>
<ci>minus_alpha2</ci>
<ci>alpha1</ci>
</apply>
<apply>
<times />
<ci>alpha4</ci>
<ci>minus_alpha2</ci>
<ci>alpha1</ci>
</apply>
<apply>
<times />
<ci>alpha4</ci>
<ci>alpha1</ci>
<ci>alpha3</ci>
</apply>
<apply>
<times />
<ci>minus_alpha3</ci>
<ci>alpha1</ci>
<ci>alpha2</ci>
</apply>
<apply>
<times />
<ci>alpha4</ci>
<ci>alpha1</ci>
<ci>alpha2</ci>
</apply>
<apply>
<times />
<ci>alpha1</ci>
<ci>alpha2</ci>
<ci>alpha3</ci>
</apply>
<apply>
<times />
<ci>minus_alpha4</ci>
<ci>minus_alpha3</ci>
<ci>minus_alpha1</ci>
</apply>
<apply>
<times />
<ci>minus_alpha4</ci>
<ci>minus_alpha3</ci>
<ci>alpha2</ci>
</apply>
<apply>
<times />
<ci>minus_alpha4</ci>
<ci>minus_alpha3</ci>
<ci>minus_alpha2</ci>
</apply>
<apply>
<times />
<ci>minus_alpha4</ci>
<ci>minus_alpha1</ci>
<ci>minus_alpha2</ci>
</apply>
<apply>
<times />
<ci>minus_alpha4</ci>
<ci>alpha2</ci>
<ci>alpha3</ci>
</apply>
<apply>
<times />
<ci>minus_alpha4</ci>
<ci>minus_alpha1</ci>
<ci>alpha3</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v_cyc_calc">
<eq />
<ci>v_cyc</ci>
<apply>
<divide />
<apply>
<minus />
<apply>
<times />
<ci>alpha1</ci>
<ci>alpha2</ci>
<ci>alpha3</ci>
<ci>alpha4</ci>
</apply>
<apply>
<times />
<ci>minus_alpha1</ci>
<ci>minus_alpha2</ci>
<ci>minus_alpha3</ci>
<ci>minus_alpha4</ci>
</apply>
</apply>
<ci>diagram_sum</ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation" />
<component_ref component="interface">
<component_ref component="NaK_pump" />
</component_ref>
</group>
<connection>
<map_components component_1="NaK_pump" component_2="interface" />
<map_variables variable_1="net_free_energy" variable_2="net_free_energy" />
<map_variables variable_1="v_cyc" variable_2="v_cyc" />
</connection>
<connection>
<map_components component_1="interface" component_2="NaK_pump" />
<map_variables variable_1="cMgADP" variable_2="cMgADP" />
<map_variables variable_1="cNa_i" variable_2="cNa_i" />
<map_variables variable_1="Vm" variable_2="Vm" />
</connection>
<rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:ro="http://www.obofoundry.org/ro/ro.owl#" xmlns:opb="http://bhi.washington.edu/OPB#" xmlns:j.0="http://imc.org/vCard/3.0#">
<rdf:Description rdf:about="#NaK_pump.k4">
<dcterms:description>Forward rate constant for sodium-potassium exchanger transition from lumped states P14-P15 to lumped states P1-P6 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#diagram_sum">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#90b178ef-1b8b-49fb-a484-273533033e62">
<rdf:value>Calculation of the diagram sum used in the denominator of the equation of cycle rate v_cyc.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dG_pump_calc_eq">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#cfa804d8-c886-480a-8416-ebfa2dfeae86">
<rdf:value>Calculation of dG_pump.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cK_e">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_5">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_6">
<ro:part_of>
<rdf:Description rdf:about="#entity_7">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/fma/FMA:70022" />
</rdf:Description>
</ro:part_of>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/chebi/CHEBI:29103" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Extracellular potassium ion concentration</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#alpha1">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#9b67e2cc-d816-4358-9f48-291b504c8afb">
<rdf:value>Calculation of the foward transition rate called alpha1 from the first to the second lumped state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dG_Na">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_4">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00378" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>The energy required to translocate a sodium ion from the intracellular cytosol to the extracellular environment</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cPi_sum">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_13">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Total intracellular concentration of bound and unbound inorganic phosphate</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dimless_K_i">
<dcterms:description>Convenience term that is the ratio of the intracellular potassium concentration to its equilibrium constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cMgADP">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_15">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_4" semsim:name="MgADP">
<ro:part_of>
<rdf:Description rdf:about="#entity_1">
<ro:part_of>
<rdf:Description rdf:about="#entity_2">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/fma/FMA:14067" />
</rdf:Description>
</ro:part_of>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/fma/FMA:66836" />
</rdf:Description>
</ro:part_of>
<dcterms:description>Magnesium-bound ADP</dcterms:description>
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular concentration of magnesium-bound ADP</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.diagram_sum">
<dcterms:description>Convencience term for expressing equation that solves v_cyc</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_Na_base_i">
<dcterms:description>Equilibrium constant for dissociation of sodium ion from intracellular-facing pump when membrane potential is zero</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dimless_Na_e">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#b63ff27d-53e4-402b-9e2e-264803036dc8">
<rdf:value>Calculation of the dimless_Na_e parameter which is a
function of Vm because the equilibrium constant is
dependent on Vm (which occurs in the denominator's exponential). Note that the partition of the
voltage dependency in the exponential corresponds to the previous calculation of dimless_Na_i.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cPi">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_7">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_9">
