- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-14 23:48:18+12:00
- Desc:
- committing version01 of noble_difrancesco_denyer_1989
- Permanent Source URI:
- http://models.cellml.org/workspace/noble_difrancesco_denyer_1989/rawfile/a444a916bd71f4173ab71983df17ace586c26f4a/noble_difrancesco_denyer_1989.cellml
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<!--
This CellML file was generated on 05/07/2005 at 16:04:08 using:
COR (0.9.31.77)
Copyright 2002-2005 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
--><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="noble_difrancesco_denyer_1989_version01" name="noble_difrancesco_denyer_1989_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<section id="sec_status">
<title>Model Status</title>
<para>
Version 01 is the original model imported from the old repository. Version 01 has been verified to run in PCEnv.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="noble_1989.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the Noble et al 1989 model.</caption>
</informalfigure>
</para>
<para>
This model was based on the article:
</para>
<para>
"Ionic Mechanisms in Normal and Abnormal Cardiac Pacemaker Activity"
</para>
<para>
This article can be found in the book "Neuronal and Cellular Oscillators"
</para>
<para>
pp. 59-85
</para>
<para>
Edited by Jon W. Jacklet
</para>
<para>
Part of the "Cellular Clocks" series, published by Marcel Dekker Inc.
</para>
<para>
Further documentation is pending a summary of this article.
</para>
</sect1>
</article>
</documentation>
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</component>
<component name="fast_sodium_current">
<variable units="nanoamp" public_interface="out" name="i_Na"/>
<variable units="microS" name="g_Na" initial_value="0.0125"/>
<variable units="millivolt" name="E_mh"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millijoule_per_mole_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="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_mh</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>Nao</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.12</cn>
<ci>Kc</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Nai</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.12</cn>
<ci>Ki</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Na</ci>
<apply>
<times/>
<ci>g_Na</ci>
<apply>
<power/>
<ci>m</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_mh</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0365"/>
<variable units="per_second" name="alpha_m"/>
<variable units="per_second" name="beta_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="dimensionless" name="delta_m" initial_value="1e-5"/>
<variable units="millivolt" name="E0_m"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_m</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">41</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_m</ci>
<piecewise>
<piece>
<cn cellml:units="per_second">2000</cn>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_m</ci>
</apply>
<ci>delta_m</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">200</cn>
<ci>E0_m</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<ci>E0_m</ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<times/>
<cn cellml:units="per_second">8000</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.056</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">66</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_m</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</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" initial_value="0.1969"/>
<variable units="per_second" name="alpha_h"/>
<variable units="per_second" name="beta_h"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_h</ci>
<apply>
<times/>
<cn cellml:units="per_second">20</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.125</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<apply>
<divide/>
<cn cellml:units="per_second">2000</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">320</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_h</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>h</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_h</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current">
<variable units="nanoamp" public_interface="out" name="i_si"/>
<variable units="nanoamp" public_interface="out" name="i_siCa"/>
<variable units="nanoamp" public_interface="out" name="i_siK"/>
<variable units="nanoamp" public_interface="out" name="i_siNa"/>
<variable units="dimensionless" name="P_si" initial_value="0.12"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millijoule_per_mole_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="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Cao"/>
<variable units="concentration_units" public_interface="in" private_interface="out" name="Cai"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_siCa</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>P_si</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Cai</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">100</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Cao</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_siK</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01</cn>
<ci>P_si</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ki</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">50</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Kc</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_siNa</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01</cn>
<ci>P_si</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Nai</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">50</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Nao</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_si</ci>
<apply>
<plus/>
<ci>i_siCa</ci>
<ci>i_siK</ci>
<ci>i_siNa</ci>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0"/>
<variable units="per_second" name="alpha_d"/>
