<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Di Francesco-Noble Purkinje Fibre Model 1985 <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Bioengineering Institute, University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status This model has been curated and unit-checked by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on. <sect1 id="sec_structure"> Model Structure During the years that followed the formulation of the McAllister-Noble-Tsien Purkinje fibre model in 1975 and the Beeler-Reuter mammalian ventricular model in 1977, many experiments were performed which provided a greater insight into the working of the ion channels in cardiac tissue. D. Di Francesco and D. Noble (1985) constructed a new model of cardiac electrical activity which sought to incorporate much of this new data (see the figure below). The complete original paper reference is cited below: A Model of the Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes - Simulations of Ionic Currents and Concentration Changes, Di Francesco, D. and Noble, D. Phil. Trans. R. Soc. Lond. , B307, 353-398. (The full text of the article is available to members on the JSTOR website.) PubMed ID: 2578676 <informalfigure float="0" id="fig_cell_diagram"> <mediaobject> <imageobject> <objectinfo> cell diagram of the DFN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum </objectinfo> <imagedata fileref="difrancesco_noble_1985.png" /> </imageobject> </mediaobject> A schematic diagram describing the current flows across the cell membrane that are captured in the DFN model. </informalfigure> <informalfigure float="0" id="fig_cellml_rendering"> <mediaobject> <imageobject> <objectinfo> the cellml rendering of the DFN model </objectinfo> <imagedata fileref="cellml_rendering.gif" /> </imageobject> </mediaobject> The network defined in the CellML description of the Di Francesco-Noble model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the notation guide . For simplicity, not all the variables are shown. </informalfigure> The membrane physically contains the currents, exchangers and pumps, as indicated by the blue arrows in . The currents act independently and are not connected to each other. Several of the channels encapsulate and contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model. The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models. </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/" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#"> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <cmeta:modification> <rdf:Description rdf:about="rdf:#307594d8-70f0-4d35-b5db-81f33862c8ab"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#003be6d0-63f8-497f-88fd-9f5db8146d3d"> <vCard:N> <rdf:Description rdf:about="rdf:#a66d4308-0f4f-4bbd-85c0-2d7200869d2e"> <vCard:Other>J</vCard:Other> <vCard:Family>Noble</vCard:Family> <vCard:Given>Penny</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Units checked, curated.</rdf:value> <dcterms:modified> <rdf:Description 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has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#7c75cf09-5016-4799-8abd-e553a35f83fe"> <vCard:FN>James Lawson</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:publisher>Department of Physiology, Anatomy & Genetics, University of Oxford</dc:publisher> <dc:creator> <rdf:Description rdf:about="rdf:#a545f1f8-a8c6-4232-aa2e-2172b402e469"> <vCard:N> <rdf:Description rdf:about="rdf:#0142cd49-c837-4e89-b067-7b3b83fcbf8a"> <vCard:Other>unknown</vCard:Other> <vCard:Family>Noble</vCard:Family> <vCard:Given>Penny</vCard:Given> </rdf:Description> </vCard:N> <vCard:EMAIL> <j.0:internet rdf:about="rdf:#69b33c19-620b-4e8b-8aea-8304ef421afa"> <rdf:value>penny.noble@physiol.ox.ac.uk</rdf:value> </j.0:internet> </vCard:EMAIL> <vCard:ORG> <rdf:Description rdf:about="rdf:#f75dd32e-bc81-42df-b5bc-9a41af37135c"> 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</cmeta:modification> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#difrancesco_noble_1985"> <cmeta:comment> <rdf:Description rdf:about="rdf:#c24be5f0-79c0-4792-ae9e-1cc26a7f086f"> <rdf:value>This is a CellML description of the model described in the paper "A Model of the Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes - Simulations of Ionic Currents and Concentration Changes," by Di Francesco, D. and Noble, D.