- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 15:19:43+12:00
- Desc:
- committing version04 of noble_noble_1984
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/noble_noble_1984/rawfile/d0e3a3809b4e28e0dd307bfafbd25ec3f91c85f3/noble_noble_1984.cellml
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<!--
This CellML file was generated on 17/09/2007 at 12:19:39 using:
COR (0.9.31.769)
Copyright 2002-2007 Dr Alan Garny
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/
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<article>
<articleinfo>
<title>Noble-Noble Model Of Sino-Atrial Node Electrical Activity, 1984</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 model has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 1984 D. Noble and S.J. Noble published a mathematical model which describes electrical activity in the sino-atrial node. Their model is based on the Purkinje fibre model developed by D. DiFrancesco and D. Noble (please see the CellML version of the DiFrancesco-Noble Purkinje Fibre Model, 1985). Most of the equations of this cardiac cell model remain unchanged. However, based on the results of experimental work, where necessary, certain parameters have been modified in order to make the model appropriate to a sino-atrial node.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A Model of Sino-Atrial Node Electrical Activity Based on a Modification of the DiFrancesco-Noble (1984) Equations, D. Noble and S.J. Noble, <ulink url="http://www.pubs.royalsoc.ac.uk/proc_bio/proc_bio.html">
<emphasis>Proceedings of the Royal Society of London. Series B, Biological Sciences</emphasis>
</ulink>, 222, 295-304. (The <ulink url="http://links.jstor.org/sici?sici=0080-4649%2819840922%29222%3A1228%3C295%3AAMOSNE%3E2.0.CO%3B2-P">full text</ulink> of the article is available to members on the JSTOR website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=6149553&dopt=Abstract">PubMed ID: 6149553</ulink>
</para>
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<mediaobject>
<imageobject>
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<title>cell diagram of the NN SAN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
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<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the NN SAN model.</caption>
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<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<minus/>
<ci>n_NaCa</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>V</ci>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Nai</ci>
<ci>n_NaCa</ci>
</apply>
<ci>Cao</ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>n_NaCa</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>V</ci>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Nao</ci>
<ci>n_NaCa</ci>
</apply>
<ci>Cai</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="millimolar4">1</cn>
<apply>
<times/>
<ci>d_NaCa</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Cai</ci>
<apply>
<power/>
<ci>Nao</ci>
<ci>n_NaCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Cao</ci>
<apply>
<power/>
<ci>Nai</ci>
<ci>n_NaCa</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Cai</ci>
<cn cellml:units="millimolar">0.0069</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="nanoA" public_interface="out" name="i_Na"/>
<variable units="microS" name="g_Na" initial_value="1.25"/>
<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="millivolt" public_interface="in" name="RTONF"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Kc"/>
<variable units="millimolar" 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/>
<ci>RTONF</ci>
<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="0.076"/>
<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="millivolt" 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="per_millivolt">0.1</cn>
</apply>
<ci>E0_m</ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<times/>
<cn cellml:units="per_second">8000</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">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="0.015"/>
<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="per_millivolt">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="per_millivolt">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="nanoA" public_interface="out" name="i_si"/>
<variable units="nanoA" public_interface="out" name="i_siCa"/>
<variable units="nanoA" public_interface="out" name="i_siK"/>
<variable units="nanoA" public_interface="out" name="i_siNa"/>
<variable units="nanoA_per_millimolar" name="P_si" initial_value="7.5"/>
<variable units="second" 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="RTONF"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Kc"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" 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>
</apply>
<apply>
<times/>
<ci>RTONF</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>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Cai</ci>
<apply>
<exp/>
<apply>
<divide/>
<cn cellml:units="millivolt">100</cn>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Cao</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_siK</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01</cn>
<ci>P_si</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<apply>
<times/>
<ci>RTONF</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>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ki</ci>
<apply>
<exp/>
<apply>
<divide/>
<cn cellml:units="millivolt">50</cn>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Kc</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_siNa</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01</cn>
<ci>P_si</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<apply>
<times/>
<ci>RTONF</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>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Nai</ci>
<apply>
<exp/>
<apply>
<divide/>
<cn cellml:units="millivolt">50</cn>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Nao</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_si</ci>
<apply>
<plus/>
<ci>i_siCa</ci>
<ci>i_siK</ci>
<ci>i_siNa</ci>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.0011"/>
<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="millivolt" 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="0.785"/>
<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="millivolt" 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="0.785"/>
<variable units="per_second" name="alpha_f2" initial_value="10"/>
<variable units="per_second" name="beta_f2"/>
<variable units="millimolar" 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="millimolar" 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="millimolar" public_interface="out" name="Nao" initial_value="140"/>
</component>
