- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2008-07-01 04:02:24+12:00
- Desc:
- committing version10 of pandit_clark_giles_demir_2001
- Permanent Source URI:
- http://models.cellml.org/workspace/pandit_clark_giles_demir_2001/rawfile/165a6747723716c6626461244350b04357522b55/pandit_clark_giles_demir_2001.cellml
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This CellML file was generated on 05/11/2007 at 19:52:40 using:
COR (0.9.31.801)
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>Adult Rat Left Ventricular Myocyte Model, 2001</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 CellML version of the model represents the epicardial cell. The model has been checked in COR, PCEnv and JSim and it runs in all three to recreate the published results. The units have been checked and are consistent. Thank you to Frank Sachse for his helpful feedback and careful code checking.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Over the past decade electrophysiological studies have revealed transmural heterogeneity, or differences in the action potential waveforms recorded in cells isolated from the epicardial and the endocardial tissues in the left ventricles of mammalian hearts.
</para>
<para>
The adult rat has been widely used as an experimental model to investigate the electrical heterogeneity in the left ventricle under normal conditions and pathophysiological states. From this biophysical, experimental data, derived from patch clamp experiments, Sandeep V. Pandit, Robert B. Clark, Wayne R. Giles and Semahat S. Demir have developed a mathematical model of action potential heterogeneity in adult rat left ventricular myocytes (see the figure below). The mathematical models for the epicardial and endocardial cells of the rat left ventricle are based on the classical formulation of Hodgkin and Huxley (please see the CellML version of The Hodgkin-Huxley Squid Axon Model, 1952 for more details), and are therefore similar to previous computational work carried out by this research group (see Demir <emphasis>et al.</emphasis> Sinoatrial Node Model 1994 and Demir <emphasis>et al.</emphasis> Sinoatrial Node Model 1999). The endocardial cell model is based on the epicardial formulation with only slight modifications in certain parameters and equations.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/81/6/3029">A Mathematical Model of Action Potential Heterogeneity in Adult Rat Left Ventricular Myocytes, </ulink>, Sandeep V. Pandit, Robert B. Clark, Wayne R. Giles and Semahat S. Demir, 2001, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 81, 3029-3051. (<ulink url="http://www.biophysj.org/cgi/content/full/81/6/3029">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/81/6/3029.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11720973&dopt=Abstract">PubMed ID: 11720973</ulink>
</para>
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<caption>A fluid compartment model of the rat epicardial/endocardial ventricular cell.</caption>
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<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>d_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">15.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.00305</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt2">0.0045</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">7</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="second">0.00105</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt2">0.002</cn>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">18</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.00025</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_infinity</ci>
<ci>d</ci>
</apply>
<ci>tau_d</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_11_gate">
<variable name="f_11" units="dimensionless" initial_value="0.9999529" public_interface="out"/>
<variable name="f_11_infinity" units="dimensionless"/>
<variable name="tau_f_11" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_11_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.7</cn>
</apply>
<cn cellml:units="millivolt">5.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_11</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.105</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45</cn>
</apply>
<cn cellml:units="millivolt">12</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="second">0.04</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">25</cn>
</apply>
<cn cellml:units="millivolt">25</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="second">0.015</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
<cn cellml:units="millivolt">25</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.0017</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_11</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_11_infinity</ci>
<ci>f_11</ci>
</apply>
<ci>tau_f_11</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_12_gate">
<variable name="f_12" units="dimensionless" initial_value="0.9999529" public_interface="out"/>
<variable name="f_12_infinity" units="dimensionless"/>
<variable name="tau_f_12" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_12_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.7</cn>
</apply>
<cn cellml:units="millivolt">5.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_12</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.041</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">47</cn>
</apply>