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#a87d6ee3-a785-42d8-a97a-9a1e6e688a6f"> <vCard:FN>James Lawson</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>Purkinje Fibre</rdf:li> <rdf:li>cardiac</rdf:li> <rdf:li>electrophysiology</rdf:li> </rdf:Bag> </rdf:value> <bqs:subject_type>keyword</bqs:subject_type> </dc:subject> </bqs:reference> <bqs:reference> 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Series B, Biological Sciences</dc:title> </rdf:Description> </bqs:Journal> <bqs:first_page>353</bqs:first_page> <bqs:volume>307</bqs:volume> <dc:title>A Model of Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#5f6d45f2-6c7c-4498-91aa-e91d130ae335"> <rdf:li> <bqs:Person rdf:about="rdf:#a4aabe00-0b1a-4b43-a15b-aaefb69a5329"> <vCard:N> <rdf:Description rdf:about="rdf:#c1a71e44-6807-4ee3-a414-9ad46fd5e910"> <vCard:Family>DiFrancesco</vCard:Family> <vCard:Given>D</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#abc3e2e8-4b95-493d-9f3b-e9234474ca70"> <vCard:N> <rdf:Description rdf:about="rdf:#ba9c58a5-d553-4953-97fc-a5852e7472a8"> <vCard:Family>Noble</vCard:Family> <vCard:Given>D</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </bqs:JournalArticle> <bqs:Pubmed_id></bqs:Pubmed_id> </rdf:Description> </bqs:reference> <ns7:simulation> <rdf:Description rdf:about="rdf:#$Hdmkf1"> <ns7:boundIntervals> <rdf:Description rdf:about="rdf:#$Idmkf1"> <rdf:first> <rdf:Description rdf:about="rdf:#$Jdmkf1"> <ns7:maximumStepSize>0.1</ns7:maximumStepSize> <ns7:nonstandard-pointDensity>10000</ns7:nonstandard-pointDensity> </rdf:Description> </rdf:first> <rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/> </rdf:Description> </ns7:boundIntervals> </rdf:Description> </ns7:simulation> </rdf:Description> </rdf:RDF>
A MODEL OF CARDIAC ELECTRICAL A C T I V I T Y INCORPORATING IONIC PUMPS AND CONCENTRATION CHANGES
C:\Users\thomp_000\Dropbox\Work Related\Annotated Models\Difrancesco_1985\difrancesco_noble_1985.cellml
Chris Thompson
difrancesco_noble_1985
Charge flow rate
Chemical concentration
Electrical potential
Sodium/calcium exchanger 2 (Na(+)/Ca(2+)-exchange protein 2) (Solute carrier family 8 member 2) (P48768)
Sodium/potassium-transporting ATPase subunit alpha-2 (Na(+)/K(+) ATPase alpha-2 subunit) (EC 3.6.3.9) (Sodium pump subunit alpha-2) (P50993)
sodium(1+)
potassium(1+)
calcium(2+)
Portion of extracellular matrix
Cardiac myocyte
Junctional sarcoplasmic reticulum of cardiac muscle cell
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.
Ca background current across plasma membrane of cardiac myocyte
Ca release from sarcoplasmic reticulum into cytosol of cardiac myocyte
Ca uptake into the sarcoplasmic reticulum
Delayed rectifier K channel current
Fast sodium channel current across plasma membrane
Hyperpolarising activated channel current
Hyperpolarizing activated K channel current
Hyperpolarizing activated Na channel current
Intercellular cleft
Channel between two tightly packed cell.
K transient outward channel current
NaCa exchange pump current across plasma membrane
NaK exchange pump current
Intracellular Ca concentration
Extracellular calcium concentration
Calcium equilibrium potential
Sodium equilibrium potential
scaling factor for i_NaCa
Intracellular Na concentration
Extracellular sodium concentration
Cardiac myocyte membrane potential
Denominator constant for i_NaCa
Position of energy barrier controlling voltage-dependence of i_NaCa
Na-Ca exchange current
Stoichiometry of Na-Ca exchange
Time solution domain
<apply> <eq /> <ci>i_NaCa</ci> <apply> <divide /> <apply> <times /> <ci>K_NaCa</ci> <apply> <minus /> <apply> <times /> <apply> <exp /> <apply> <divide /> <apply> <times /> <ci>gamma</ci> <apply> <minus /> <ci>n_NaCa</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>V</ci> </apply> <ci>RTONF</ci> </apply> </apply> <apply> <power /> <ci>Nai</ci> <ci>n_NaCa</ci> </apply> <ci>Cao</ci> </apply> <apply> <times /> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <ci>gamma</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <minus /> <ci>n_NaCa</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>V</ci> </apply> <ci>RTONF</ci> </apply> </apply> <apply> <power /> <ci>Nao</ci> <ci>n_NaCa</ci> </apply> <ci>Cai</ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar4">1</cn> <apply> <times /> <ci>d_NaCa</ci> <apply> <plus /> <apply> <times /> <ci>Cai</ci> <apply> <power /> <ci>Nao</ci> <ci>n_NaCa</ci> </apply> </apply> <apply> <times /> <ci>Cao</ci> <apply> <power /> <ci>Nai</ci> <ci>n_NaCa</ci> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <ci>Cai</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.0069</cn> </apply> </apply> </apply> </apply> </apply>
Na background current across plasma membrane of cardiac myocyte
Sarcoplasmic Ca transfer current
Sarcoplasmic reticulum uptake store
Secondary Ca channel inward current
Secondary K channel inward current
Secondary Na channel inward current
Secondary channel inward current
Time independent K channel current
Calcium background conductance
Calcium background current
<apply> <eq /> <ci>E_Ca</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn> <ci>RTONF</ci> <apply> <ln /> <apply> <divide /> <ci>Cao</ci> <ci>Cai</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_Ca_b</ci> <apply> <times /> <ci>g_Cab</ci> <apply> <minus /> <ci>V</ci> <ci>E_Ca</ci> </apply> </apply> </apply>
Faraday Constant
