<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Hilemann-Noble Atrial Cell Model 1987 <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status This model is known to run in OpenCell and COR and reproduce the published results. <sect1 id="sec_structure"> Model Structure ABSTRACT: Interactions of electrogenic sodium-calcium exchange, calcium channel and sarcoplasmic reticulum in the mammalian heart have been explored by simulation of extracellular calcium transients measured with tetramethylmurexide in rabbit atrium. The approach has been to use the simplest possible formulations of these mechanisms, which together with a minimum number of additional mechanisms allow reconstruction of action potentials, intracellular calcium transients and extracellular calcium transients. A 3:1 sodium-calcium exchange stoichiometry is assumed. Calcium-channel inactivation is assumed to take place by a voltage-dependent mechanism, which is accelerated by a rise in intracellular calcium; intracellular calcium release becomes a major physiological regulator of calcium influx via calcium channels. A calcium release mechanism is assumed, which is both calcium- and voltage-sensitive, and which undergoes prolonged inactivation. 200 microM cytosolic calcium buffer is assumed. For most simulations only instantaneous potassium conductances are simulated so as to study the other mechanisms independently of time- and calcium-dependent outward current. Thus, the model reconstructs extracellular calcium transients and typical action-potential configuration changes during steady-state and non-steady-state stimulation from the mechanisms directly involved in trans-sarcolemmal calcium movements. The model predicts relatively small trans-sarcolemmal calcium movements during regular stimulation (ca. 2 mumol kg-1 fresh mass per excitation); calcium current is fully activated within 2 ms of excitation, inactivation is substantially complete within 30 ms, and sodium-calcium exchange significantly resists repolarization from approximately -30 mV. Net calcium movements many times larger are possible during non-steady-state stimulation. Long action potentials at premature excitations or after inhibition of calcium release can be supported almost exclusively by calcium current (net calcium influx 5-30 mumol kg-1 fresh mass); action potentials during potentiated post-stimulatory contractions can be supported almost exclusively by sodium-calcium exchange (net calcium efflux 4-20 mumol kg-1 fresh mass). Large calcium movements between the extracellular space and the sarcoplasmic reticulum can take place through the cytosol with virtually no contractile activation. The simulations provide integrated explanations of electrical activity, contractile function and trans-sarcolemmal calcium movements, which were outside the explanatory range of previous models. The original paper reference is cited below: Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of the basic cellular mechanisms, Hilemann, D.W. and Noble, D. 1987, Proc. R. Soc. Lond. , B230, 163-205. PubMed ID: 2884668 <informalfigure float="0" id="fig_cell_diagram"> <mediaobject> <imageobject> <objectinfo> cell diagram of the Hilemann-Noble model showing ionic currents across the sarcolemma </objectinfo> <imagedata fileref="hilgemann_noble_1987.png" /> </imageobject> </mediaobject> A schematic diagram describing the current flows across the cell membrane that are captured in the Hilemann-Noble model. </informalfigure> </sect1> </documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:j.0="http://imc.org/vCard/3.0#"> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <cmeta:modification> <rdf:Description rdf:about="rdf:#d134371a-7ca9-4bc9-b15c-8311d6159199"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#b8bd0ccd-2a3d-467d-a4e8-4baeb73e1139"> <vCard:N> <rdf:Description rdf:about="rdf:#53f5e968-5a33-41dc-a08d-abf75f7a4684"> <vCard:Other>Richard</vCard:Other> <vCard:Family>Lawson</vCard:Family> <vCard:Given>James</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Made 2 new variables - dCaCalmoddt and dCaTropdt in component "intracellular_calcium_concentration," equated these variables to d(CaCalmod)/d(time) and d(CaTrop)/d(time), respectively. This was done to allow PCEnv 0.2 to run the model.