- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:15:26+12:00
- Desc:
- committing version01 of courtemanche_ramirez_nattel_1998
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/courtemanche_ramirez_nattel_1998/rawfile/7b614643af6f457c2b8aef5dccdea9adc5bcc4d4/courtemanche_ramirez_nattel_1998.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : courtemanche_atrial_model_1998.xml
CREATED : 27th March 2002
LAST MODIFIED : 4th June 2003
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 Courtemanche et al's 1998 mathematical model of a human atrial cell.
CHANGES:
18/07/2002 - CML - Added more metadata.
28/03/2003 - AAC - Changed the name and cmeta:id of the model to reflect the
proper spelling of Courtemanche.
09/04/2003 - AAC - Added publication date information.
04/06/2003 - CML - Fixed MathML in a few components.
--><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="courtemanche_ramirez_nattel_1998_version01" name="courtemanche_ramirez_nattel_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical Model Of A Human Atrial Action Potential, 1998</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>
The ionic mechanisms underlying many important properties of the human atrial action potential are poorly understood. Using specific formulations of the K<superscript>+</superscript>, Na<superscript>+</superscript> and Ca<superscript>2+</superscript> currents based on experimental data recorded from human atrial myocytes, along with representations of pump, exchange and background currents, Marc Courtemanche, Rafael J. Ramirez and Stanley Nattel developed a mathematical model of the action potential (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
This mathematical model builds mostly on the classical work of Luo and Rudy (see <ulink url="${HTML_EXMPL_LR_II_MODEL}">The Luo-Rudy Ventricular Model II (dynamic), 1994</ulink>). Courtemanche <emphasis>et al</emphasis> effectively develop a working model of the human atrial action potential from the Luo-Rudy model which is based on guinea pig ventricular cells. Their primary goal was to develop a useful model of the action potential from which they could gain insights into experimental observations made on human atrial cells and tissues and make predictions regarding the behaviour of these cells under previously untested conditions
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://ajpheart.physiology.org/cgi/content/abstract/275/1/H301">Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model,</ulink> Marc Courtemanche, Rafael J. Ramirez and Stanley Nattel, 1998, <ulink url="http://ajpheart.physiology.org/">
<emphasis>American Journal of Physiology</emphasis>
</ulink>, 275, H301-H321. (<ulink url="http://ajpheart.physiology.org/cgi/content/full/275/1/H301">Full text</ulink> and <ulink url="http://ajpheart.physiology.org/cgi/reprint/275/1/H301.pdf">PDF</ulink> versions of the article are available for Journal Members on the AJP website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9688927&dopt=Abstract">PubMed ID: 9688927</ulink>
</para>
<para>
The raw CellML description of the Courtemanche <emphasis>et al</emphasis> 1998 mathematical model of a human atrial action potential can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram of a human atrial myocyte</title>
</objectinfo>
<imagedata fileref="cell_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic representation of currents, pumps and exchangers included in the model. The cell includes three intracellular compartments: cytoplasm, sarcoplasmic reticulum (SR) release compartment [junctional SR (JSR)], and SR uptake compartment [network SR (NSR)].</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="millisecond" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="millivolt" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="millimolar_per_millisecond">
<unit units="millimolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="picoA_per_picoF">
<unit units="ampere" prefix="pico"/>
<unit units="farad" prefix="pico" exponent="-1"/>
</units>
<units name="nanoS_per_picoF">
<unit units="siemens" prefix="nano"/>
<unit units="farad" prefix="pico" exponent="-1"/>
</units>
<units name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units name="micrometre_3">
<unit units="metre" prefix="micro" exponent="3"/>
</units>
<units name="joule_per_mole_kelvin">
<unit units="joule"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_millimole">
<unit units="coulomb"/>
<unit units="mole" prefix="milli" exponent="-1"/>
</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="-81.20"/>
<variable units="joule_per_mole_kelvin" public_interface="out" name="R" initial_value="8.3143"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_millimole" public_interface="out" name="F" initial_value="96.4867"/>
<variable units="picoF" name="Cm" initial_value="100.0"/>
<variable units="picoA_per_picoF" name="i_st"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_K1"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_to"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Kur"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Kr"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ks"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ca_L"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_CaP"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_B_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_B_Ca"/>