<variable units="per_second" name="beta_d"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="dimensionless" name="delta_d" initial_value="0.0001"/>
<variable units="millivolt" name="E0_d"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_d</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">24</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d</ci>
<piecewise>
<piece>
<cn cellml:units="per_second">120</cn>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_d</ci>
</apply>
<ci>delta_d</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">30</cn>
<ci>E0_d</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>E0_d</ci>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_d</ci>
<piecewise>
<piece>
<cn cellml:units="per_second">120</cn>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_d</ci>
</apply>
<ci>delta_d</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">12</cn>
<ci>E0_d</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_d</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_d</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>d</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_d</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.9997"/>
<variable units="per_second" name="alpha_f"/>
<variable units="per_second" name="beta_f"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="dimensionless" name="delta_f" initial_value="0.0001"/>
<variable units="millivolt" name="E0_f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_f</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">34</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f</ci>
<piecewise>
<piece>
<cn cellml:units="per_second">25</cn>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_f</ci>
</apply>
<ci>delta_f</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">6.25</cn>
<ci>E0_f</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_f</ci>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_f</ci>
<apply>
<divide/>
<cn cellml:units="per_second">50</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">34</cn>
</apply>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_f</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_f</ci>
<ci>f</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_f2_gate">
<variable units="dimensionless" public_interface="out" name="f2" initial_value="0.5765"/>
<variable units="per_second" name="alpha_f2" initial_value="10"/>
<variable units="per_second" name="beta_f2"/>
<variable units="concentration_units" name="K_mf2" initial_value="0.0005"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>beta_f2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Cai</ci>
<ci>alpha_f2</ci>
</apply>
<ci>K_mf2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f2</ci>
</apply>
<apply>
<minus/>
<ci>alpha_f2</ci>
<apply>
<times/>
<ci>f2</ci>
<apply>
<plus/>
<ci>alpha_f2</ci>
<ci>beta_f2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_sodium_concentration">
<variable units="concentration_units" public_interface="out" name="Nao" initial_value="140"/>
</component>
<component name="intracellular_sodium_concentration">
<variable units="concentration_units" public_interface="out" name="Nai" initial_value="7.5"/>
<variable units="micrometre" name="radius" initial_value="10"/>
<variable units="micrometre" name="length" initial_value="28"/>
<variable units="dimensionless" name="V_e_ratio" initial_value="0.1"/>
<variable units="microlitre" name="V_Cell"/>
<variable units="microlitre" public_interface="out" name="Vi"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="nanoamp" public_interface="in" name="i_Na"/>
<variable units="nanoamp" public_interface="in" name="i_Na_b"/>
<variable units="nanoamp" public_interface="in" name="i_siNa"/>
<variable units="nanoamp" public_interface="in" name="i_p"/>
<variable units="nanoamp" public_interface="in" name="i_fNa"/>
<variable units="nanoamp" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_Cell</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3.141592654</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>radius</ci>
<cn cellml:units="dimensionless">1000</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>length</ci>
</apply>
<cn cellml:units="dimensionless">1000</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>Vi</ci>
<apply>
<times/>
<ci>V_Cell</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>V_e_ratio</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Nai</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_Na_b</ci>
<ci>i_fNa</ci>
<ci>i_siNa</ci>
<apply>
<times/>
<ci>i_p</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaCa</ci>
<ci>n_NaCa</ci>
</apply>
<apply>
<minus/>
<ci>n_NaCa</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_calcium_concentration">
<variable units="concentration_units" public_interface="out" name="Cao" initial_value="2"/>
</component>
<component name="intracellular_calcium_concentration">
<variable units="concentration_units" public_interface="out" name="Cai" initial_value="5.6e-5"/>
<variable units="microlitre" name="V_up"/>
<variable units="microlitre" name="V_rel"/>
<variable units="microlitre" public_interface="in" name="Vi"/>
<variable units="nanoamp" name="i_up"/>
<variable units="nanoamp" name="i_tr"/>
<variable units="nanoamp" name="i_rel"/>
<variable units="per_second" name="alpha_up"/>
<variable units="per_second" name="alpha_tr"/>
<variable units="per_second" name="alpha_rel"/>
<variable units="concentration_units" name="Ca_up" initial_value="2.3909"/>
<variable units="concentration_units" name="Ca_rel" initial_value="0.2207"/>
<variable units="concentration_units" name="Ca_up_max" initial_value="5"/>
<variable units="concentration_units" name="K_mCa" initial_value="0.002"/>
<variable units="dimensionless" name="p" initial_value="0.237"/>
<variable units="per_second" name="alpha_p"/>
<variable units="per_second" name="beta_p"/>
<variable units="millivolt" name="E0_p"/>
<variable units="second" name="tau_up" initial_value="0.005"/>
<variable units="second" name="tau_rep" initial_value="0.2"/>