<cn cellml:units="millivolt">12</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="second">0.08</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">55</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="second">0.015</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
<cn cellml:units="millivolt">25</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.0017</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_12</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_12_infinity</ci>
<ci>f_12</ci>
</apply>
<ci>tau_f_12</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_Ca_inact_gate">
<variable name="Ca_inact" units="dimensionless" initial_value="0.9913102" public_interface="out"/>
<variable name="tau_Ca_inact" units="second" initial_value="0.009"/>
<variable name="Ca_inact_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_ss" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ca_inact_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">0.01</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_inact</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_inact_infinity</ci>
<ci>Ca_inact</ci>
</apply>
<ci>tau_Ca_inact</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current">
<variable name="i_t" units="nanoA" public_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="out"/>
<variable name="g_t" units="microS" initial_value="0.035"/>
<variable name="a" units="dimensionless" initial_value="0.886"/>
<variable name="b" units="dimensionless" initial_value="0.114"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="K_o" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="r" units="dimensionless" private_interface="in"/>
<variable name="s" units="dimensionless" private_interface="in"/>
<variable name="s_slow" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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>
<apply>
<eq/>
<ci>i_t</ci>
<apply>
<times/>
<ci>g_t</ci>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<ci>s</ci>
</apply>
<apply>
<times/>
<ci>b</ci>
<ci>s_slow</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_r_gate">
<variable name="r" units="dimensionless" initial_value="0.002191519" public_interface="out"/>
<variable name="tau_r" units="second"/>
<variable name="r_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10.6</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">11.42</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">45.16</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.03577</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">98.9</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">38</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_infinity</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s_gate">
<variable name="s" units="dimensionless" initial_value="0.9842542" public_interface="out"/>
<variable name="tau_s" units="second"/>
<variable name="s_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45.3</cn>
</apply>
<cn cellml:units="millivolt">6.8841</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.35</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">70</cn>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.035</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_infinity</ci>
<ci>s</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s_slow_gate">
<variable name="s_slow" units="dimensionless" initial_value="0.6421196" public_interface="out"/>
<variable name="tau_s_slow" units="second"/>
<variable name="s_slow_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s_slow_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45.3</cn>
</apply>
<cn cellml:units="millivolt">6.8841</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s_slow</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">3.7</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">70</cn>
</apply>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.035</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s_slow</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_slow_infinity</ci>
<ci>s_slow</ci>
</apply>
<ci>tau_s_slow</ci>
</apply>
</apply>
</math>
</component>
<component name="steady_state_outward_K_current">
<variable name="i_ss" units="nanoA" public_interface="out"/>
<variable name="g_ss" units="microS" initial_value="0.007"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="r_ss" units="dimensionless" private_interface="in"/>
<variable name="s_ss" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_ss</ci>
<apply>
<times/>
<ci>g_ss</ci>
<ci>r_ss</ci>
<ci>s_ss</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="steady_state_outward_K_current_r_ss_gate">
<variable name="r_ss" units="dimensionless" initial_value="0.002907171" public_interface="out"/>
<variable name="tau_r_ss" units="second"/>
<variable name="r_ss_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_ss_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">11.5</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">11.82</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r_ss</ci>
<apply>
<divide/>
<cn cellml:units="second">10</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">45.16</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.03577</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">98.9</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">38</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r_ss</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_ss_infinity</ci>
<ci>r_ss</ci>
</apply>
<ci>tau_r_ss</ci>