<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>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_K1 </ci>
<ci> i_to </ci>
<ci> i_Kur </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_B_Na </ci>
<ci> i_B_Ca </ci>
<ci> i_NaK </ci>
<ci> i_CaP </ci>
<ci> i_NaCa </ci>
<ci> i_Ca_L </ci>
<ci> i_st </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="nanoS_per_picoF" name="g_Na" initial_value="7.8"/>
<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="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<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> Na_o </ci>
<ci> Na_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.00291"/>
<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>
<piecewise>
<piece>
<cn cellml:units="per_millisecond"> 3.2 </cn>
<apply>
<eq/>
<ci> V </ci>
<cn cellml:units="millivolt"> -47.13 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.32 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</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>
</otherwise>
</piecewise>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.08 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.965"/>
<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>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.8 </cn>
</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_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>
<minus/>
<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>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="fast_sodium_current_j_gate">
<variable units="dimensionless" public_interface="out" name="j" initial_value="0.978"/>
<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>
<times/>
<cn cellml:units="per_millisecond"> 0.1212 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.01052 </cn>
<ci> V </ci>
</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>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.3 </cn>
<apply>
<divide/>
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<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.0000002535 </cn>
<ci> V </ci>
</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>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="time_independent_potassium_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_K1"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="nanoS_per_picoF" name="g_K1" initial_value="0.09"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> g_K1 </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.07 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
</apply>
</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/>
<ci> K_o </ci>
<ci> K_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_K_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_to"/>
<variable units="dimensionless" public_interface="out" private_interface="out" name="K_Q10" initial_value="3.0"/>
<variable units="nanoS_per_picoF" name="g_to" initial_value="0.1652"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="oa"/>
<variable units="dimensionless" private_interface="in" name="oi"/>
<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> oa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> oi </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_K_current_oa_gate">
<variable units="dimensionless" public_interface="out" name="oa" initial_value="0.0304"/>
<variable units="per_millisecond" name="alpha_oa"/>
<variable units="per_millisecond" name="beta_oa"/>
<variable units="millisecond" name="tau_oa"/>
<variable units="dimensionless" name="oa_infinity"/>
<variable units="dimensionless" public_interface="in" name="K_Q10"/>
<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_oa_calculation">
<eq/>
<ci> alpha_oa </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.65 </cn>
<apply>
<power/>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 8.5 </cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 59.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
<apply id="beta_oa_calculation">
<eq/>
<ci> beta_oa </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.65 </cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 2.5 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 82.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
<apply id="tau_oa_calculation">
<eq/>
<ci> tau_oa </ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<plus/>
<ci> alpha_oa </ci>
<ci> beta_oa </ci>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
<ci> K_Q10 </ci>
</apply>
</apply>
<apply id="oa_infinity_calculation">
<eq/>
<ci> oa_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.47 </cn>
</apply>
<cn cellml:units="millivolt"> 17.54 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_K_current_oi_gate">
<variable units="dimensionless" public_interface="out" name="oi" initial_value="0.999"/>
<variable units="per_millisecond" name="alpha_oi"/>
<variable units="per_millisecond" name="beta_oi"/>
<variable units="millisecond" name="tau_oi"/>
<variable units="dimensionless" name="oi_infinity"/>
<variable units="dimensionless" public_interface="in" name="K_Q10"/>
<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_oi_calculation">
<eq/>
<ci> alpha_oi </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="millisecond"> 18.53 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 133.7 </cn>
</apply>
