<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : dumaine_model_1999.xml
CREATED : 18th August 2003
LAST MODIFIED : 27th April 2005
AUTHOR : Catherine Lloyd
The Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th
January, 2002.
DESCRIPTION : This file contains a CellML description of Dumaine et al.'s 1999 mathematical model of ventricular action potentials in Brugada syndrome.
CHANGES:
27/04/2005 - PJV - Removed excessive lines at the end of the
model.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="dumaine_towbin_brugada_vatta_nesterenko_nesterenko_brugada_brugada_antzelevitch_1999_version01" name="dumaine_towbin_brugada_vatta_nesterenko_nesterenko_brugada_brugada_antzelevitch_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Ionic Mechanisms Underlying Brugada Syndrome</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Of the 300,000 sudden deaths that occur in America each year, 5 to 12 percent are due to polymorphic ventricular tachycardia (VT) and ventricular fibrillation (VF) developing in patients with structurally normal hearts. About half of these cases are attributed to the Brugada syndrome, which is characterised by an ST-segment elevation in V1 through V3 and a rapid VT that can degenerate into VF. The disease has been linked to mutations in the <emphasis>SCN5A</emphasis> gene, which encodes the alpha subunit of the cardiac sodium channel. This temperature dependent mutation appears to change the gating kinetics of the sodium channel, such that the net outward current is augmented during the early phases of the right ventricular action potential.
</para>
<para>
In their 1999 study, Dumaine <emphasis>et al.</emphasis> tested this temperature dependence hypothesis. They studied cardiac action potentials by using a modified version of the Luo-Rudy II model. The modification involved adding a transient outward potassium current (<emphasis>I<subscript>to</subscript>
</emphasis>) to the original model, and reducing the conductance of the L-type calcium channel by 20 to 50 percent. For a diagram of the model, please see the figure below.
</para>
<para>
The results of their study showed that this mutation is only expressed at physiological temperatures. This explained why the mutation phenotype had not been observed in previous experiments which had been carried out at room temperature. Their findings also suggest that some patients may be more at risk during febrile states when their body temperature is elevated.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/85/9/803">Ionic Mechanisms Responsible for the Electrocardiographic Phenotype of the Brugada Syndrome Are Temperature Dependent</ulink>, Robert Dumaine, Jeffrey A. Towbin, Pedro Brugada, Matteo Vatta, Dmitri V. Nesterenko, Vladislav V. Nesterenko, Josep Brugada, Ramon Brugada, and Charles Antzelevitch, 1999, <ulink url="http://circres.ahajournals.org/">
<emphasis>Circulation Research</emphasis>
</ulink>, 85, 803-809. (<ulink url="http://circres.ahajournals.org/cgi/content/full/85/9/803">Full text</ulink> and <ulink url="http://circres.ahajournals.org/cgi/reprint/85/9/803.pdf">PDF</ulink> versions of this article are available to subscribers on the <emphasis>Circulation Research</emphasis> website). <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10532948&dopt=Abstract">PubMed ID: 10532948</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="dumaine_1999.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the ionic currents, pumps and exchangers that are captured in the Dumaine <emphasis>et al.</emphasis> 1999 model. The intracellular compartment is the sarcoplasmic reticulum (SR), which is divided into the two subcompartments, the network SR (NSR) and the junctional SR (JSR). Ca<superscript>2+</superscript> buffers are present in both the cytoplasm and the JSR.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="milliS_per_microF">
<unit units="siemens" prefix="milli"/>
<unit units="farad" prefix="milli" exponent="-1"/>
</units>
<units name="milliS_per_cm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="nanoS_per_cm2">
<unit units="siemens" prefix="nano"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF">
<unit units="farad" prefix="micro"/>
</units>
<units name="microA_per_microF">
<unit units="ampere" prefix="micro"/>
<unit units="farad" prefix="micro" exponent="-1"/>
</units>
<units name="millimolar_per_millisecond">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule"/>
<unit units="mole" prefix="kilo" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</units>
<units name="cm_per_second">
<unit units="metre" prefix="centi"/>
<unit units="second" exponent="-1"/>
</units>
<units name="mm2">
<unit units="metre" prefix="milli" exponent="2"/>
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_value="-84.624"/>
<variable units="joule_per_kilomole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96500.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microF" name="Cm" initial_value="1.0"/>
<variable units="microA_per_microF" name="I_st" initial_value="-100.0"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L"/>
<variable units="microA_per_microF" public_interface="in" name="i_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_to"/>
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Cm </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca_L </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_NaCa </ci>
<ci> i_p_Ca </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_ns_Ca </ci>
<ci> i_to </ci>
<ci> I_st </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_to"/>
<variable units="milliS_per_microF" name="g_to" initial_value="0.5"/>
<variable units="dimensionless" name="R_to"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="z"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_to_calculation">