Bulk extracellular potassium
Potassium concentration in the extracellular cleft
Total extracellular volume
Delayed K current
Time independent K current
K component of hyperpolarising activated current
Net membrane potassium flux
Potassium component of fast Ca current
Transient outward current
Rate constant for K exchange between bulk and cleft space
<apply> <eq /> <ci>i_mK</ci> <apply> <minus /> <apply> <plus /> <ci>i_K1</ci> <ci>i_K</ci> <ci>i_fK</ci> <ci>i_siK</ci> <ci>i_to</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <ci>i_p</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Kc</ci> </apply> <apply> <plus /> <apply> <times /> <apply> <minus /> <ci>pf</ci> </apply> <apply> <minus /> <ci>Kc</ci> <ci>Kb</ci> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <ci>i_mK</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>Ve</ci> <ci>F</ci> </apply> </apply> </apply> </apply>
Reversal potential for sodium channel
Potassium intracellular concentration
Conductance of fast sodium current channels
Gating variable for h gate
TTX sensittive fast Na current
Activation gate and rate coefficient
<apply> <eq /> <ci>E_mh</ci> <apply> <times /> <ci>RTONF</ci> <apply> <ln /> <apply> <divide /> <apply> <plus /> <ci>Nao</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn> <ci>Kc</ci> </apply> </apply> <apply> <plus /> <ci>Nai</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn> <ci>Ki</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_Na</ci> <apply> <times /> <ci>g_Na</ci> <apply> <power /> <ci>m</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> <ci>h</ci> <apply> <minus /> <ci>V</ci> <ci>E_mh</ci> </apply> </apply> </apply>
Inactivation gate and rate coefficient
<apply> <eq /> <ci>alpha_h</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">20</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.125</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>beta_h</ci> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2000</cn> <apply> <plus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">320</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn> </apply> </apply> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>h</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_h</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>h</ci> </apply> </apply> <apply> <times /> <ci>beta_h</ci> <ci>h</ci> </apply> </apply> </apply>
<apply> <eq /> <ci>E0_m</ci> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">41</cn> </apply> </apply> <apply> <eq /> <ci>alpha_m</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2000</cn> <apply> <lt /> <apply> <abs /> <ci>E0_m</ci> </apply> <ci>delta_m</ci> </apply> </piece> <otherwise> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">200</cn> <ci>E0_m</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn> </apply> <ci>E0_m</ci> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>beta_m</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">8000</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.056</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">66</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>m</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_m</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>m</ci> </apply> </apply> <apply> <times /> <ci>beta_m</ci> <ci>m</ci> </apply> </apply> </apply>
Potassium equilibrium potential
Ionic half-activation concentration for hyperpolarising current
K conductance of if channels
Na conductance of if channels
Hyperpolarizing-activated NaK current
Na component of hyperpolarising activated current
Gating variable for Hyperpolarizing-activated NaK current
<apply> <eq /> <ci>E_Na</ci> <apply> <times /> <ci>RTONF</ci> <apply> <ln /> <apply> <divide /> <ci>Nao</ci> <ci>Nai</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>E_K</ci> <apply> <times /> <ci>RTONF</ci> <apply> <ln /> <apply> <divide /> <ci>Kc</ci> <ci>Ki</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_fNa</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>y</ci> <ci>Kc</ci> </apply> <apply> <plus /> <ci>Kc</ci> <ci>Km_f</ci> </apply> </apply> <ci>g_f_Na</ci> <apply> <minus /> <ci>V</ci> <ci>E_Na</ci> </apply> </apply> </apply> <apply> <eq /> <ci>i_fK</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>y</ci> <ci>Kc</ci> </apply> <apply> <plus /> <ci>Kc</ci> <ci>Km_f</ci> </apply> </apply> <ci>g_f_K</ci> <apply> <minus /> <ci>V</ci> <ci>E_K</ci> </apply> </apply> </apply> <apply> <eq /> <ci>i_f</ci> <apply> <plus /> <ci>i_fNa</ci> <ci>i_fK</ci> </apply> </apply>
Rate coefficient for hyperpolarizing-activated NaK current