<cn cellml:units="millivolt"> 10.95 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="beta_oi_calculation">
<eq/>
<ci> beta_oi </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="millisecond"> 35.56 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 1.26 </cn>
</apply>
<cn cellml:units="millivolt"> 7.44 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="tau_oi_calculation">
<eq/>
<ci> tau_oi </ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<plus/>
<ci> alpha_oi </ci>
<ci> beta_oi </ci>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
<ci> K_Q10 </ci>
</apply>
</apply>
<apply id="oi_infinity_calculation">
<eq/>
<ci> oi_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 43.1 </cn>
</apply>
<cn cellml:units="millivolt"> 5.3 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="ultrarapid_delayed_rectifier_K_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Kur"/>
<variable units="nanoS_per_picoF" name="g_Kur"/>
<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" public_interface="in" private_interface="out" name="K_Q10"/>
<variable units="dimensionless" private_interface="in" name="ua"/>
<variable units="dimensionless" private_interface="in" name="ui"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Kur_calculation">
<eq/>
<ci> i_Kur </ci>
<apply>
<times/>
<ci> g_Kur </ci>
<apply>
<power/>
<ci> ua </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> ui </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="g_Kur_calculation">
<eq/>
<ci> g_Kur </ci>
<apply>
<plus/>
<cn cellml:units="nanoS_per_picoF"> 0.005 </cn>
<apply>
<divide/>
<cn cellml:units="nanoS_per_picoF"> 0.05 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
<cn cellml:units="millivolt"> 13.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ultrarapid_delayed_rectifier_K_current_ua_gate">
<variable units="dimensionless" public_interface="out" name="ua" initial_value="0.00496"/>
<variable units="per_millisecond" name="alpha_ua"/>
<variable units="per_millisecond" name="beta_ua"/>
<variable units="millisecond" name="tau_ua"/>
<variable units="dimensionless" name="ua_infinity"/>
<variable units="dimensionless" public_interface="in" name="K_Q10"/>
<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_ua_calculation">
<eq/>
<ci> alpha_ua </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.65 </cn>
<apply>
<power/>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 8.5 </cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 59.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
<apply id="beta_ua_calculation">
<eq/>
<ci> beta_ua </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.65 </cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 2.5 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 82.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
<apply id="tau_ua_calculation">
<eq/>
<ci> tau_ua </ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<plus/>
<ci> alpha_ua </ci>
<ci> beta_ua </ci>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
<ci> K_Q10 </ci>
</apply>
</apply>
<apply id="ua_infinity_calculation">
<eq/>
<ci> ua_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.3 </cn>
</apply>
<cn cellml:units="millivolt"> 9.6 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="ultrarapid_delayed_rectifier_K_current_ui_gate">
<variable units="dimensionless" public_interface="out" name="ui" initial_value="0.999"/>
<variable units="per_millisecond" name="alpha_ui"/>
<variable units="per_millisecond" name="beta_ui"/>
<variable units="millisecond" name="tau_ui"/>
<variable units="dimensionless" name="ui_infinity"/>
<variable units="dimensionless" public_interface="in" name="K_Q10"/>
<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_ui_calculation">
<eq/>
<ci> alpha_ui </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="millisecond"> 21.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 185.0 </cn>
</apply>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="beta_ui_calculation">
<eq/>
<ci> beta_ui </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 158.0 </cn>
</apply>
<cn cellml:units="millivolt"> 16.0 </cn>
</apply>
</apply>
</apply>
<apply id="tau_ui_calculation">
<eq/>
<ci> tau_ui </ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<plus/>
<ci> alpha_ui </ci>
<ci> beta_ui </ci>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
<ci> K_Q10 </ci>
</apply>
</apply>
<apply id="ui_infinity_calculation">
<eq/>
<ci> ui_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 99.45 </cn>
</apply>
<cn cellml:units="millivolt"> 27.48 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifier_K_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Kr"/>
<variable units="nanoS_per_picoF" name="g_Kr" initial_value="0.0294"/>
<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="xr"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Kr_calculation">
<eq/>
<ci> i_Kr </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> g_Kr </ci>
<ci> xr </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
<cn cellml:units="millivolt"> 22.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifier_K_current_xr_gate">
<variable units="dimensionless" public_interface="out" name="xr" initial_value="0.0000329"/>
<variable units="per_millisecond" name="alpha_xr"/>
<variable units="per_millisecond" name="beta_xr"/>
<variable units="millisecond" name="tau_xr"/>
<variable units="dimensionless" name="xr_infinity"/>