</apply>
</apply>
</math>
</component>
<component name="steady_state_outward_K_current_s_ss_gate">
<variable name="s_ss" units="dimensionless" initial_value="0.3142767" public_interface="out"/>
<variable name="tau_s_ss" units="second"/>
<variable name="s_ss_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s_ss_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">87.5</cn>
</apply>
<cn cellml:units="millivolt">10.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s_ss</ci>
<cn cellml:units="second">2.1</cn>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s_ss</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_ss_infinity</ci>
<ci>s_ss</ci>
</apply>
<ci>tau_s_ss</ci>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier">
<variable name="i_K1" units="nanoA" public_interface="out"/>
<variable name="g_K1" units="microS" initial_value="0.024"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="K_o" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="nanoA">48</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37</cn>
</apply>
<cn cellml:units="millivolt">25</cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="nanoA">10</cn>
</apply>
<cn cellml:units="dimensionless">0.0001</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<apply>
<plus/>
<ci>E_K</ci>
<cn cellml:units="millivolt">76.77</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<apply>
<minus/>
<ci>V</ci>
<apply>
<plus/>
<ci>E_K</ci>
<cn cellml:units="millivolt">1.73</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.613</cn>
<ci>F</ci>
<apply>
<minus/>
<ci>V</ci>
<apply>
<plus/>
<ci>E_K</ci>
<cn cellml:units="millivolt">1.73</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>K_o</ci>
<cn cellml:units="millimolar">0.9988</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millimolar">0.124</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current">
<variable name="i_f" units="nanoA" public_interface="out"/>
<variable name="i_f_Na" units="nanoA" public_interface="out"/>
<variable name="i_f_K" units="nanoA" public_interface="out"/>
<variable name="g_f" units="microS" initial_value="0.00145"/>
<variable name="f_Na" units="dimensionless" initial_value="0.2"/>
<variable name="f_K" units="dimensionless"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="E_Na" units="millivolt" public_interface="in"/>
<variable name="y" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_K</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f_Na</ci>
<apply>
<times/>
<ci>g_f</ci>
<ci>y</ci>
<ci>f_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f_K</ci>
<apply>
<times/>
<ci>g_f</ci>
<ci>y</ci>
<ci>f_K</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f</ci>
<apply>
<plus/>
<ci>i_f_Na</ci>
<ci>i_f_K</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current_y_gate">
<variable name="y" units="dimensionless" initial_value="0.003578708" public_interface="out"/>
<variable name="tau_y" units="second"/>
<variable name="y_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>y_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">138.6</cn>
</apply>
<cn cellml:units="millivolt">10.48</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_y</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.11885</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">80</cn>
</apply>
<cn cellml:units="millivolt">28.37</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5623</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">80</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">14.19</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>y_infinity</ci>
<ci>y</ci>
</apply>
<ci>tau_y</ci>
</apply>
</apply>
</math>
</component>
<component name="background_currents">
<variable name="i_B" units="nanoA" public_interface="out"/>
<variable name="i_B_Na" units="nanoA" public_interface="out"/>
<variable name="i_B_Ca" units="nanoA" public_interface="out"/>
<variable name="i_B_K" units="nanoA" public_interface="out"/>
<variable name="g_B_Na" units="microS" initial_value="0.00008015"/>
<variable name="g_B_Ca" units="microS" initial_value="0.0000324"/>
<variable name="g_B_K" units="microS" initial_value="0.000138"/>
<variable name="E_Ca" units="millivolt"/>
<variable name="E_Na" units="millivolt" public_interface="in"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="Ca_o" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_o</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_Na</ci>
<apply>
<times/>
<ci>g_B_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_Ca</ci>
<apply>
<times/>
<ci>g_B_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_K</ci>
<apply>
<times/>
<ci>g_B_K</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B</ci>
<apply>
<plus/>
<ci>i_B_Na</ci>
<ci>i_B_Ca</ci>
<ci>i_B_K</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable name="i_NaK" units="nanoA" public_interface="out"/>
<variable name="i_NaK_max" units="nanoA" initial_value="0.08"/>
<variable name="K_m_K" units="millimolar" initial_value="1.5"/>
<variable name="K_m_Na" units="millimolar" initial_value="10"/>
<variable name="sigma" units="dimensionless"/>
<variable name="K_o" units="millimolar" public_interface="in"/>
<variable name="Na_o" units="millimolar" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="R" units="millijoule_per_mole_kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>sigma</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Na_o</ci>