<component name="intracellular_sodium_concentration">
<variable units="millimolar" public_interface="out" name="Nai" initial_value="7.5"/>
<variable units="micrometre" name="radius" initial_value="0.08"/>
<variable units="micrometre" name="length" initial_value="0.08"/>
<variable units="dimensionless" name="V_e_ratio" initial_value="0.1"/>
<variable units="micrometre3" name="V_Cell"/>
<variable units="micrometre3" 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="nanoA" public_interface="in" name="i_Na"/>
<variable units="nanoA" public_interface="in" name="i_Na_b"/>
<variable units="nanoA" public_interface="in" name="i_siNa"/>
<variable units="nanoA" public_interface="in" name="i_p"/>
<variable units="nanoA" public_interface="in" name="i_fNa"/>
<variable units="nanoA" 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>
<times/>
<cn cellml:units="dimensionless">3.141592654</cn>
<apply>
<power/>
<ci>radius</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>length</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vi</ci>
<apply>
<times/>
<ci>V_Cell</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>V_e_ratio</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Nai</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_nA">1</cn>
</apply>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_Na_b</ci>
<ci>i_fNa</ci>
<ci>i_siNa</ci>
<apply>
<times/>
<ci>i_p</ci>
<cn 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/>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_calcium_concentration">
<variable units="millimolar" public_interface="out" name="Cao" initial_value="2"/>
</component>
<component name="intracellular_calcium_concentration">
<variable units="millimolar" public_interface="out" name="Cai" initial_value="5.8e-5"/>
<variable units="micrometre3" name="V_up"/>
<variable units="micrometre3" name="V_rel"/>
<variable units="micrometre3" public_interface="in" name="Vi"/>
<variable units="nanoA" name="i_up"/>
<variable units="nanoA" name="i_tr"/>
<variable units="nanoA" name="i_rel"/>
<variable units="millimolar" name="Ca_up" initial_value="1.98"/>
<variable units="millimolar" name="Ca_rel" initial_value="0.55"/>
<variable units="millimolar" name="Ca_up_max" initial_value="5"/>
<variable units="millimolar" name="K_mCa" initial_value="0.002"/>
<variable units="dimensionless" name="p" initial_value="0.785"/>
<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="nanoA" public_interface="in" name="i_Ca_b"/>
<variable units="nanoA" public_interface="in" name="i_siCa"/>
<variable units="nanoA" 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/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="mA_nA">1</cn>
<ci>tau_up</ci>
<ci>Ca_up_max</ci>
</apply>
</apply>
<ci>Cai</ci>
<apply>
<minus/>
<ci>Ca_up_max</ci>
<ci>Ca_up</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_tr</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="mA_nA">1</cn>
<ci>tau_rep</ci>
</apply>
</apply>
<ci>p</ci>
<apply>
<minus/>
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>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/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="mA_nA">1</cn>
<ci>tau_rel</ci>
</apply>
</apply>
<ci>Ca_rel</ci>
<apply>
<power/>
<ci>Cai</ci>
<ci>rCa</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Cai</ci>
<ci>rCa</ci>
</apply>
<apply>
<power/>
<ci>K_mCa</ci>
<ci>rCa</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_p</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>p</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_p</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_nA">1</cn>
<apply>
<minus/>
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_up</ci>
<apply>
<times/>
<ci>Vi</ci>
<cn cellml:units="dimensionless">0.05</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_nA">1</cn>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_rel</ci>
<apply>
<times/>
<ci>Vi</ci>
<cn cellml:units="dimensionless">0.02</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cai</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_nA">1</cn>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_siCa</ci>
<ci>i_Ca_b</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn 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>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_potassium_concentration">
<variable units="millimolar" public_interface="out" name="Kc" initial_value="3"/>
<variable units="micrometre3" name="V_e" initial_value="0.00016077"/>
<variable units="millimolar" name="Kb" initial_value="3"/>
<variable units="nanoA" public_interface="out" name="i_mK"/>
<variable units="per_second" name="pf" initial_value="1"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="nanoA" public_interface="in" name="i_K1"/>
<variable units="nanoA" public_interface="in" name="i_K"/>
<variable units="nanoA" public_interface="in" name="i_fK"/>
<variable units="nanoA" public_interface="in" name="i_siK"/>
<variable units="nanoA" public_interface="in" name="i_p"/>
<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>Kc</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>pf</ci>
</apply>
<apply>
<minus/>
<ci>Kc</ci>
<ci>Kb</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_nA">1</cn>
<ci>i_mK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_e</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_potassium_concentration">
<variable units="millimolar" public_interface="out" name="Ki" initial_value="140"/>
<variable units="micrometre3" public_interface="in" name="Vi"/>
<variable units="nanoA" public_interface="in" 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/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ki</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_nA">1</cn>
</apply>
<ci>i_mK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="litre_micrometre3">1</cn>
<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="extracellular_potassium_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="RTONF" variable_1="RTONF"/>
<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="RTONF" variable_1="RTONF"/>
<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="RTONF" variable_1="RTONF"/>
<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="RTONF" variable_1="RTONF"/>
</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="RTONF" variable_1="RTONF"/>
</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="RTONF" variable_1="RTONF"/>
</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="extracellular_potassium_concentration"/>
<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"/>
<map_variables variable_2="i_fK" variable_1="i_fK"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</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"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
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