<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_xr_calculation">
<eq/>
<ci> alpha_xr </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.0003 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.1 </cn>
</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"> 14.1 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_xr_calculation">
<eq/>
<ci> beta_xr </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.000073898 </cn>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 3.3328 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 3.3328 </cn>
</apply>
<cn cellml:units="millivolt"> 5.1237 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_xr_calculation">
<eq/>
<ci> tau_xr </ci>
<apply>
<power/>
<apply>
<plus/>
<ci> alpha_xr </ci>
<ci> beta_xr </ci>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="xr_infinity_calculation">
<eq/>
<ci> xr_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.1 </cn>
</apply>
<cn cellml:units="millivolt"> 6.5 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="slow_delayed_rectifier_K_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Ks"/>
<variable units="nanoS_per_picoF" name="g_Ks" initial_value="0.129"/>
<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="xs"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ks_calculation">
<eq/>
<ci> i_Ks </ci>
<apply>
<times/>
<ci> g_Ks </ci>
<apply>
<power/>
<ci> xs </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_delayed_rectifier_K_current_xs_gate">
<variable units="dimensionless" public_interface="out" name="xs" initial_value="0.0187"/>
<variable units="per_millisecond" name="alpha_xs"/>
<variable units="per_millisecond" name="beta_xs"/>
<variable units="millisecond" name="tau_xs"/>
<variable units="dimensionless" name="xs_infinity"/>
<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_xs_calculation">
<eq/>
<ci> alpha_xs </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.00004 </cn>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 19.9 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 17.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 19.9 </cn>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_xs_calculation">
<eq/>
<ci> beta_xs </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.000035 </cn>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 19.9 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 19.9 </cn>
</apply>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_xs_calculation">
<eq/>
<ci> tau_xs </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.5 </cn>
<apply>
<power/>
<apply>
<plus/>
<ci> alpha_xs </ci>
<ci> beta_xs </ci>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
<apply id="xs_infinity_calculation">
<eq/>
<ci> xs_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 19.9 </cn>
</apply>
<cn cellml:units="millivolt"> 12.7 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -0.5 </cn>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel">
<variable units="picoA_per_picoF" public_interface="out" name="i_Ca_L"/>
<variable units="nanoS_per_picoF" name="g_Ca_L" initial_value="0.1238"/>
<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" private_interface="out" name="Ca_i"/>
<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_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply>
<times/>
<ci> g_Ca_L </ci>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 65.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.000137"/>
<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="d_infinity_calculation">
<eq/>
<ci> d_infinity </ci>
<apply>
<power/>
<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"> 8.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="tau_d_calculation">
<eq/>
<ci> tau_d </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millisecond"> 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"> 0.035 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</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"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.999"/>
<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="f_infinity_calculation">
<eq/>
<ci> f_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.9 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="tau_f_calculation">
<eq/>
<ci> tau_f </ci>
<apply>
<times/>
<cn cellml:units="millisecond"> 9.0 </cn>
<apply>
<power/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0197 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<power/>
<cn cellml:units="dimensionless"> 0.0337 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_Ca_gate">
<variable units="dimensionless" public_interface="out" name="f_Ca" initial_value="0.775"/>
<variable units="dimensionless" name="f_Ca_infinity"/>
<variable units="millisecond" name="tau_f_Ca"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<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="f_Ca_infinity_calculation">
<eq/>
<ci> f_Ca_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Ca_i </ci>
<cn cellml:units="millimolar"> 0.00035 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="tau_f_Ca_calculation">
<eq/>
<ci> tau_f_Ca </ci>
<cn cellml:units="millisecond"> 2.0 </cn>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="picoA_per_picoF" public_interface="out" name="i_NaK"/>
<variable units="millimolar" name="Km_Na_i" initial_value="10.0"/>