<apply> <eq /> <ci>alpha_y</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">0.05</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.067</cn> </apply> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">52</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>E0_y</ci> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">52</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <apply> <eq /> <ci>beta_y</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2.5</cn> <apply> <lt /> <apply> <abs /> <ci>E0_y</ci> </apply> <ci>delta_y</ci> </apply> </piece> <otherwise> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">1</cn> <ci>E0_y</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn> </apply> <ci>E0_y</ci> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>y</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_y</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>y</ci> </apply> </apply> <apply> <times /> <ci>beta_y</ci> <ci>y</ci> </apply> </apply> </apply>
Ca concentrations in s.r. release store
Ca concentration in s.r. uptake store
Maximum Ca concentration in s.r. uptake store
Half activation concentration for Ca binding to release site
Volume of store of releasable calcium
Volume of sarcoplasmic reticulum (s.r.) uptake store
Total intracellular volume
Rate coefficient of p
Ca release from junctional sarcoplasmic reticulum into cytosol
Calcium component of fast current
Ca transferred into releasable form
Ca uptake into s.r. expressed as a current
Time- and voltage-dependence of the exchange between storage and release sites.
Number of Ca ions required to bind to activate release
Time constant for Ca release
Time constant for repriming release store
Time constant for s.r. uptake of calcium
<apply> <eq /> <ci>i_up</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>Vi</ci> <ci>F</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <ci>tau_up</ci> <ci>Ca_up_max</ci> </apply> </apply> <ci>Cai</ci> <apply> <minus /> <ci>Ca_up_max</ci> <ci>Ca_up</ci> </apply> </apply> </apply> <apply> <eq /> <ci>i_tr</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>V_rel</ci> <ci>F</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <ci>tau_rep</ci> </apply> </apply> <ci>p</ci> <apply> <minus /> <ci>Ca_up</ci> <ci>Ca_rel</ci> </apply> </apply> </apply> <apply> <eq /> <ci>alpha_p</ci> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">0.625</cn> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn> </apply> </apply> <apply> <minus /> <apply> <exp /> <apply> <divide /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <eq /> <ci>beta_p</ci> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">5</cn> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_rel</ci> <apply> <divide /> <apply> <times /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>V_rel</ci> <ci>F</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <ci>tau_rel</ci> </apply> </apply> <ci>Ca_rel</ci> <apply> <power /> <ci>Cai</ci> <ci>rCa</ci> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>Cai</ci> <ci>rCa</ci> </apply> <apply> <power /> <ci>K_mCa</ci> <ci>rCa</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>p</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_p</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>p</ci> </apply> </apply> <apply> <times /> <ci>beta_p</ci> <ci>p</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_up</ci> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <apply> <minus /> <ci>i_up</ci> <ci>i_tr</ci> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>V_up</ci> <ci>F</ci> </apply> </apply> </apply> <apply> <eq /> <ci>V_up</ci> <apply> <times /> <ci>Vi</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_rel</ci> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <apply> <minus /> <ci>i_tr</ci> <ci>i_rel</ci> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>V_rel</ci> <ci>F</ci> </apply> </apply> </apply> <apply> <eq /> <ci>V_rel</ci> <apply> <times /> <ci>Vi</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.02</cn> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Cai</ci> </apply> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> </apply> <apply> <plus /> <apply> <minus /> <apply> <minus /> <apply> <plus /> <ci>i_siCa</ci> <ci>i_Ca_b</ci> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <ci>i_NaCa</ci> </apply> <apply> <minus /> <ci>n_NaCa</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <ci>i_rel</ci> </apply> <ci>i_up</ci> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>Vi</ci> <ci>F</ci> </apply> </apply> </apply>
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ki</ci> </apply> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> </apply> <ci>i_mK</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>Vi</ci> <ci>F</ci> </apply> </apply> </apply>
Fraction occupied by extracellular space
Sodium background current
Sodium component of fast Ca current
Length of preparation
Radius of preparation
