/Users/max_neal/Dropbox/Semantic Project/Annotated CellML models/smith_crampin_2004/smith_crampin_2004.cellml
<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study <author> <firstname>Alice</firstname> <surname>Boit</surname> <affiliation> <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status This CellML model runs in both OpenCell and COR. <sect1 id="sec_structure"> Model Structure 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. The original paper reference is cited below: 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, Progress in Biophysics and Molecular Biology PubMed ID: 15142754 <informalfigure float="0" id="fig_smith_crampin_state_diagram"> <mediaobject> <imageobject> <objectinfo> 15-state State Diagram </objectinfo> <imagedata fileref="smith_2004.png" /> </imageobject> </mediaobject> The 15 states of the original model. </informalfigure> <informalfigure float="0" id="fig_smith_crampin_lumped_state_diagram"> <mediaobject> <imageobject> <objectinfo> Smith-Crampin 4-state lumping scheme </objectinfo> <imagedata fileref="smith_2004b.png" /> </imageobject> </mediaobject> The 4 states of the Smith-Crampin model. </informalfigure> </sect1> </documentation>
<rdf:RDF xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:j.0="http://imc.org/vCard/3.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/"> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <dc:creator> <rdf:Description rdf:about="rdf:#bb0e207c-146d-4039-9f7c-d06ad25bd9c6"> <vCard:N> <rdf:Description rdf:about="rdf:#6ba26935-1582-4d2c-8d63-b5fe38631905"> <vCard:Other></vCard:Other> <vCard:Family>Boit</vCard:Family> <vCard:Given>Alice</vCard:Given> </rdf:Description> </vCard:N> <vCard:EMAIL> <j.0:internet rdf:about="rdf:#9a0073c8-2718-41c3-991a-5f3bb96b7e15"> <rdf:value>a.boit@auckland.ac.nz</rdf:value> </j.0:internet> </vCard:EMAIL> <vCard:ORG> <rdf:Description rdf:about="rdf:#bcf6b23d-9335-449b-83be-c2e0c4ac4d75"> <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:#93a24e90-c784-407e-8e0a-56b5e3ab32a5"> <dcterms:W3CDTF>2004-04-26T00:00:00+00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:created> <cmeta:comment> <rdf:Description rdf:about="rdf:#59a55738-0e3b-48a0-9a7e-572dc6ab43fe"> <rdf:value></rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#6496b573-b950-4d87-9d53-de4874253a31"> <vCard:FN></vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:publisher>The University of Auckland, Auckland Bioengineering Institute</dc:publisher> </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="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="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="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#dG_ATP_calc"> <cmeta:comment> <rdf:Description rdf:about="rdf:#7eda74c9-eee6-4811-90f5-a8551c930b04"> <rdf:value>Calculation the energy released by ATP hydrolysis.</rdf:value> </rdf:Description> </cmeta:comment> <cmeta:comment> <rdf:Description rdf:about="rdf:#07acefc0-d7da-4103-80e7-5e9b45616ad3"> <rdf:value>Calculation the net free energy of the cycle.</rdf:value> </rdf:Description> </cmeta:comment> </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="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="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="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="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="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="http://www.cellml.org/cellml/1.0#minus_alpha4"> <cmeta:comment> <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="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#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#dimless_Na_i"> <cmeta:comment> <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="http://www.cellml.org/cellml/1.0#smith_2004"> <bqs:reference> <rdf:Description rdf:about="rdf:#53e59201-e39b-4906-b3ac-6ef2d4277a0d"> <dc:subject> <rdf:Description rdf:about="rdf:#98bc0d3c-d6c3-4da2-ab38-3e3ffac938e4"> <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> <bqs:subject_type>keyword</bqs:subject_type> </rdf:Description> </dc:subject> </rdf:Description> </bqs:reference> <bqs:reference> <rdf:Description rdf:about="rdf:#378e8f91-8f18-4deb-a171-8252e74c529a"> <bqs:JournalArticle> <rdf:Description rdf:about="rdf:#b5a46cc0-fa43-429a-ad0e-7fc775c1802a"> <bqs:last_page>405</bqs:last_page> <dcterms:issued> <rdf:Description rdf:about="rdf:#decab482-727d-4572-b04c-40302d5a17c6"> <dcterms:W3CDTF>2004</dcterms:W3CDTF> </rdf:Description> </dcterms:issued> <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> <bqs:first_page>387</bqs:first_page> <bqs:volume>85(2-3)</bqs:volume> <dc:title>Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#b182e5c9-9979-410b-9142-51f6d6c5b2b4"> <rdf:li> <bqs:Person rdf:about="rdf:#98f3e49f-00aa-4fd6-9112-b3236b124303"> <vCard:N> <rdf:Description rdf:about="rdf:#3360fe81-1f36-4dd7-beaf-ea692b63ce5a"> <vCard:Other>P</vCard:Other> <vCard:Family>Smith</vCard:Family> <vCard:Given>N</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#4ccf58bb-7f92-4793-84b4-03efb6e3c6a5"> <vCard:N> <rdf:Description rdf:about="rdf:#1359ec4c-5e0b-40c4-b30e-4c5e6895cd5e"> <vCard:Other>J</vCard:Other> <vCard:Family>Crampin</vCard:Family> <vCard:Given>E</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </bqs:JournalArticle> <bqs:Pubmed_id>15142754</bqs:Pubmed_id> </rdf:Description> </bqs:reference> <cmeta:comment> <rdf:Description rdf:about="rdf:#da7ec15b-087d-4b57-a579-bff0adc67588"> <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> <dc:creator> <rdf:Description rdf:about="rdf:#21f8e3dd-bbab-4ff0-80b1-901122c5788a"> <vCard:FN>Alice Boit</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity> <dc:title>N. P. Smith' and E. Crampin's 2004 mathematical model of the cardiac sodium-potassium pump.</dc:title> </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="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="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="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="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#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:RDF>
smith_2004
Temperature
Chemical concentration
Chemical potential
Electrochemical potential
proton
inorganic phosphate
sodium(1+)
potassium(1+)
MgATP(2-)
Cardiac myocyte
Extracellular space
Human body
Plasma membrane
Portion of cytosol
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.