<ro:part_of rdf:resource="#entity_1" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/chebi/CHEBI:24838" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular concentration of inorganic phosphate</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#cPi">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#92ebf8ec-5316-4957-9904-1e14495c7df0">
<rdf:value>Calculation of the concentration of free inorganic phosphate cPi
related to the total measurable concentration given by cPi_sum.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.net_free_energy">
<dcterms:description>The net free energy of a sodium-potassium pump cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cMgATP">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_17">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_12">
<ro:part_of rdf:resource="#entity_1" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/chebi/CHEBI:30617" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular concentration of magnesium-bound ATP</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#alpha2">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#8e9e9a79-54ca-4a22-89bb-31588b852e8c">
<rdf:value>Calculation of the foward transition rate called alpha2 from the second to the third state.
Note that this transition rate is identical to k2 because state P7 (see paper) is not a lumped state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#interface.cNa_i">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_0">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_0">
<ro:part_of rdf:resource="#entity_1" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/chebi/CHEBI:29101" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular sodium ion concentration</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dimless_Na_e">
<dcterms:description>Convenience term that is the ratio of the extracellular sodium concentration to its equilibrium constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dimless_MgATP">
<dcterms:description>Convenience term that is the ratio of the intracellular MgATP concentration to its equilibrium constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.Vm">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_8">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_3">
<ro:part_of rdf:resource="#entity_2" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/fma/FMA:63841" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01364" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_NaPi">
<dcterms:description>Equilibrium constant for dissociation of sodium ion from inorganic phosphate</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_HPi">
<dcterms:description>Equilibrium constant for dissociation of proton from inorganic phosphate</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#smith_crampin_2004" semsim:modelId="smith_2004" semsim:modelName="smith_2004" />
<rdf:Description rdf:about="#NaK_pump.alpha1">
<dcterms:description>Apparent first-order forward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#NaK_pump">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#7c073ba1-627f-4f0d-b8cc-f1959eee1dbd">
<rdf:value>The Na/K-pump is an energy-consuming transporter channel within the membrane.
It is indispensible for maintaining the electrochemical gradients of the involved ions
across the membrane which result in resting Vm. The pump splits up one ATP molecule as it undergoes a
conformational change transporting 3Na outwards and 2K inwards in each cycle.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_k1">
<dcterms:description>Backward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#alpha3">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#a9d5a14c-a97d-456c-b0d8-8b76c7c3e19d">
<rdf:value>Calculation of the foward transition rate called alpha3 from the third to the fourth state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dG_Na_calc_eq">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#f6f58a55-01db-45ff-9a37-b8fc810b4e5d">
<rdf:value>Calculation of the Na contribution to dG_pump.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#v_cyc">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#aa877685-c275-475e-a620-83e870461e32">
<rdf:value>Calculation of the clockwise cycle rate v_cyc.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dG_K">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_11">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00378" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>The energy required to translocate a potassium ion from the extracellular environment to the intracellular cytosol</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dimless_K_e">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#06ec35f5-3dfe-4cf9-ba33-52ebeda01fe2">
<rdf:value>Calculation of the dimless_K_e parameter.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_K_e">
<dcterms:description>Equilibrium constant for dissociation of potassium ion from extracellular-facing pump</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_MgATP">
<dcterms:description>Equilibrium constant for MgATP hydrolysis</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cH">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_9">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_10">
<ro:part_of rdf:resource="#entity_1" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/chebi/CHEBI:24636" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular proton concentration</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dG_K_calc_eq">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#436c5416-0a14-41b1-b7bb-c1fc3ed3ccac">
<rdf:value>Calculation of the K contribution to dG_pump.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#alpha4">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#b63db052-a29a-4645-ae22-6c7a8d394691">
<rdf:value>Calculation of the foward transition rate called alpha4 from the fourth to the first state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_KPi">