<apply> <eq /> <ci>V_Cell</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.141592654</cn> <apply> <power /> <ci>radius</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>length</ci> </apply> </apply> <apply> <eq /> <ci>Vi</ci> <apply> <times /> <ci>V_Cell</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>V_e_ratio</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Nai</ci> </apply> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> </apply> <apply> <plus /> <ci>i_Na</ci> <ci>i_Na_b</ci> <ci>i_fNa</ci> <ci>i_siNa</ci> <apply> <times /> <ci>i_p</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> <apply> <divide /> <apply> <times /> <ci>i_NaCa</ci> <ci>n_NaCa</ci> </apply> <apply> <minus /> <ci>n_NaCa</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>Vi</ci> <ci>F</ci> </apply> </apply> </apply>
Membrane capacitance
Boltzmann constant
Temperature
Experimental stimulation current
Total TTX-insensitive inward current
<apply> <eq /> <ci>RTONF</ci> <apply> <divide /> <apply> <times /> <ci>R</ci> <ci>T</ci> </apply> <ci>F</ci> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>V</ci> </apply> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>i_f</ci> <ci>i_K</ci> <ci>i_K1</ci> <ci>i_to</ci> <ci>i_Na_b</ci> <ci>i_Ca_b</ci> <ci>i_p</ci> <ci>i_NaCa</ci> <ci>i_Na</ci> <ci>i_si</ci> <ci>i_pulse</ci> </apply> </apply> <ci>C</ci> </apply> </apply>
Gating variable for fast Ca current channel d gate
Gating variable for fast Ca current channel f gate
Intracellular Ca dependent inactivation of fast calcium current
<apply> <eq /> <ci>i_siCa</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn> <ci>P_si</ci> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <apply> <times /> <ci>RTONF</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> </apply> <apply> <minus /> <apply> <times /> <ci>Cai</ci> <apply> <exp /> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">100</cn> <ci>RTONF</ci> </apply> </apply> </apply> <apply> <times /> <ci>Cao</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> <ci>d</ci> <ci>f</ci> <ci>f2</ci> </apply> </apply> <apply> <eq /> <ci>i_siK</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn> <ci>P_si</ci> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <apply> <times /> <ci>RTONF</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> </apply> <apply> <minus /> <apply> <times /> <ci>Ki</ci> <apply> <exp /> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> <ci>RTONF</ci> </apply> </apply> </apply> <apply> <times /> <ci>Kc</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> <ci>d</ci> <ci>f</ci> <ci>f2</ci> </apply> </apply> <apply> <eq /> <ci>i_siNa</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn> <ci>P_si</ci> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <apply> <times /> <ci>RTONF</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> </apply> <apply> <minus /> <apply> <times /> <ci>Nai</ci> <apply> <exp /> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> <ci>RTONF</ci> </apply> </apply> </apply> <apply> <times /> <ci>Nao</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> <ci>d</ci> <ci>f</ci> <ci>f2</ci> </apply> </apply> <apply> <eq /> <ci>i_si</ci> <apply> <plus /> <ci>i_siCa</ci> <ci>i_siK</ci> <ci>i_siNa</ci> </apply> </apply>
Activation gating and rate coefficient for fast Ca current channel
Inactivation gating and rate coefficient for fast Ca current channel d gate
<apply> <eq /> <ci>E0_d</ci> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">24</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn> </apply> </apply> <apply> <eq /> <ci>alpha_d</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">120</cn> <apply> <lt /> <apply> <abs /> <ci>E0_d</ci> </apply> <ci>delta_d</ci> </apply> </piece> <otherwise> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">30</cn> <ci>E0_d</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <ci>E0_d</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>beta_d</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">120</cn> <apply> <lt /> <apply> <abs /> <ci>E0_d</ci> </apply> <ci>delta_d</ci> </apply> </piece> <otherwise> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">12</cn> <ci>E0_d</ci> </apply> <apply> <minus /> <apply> <exp /> <apply> <divide /> <ci>E0_d</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>d</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_d</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>d</ci> </apply> </apply> <apply> <times /> <ci>beta_d</ci> <ci>d</ci> </apply> </apply> </apply>
Half activation concentration for extracellular K activation of hyperpolarizing-activated NaK current
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>f2</ci> </apply> <apply> <minus /> <ci>alpha_f2</ci> <apply> <times /> <ci>f2</ci> <apply> <plus /> <ci>alpha_f2</ci> <ci>beta_f2</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>beta_f2</ci> <apply> <divide /> <apply> <times /> <ci>Cai</ci> <ci>alpha_f2</ci> </apply> <ci>K_mf2</ci> </apply> </apply>