MgADP
Magnesium-bound ADP
Membrane potential
Apparent first-order forward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle
Apparent first-order forward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle
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
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
Ambient temperature
Intracellular proton concentration
Extracellular potassium ion concentration
Intracellular potassium ion concentration
Intracellular concentration of magnesium-bound ADP
Intracellular concentration of magnesium-bound ATP
Extracellular sodium ion concentration
Intracellular sodium ion concentration
Intracellular concentration of inorganic phosphate
Total intracellular concentration of bound and unbound inorganic phosphate
The free energy of MgATP hydroysis
The energy required to translocate a potassium ion from the extracellular environment to the intracellular cytosol
The energy required to translocate a sodium ion from the intracellular cytosol to the extracellular environment
Energy consumed for each pump cycle
Convencience term for expressing equation that solves v_cyc
Convenience term that is the ratio of the extracellular potassium concentration to its equilibrium constant
Convenience term that is the ratio of the intracellular potassium concentration to its equilibrium constant
Convenience term that is the ratio of the intracellular MgATP concentration to its equilibrium constant
Convenience term that is the ratio of the extracellular sodium concentration to its equilibrium constant
Convenience term that is the ratio of the intracellular sodium concentration to its equilibrium constant
Equilibrium constant for dissociation of proton from inorganic phosphate
Equilibrium constant for dissociation of potassium ion from inorganic phosphate
Equilibrium constant for dissociation of potassium ion from extracellular-facing pump
Equilibrium constant for dissociation of potassium ion from intracellular-facing pump
Equilibrium constant for MgATP hydrolysis
Equilibrium constant for dissociation of sodium ion from inorganic phosphate
Equilibrium constant for dissociation of sodium ion from extracellular-facing pump when membrane potential is zero
Equilibrium constant for dissociation of sodium ion from intracellular-facing pump when membrane potential is zero
Faraday constant
Gas constant
Universal gas constant
Forward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle
Forward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle
Forward rate constant for sodium-potassium exchanger transition from lumped states P8-P13 to lumped states P14-P15 of the Post-Albers cycle
Forward rate constant for sodium-potassium exchanger transition from lumped states P14-P15 to lumped states P1-P6 of the Post-Albers cycle
Psuedo-first-order backward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle
Psuedo-first-order backward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle
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
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
Backward rate constant for sodium-potassium exchanger transition from lumped states P1-P6 to state P7 of the Post-Albers cycle
Backward rate constant for sodium-potassium exchanger transition from state P7 to lumped states P8-P13 of the Post-Albers cycle
Backward rate constant for sodium-potassium exchanger transition from lumped states P8-P13 to lumped states P14-P15 of the Post-Albers cycle
Backward rate constant for sodium-potassium exchanger transition from lumped states P14-P15 to lumped states P1-P6 of the Post-Albers cycle
The net free energy of a sodium-potassium pump cycle
Factor for determining how voltage dependence is partitioned between the intra- and extracellular sodium ion dissociation reactions
Steady-state cycle rate of sodium-potassium pump
<apply id="cPi"> <eq /> <ci>cPi</ci> <apply> <divide /> <ci>cPi_sum</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn> <apply> <divide /> <ci>cK_i</ci> <ci>eq_KPi</ci> </apply> <apply> <divide /> <ci>cH</ci> <ci>eq_HPi</ci> </apply> <apply> <divide /> <ci>cNa_i</ci> <ci>eq_NaPi</ci> </apply> </apply> </apply> </apply> <apply id="dG_Na_calc"> <eq /> <ci>dG_Na</ci> <apply> <minus /> <apply> <times /> <ci>gas_const</ci> <ci>body_temp</ci> <apply> <ln /> <apply> <divide /> <ci>cNa_e</ci> <ci>cNa_i</ci> </apply> </apply> </apply> <apply> <times /> <ci>faraday_const</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.001</cn> <ci>Vm</ci> </apply> </apply> </apply> <apply id="dG_K_calc"> <eq /> <ci>dG_K</ci> <apply> <plus /> <apply> <times /> <ci>gas_const</ci> <ci>body_temp</ci> <apply> <ln /> <apply> <divide /> <ci>cK_i</ci> <ci>cK_e</ci> </apply> </apply> </apply> <apply> <times /> <ci>faraday_const</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.001</cn> <ci>Vm</ci> </apply> </apply> </apply> <apply id="dG_pump_calc"> <eq /> <ci>dG_pump</ci> <apply> <plus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> <ci>dG_K</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.0</cn> <ci>dG_Na</ci> </apply> </apply> </apply> <apply id="dG_ATP_calc"> <eq /> <ci>dG_ATP</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="energy">-29600.