<dcterms:description>Equilibrium constant for dissociation of potassium ion from inorganic phosphate</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#interface.cMgADP">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_2">
<semsim:physicalPropertyOf rdf:resource="#entity_4" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular concentration of magnesium-bound ADP</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.v_cyc">
<dcterms:description>Steady-state cycle rate of sodium-potassium pump</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.gas_const">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00410" />
<dcterms:description>Universal gas constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dimless_MgATP">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#fdb8d672-10b8-4fba-b93b-af2bf9c89e11">
<rdf:value>Calculation of the dimless_MgATP parameter.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cK_i">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_3">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_5">
<ro:part_of rdf:resource="#entity_1" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/chebi/CHEBI:29103" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular potassium ion concentration</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_k3">
<dcterms:description>Backward rate constant for sodium-potassium exchanger transition from lumped states P8-P13 to lumped states P14-P15 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#interface.v_cyc">
<dcterms:description>Steady-state cycle rate of sodium-potassium pump</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#interface.Vm">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_1">
<semsim:physicalPropertyOf rdf:resource="#entity_3" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01364" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Membrane potential</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0">
<dc:publisher>The University of Auckland, Auckland Bioengineering Institute</dc:publisher>
<cmeta:comment>
<rdf:Description rdf:about="rdf:#59a55738-0e3b-48a0-9a7e-572dc6ab43fe" rdf:value="">
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<dcterms:created rdf:resource="rdf:#93a24e90-c784-407e-8e0a-56b5e3ab32a5" dcterms:W3CDTF="2004-04-26T00:00:00+00:00" />
<dc:creator>
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<vCard:ORG>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
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</vCard:ORG>
<vCard:EMAIL rdf:resource="rdf:#9a0073c8-2718-41c3-991a-5f3bb96b7e15" rdf:value="a.boit@auckland.ac.nz" rdf:type="http://imc.org/vCard/3.0#internet" />
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</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#minus_alpha3">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#df417b59-a805-4786-8a85-33da54677f6b">
<rdf:value>Calculation of the reverse transition rate called minus_alpha3 from the fourth to the 3rd state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_alpha1">
<dcterms:description>Psuedo-first-order backward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dimless_K_e">
<dcterms:description>Convenience term that is the ratio of the extracellular potassium concentration to its equilibrium constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_Na_base_e">
<dcterms:description>Equilibrium constant for dissociation of sodium ion from extracellular-facing pump when membrane potential is zero</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.alpha3">
<dcterms:description>Apparent first-order forward rate constant for sodium-potassium exchanger transition from lumped states P8-P13 to lumped states P14-P15 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#interface.net_free_energy">
<dcterms:description>The net free energy of a sodium-potassium pump cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.alpha2">
<dcterms:description>Apparent first-order forward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle</dcterms:description>
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<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dG_ATP_calc">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#07acefc0-d7da-4103-80e7-5e9b45616ad3">
<rdf:value>Calculation the net free energy of the cycle.</rdf:value>
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</cmeta:comment>
<cmeta:comment>
<rdf:Description rdf:about="rdf:#7eda74c9-eee6-4811-90f5-a8551c930b04">
<rdf:value>Calculation the energy released by ATP hydrolysis.</rdf:value>
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<rdf:Description rdf:about="#NaK_pump.k1">
<dcterms:description>Forward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle</dcterms:description>
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<rdf:Description rdf:about="#NaK_pump.minus_k2">
<dcterms:description>Backward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle</dcterms:description>
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<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dimless_Na_i">
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<rdf:Description rdf:about="rdf:#fe1d39b5-c55d-4626-aef5-1d4ef879cd42">
<rdf:value>Calculation of the dimless_Na_i parameter which is a function of Vm because the equilibrium constant is
dependent on Vm (which occurs in the denominator's exponential).</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.faraday_const">
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<dcterms:description>Faraday constant</dcterms:description>
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<rdf:Description rdf:about="#NaK_pump.dimless_Na_i">
<dcterms:description>Convenience term that is the ratio of the intracellular sodium concentration to its equilibrium constant</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cNa_e">
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<dcterms:description>Extracellular sodium ion concentration</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#minus_alpha4">