<variable units="millimolar" name="Km_K_o" initial_value="1.5"/>
<variable units="picoA_per_picoF" name="i_NaK_max" initial_value="0.6"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="dimensionless" name="sigma"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> i_NaK_max </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> Km_Na_i </ci>
<ci> Na_i </ci>
</apply>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> K_o </ci>
<apply>
<plus/>
<ci> K_o </ci>
<ci> Km_K_o </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="f_NaK_calculation">
<eq/>
<ci> f_NaK </ci>
<apply>
<power/>
<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> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</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> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</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> Na_o </ci>
<cn cellml:units="millimolar"> 67.3 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_currents">
<variable units="picoA_per_picoF" public_interface="out" name="i_B_Na"/>
<variable units="picoA_per_picoF" public_interface="out" name="i_B_Ca"/>
<variable units="picoA_per_picoF" public_interface="out" name="i_B_K"/>
<variable units="nanoS_per_picoF" name="g_B_Na" initial_value="0.000674"/>
<variable units="nanoS_per_picoF" name="g_B_Ca" initial_value="0.00113"/>
<variable units="nanoS_per_picoF" name="g_B_K" initial_value="0.0"/>
<variable units="millivolt" name="E_Ca"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_B_Na_calculation">
<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>
<apply id="i_B_Ca_calculation">
<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>
<apply id="i_B_K_calculation">
<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>
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </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> Ca_o </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_exchanger_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_NaCa"/>
<variable units="picoA_per_picoF" name="I_NaCa_max" initial_value="1600.0"/>
<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="gamma" initial_value="0.35"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger">
<eq/>
<ci> i_NaCa </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> I_NaCa_max </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> gamma </ci>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_o </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> gamma </ci>
</apply>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Na_o </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> Na_o </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<ci> K_mCa </ci>
<ci> Ca_o </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> K_sat </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> gamma </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_CaP"/>
<variable units="picoA_per_picoF" name="i_CaP_max" initial_value="0.275"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_CaP_calculation">
<eq/>
<ci> i_CaP </ci>
<apply>
<times/>
<ci> i_CaP_max </ci>
<apply>
<divide/>
<ci> Ca_i </ci>
<apply>
<plus/>
<cn cellml:units="millimolar"> 0.0005 </cn>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_release_current_from_JSR">
<variable units="picoA_per_picoF" public_interface="out" name="i_rel"/>
<variable units="dimensionless" private_interface="out" name="Fn"/>
<variable units="per_millisecond" name="K_rel" initial_value="30.0"/>
<variable units="micrometre_3" name="V_rel" initial_value="96.48"/>
<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="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_rel"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ca_L"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="u"/>
<variable units="dimensionless" private_interface="in" name="v"/>
<variable units="dimensionless" private_interface="in" name="w"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> K_rel </ci>
<apply>
<power/>
<ci> u </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> v </ci>
<ci> w </ci>
<apply>
<minus/>
<ci> Ca_rel </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply id="Fn_calculation">
<eq/>
<ci> Fn </ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.000000000001 </cn>
<ci> V_rel </ci>
<ci> i_rel </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.0000000000005 </cn>
<ci> F </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.5 </cn>
<ci> i_Ca_L </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<ci> i_NaCa </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_release_current_from_JSR_u_gate">
<variable units="dimensionless" public_interface="out" name="u" initial_value="0.0"/>
<variable units="millisecond" name="tau_u"/>
<variable units="dimensionless" name="u_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" public_interface="in" name="Fn"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="tau_u_calculation">
<eq/>
<ci> tau_u </ci>
<cn cellml:units="millisecond"> 8.0 </cn>
</apply>
<apply id="u_infinity_calculation">
<eq/>
<ci> u_infinity </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Fn </ci>
<cn cellml:units="dimensionless"> 0.00000000000034175 </cn>
</apply>
<cn cellml:units="dimensionless"> 0.000000000000001367 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_release_current_from_JSR_v_gate">
<variable units="dimensionless" public_interface="out" name="v" initial_value="1.0"/>