</cn> <apply> <times /> <ci>gas_const</ci> <ci>body_temp</ci> <apply> <ln /> <apply> <divide /> <ci>cMgATP</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_concentration">0.001</cn> <ci>cMgADP</ci> <ci>cPi</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply id="net_free_energy_calc"> <eq /> <ci>net_free_energy</ci> <apply> <plus /> <ci>dG_ATP</ci> <ci>dG_pump</ci> </apply> </apply> <apply id="dimless_Na_i_calc"> <eq /> <ci>dimless_Na_i</ci> <apply> <divide /> <ci>cNa_i</ci> <apply> <times /> <ci>eq_Na_base_i</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <ci>partition_factor</ci> <ci>faraday_const</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.001</cn> <ci>Vm</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.0</cn> <ci>gas_const</ci> <ci>body_temp</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply id="dimless_Na_e_calc"> <eq /> <ci>dimless_Na_e</ci> <apply> <divide /> <ci>cNa_e</ci> <apply> <times /> <ci>eq_Na_base_e</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.</cn> <ci>partition_factor</ci> </apply> <ci>faraday_const</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.001</cn> <ci>Vm</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.0</cn> <ci>gas_const</ci> <ci>body_temp</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply id="dimless_K_i_calc"> <eq /> <ci>dimless_K_i</ci> <apply> <divide /> <ci>cK_i</ci> <ci>eq_K_i</ci> </apply> </apply> <apply id="dimless_K_e_calc"> <eq /> <ci>dimless_K_e</ci> <apply> <divide /> <ci>cK_e</ci> <ci>eq_K_e</ci> </apply> </apply> <apply id="dimless_MgATP_calc"> <eq /> <ci>dimless_MgATP</ci> <apply> <divide /> <ci>cMgATP</ci> <ci>eq_MgATP</ci> </apply> </apply> <apply id="alpha1_calc"> <eq /> <ci>alpha1</ci> <apply> <divide /> <apply> <times /> <ci>k1</ci> <apply> <power /> <ci>dimless_Na_i</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</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> <apply id="alpha2_calc"> <eq /> <ci>alpha2</ci> <ci>k2</ci> </apply> <apply id="alpha3_calc"> <eq /> <ci>alpha3</ci> <apply> <divide /> <apply> <times /> <ci>k3</ci> <apply> <power /> <ci>dimless_K_e</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_e</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_e</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> <apply id="alpha4_calc"> <eq /> <ci>alpha4</ci> <apply> <divide /> <apply> <times /> <ci>k4</ci> <ci>dimless_MgATP</ci> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn> <ci>dimless_MgATP</ci> </apply> </apply> </apply> <apply id="minus_alpha1_calc"> <eq /> <ci>minus_alpha1</ci> <apply> <times /> <ci>minus_k1</ci> <ci>cMgADP</ci> </apply> </apply> <apply id="minus_alpha2_calc"> <eq /> <ci>minus_alpha2</ci> <apply> <divide /> <apply> <times /> <ci>minus_k2</ci> <apply> <power /> <ci>dimless_Na_e</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</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_e</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_e</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> <apply id="minus_alpha3_calc"> <eq /> <ci>minus_alpha3</ci> <apply> <divide /> <apply> <times /> <ci>minus_k3</ci> <ci>cPi</ci> <ci>cH</ci> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn> <ci>dimless_MgATP</ci> </apply> </apply> </apply> <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> <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> <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>
Time
Time domain for simulation
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Vm</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV_per_ms">1.0</cn> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>cMgADP</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="concentration_per_ms">0.0</cn> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>cNa_i</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="concentration_per_ms">0.0</cn> </apply>