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#eb2cd150-322c-4782-8f7f-61662395f5f0"> <dcterms:W3CDTF>2007-09-20T12:40:08+12:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#0a11824d-79bb-4c95-bf67-f2a0c00a1ab1"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#7500468a-4c03-4b44-93f7-84fcc577f8d6"> <vCard:N> <rdf:Description rdf:about="rdf:#9e7662b0-bfb4-4bb5-9d56-3c5f91e06e18"> <vCard:Other>Richard</vCard:Other> <vCard:Family>Lawson</vCard:Family> <vCard:Given>James</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Added stimulus protocol to allow simulation of trains of action potentials.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#eee2dffe-700f-4485-9feb-f7ba7a90abc2"> <dcterms:W3CDTF>2007-06-20T15:15:35+12:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#20f85be5-33d5-4183-8900-c02eccab3b39"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#5385f45f-9928-4da2-9654-e9c8651cbf57"> <vCard:N> <rdf:Description rdf:about="rdf:#ad840cb5-5971-40f0-9319-0e4030e77505"> <vCard:Other>Richard</vCard:Other> <vCard:Family>Lawson</vCard:Family> <vCard:Given>James</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>added cmeta:id's to some variables to facilitate creation of PCEnv session file</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#4ae6dde3-74ce-4ca7-b5f7-dc7e62c7db98"> <dcterms:W3CDTF>2008-01-10T13:06:42+13:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <dc:creator> <rdf:Description rdf:about="rdf:#03dc2785-2130-4236-8a8f-f6a446d778d6"> <vCard:N> <rdf:Description rdf:about="rdf:#abf72336-d61e-48a4-98b5-a93673fcbbfd"> <vCard:Other>J</vCard:Other> <vCard:Family>Noble</vCard:Family> <vCard:Given>Penny</vCard:Given> </rdf:Description> </vCard:N> <vCard:EMAIL> <j.0:internet rdf:about="rdf:#40a75966-f864-4887-9e5c-aeb89bff221a"> <rdf:value>penny.noble@dpag.ox.ac.uk</rdf:value> </j.0:internet> </vCard:EMAIL> <vCard:ORG> <rdf:Description rdf:about="rdf:#3af4e6f4-646d-4682-9e52-9556553ead7e"> <vCard:Orgunit>Department of Physiology, Anatomy & Genetics</vCard:Orgunit> <vCard:Orgname>Oxford University</vCard:Orgname> </rdf:Description> </vCard:ORG> </rdf:Description> </dc:creator> <dcterms:created> <rdf:Description rdf:about="rdf:#2b7e8a86-6166-4fd5-87da-24c9bd125230"> <dcterms:W3CDTF>2006-08-08T00:00:00+00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:created> <cmeta:comment> <rdf:Description rdf:about="rdf:#db0c3b92-9d2c-496f-94a3-598d24393808"> <rdf:value>This version was created by Penny Noble of Oxford University and is known to run in both COR and PCEnv. The integration problems experienced with Version 03 are fixed in this version. A predefined operator diff error produced by PCEnv in the component intracellular_calcium_concentration of Penny Noble's version was fixed by James Lawson on 19/04/07. Due to the small stimulus duration, for this model to produce a train of action potentials, the max step size must be set at 0.001 or below and the number of points per graph must be over 10k.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#e890b153-d092-4b49-82f2-f9911da9f012"> <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> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#hilgemann_noble_1987"> <bqs:reference rdf:parseType="Resource"> <dc:subject rdf:parseType="Resource"> <rdf:value> <rdf:Bag> <rdf:li>calcium dynamics</rdf:li> <rdf:li>electrophysiology</rdf:li> <rdf:li>mouse</rdf:li> <rdf:li>atrial myocyte</rdf:li> <rdf:li>excitation-contraction coupling</rdf:li> </rdf:Bag> </rdf:value> <bqs:subject_type>keyword</bqs:subject_type> </dc:subject> </bqs:reference> <bqs:reference> <rdf:Description rdf:about="rdf:#04232c45-04f0-41b0-9715-172331d0657b"> <bqs:JournalArticle> <rdf:Description rdf:about="rdf:#bc289a91-bdb7-40f3-b536-3d42cfc72a10"> <bqs:last_page>205</bqs:last_page> <dcterms:issued> <rdf:Description