<eq/>
<ci> i_to </ci>
<apply>
<times/>
<ci> g_to </ci>
<apply>
<power/>
<ci> z </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> y </ci>
<ci> R_to </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="R_to_calculation">
<eq/>
<ci> R_to </ci>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 100.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_z_gate">
<variable units="dimensionless" public_interface="out" name="z"/>
<variable units="per_millisecond" name="alpha_z"/>
<variable units="per_millisecond" name="beta_z"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dz_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> z </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_z </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> z </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_z </ci>
<ci> z </ci>
</apply>
</apply>
</apply>
<apply id="alpha_z_calculation">
<eq/>
<ci> alpha_z </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 10.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_z_calculation">
<eq/>
<ci> beta_z </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 10.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 90.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 90.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y"/>
<variable units="per_millisecond" name="alpha_y"/>
<variable units="per_millisecond" name="beta_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dy_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_y </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> y </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_y </ci>
<ci> y </ci>
</apply>
</apply>
</apply>
<apply id="alpha_y_calculation">
<eq/>
<ci> alpha_y </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 0.015 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_y_calculation">
<eq/>
<ci> beta_y </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="milliS_per_microF" name="g_Na" initial_value="16.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<variable units="dimensionless" private_interface="in" name="j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<ci> j </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
<apply id="E_Na_calculation">
<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m"/>
<variable units="per_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.32 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.08 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.135 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 80.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> -6.8 </cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 3.56 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.079 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 310000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.35 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="millisecond"> 0.13 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.66 </cn>
</apply>
<cn cellml:units="millivolt"> -11.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_j_gate">
<variable units="dimensionless" public_interface="out" name="j"/>
<variable units="per_millisecond" name="alpha_j"/>
<variable units="per_millisecond" name="beta_j"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_j_calculation">
<eq/>
<ci> alpha_j </ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -127140.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2444 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.00003474 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.04391 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 37.78 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.311 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 79.23 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_j_calculation">
<eq/>
<ci> beta_j </ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1212 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.01052 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1378 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.14 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.3 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.0000002535 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 32.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dj_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> j </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_j </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> j </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_j </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_L"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaCa"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaK"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaNa"/>
<variable units="dimensionless" public_interface="out" name="gamma_Nai" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Nao" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Ki" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Ko" initial_value="0.75"/>
<variable units="microA_per_microF" name="I_CaCa"/>
<variable units="microA_per_microF" name="I_CaK"/>
<variable units="microA_per_microF" name="I_CaNa"/>
<variable units="cm_per_second" name="P_Ca" initial_value="0.00054"/>
<variable units="cm_per_second" name="P_Na" initial_value="0.000000675"/>
<variable units="cm_per_second" name="P_K" initial_value="0.000000193"/>
<variable units="dimensionless" name="gamma_Cai" initial_value="1.0"/>
<variable units="dimensionless" name="gamma_Cao" initial_value="0.34"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="micromolar" public_interface="in" private_interface="out" name="Cai"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_CaCa_calculation">