<cn cellml:units="millimolar">67.3</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<cn cellml:units="dimensionless">7</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>i_NaK_max</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1245</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0365</cn>
<ci>sigma</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_m_K</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>K_m_Na</ci>
<ci>Na_i</ci>
</apply>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump_current">
<variable name="i_Ca_P" units="nanoA" public_interface="out"/>
<variable name="i_Ca_P_max" units="nanoA" initial_value="0.004"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca_P</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_Ca_P_max</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.0004</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_ion_exchanger_current">
<variable name="i_NaCa" units="nanoA" public_interface="out"/>
<variable name="K_NaCa" units="nanoA_millimolar_4" initial_value="0.000009984"/>
<variable name="d_NaCa" units="millimolar_4" initial_value="0.0001"/>
<variable name="gamma_NaCa" units="dimensionless" initial_value="0.5"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_o" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="Ca_o" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.03743</cn>
<ci>V</ci>
<ci>gamma_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.03743</cn>
<ci>V</ci>
<apply>
<minus/>
<ci>gamma_NaCa</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>d_NaCa</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SR_Ca_release_channel">
<variable name="J_rel" units="millimolar_per_second" public_interface="out"/>
<variable name="v1" units="per_second" initial_value="1.8e3"/>
<variable name="k_a_plus" units="per_second" initial_value="12.15e12"/>
<variable name="k_a_minus" units="per_second" initial_value="576"/>
<variable name="k_b_plus" units="per_second" initial_value="4.05e9"/>
<variable name="k_b_minus" units="per_second" initial_value="1930"/>
<variable name="k_c_plus" units="per_second" initial_value="100"/>
<variable name="k_c_minus" units="per_second" initial_value="0.8"/>
<variable name="P_O1" units="dimensionless" initial_value="0.0004327548"/>
<variable name="P_O2" units="dimensionless" initial_value="0.000000000606254"/>
<variable name="P_C1" units="dimensionless" initial_value="0.6348229"/>
<variable name="P_C2" units="dimensionless" initial_value="0.3647471"/>
<variable name="n" units="dimensionless" initial_value="4"/>
<variable name="m" units="dimensionless" initial_value="3"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_ss" units="millimolar" public_interface="in"/>
<variable name="Ca_JSR" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_C1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k_a_plus</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<ci>n</ci>
</apply>
<ci>P_C1</ci>
</apply>
<apply>
<times/>
<ci>k_a_minus</ci>
<ci>P_O1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_O1</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_a_plus</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<ci>n</ci>
</apply>
<ci>P_C1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k_a_minus</ci>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_b_plus</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<ci>m</ci>
</apply>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_c_plus</ci>
<ci>P_O1</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>k_b_minus</ci>
<ci>P_O2</ci>
</apply>
<apply>
<times/>
<ci>k_c_minus</ci>
<ci>P_C2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_O2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_b_plus</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<ci>m</ci>
</apply>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_b_minus</ci>
<ci>P_O2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_C2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_c_plus</ci>
<ci>P_O1</ci>
</apply>
<apply>
<times/>
<ci>k_c_minus</ci>
<ci>P_C2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_rel</ci>
<apply>
<times/>
<ci>v1</ci>
<apply>
<plus/>
<ci>P_O1</ci>
<ci>P_O2</ci>
</apply>
<apply>
<minus/>
<ci>Ca_JSR</ci>
<ci>Ca_ss</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SERCA2a_pump">
<variable name="J_up" units="millimolar_per_second" public_interface="out"/>
<variable name="K_fb" units="millimolar" initial_value="0.000168"/>
<variable name="K_rb" units="millimolar" initial_value="3.29"/>
<variable name="fb" units="dimensionless"/>
<variable name="rb" units="dimensionless"/>
<variable name="Vmaxf" units="millimolar_per_second" initial_value="0.04"/>
<variable name="Vmaxr" units="millimolar_per_second" initial_value="0.9"/>
<variable name="K_SR" units="dimensionless" initial_value="1"/>
<variable name="N_fb" units="dimensionless" initial_value="1.2"/>
<variable name="N_rb" units="dimensionless" initial_value="1"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="Ca_NSR" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>fb</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>K_fb</ci>
</apply>
<ci>N_fb</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rb</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_NSR</ci>
<ci>K_rb</ci>
</apply>
<ci>N_rb</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_up</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_SR</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>Vmaxf</ci>
<ci>fb</ci>
</apply>
<apply>
<times/>