<variable units="millisecond" name="tau_v"/>
<variable units="dimensionless" name="v_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" public_interface="in" name="Fn"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="tau_v_calculation">
<eq/>
<ci> tau_v </ci>
<apply>
<plus/>
<cn cellml:units="millisecond"> 1.91 </cn>
<apply>
<times/>
<cn cellml:units="millisecond"> 2.09 </cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Fn </ci>
<cn cellml:units="dimensionless"> 0.00000000000034175 </cn>
</apply>
<cn cellml:units="dimensionless"> 0.000000000000001367 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="v_infinity_calculation">
<eq/>
<ci> v_infinity </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Fn </ci>
<cn cellml:units="dimensionless"> 0.000000000000034175 </cn>
</apply>
<cn cellml:units="dimensionless"> 0.000000000000001367 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_release_current_from_JSR_w_gate">
<variable units="dimensionless" public_interface="out" name="w" initial_value="0.999"/>
<variable units="millisecond" name="tau_w"/>
<variable units="dimensionless" name="w_infinity"/>
<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="tau_w_calculation">
<eq/>
<ci> tau_w </ci>
<apply>
<times/>
<cn cellml:units="millisecond"> 6.0 </cn>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 7.9 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.3 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 7.9 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 7.9 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="w_infinity_calculation">
<eq/>
<ci> w_infinity </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transfer_current_from_NSR_to_JSR">
<variable units="picoA_per_picoF" public_interface="out" name="i_tr"/>
<variable units="millisecond" name="tau_tr" initial_value="180.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_rel"/>
<variable units="millimolar" public_interface="in" name="Ca_up"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_up </ci>
<ci> Ca_rel </ci>
</apply>
<ci> tau_tr </ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_uptake_current_by_the_NSR">
<variable units="picoA_per_picoF" public_interface="out" name="I_up_max" initial_value="0.005"/>
<variable units="picoA_per_picoF" public_interface="out" name="i_up"/>
<variable units="millimolar" name="K_up" initial_value="0.00092"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<divide/>
<ci> I_up_max </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> K_up </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_leak_current_by_the_NSR">
<variable units="picoA_per_picoF" public_interface="out" name="i_up_leak"/>
<variable units="millimolar" name="Ca_up_max" initial_value="15.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_up"/>
<variable units="picoA_per_picoF" public_interface="in" name="I_up_max"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_up_leak_calculation">
<eq/>
<ci> i_up_leak </ci>
<apply>
<times/>
<ci> I_up_max </ci>
<apply>
<divide/>
<ci> Ca_up </ci>
<ci> Ca_up_max </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_buffers">
<variable units="millimolar" public_interface="out" name="CMDN_max" initial_value="0.05"/>
<variable units="millimolar" public_interface="out" name="TRPN_max" initial_value="0.07"/>
<variable units="millimolar" public_interface="out" name="CSQN_max" initial_value="10.0"/>
<variable units="millimolar" public_interface="out" name="Km_CMDN" initial_value="0.00238"/>
<variable units="millimolar" public_interface="out" name="Km_TRPN" initial_value="0.0005"/>
<variable units="millimolar" public_interface="out" name="Km_CSQN" initial_value="0.8"/>
<variable units="millimolar" name="Ca_CMDN" initial_value="0.00205"/>
<variable units="millimolar" name="Ca_TRPN" initial_value="0.0118"/>
<variable units="millimolar" name="Ca_CSQN" initial_value="6.51"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_rel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_CMDN_calculation">
<eq/>
<ci> Ca_CMDN </ci>
<apply>
<times/>
<ci> CMDN_max </ci>
<apply>
<divide/>
<ci> Ca_i </ci>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> Km_CMDN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_TRPN_calculation">
<eq/>
<ci> Ca_TRPN </ci>
<apply>
<times/>
<ci> TRPN_max </ci>
<apply>
<divide/>
<ci> Ca_i </ci>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> Km_TRPN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_CSQN_calculation">
<eq/>
<ci> Ca_CSQN </ci>
<apply>
<times/>
<ci> CSQN_max </ci>
<apply>
<divide/>
<ci> Ca_rel </ci>
<apply>
<plus/>
<ci> Ca_rel </ci>
<ci> Km_CSQN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="11.20"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="0.000102"/>
<variable units="millimolar" public_interface="out" name="K_i" initial_value="139.0"/>
<variable units="millimolar" public_interface="out" name="Ca_rel" initial_value="1.49"/>
<variable units="millimolar" public_interface="out" name="Ca_up" initial_value="1.49"/>
<variable units="micrometre_3" name="V_i" initial_value="13668.0"/>
<variable units="micrometre_3" name="V_rel" initial_value="96.48"/>
<variable units="micrometre_3" name="V_up" initial_value="1109.52"/>
<variable units="dimensionless" name="B1"/>