<eq/>
<ci> i_CaCa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaCa </ci>
</apply>
</apply>
<apply id="i_CaNa_calculation">
<eq/>
<ci> i_CaNa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaNa </ci>
</apply>
</apply>
<apply id="i_CaK_calculation">
<eq/>
<ci> i_CaK </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaK </ci>
</apply>
</apply>
<apply id="I_CaCa_calculation">
<eq/>
<ci> I_CaCa </ci>
<apply>
<times/>
<ci> P_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Cai </ci>
<ci> Cai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Cao </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_CaNa_calculation">
<eq/>
<ci> I_CaNa </ci>
<apply>
<times/>
<ci> P_Na </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Nai </ci>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Nao </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_CaK_calculation">
<eq/>
<ci> I_CaK </ci>
<apply>
<times/>
<ci> P_K </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Ki </ci>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Ko </ci>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply> <plus/>
<ci> i_CaCa </ci>
<ci> i_CaK </ci>
<ci> i_CaNa </ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d"/>
<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<variable units="dimensionless" name="d_infinity"/>
<variable units="millisecond" name="tau_d"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<divide/>
<ci> d_infinity </ci>
<ci> tau_d </ci>
</apply>
</apply>
<apply id="d_infinity_calculation">
<eq/>
<ci> d_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_calculation">
<eq/>
<ci> tau_d </ci>
<apply>
<times/>
<ci> d_infinity </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.035 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d_infinity </ci>
</apply>
<ci> tau_d </ci>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f"/>
<variable units="per_millisecond" name="alpha_f"/>
<variable units="per_millisecond" name="beta_f"/>
<variable units="dimensionless" name="f_infinity"/>
<variable units="millisecond" name="tau_f"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<ci> f_infinity </ci>
<ci> tau_f </ci>
</apply>
</apply>
<apply id="f_infinity_calculation">
<eq/>
<ci> f_infinity </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.06 </cn>
</apply>
<cn cellml:units="millivolt"> 8.6 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.6 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 50.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_f_calculation">
<eq/>
<ci> tau_f </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0197 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.0337 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f_infinity </ci>
</apply>
<ci> tau_f </ci>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_Ca_gate">
<variable units="dimensionless" public_interface="out" name="f_Ca"/>
<variable units="micromolar" name="Km_Ca" initial_value="0.6"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_Ca_calculation">
<eq/>
<ci> f_Ca </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Cai </ci>
<ci> Km_Ca </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="milliS_per_microF" name="g_K" initial_value="0.282"/>
<variable units="dimensionless" name="PR_NaK" initial_value="0.01833"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="dimensionless" private_interface="in" name="X"/>
<variable units="dimensionless" private_interface="in" name="Xi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_K_calculation">
<eq/>
<ci> g_K </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_cm2"> 0.282 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K_calculation">
<eq/>
<ci> E_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci> Ko </ci>
<apply>
<times/>
<ci> PR_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> PR_NaK </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<power/>
<ci> X </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> Xi </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current_X_gate">
<variable units="dimensionless" public_interface="out" name="X"/>
<variable units="per_millisecond" name="alpha_X"/>
<variable units="per_millisecond" name="beta_X"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_X_calculation">
<eq/>
<ci> alpha_X </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.0000719 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.148 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_X_calculation">
<eq/>
<ci> beta_X </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.000131 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0687 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dX_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> X </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_X </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> X </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_X </ci>
<ci> X </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current_Xi_gate">
<variable units="dimensionless" public_interface="out" name="Xi"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Xi_calculation">
<eq/>
<ci> Xi </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 56.26 </cn>
</apply>
<cn cellml:units="millivolt"> 32.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K1"/>
<variable units="millivolt" public_interface="out" private_interface="out" name="E_K1"/>
<variable units="milliS_per_cm2" name="g_K1"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="K1_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_K1_calculation">
<eq/>
<ci> g_K1 </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.75 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K1_calculation">
<eq/>