rdf:about="rdf:#5cff8ec6-0045-4d69-8e94-d289fbe399b8"> <dcterms:W3CDTF>1987-03-23</dcterms:W3CDTF> </rdf:Description> </dcterms:issued> <bqs:Journal> <rdf:Description rdf:about="rdf:#fbdca4db-2aa1-43f8-8403-6e0ff21c31c7"> <dc:title>Proceedings of the Royal Society of London - Series B</dc:title> </rdf:Description> </bqs:Journal> <bqs:first_page>163</bqs:first_page> <bqs:volume>230 1259</bqs:volume> <dc:title>Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#ad4f3cee-6ff9-4cca-87c8-e8787cba2d16"> <rdf:li> <bqs:Person rdf:about="rdf:#f996572c-60c3-4ed7-b85d-3f4384e790c5"> <vCard:N> <rdf:Description rdf:about="rdf:#faf2c2c4-d017-469b-8b58-376884f7920e"> <vCard:Other>W</vCard:Other> <vCard:Family>Hilgemann</vCard:Family> <vCard:Given>D</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#acb80eaf-a6c7-4c8e-bb3c-eb755296fc47"> <vCard:N> <rdf:Description rdf:about="rdf:#a7f52ec9-28dd-4894-ad57-458b1c993791"> <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>2884668</bqs:Pubmed_id> </rdf:Description> </bqs:reference> <cmeta:comment> <rdf:Description rdf:about="rdf:#ad850d69-f419-4ac2-a62f-2dda69b76bb0"> <rdf:value>This is a CellML representation of Hilgeman et al.'s 1987 model of the basic cellular mechanisms of excitation-contraction coupling and Ca++ handling in the rabbit atrial myocyte.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#a708b6db-13cb-42be-878b-a4151c035753"> <vCard:FN>James Lawson</vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:title>unknown</dc:title> <ns7:simulation> <rdf:Description rdf:about="rdf:#$lPjdE1"> <ns7:boundIntervals> <rdf:Description rdf:about="rdf:#$mPjdE1"> <rdf:first> <rdf:Description rdf:about="rdf:#$nPjdE1"> <ns7:maximumStepSize>0.001</ns7:maximumStepSize> <ns7:nonstandard-pointDensity>200000</ns7:nonstandard-pointDensity> <ns7:endingValue>5</ns7:endingValue> </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>
C:\Users\Christopher\Dropbox\Work Related\Annotated Models\Hilgemann_1987\hilgemann_noble_1987.cellml
Chris Thompson
Charge flow rate
Chemical concentration
Electrical potential
Chemical molar flow rate
Sodium/potassium-transporting ATPase subunit alpha-2 (Na(+)/K(+) ATPase alpha-2 subunit) (EC 3.6.3.9) (Sodium pump subunit alpha-2) (P50993)
Ryanodine receptor 2 (RYR-2) (RyR2) (hRYR-2) (Cardiac muscle ryanodine receptor) (Cardiac muscle ryanodine receptor-calcium release channel) (Type 2 ryanodine receptor) (Q92736)
sodium(1+)
potassium(1+)
calcium(2+)
Troponin
Calmodulin
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
Fast sodium channel current across plasma membrane
Intercellular cleft
Channel between two tightly packed cell.
K background current across plasma membrane of the cardiac myocyte
Muscle Bath
NaCa exchange pump current across plasma membrane
Intracellular Ca concentration
Extracellular calcium concentration
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
scaling factor for i_NaCa
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>Na_i</ci> <ci>n_NaCa</ci> </apply> <ci>Ca_o</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>Na_o</ci> <ci>n_NaCa</ci> </apply> <ci>Ca_i</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>Ca_i</ci> <apply> <power /> <ci>Na_o</ci> <ci>n_NaCa</ci> </apply> </apply> <apply> <times /> <ci>Ca_o</ci> <apply> <power /> <ci>Na_i</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>Ca_i</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
Sodium-Potassium Pump Current
Time independent K channel current
Calcium reversal potential
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>Ca_o</ci> <ci>Ca_i</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_b_Ca</ci> <apply> <times /> <ci>g_b_Ca</ci> <apply> <minus /> <ci>V</ci> <ci>E_Ca</ci> </apply> </apply> </apply>
Activator molecule fraction
Release channel activation rate
Ca concentrations in s.r. release store
Release channel inactivation rate
Release channel Ca leak rate
SR Ca release current maximal release rate
Activator precursor molecule fraction
Activator molecule inactive product fraction
Regulatory binding sites occupied by Ca.