<variable units="second" name="tau_rel" initial_value="0.01"/>
<variable units="dimensionless" name="rCa" initial_value="2"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="nanoamp" public_interface="in" name="i_Ca_b"/>
<variable units="nanoamp" public_interface="in" name="i_siCa"/>
<variable units="nanoamp" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<times/>
<ci>alpha_up</ci>
<ci>Cai</ci>
<apply>
<minus/>
<ci>Ca_up_max</ci>
<ci>Ca_up</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_up</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>tau_up</ci>
<ci>Ca_up_max</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_tr</ci>
<apply>
<times/>
<ci>alpha_tr</ci>
<ci>p</ci>
<apply>
<minus/>
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_tr</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<ci>tau_rep</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>E0_p</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">34</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_p</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">0.625</cn>
<ci>E0_p</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_p</ci>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_p</ci>
<apply>
<divide/>
<cn cellml:units="per_second">5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>E0_p</ci>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_rel</ci>
<ci>Ca_rel</ci>
<apply>
<power/>
<ci>Cai</ci>
<ci>rCa</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Cai</ci>
<ci>rCa</ci>
</apply>
<apply>
<power/>
<ci>K_mCa</ci>
<ci>rCa</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_rel</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<ci>tau_rel</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_p</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>p</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_p</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_up</ci>
<apply>
<times/>
<ci>Vi</ci>
<cn cellml:units="dimensionless">0.05</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_rel</ci>
<apply>
<times/>
<ci>Vi</ci>
<cn cellml:units="dimensionless">0.02</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cai</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_siCa</ci>
<ci>i_Ca_b</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
<apply>
<minus/>
<ci>n_NaCa</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>i_rel</ci>
</apply>
<ci>i_up</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_potassium_concentration">
<variable units="concentration_units" public_interface="out" name="Kc" initial_value="3"/>
</component>
<component name="intracellular_potassium_concentration">
<variable units="concentration_units" public_interface="out" name="Ki" initial_value="140"/>
<variable units="microlitre" public_interface="in" name="Vi"/>
<variable units="nanoamp" public_interface="in" name="i_K1"/>
<variable units="nanoamp" public_interface="in" name="i_K"/>
<variable units="nanoamp" public_interface="in" name="i_fK"/>
<variable units="nanoamp" public_interface="in" name="i_siK"/>
<variable units="nanoamp" public_interface="in" name="i_p"/>
<variable units="nanoamp" name="i_mK"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_mK</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_K1</ci>
<ci>i_K</ci>
<ci>i_fK</ci>
<ci>i_siK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ki</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_mK</ci>
</apply>
<apply>
<times/>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current"/>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="Na_Ca_exchanger"/>
<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_ref component="second_inward_current">
<component_ref component="second_inward_current_d_gate"/>
<component_ref component="second_inward_current_f_gate"/>
<component_ref component="second_inward_current_f2_gate"/>
</component_ref>
<component_ref component="intracellular_sodium_concentration"/>
<component_ref component="extracellular_sodium_concentration"/>
<component_ref component="intracellular_calcium_concentration"/>
<component_ref component="extracellular_calcium_concentration"/>
<component_ref component="extracellular_potassium_concentration"/>
<component_ref component="intracellular_potassium_concentration"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_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_ref component="second_inward_current">
<component_ref component="second_inward_current_d_gate"/>
<component_ref component="second_inward_current_f_gate"/>
<component_ref component="second_inward_current_f2_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="hyperpolarising_activated_current"/>
<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="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="Na_Ca_exchanger"/>
<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="second_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_f" variable_1="i_f"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
<map_variables variable_2="RTONF" variable_1="RTONF"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_independent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="calcium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_potassium_pump"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Na_Ca_exchanger"/>
<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="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="fast_sodium_current"/>
<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="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="second_inward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_si" variable_1="i_si"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="i_fK" variable_1="i_fK"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="i_fNa" variable_1="i_fNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="time_independent_potassium_current"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="fast_sodium_current"/>
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