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<rdf:Description rdf:about="rdf:#e111190b-c9ab-4532-a37b-602af3eca18b">
<rdf:value>Calculation of the reverse transition rate called minus_alpha4 from the first to the fourth lumped state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dG_pump">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_14">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00378" />
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</semsim:isComputationalComponentFor>
<dcterms:description>Energy consumed for each pump cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.body_temp">
<semsim:isComputationalComponentFor>
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<semsim:physicalPropertyOf>
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<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/fma/FMA:305853" />
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<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00293" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Ambient temperature</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.k2">
<dcterms:description>Forward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_alpha4">
<dcterms:description>Psuedo-first-order backward rate constant for sodium-potassium exchanger transition from lumped states P14-P15 to lumped states P1-P6 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.cNa_i">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_10">
<semsim:physicalPropertyOf rdf:resource="#entity_0" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00340" />
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</semsim:isComputationalComponentFor>
<dcterms:description>Intracellular sodium ion concentration</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#dimless_K_i">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#0c4e2915-1b40-49a5-af44-8642b560477c">
<rdf:value>Calculation of the dimless_K_i parameter.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_alpha3">
<dcterms:description>Psuedo-first-order backward rate constant for sodium-potassium exchanger transition from lumped states P8-P13 to lumped states P14-P15 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#minus_alpha1">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#5d649588-1214-4bf4-ae80-ecee3fae16ad">
<rdf:value>Calculation of the reverse transition rate called minus_alpha1 from the second to the first state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.eq_K_i">
<dcterms:description>Equilibrium constant for dissociation of potassium ion from intracellular-facing pump</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.dG_ATP">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_16">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_00378" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>The free energy of MgATP hydroysis</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#smith_2004">
<dc:title>N. P. Smith' and E. Crampin's 2004 mathematical model of the cardiac sodium-potassium pump.</dc:title>
<cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity>
<cmeta:comment>
<rdf:Description rdf:about="rdf:#da7ec15b-087d-4b57-a579-bff0adc67588">
<dc:creator>
<rdf:Description rdf:about="rdf:#21f8e3dd-bbab-4ff0-80b1-901122c5788a">
<vCard:FN>Alice Boit</vCard:FN>
</rdf:Description>
</dc:creator>
<rdf:value>This is the CellML description of N. P. Smith' and E. Crampin's 2004
mathematical model of the cardiac sodium-potassium pump.</rdf:value>
</rdf:Description>
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</bqs:Person>
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</dc:creator>
<dc:title>Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study</dc:title>
<bqs:Journal>
<rdf:Description rdf:about="rdf:#12528523-5983-4b5e-93f6-279a4ff091f0">
<dc:title>Progress in Biophysics & Molecular Biology</dc:title>
</rdf:Description>
</bqs:Journal>
<dcterms:issued rdf:resource="rdf:#decab482-727d-4572-b04c-40302d5a17c6" dcterms:W3CDTF="2004" />
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<bqs:reference>
<rdf:Description rdf:about="rdf:#53e59201-e39b-4906-b3ac-6ef2d4277a0d">
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<rdf:value>
<rdf:Bag rdf:about="rdf:#b6c23be5-05a3-4e34-b31f-d00db0737132">
<rdf:li>active transport</rdf:li>
<rdf:li>cardiac myocyte</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>na/k pump</rdf:li>
</rdf:Bag>
</rdf:value>
</rdf:Description>
</dc:subject>
</rdf:Description>
</bqs:reference>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.k3">
<dcterms:description>Forward rate constant for sodium-potassium exchanger transition from lumped states P8-P13 to lumped states P14-P15 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_k4">
<dcterms:description>Backward rate constant for sodium-potassium exchanger transition from lumped states P14-P15 to lumped states P1-P6 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#interface.time">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01023" />
<dcterms:description>Time domain for simulation</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.minus_alpha2">
<dcterms:description>Psuedo-first-order backward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#minus_alpha2">
<cmeta:comment>
<rdf:Description rdf:about="rdf:#8f94dcfc-58fb-4b79-bfe5-545db58f0d46">
<rdf:value>Calculation of the reverse transition rate called minus_alpha2 from the 3rd to the second state.</rdf:value>
</rdf:Description>
</cmeta:comment>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.partition_factor">
<dcterms:description>Factor for determining how voltage dependence is partitioned between the intra- and extracellular sodium ion dissociation reactions</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#NaK_pump.alpha4">
<dcterms:description>Apparent first-order forward rate constant for sodium-potassium exchanger transition from lumped states P14-P15 to lumped states P1-P6 of the Post-Albers cycle</dcterms:description>
</rdf:Description>
</rdf:RDF>
</model>