Voltage dependence of release
Ca release from junctional sarcoplasmic reticulum into cytosol
Time - Solution Domain
<apply> <eq /> <ci>PrecFrac</ci> <apply> <minus /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>ActFrac</ci> </apply> <ci>ProdFrac</ci> </apply> </apply> <apply> <eq /> <ci>VoltDep</ci> <apply> <exp /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.08</cn> <apply> <minus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>RegBindSite</ci> <apply> <power /> <apply> <divide /> <ci>Ca_i</ci> <apply> <plus /> <ci>Ca_i</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.0005</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> <apply> <eq /> <ci>ActRate</ci> <apply> <plus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">600</cn> <ci>VoltDep</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">500</cn> <ci>RegBindSite</ci> </apply> </apply> </apply> <apply> <eq /> <ci>InactRate</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">60</cn> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">500</cn> <ci>RegBindSite</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>ActFrac</ci> </apply> <apply> <minus /> <apply> <times /> <ci>PrecFrac</ci> <ci>ActRate</ci> </apply> <apply> <times /> <ci>ActFrac</ci> <ci>InactRate</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>ProdFrac</ci> </apply> <apply> <minus /> <apply> <times /> <ci>ActFrac</ci> <ci>InactRate</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">0.6</cn> <ci>ProdFrac</ci> </apply> </apply> </apply> <apply> <eq /> <ci>i_rel</ci> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <divide /> <ci>ActFrac</ci> <apply> <plus /> <ci>ActFrac</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.25</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> <ci>K_m_rel</ci> </apply> <ci>K_leak_rate</ci> </apply> <ci>Ca_rel</ci> </apply> </apply>
Ca concentration in s.r. uptake store
Rate coefficient for Ca translocation
Ca transferred into releasable form
<apply> <eq /> <ci>i_trans</ci> <apply> <times /> <apply> <minus /> <ci>Ca_up</ci> <ci>Ca_rel</ci> </apply> <ci>alpha_tr</ci> </apply> </apply>
Ca concentration in the muscle bath
Faraday Constant
Rate constant of exchange between extracellular space and the muscle bath
Total extracellular volume
Calcium component of fast Ca current
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_o</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <minus /> <ci>Cab</ci> <ci>Ca_o</ci> </apply> <ci>K_diff</ci> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> <apply> <plus /> <ci>i_siCa</ci> <ci>i_NaCa</ci> <ci>i_b_Ca</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>Ve</ci> <ci>F</ci> </apply> </apply> </apply> </apply>
Potassium concentration in the extracellular cleft
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>Na_o</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn> <ci>K_c</ci> </apply> </apply> <apply> <plus /> <ci>Na_i</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn> <ci>K_i</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 /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <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> </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>
Concentration of Ca bound calmodulin in the cytosol
Concentration of Ca bound troponin in the cytosol
Total calmodulin concentration in the cytosol
Total troponin concentration in the cytosol
Cell volume
Fraction of volume taken by extracellular space
Total intracellular volume
Ratio of intracellular volume and total cell volume
Ratio of JSR volume and total cell volume
Ratio of SR uptake component volume and total cell volume
Ca-calmodulin binding rate constant
Ca-troponin binding rate constant
Ca-calmodulin dissociation rate constant
Ca-troponin dissociation rate constant
Redundant and unused codeword
Ca uptake into SR expressed as a 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>V_i_ratio</ci> <apply> <minus /> <apply> <minus /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>V_e_ratio</ci> </apply> <ci>V_up_ratio</ci> </apply> <ci>V_rel_ratio</ci> </apply> </apply> <apply> <eq /> <ci>V_i</ci> <apply> <times /> <ci>V_Cell</ci> <ci>V_i_ratio</ci> </apply> </apply> <apply> <eq /> <ci>Ve</ci> <apply> <times /> <ci>V_Cell</ci> <ci>V_e_ratio</ci> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_i</ci> </apply> <apply> <minus /> <apply> <minus /> <apply> <minus /> <apply> <plus /> <apply> <times /> <apply> <divide /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> </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_i</ci> <ci>F</ci> </apply> </apply> <apply> <minus /> <apply> <plus /> <ci>i_siCa</ci> <ci>i_b_Ca</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <ci>i_NaCa</ci> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <ci>i_rel</ci> <ci>V_rel_ratio</ci> </apply> <ci>V_i_ratio</ci> </apply> </apply> <ci>dCaCalmoddt</ci> </apply> <ci>dCaTropdt</ci> </apply> <ci>i_up</ci> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_up</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <ci>V_i_ratio</ci> <ci>V_up_ratio</ci> </apply> <ci>i_up</ci> </apply> <ci>i_trans</ci> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_rel</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <divide /> <ci>V_up_ratio</ci> <ci>V_rel_ratio</ci> </apply> <ci>i_trans</ci> </apply> <ci>i_rel</ci> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_Calmod</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_Calmod</ci> <ci>Ca_i</ci> <apply> <minus /> <ci>Calmod</ci> <ci>Ca_Calmod</ci> </apply> </apply> <apply> <times /> <ci>beta_Calmod</ci> <ci>Ca_Calmod</ci> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Ca_Trop</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_Trop</ci> <ci>Ca_i</ci> <apply> <minus /> <ci>Trop</ci> <ci>Ca_Trop</ci> </apply> </apply> <apply> <times /> <ci>beta_Trop</ci> <ci>Ca_Trop</ci> </apply> </apply> </apply> <apply> <eq /> <ci>dCaCalmoddt</ci> <apply> <minus /> <apply> <times /> <ci>alpha_Calmod</ci> <ci>Ca_i</ci> <apply> <minus /> <ci>Calmod</ci> <ci>Ca_Calmod</ci> </apply> </apply> <apply> <times /> <ci>beta_Calmod</ci> <ci>Ca_Calmod</ci> </apply> </apply> </apply> <apply> <eq /> <ci>dCaTropdt</ci> <apply> <minus /> <apply> <times /> <ci>alpha_Trop</ci> <ci>Ca_i</ci> <apply> <minus /> <ci>Trop</ci> <ci>Ca_Trop</ci> </apply> </apply> <apply> <times /> <ci>beta_Trop</ci> <ci>Ca_Trop</ci> </apply> </apply> </apply>
Time independent K current
NaK exchange pump current
Background K current
Potassium component of fast Ca current
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>K_i</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>V_i</ci> <ci>F</ci> </apply> </apply> <apply> <minus /> <apply> <plus /> <ci>i_K1</ci> <ci>i_siK</ci> <ci>i_b_K</ci> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> <ci>i_NaK</ci> </apply> </apply> </apply> </apply>
Sodium background current
Sodium component of fast Ca current
<apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>Na_i</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn> <ci>V_i</ci> <ci>F</ci> </apply> </apply> <apply> <plus /> <ci>i_Na</ci> <ci>i_b_Na</ci> <apply> <times /> <ci>i_NaK</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> <apply> <times /> <ci>i_NaCa</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> <ci>i_siNa</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 /> <ci>i_Stim</ci> <piecewise> <piece> <ci>stim_amplitude</ci> <apply> <and /> <apply> <geq /> <ci>time</ci> <ci>stim_start</ci> </apply> <apply> <leq /> <ci>time</ci> <ci>stim_end</ci> </apply> <apply> <leq /> <apply> <minus /> <apply> <minus /> <ci>time</ci> <ci>stim_start</ci> </apply> <apply> <times /> <apply> <floor /> <apply> <divide /> <apply> <minus /> <ci>time</ci> <ci>stim_start</ci> </apply> <ci>stim_period</ci> </apply> </apply> <ci>stim_period</ci> </apply> </apply> <ci>stim_duration</ci> </apply> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="nanoA">0</cn> </otherwise> </piecewise> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>V</ci> </apply> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>i_Stim</ci> <ci>i_K1</ci> <ci>i_b_Na</ci> <ci>i_b_Ca</ci> <ci>i_b_K</ci> <ci>i_NaK</ci> <ci>i_NaCa</ci> <ci>i_Na</ci> <ci>i_si</ci> </apply> </apply> <ci>C_m</ci> </apply> </apply>
Potassium reversal potential
Potassium background conductance
<apply> <eq /> <ci>i_b_K</ci> <apply> <times /> <ci>g_b_K</ci> <apply> <minus /> <ci>V</ci> <ci>E_K</ci> </apply> </apply> </apply>
Cytosolic Ca/enzyme reaction rate
SR Ca/enzyme reaction rate
SR Ca uptake forward reaction rate constant
SR Ca uptake back ard reaction rate constant
<apply> <eq /> <ci>K_1</ci> <apply> <divide /> <apply> <times /> <ci>K_cyca</ci> <ci>K_xcs</ci> </apply> <ci>K_srca</ci> </apply> </apply> <apply> <eq /> <ci>K_2</ci> <apply> <plus /> <ci>Ca_i</ci> <apply> <times /> <ci>Ca_up</ci> <ci>K_1</ci> </apply> <apply> <times /> <ci>K_cyca</ci> <ci>K_xcs</ci> </apply> <ci>K_cyca</ci> </apply> </apply> <apply> <eq /> <ci>i_up</ci> <apply> <minus /> <apply> <times /> <apply> <divide /> <ci>Ca_i</ci> <ci>K_2</ci> </apply> <ci>alpha_up</ci> </apply> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>Ca_up</ci> <ci>K_1</ci> </apply> <ci>K_2</ci> </apply> <ci>beta_up</ci> </apply> </apply> </apply>
Active, unbound regulatory states
Activation gating and rate coefficient for fast Ca current channel
Fraction of channels inactivated by voltage-dependent process.