<ci> E_K1 </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<ci> K1_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current_K1_gate">
<variable units="dimensionless" public_interface="out" name="K1_infinity"/>
<variable units="per_millisecond" name="alpha_K1"/>
<variable units="per_millisecond" name="beta_K1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_K1_calculation">
<eq/>
<ci> alpha_K1 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 1.02 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2385 </cn>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="millivolt"> 59.215 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_K1_calculation">
<eq/>
<ci> beta_K1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.49124 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08032 </cn>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.476 </cn>
</apply>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.06175 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 594.31 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.5143 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 4.753 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="K1_infinity_calculation">
<eq/>
<ci> K1_infinity </ci>
<apply>
<divide/>
<ci> alpha_K1 </ci>
<apply>
<plus/>
<ci> alpha_K1 </ci>
<ci> beta_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
<variable units="millivolt" name="E_Kp"/>
<variable units="milliS_per_microF" name="g_Kp" initial_value="0.0183"/>
<variable units="dimensionless" name="Kp"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_Kp_calculation">
<eq/>
<ci> E_Kp </ci>
<ci> E_K1 </ci>
</apply>
<apply id="Kp_calculation">
<eq/>
<ci> Kp </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 7.488 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 5.98 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Kp_calculation">
<eq/>
<ci> i_Kp </ci>
<apply>
<times/>
<ci> g_Kp </ci>
<ci> Kp </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Kp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
<variable units="micromolar" name="K_mpCa" initial_value="0.5"/>
<variable units="microA_per_microF" name="I_pCa" initial_value="1.15"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_Ca_calculation">
<eq/>
<ci> i_p_Ca </ci>
<apply>
<times/>
<ci> I_pCa </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> K_mpCa </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Na_b"/>
<variable units="milliS_per_microF" name="g_Nab" initial_value="0.00141"/>
<variable units="millivolt" name="E_NaN"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_NaN_calculation">
<eq/>
<ci> E_NaN </ci>
<ci> E_Na </ci>
</apply>
<apply id="i_Na_b_calculation">
<eq/>
<ci> i_Na_b </ci>
<apply>
<times/>
<ci> g_Nab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_NaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
<variable units="milliS_per_microF" name="g_Cab" initial_value="0.003016"/>
<variable units="millivolt" name="E_CaN"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_CaN_calculation">
<eq/>
<ci> E_CaN </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_b_calculation">
<eq/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<ci> g_Cab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_CaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
<variable units="microA_per_microF" name="I_NaK" initial_value="1.5"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="millimolar" name="K_mNai" initial_value="10.0"/>
<variable units="millimolar" name="K_mKo" initial_value="1.5"/>
<variable units="dimensionless" name="sigma"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_NaK_calculation">
<eq/>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1245 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0365 </cn>
<ci> sigma </ci>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="sigma_calculation">
<eq/>
<ci> sigma </ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 7.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 67.3 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> I_NaK </ci>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_mNai </ci>
<ci> Nai </ci>
</apply>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Ko </ci>
<apply>
<plus/>
<ci> Ko </ci>
<ci> K_mKo </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="non_specific_calcium_activated_current">
<variable units="microA_per_microF" public_interface="out" name="i_ns_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_Na"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_K"/>
<variable units="cm_per_second" name="P_ns_Ca" initial_value="1.75E-7"/>
<variable units="dimensionless" public_interface="in" name="gamma_Nai"/>
<variable units="dimensionless" public_interface="in" name="gamma_Nao"/>
<variable units="dimensionless" public_interface="in" name="gamma_Ki"/>
<variable units="dimensionless" public_interface="in" name="gamma_Ko"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="microA_per_microF" name="I_ns_Na"/>
<variable units="microA_per_microF" name="I_ns_K"/>
<variable units="micromolar" name="K_m_ns_Ca" initial_value="1.2"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_ns_Na_calculation">
<eq/>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> I_ns_Na </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_K_calculation">
<eq/>
<ci> i_ns_K </ci>
<apply>
<times/>
<ci> I_ns_K </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_Ca_calculation">
<eq/>
<ci> i_ns_Ca </ci>
<apply>
<plus/>
<ci> i_ns_Na </ci>
<ci> i_ns_K </ci>
</apply>
</apply>
<apply id="I_ns_Na_calculation">
<eq/>
<ci> I_ns_Na </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Nai </ci>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Nao </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_ns_K_calculation">