Inactivation gating and rate coefficient for fast Ca current channel
<apply> <eq /> <ci>E0_f</ci> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn> </apply> </apply> <apply> <eq /> <ci>alpha_f</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">25</cn> <apply> <lt /> <apply> <abs /> <ci>E0_f</ci> </apply> <ci>delta_f</ci> </apply> </piece> <otherwise> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">6.25</cn> <ci>E0_f</ci> </apply> <apply> <minus /> <apply> <exp /> <apply> <divide /> <ci>E0_f</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>beta_f</ci> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">50</cn> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>f</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_f</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>f</ci> </apply> </apply> <apply> <times /> <ci>beta_f</ci> <ci>f</ci> </apply> </apply> </apply>
Sodium background conductance
<apply> <eq /> <ci>i_Na_b</ci> <apply> <times /> <ci>g_Nab</ci> <apply> <minus /> <ci>V</ci> <ci>E_Na</ci> </apply> </apply> </apply>
Maximum NaK exchane pump current
NaK pump K half activation concentration
NaK pump Na half activation concentration
<apply> <eq /> <ci>i_p</ci> <apply> <divide /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>I_p</ci> <ci>Kc</ci> </apply> <apply> <plus /> <ci>K_mK</ci> <ci>Kc</ci> </apply> </apply> <ci>Nai</ci> </apply> <apply> <plus /> <ci>K_mNa</ci> <ci>Nai</ci> </apply> </apply> </apply>
Fully activated value of delayed K current
Maximum outward potassium current
Delayed K current gating variable
<apply> <eq /> <ci>I_K</ci> <apply> <divide /> <apply> <times /> <ci>i_K_max</ci> <apply> <minus /> <ci>Ki</ci> <apply> <times /> <ci>Kc</ci> <apply> <exp /> <apply> <divide /> <apply> <minus /> <ci>V</ci> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">140</cn> </apply> </apply> <apply> <eq /> <ci>i_K</ci> <apply> <times /> <ci>x</ci> <ci>I_K</ci> </apply> </apply>
Delayed K rate coefficient
<apply> <eq /> <ci>alpha_x</ci> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">0.5</cn> <apply> <exp /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.0826</cn> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.057</cn> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>beta_x</ci> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">1.3</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.06</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.04</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>x</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_x</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>x</ci> </apply> </apply> <apply> <times /> <ci>beta_x</ci> <ci>x</ci> </apply> </apply> </apply>
K half-activation concentration for inward K rectifier
Inward K rectifier conductance
<apply> <eq /> <ci>i_K1</ci> <apply> <divide /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>g_K1</ci> <ci>Kc</ci> </apply> <apply> <plus /> <ci>Kc</ci> <ci>Km_K1</ci> </apply> </apply> <apply> <minus /> <ci>V</ci> <ci>E_K</ci> </apply> </apply> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> <ci>E_K</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> </apply>
Ca half activation concentration for transient outward current
K half activation concentration for transient outward current
Conductance for transient outward K rectification
Gating variable for transient outward current
<apply> <eq /> <ci>i_to</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>s</ci> <ci>g_to</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.2</cn> <apply> <divide /> <ci>Kc</ci> <apply> <plus /> <ci>Km_to</ci> <ci>Kc</ci> </apply> </apply> </apply> <ci>Cai</ci> </apply> <apply> <plus /> <ci>Km_Ca</ci> <ci>Cai</ci> </apply> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> </apply> </apply> </apply> <apply> <minus /> <apply> <times /> <ci>Ki</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn> <ci>V</ci> </apply> <ci>RTONF</ci> </apply> </apply> </apply> <apply> <times /> <ci>Kc</ci> <apply> <exp /> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn> </apply> <ci>V</ci> </apply> <ci>RTONF</ci> </apply> </apply> </apply> </apply> </apply> </apply>
Rate coefficient for transient outward current
<apply> <eq /> <ci>alpha_s</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">0.033</cn> <apply> <exp /> <apply> <divide /> <apply> <minus /> <ci>V</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">17</cn> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>beta_s</ci> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">33</cn> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">8</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>s</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_s</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>s</ci> </apply> </apply> <apply> <times /> <ci>beta_s</ci> <ci>s</ci> </apply> </apply> </apply>