<apply> <eq /> <ci>i_si</ci> <apply> <plus /> <ci>i_siCa</ci> <ci>i_siK</ci> <ci>i_siNa</ci> </apply> </apply> <apply> <eq /> <ci>i_siCa</ci> <apply> <times /> <apply> <divide /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn> <ci>P_si</ci> <ci>d</ci> <ci>CaChon</ci> <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> <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> <minus /> <apply> <times /> <ci>Ca_i</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>Ca_o</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> </apply> </apply> <apply> <eq /> <ci>i_siK</ci> <apply> <times /> <apply> <divide /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.002</cn> <ci>P_si</ci> <ci>d</ci> <ci>CaChon</ci> <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> <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> <minus /> <apply> <times /> <ci>K_i</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>K_c</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> </apply> </apply> <apply> <eq /> <ci>i_siNa</ci> <apply> <times /> <apply> <divide /> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn> <ci>P_si</ci> <ci>d</ci> <ci>CaChon</ci> <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> <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> <minus /> <apply> <times /> <ci>Na_i</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>Na_o</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> </apply> </apply>
<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>
Fraction of regulatory sites occupied by Ca
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_Ca</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_Ca</ci> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">12</cn> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <exp /> <apply> <divide /> <apply> <minus /> <ci>E0_f</ci> </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_Ca</ci> </apply> <apply> <minus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">120</cn> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>f_Ca</ci> </apply> <ci>CaChoff</ci> </apply> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>f_Ca</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>CaChoff</ci> </apply> </apply> </apply> <ci>beta_f_Ca</ci> </apply> <apply> <times /> <ci>alpha_f_Ca</ci> <ci>f_Ca</ci> </apply> </apply> </apply> <apply> <eq /> <ci>CaChoff</ci> <apply> <divide /> <ci>Ca_i</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.001</cn> <ci>Ca_i</ci> </apply> </apply> </apply> <apply> <eq /> <ci>CaChon</ci> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>f_Ca</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>CaChoff</ci> </apply> </apply> </apply>
Sodium reversal potential
Sodium background conductance
<apply> <eq /> <ci>E_Na</ci> <apply> <times /> <ci>RTONF</ci> <apply> <ln /> <apply> <divide /> <ci>Na_o</ci> <ci>Na_i</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_b_Na</ci> <apply> <times /> <ci>g_b_Na</ci> <apply> <minus /> <ci>V</ci> <ci>E_Na</ci> </apply> </apply> </apply>
NaK pump K half activation concentration
NaK pump Na half activation concentration
Maximum NaK exchane pump current
<apply> <eq /> <ci>i_NaK</ci> <apply> <divide /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>i_NaK_max</ci> <ci>K_c</ci> </apply> <apply> <plus /> <ci>K_mK</ci> <ci>K_c</ci> </apply> </apply> <ci>Na_i</ci> </apply> <apply> <plus /> <ci>K_mNa</ci> <ci>Na_i</ci> </apply> </apply> </apply>
K half-activation concentration for inward K rectifier
Inward K rectifier conductance
<apply> <eq /> <ci>E_K</ci> <apply> <times /> <ci>RTONF</ci> <apply> <ln /> <apply> <divide /> <ci>K_c</ci> <ci>K_i</ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>i_K1</ci> <apply> <divide /> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>g_K1</ci> <ci>K_c</ci> </apply> <apply> <plus /> <ci>K_c</ci> <ci>K_m_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> <minus /> <ci>V</ci> <ci>E_K</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</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>