<eq/>
<ci> I_ns_K </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Ki </ci>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Ko </ci>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_exchanger">
<variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
<variable units="microA_per_microF" name="K_NaCa" initial_value="2000.0"/>
<variable units="millimolar" name="K_mNa" initial_value="87.5"/>
<variable units="millimolar" name="K_mCa" initial_value="1.38"/>
<variable units="dimensionless" name="K_sat" initial_value="0.1"/>
<variable units="dimensionless" name="eta" initial_value="0.35"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> K_mCa </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> K_sat </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<ci> eta </ci>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_buffers_in_the_myoplasm">
<variable units="micromolar" name="K_mTn" initial_value="0.5"/>
<variable units="micromolar" name="K_mCMDN" initial_value="2.38"/>
<variable units="micromolar" name="Tn_max" initial_value="70.0"/>
<variable units="micromolar" name="CMDN_max" initial_value="50.0"/>
<variable units="micromolar" name="Tn_buff"/>
<variable units="micromolar" name="CMDN_buff"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Tn_buff_calculation">
<eq/>
<ci> Tn_buff </ci>
<apply>
<times/>
<ci> Tn_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mTn </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="CMDN_buff_calculation">
<eq/>
<ci> CMDN_buff </ci>
<apply>
<times/>
<ci> CMDN_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mCMDN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_fluxes_in_the_SR">
<variable units="millimolar_per_millisecond" public_interface="out" name="i_rel"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_up"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_leak"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_tr"/>
<variable units="per_millisecond" name="G_rel"/>
<variable units="per_millisecond" name="G_rel_max"/>
<variable units="millisecond" name="tau_on" initial_value="2.0"/>
<variable units="millisecond" name="tau_off" initial_value="2.0"/>
<variable units="millisecond" name="tau_tr" initial_value="180.0"/>
<variable units="millisecond" name="t" initial_value="0.0"/>
<variable units="micromolar" name="K_mrel" initial_value="0.8"/>
<variable units="micromolar" name="delta_Ca_i2"/>
<variable units="micromolar" name="delta_Ca_ith" initial_value="0.18"/>
<variable units="millimolar" name="CSQN_buff"/>
<variable units="millimolar" name="CSQN_max" initial_value="10.0"/>
<variable units="millimolar" name="CSQN_th" initial_value="0.7"/>
<variable units="millimolar" name="K_mCSQN" initial_value="0.8"/>
<variable units="micromolar" name="K_mup" initial_value="0.92"/>
<variable units="per_millisecond" name="K_leak"/>
<variable units="millimolar_per_millisecond" name="I_up" initial_value="0.005"/>
<variable units="millimolar" name="Ca_NSR_max" initial_value="0.15"/>
<variable units="dimensionless" name="calcium_overload"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR"/>
<variable units="millimolar" public_interface="in" name="Ca_NSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> G_rel </ci>
<apply>
<minus/>
<ci> Ca_JSR </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
<apply id="G_rel_calculation">
<eq/>
<ci> G_rel </ci>
<piecewise>
<piece>
<apply>
<times/>
<ci> G_rel_max </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_Ca_i2 </ci>
<ci> delta_Ca_ith </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> K_mrel </ci>
<ci> delta_Ca_i2 </ci>
</apply>
<ci> delta_Ca_ith </ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_on </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_off </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> calcium_overload </ci>
<cn cellml:units="dimensionless"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci> G_rel_max </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_on </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_off </ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="G_rel_max_calculation">
<eq/>
<ci> G_rel_max </ci>
<piecewise>
<piece>
<piecewise>
<piece>
<cn cellml:units="per_millisecond"> 0.0 </cn>
<apply>
<lt/>
<ci> delta_Ca_i2 </ci>
<ci> delta_Ca_ith </ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 60.0 </cn>
</otherwise>
</piecewise>
<apply>
<eq/>
<ci> calcium_overload </ci>
<cn cellml:units="dimensionless"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<piecewise>
<piece>
<cn cellml:units="per_millisecond"> 0.0 </cn>
<apply>
<lt/>
<ci> CSQN_buff </ci>
<ci> CSQN_th </ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 4.0 </cn>
</otherwise>
</piecewise>
</otherwise>
</piecewise>
</apply>
<apply id="CSQN_buff_calculation">
<eq/>
<ci> CSQN_buff </ci>
<apply>
<times/>
<ci> CSQN_max </ci>
<apply>
<divide/>
<ci> Ca_JSR </ci>
<apply>
<plus/>
<ci> Ca_JSR </ci>
<ci> K_mCSQN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> I_up </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mup </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_leak_calcualtion">
<eq/>
<ci> i_leak </ci>
<apply>
<times/>
<ci> K_leak </ci>
<ci> Ca_NSR </ci>
</apply>
</apply>
<apply id="K_leak_calculation">
<eq/>
<ci> K_leak </ci>
<apply>
<divide/>
<ci> I_up </ci>
<ci> Ca_NSR_max </ci>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Ca_JSR </ci>
</apply>
<ci> tau_tr </ci>
</apply>
</apply>
</math>
</component>
<component name="ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Nai" initial_value="10.0"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="140.0"/>
<variable units="micromolar" public_interface="out" name="Cai" initial_value="0.12"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="1.8"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="145.0"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4"/>