<variable units="dimensionless" name="B2"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_B_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_K1"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_to"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Kur"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Kr"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ks"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_CaP"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ca_L"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_B_Ca"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_B_K"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_up"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_up_leak"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_tr"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_rel"/>
<variable units="millimolar" public_interface="in" name="Km_CMDN"/>
<variable units="millimolar" public_interface="in" name="Km_CSQN"/>
<variable units="millimolar" public_interface="in" name="Km_TRPN"/>
<variable units="millimolar" public_interface="in" name="CMDN_max"/>
<variable units="millimolar" public_interface="in" name="CSQN_max"/>
<variable units="millimolar" public_interface="in" name="TRPN_max"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Na_i </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -3.0 </cn>
<ci> i_NaK </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaCa </ci>
</apply>
<ci> i_B_Na </ci>
<ci> i_Na </ci>
</apply>
</apply>
<apply>
<times/>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="K_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> K_i </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaK </ci>
</apply>
<apply>
<plus/>
<ci> i_K1 </ci>
<ci> i_to </ci>
<ci> i_Kur </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_B_K </ci>
</apply>
</apply>
<apply>
<times/>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="Ca_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<divide/>
<ci> B1 </ci>
<ci> B2 </ci>
</apply>
</apply>
<apply id="B1_calculation">
<eq/>
<ci> B1 </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<apply>
<plus/>
<ci> i_CaP </ci>
<ci> i_Ca_L </ci>
<ci> i_B_Ca </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci> V_up </ci>
<apply>
<minus/>
<ci> i_up_leak </ci>
<ci> i_up </ci>
</apply>
</apply>
<apply>
<times/>
<ci> i_rel </ci>
<ci> V_rel </ci>
</apply>
</apply>
<ci> V_i </ci>
</apply>
</apply>
</apply>
<apply id="B2_calculation">
<eq/>
<ci> B2 </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> TRPN_max </ci>
<ci> Km_TRPN </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> Km_TRPN </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> CMDN_max </ci>
<ci> Km_CMDN </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> Km_CMDN </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_up_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_up </ci>
</apply>
<apply>
<minus/>
<ci> i_up </ci>
<apply>
<plus/>
<ci> i_up_leak </ci>
<apply>
<times/>
<ci> i_tr </ci>
<apply>
<divide/>
<ci> V_rel </ci>
<ci> V_up </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_rel_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_rel </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_tr </ci>
<ci> i_rel </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CSQN_max </ci>
<ci> Km_CSQN </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_rel </ci>
<ci> Km_CSQN </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="standard_ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="Ca_o" initial_value="1.8"/>
<variable units="millimolar" public_interface="out" name="K_o" initial_value="5.4"/>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<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="time_independent_potassium_current"/>
<component_ref component="transient_outward_K_current">
<component_ref component="transient_outward_K_current_oa_gate"/>
<component_ref component="transient_outward_K_current_oi_gate"/>
</component_ref>
<component_ref component="ultrarapid_delayed_rectifier_K_current">
<component_ref component="ultrarapid_delayed_rectifier_K_current_ua_gate"/>
<component_ref component="ultrarapid_delayed_rectifier_K_current_ui_gate"/>
</component_ref>
<component_ref component="rapid_delayed_rectifier_K_current">
<component_ref component="rapid_delayed_rectifier_K_current_xr_gate"/>
</component_ref>
<component_ref component="slow_delayed_rectifier_K_current">
<component_ref component="slow_delayed_rectifier_K_current_xs_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="sodium_potassium_pump"/>
<component_ref component="background_currents"/>
<component_ref component="Na_Ca_exchanger_current"/>
<component_ref component="sarcolemmal_calcium_pump_current"/>
<component_ref component="Ca_release_current_from_JSR">
<component_ref component="Ca_release_current_from_JSR_u_gate"/>
<component_ref component="Ca_release_current_from_JSR_v_gate"/>
<component_ref component="Ca_release_current_from_JSR_w_gate"/>
</component_ref>
<component_ref component="transfer_current_from_NSR_to_JSR"/>
<component_ref component="Ca_uptake_current_by_the_NSR"/>
<component_ref component="Ca_leak_current_by_the_NSR"/>
<component_ref component="Ca_buffers"/>
<component_ref component="intracellular_ion_concentrations"/>
<component_ref component="standard_ionic_concentrations"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<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="transient_outward_K_current">