<variable units="millimolar" public_interface="out" name="Ca_JSR"/>
<variable units="millimolar" public_interface="out" name="Ca_NSR" initial_value="15.0"/>
<variable units="micromolar" name="Ca_foot"/>
<variable units="mm2" name="A_cap" initial_value="0.000153"/>
<variable units="dimensionless" name="R_A_V"/>
<variable units="micro_litre" name="V_myo"/>
<variable units="micro_litre" name="V_cleft"/>
<variable units="micro_litre" name="V_JSR"/>
<variable units="micro_litre" name="V_NSR"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_CaNa"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_CaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_CaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/> <variable units="microA_per_microF" public_interface="in" name="i_ns_K"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_tr"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_rel"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_leak"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_up"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_CaNa </ci>
<ci> i_Na_b </ci>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaCa </ci>
<ci> i_p_Ca </ci>
<ci> i_Ca_b </ci>
</apply>
<ci> i_NaCa </ci>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> i_rel </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_myo </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_leak </ci>
<ci> i_up </ci>
</apply>
<apply>
<divide/>
<ci> V_NSR </ci>
<ci> V_myo </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaK </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_external_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ko </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> i_CaK </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_cleft </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_JSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_JSR </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> i_tr </ci>
<apply>
<divide/>
<ci> V_NSR </ci>
<ci> V_JSR </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_NSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_NSR </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_leak </ci>
<ci> i_tr </ci>
</apply>
<ci> i_up </ci>
</apply>
</apply>
</apply>
<apply id="calcium_foot_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_foot </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_CaCa </ci>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
<ci> R_A_V </ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="transient_outward_potassium_current">
<component_ref component="transient_outward_potassium_current_z_gate"/>
<component_ref component="transient_outward_potassium_current_y_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
<component_ref component="L_type_Ca_channel_f_Ca_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate"/>
<component_ref component="time_dependent_potassium_current_Xi_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="plateau_potassium_current"/>
<component_ref component="sarcolemmal_calcium_pump"/>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="non_specific_calcium_activated_current"/>
<component_ref component="ionic_concentrations"/>
<component_ref component="calcium_buffers_in_the_myoplasm"/>
<component_ref component="calcium_fluxes_in_the_SR"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="transient_outward_potassium_current">
<component_ref component="transient_outward_potassium_current_z_gate"/>
<component_ref component="transient_outward_potassium_current_y_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
<component_ref component="L_type_Ca_channel_f_Ca_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate"/>
<component_ref component="time_dependent_potassium_current_Xi_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_outward_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sarcolemmal_calcium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="non_specific_calcium_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ionic_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_buffers_in_the_myoplasm"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_fluxes_in_the_SR"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>transient_outward_potassium
<connection>
<map_components component_2="transient_outward_potassium_current" component_1="membrane"/>
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Ionic mechanisms responsible for the electrocardiographic phenotype
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The University of Auckland, The Bioengineering Institute
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Dumaine et al.'s 1999 mathematical model of ventricular action
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<vCard:Given>Josep</vCard:Given>
<vCard:Family>Brugada</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5a57adad-19cd-49f6-90dd-8247384ddf4b">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#6ab245d4-99d4-4508-8bb9-5e33fa479a21"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e21dcef9-78b6-4a5c-9438-477caff57cb3">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#29a9c106-d0be-4ff6-a155-1ed95bee87bd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#83321ccf-9698-4af0-8182-242183351da3">
<dc:subject rdf:resource="rdf:#2a046ab6-6715-431c-bc75-b17b845bfcad"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1d6b4df6-29a5-4bbb-8a0a-85b8e60a5715">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a9bc3d7f-562f-4837-bed0-6a08eee7e4bd">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#3981d1cb-14b2-4528-b7d1-814ff69fc048"/>
</rdf:Description>
</rdf:RDF>
</model>