<component_ref component="transient_outward_K_current_oa_gate"/>
<component_ref component="transient_outward_K_current_oi_gate"/>
</component_ref>
<component_ref component="ultrarapid_delayed_rectifier_K_current">
<component_ref component="ultrarapid_delayed_rectifier_K_current_ua_gate"/>
<component_ref component="ultrarapid_delayed_rectifier_K_current_ui_gate"/>
</component_ref>
<component_ref component="rapid_delayed_rectifier_K_current">
<component_ref component="rapid_delayed_rectifier_K_current_xr_gate"/>
</component_ref>
<component_ref component="slow_delayed_rectifier_K_current">
<component_ref component="slow_delayed_rectifier_K_current_xs_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="Ca_release_current_from_JSR">
<component_ref component="Ca_release_current_from_JSR_u_gate"/>
<component_ref component="Ca_release_current_from_JSR_v_gate"/>
<component_ref component="Ca_release_current_from_JSR_w_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="fast_sodium_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="transient_outward_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ultrarapid_delayed_rectifier_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_delayed_rectifier_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_delayed_rectifier_K_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="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="background_currents"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sarcolemmal_calcium_pump_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_release_current_from_JSR"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transfer_current_from_NSR_to_JSR"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_uptake_current_by_the_NSR"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_leak_current_by_the_NSR"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_buffers"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_ion_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="transient_outward_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
</connection>
<connection>
<map_components component_2="ultrarapid_delayed_rectifier_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kur" variable_1="i_Kur"/>
</connection>
<connection>
<map_components component_2="rapid_delayed_rectifier_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
</connection>
<connection>
<map_components component_2="slow_delayed_rectifier_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="background_currents" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_B_Ca" variable_1="i_B_Ca"/>
<map_variables variable_2="i_B_Na" variable_1="i_B_Na"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sarcolemmal_calcium_pump_current" component_1="membrane"/>
<map_variables variable_2="i_CaP" variable_1="i_CaP"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Ca_release_current_from_JSR"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
</connection>
<connection>
<map_components component_2="standard_ionic_concentrations" component_1="fast_sodium_current"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
</connection>
<connection>
<map_components component_2="background_currents" component_1="fast_sodium_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="time_independent_potassium_current"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
</connection>
<connection>
<map_components component_2="standard_ionic_concentrations" component_1="time_independent_potassium_current"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
</connection>
<connection>
<map_components component_2="transient_outward_K_current" component_1="time_independent_potassium_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="background_currents" component_1="time_independent_potassium_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
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Changed the name and cmeta:id of the model to reflect the proper
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Courtemanche et al's 1998 Mathematical Model of the Ionic Mechanisms
Underlying Human Atrial Acton Potential Properties.
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Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model
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<dc:title>American Journal of Physiology</dc:title>
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The University of Auckland, The Bioengineering Institute
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<vCard:Given>Autumn</vCard:Given>
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This is the CellML description of Courtemanche et al's mathematical
model of the ionic mechanisms underlying human atrial action potential properties.
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<vCard:Given>Stanley</vCard:Given>
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<vCard:Given>Rafael</vCard:Given>
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Corrected equations: alpha_j_calculation and beta_j_calculation in
fast_sodium_current_j_gate, oa_infinity_calculation in
transient_outward_K_current_oa_gate, alpha_ui_calculation in
ultrarapid_delayed_rectifier_K_current_ui_gate, i_Ca_L_calculation in
L_type_Ca_channel, and i_rel_calculation in
Ca_release_current_from_JSR.
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