<ci>Vmaxr</ci>
<ci>rb</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>fb</ci>
<ci>rb</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_and_SR_Ca_fluxes">
<variable name="J_tr" units="millimolar_per_second" public_interface="out"/>
<variable name="J_xfer" units="millimolar_per_second" public_interface="out"/>
<variable name="J_trpn" units="millimolar_per_second" public_interface="out"/>
<variable name="tau_tr" units="second" initial_value="0.0005747"/>
<variable name="tau_xfer" units="second" initial_value="0.0267"/>
<variable name="HTRPNCa" units="millimolar" initial_value="1.394301e-1"/>
<variable name="LTRPNCa" units="millimolar" initial_value="5.1619e-3"/>
<variable name="J_HTRPNCa" units="millimolar_per_second"/>
<variable name="J_LTRPNCa" units="millimolar_per_second"/>
<variable name="HTRPN_tot" units="millimolar" initial_value="0.14"/>
<variable name="LTRPN_tot" units="millimolar" initial_value="0.07"/>
<variable name="k_htrpn_plus" units="per_millimolar_per_second" initial_value="200000"/>
<variable name="k_htrpn_minus" units="per_second" initial_value="0.066"/>
<variable name="k_ltrpn_plus" units="per_millimolar_per_second" initial_value="40000"/>
<variable name="k_ltrpn_minus" units="per_second" initial_value="40"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="Ca_ss" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="Ca_NSR" units="millimolar" public_interface="in"/>
<variable name="Ca_JSR" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_tr</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_NSR</ci>
<ci>Ca_JSR</ci>
</apply>
<ci>tau_tr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_xfer</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_ss</ci>
<ci>Ca_i</ci>
</apply>
<ci>tau_xfer</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_HTRPNCa</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_htrpn_plus</ci>
<ci>Ca_i</ci>
<apply>
<minus/>
<ci>HTRPN_tot</ci>
<ci>HTRPNCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_htrpn_minus</ci>
<ci>HTRPNCa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HTRPNCa</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_htrpn_plus</ci>
<ci>Ca_i</ci>
<apply>
<minus/>
<ci>HTRPN_tot</ci>
<ci>HTRPNCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_htrpn_minus</ci>
<ci>HTRPNCa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_LTRPNCa</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_ltrpn_plus</ci>
<ci>Ca_i</ci>
<apply>
<minus/>
<ci>LTRPN_tot</ci>
<ci>LTRPNCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_ltrpn_minus</ci>
<ci>LTRPNCa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>LTRPNCa</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_ltrpn_plus</ci>
<ci>Ca_i</ci>
<apply>
<minus/>
<ci>LTRPN_tot</ci>
<ci>LTRPNCa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_ltrpn_minus</ci>
<ci>LTRPNCa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_trpn</ci>
<apply>
<plus/>
<ci>J_HTRPNCa</ci>
<ci>J_LTRPNCa</ci>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable name="Na_i" units="millimolar" initial_value="10.73519" public_interface="out"/>
<variable name="Ca_i" units="millimolar" initial_value="0.00007901351" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="139.2751" public_interface="out"/>
<variable name="Ca_ss" units="millimolar" initial_value="0.00008737212" public_interface="out"/>
<variable name="Ca_JSR" units="millimolar" initial_value="0.06607948" public_interface="out"/>
<variable name="Ca_NSR" units="millimolar" initial_value="0.06600742" public_interface="out"/>
<variable name="V_myo" units="micro_litre" initial_value="0.00000936"/>
<variable name="V_JSR" units="micro_litre" initial_value="0.00000056"/>
<variable name="V_NSR" units="micro_litre" initial_value="0.00000504"/>
<variable name="V_SS" units="micro_litre" initial_value="0.000000012"/>
<variable name="K_mCMDN" units="millimolar" initial_value="0.00238"/>
<variable name="K_mCSQN" units="millimolar" initial_value="0.8"/>
<variable name="K_mEGTA" units="millimolar" initial_value="0.00015"/>
<variable name="CMDN_tot" units="millimolar" initial_value="0.05"/>
<variable name="CSQN_tot" units="millimolar" initial_value="15"/>
<variable name="EGTA_tot" units="millimolar" initial_value="10"/>
<variable name="beta_i" units="dimensionless"/>
<variable name="beta_SS" units="dimensionless"/>
<variable name="beta_JSR" units="dimensionless"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="i_Na" units="nanoA" public_interface="in"/>
<variable name="i_Ca_L" units="nanoA" public_interface="in"/>
<variable name="i_B_Na" units="nanoA" public_interface="in"/>
<variable name="i_NaCa" units="nanoA" public_interface="in"/>
<variable name="i_NaK" units="nanoA" public_interface="in"/>
<variable name="i_f_Na" units="nanoA" public_interface="in"/>
<variable name="i_f_K" units="nanoA" public_interface="in"/>
<variable name="i_B_K" units="nanoA" public_interface="in"/>
<variable name="i_K1" units="nanoA" public_interface="in"/>
<variable name="i_t" units="nanoA" public_interface="in"/>
<variable name="i_ss" units="nanoA" public_interface="in"/>
<variable name="i_Ca_P" units="nanoA" public_interface="in"/>
<variable name="i_B_Ca" units="nanoA" public_interface="in"/>
<variable name="J_up" units="millimolar_per_second" public_interface="in"/>
<variable name="J_rel" units="millimolar_per_second" public_interface="in"/>
<variable name="J_xfer" units="millimolar_per_second" public_interface="in"/>
<variable name="J_trpn" units="millimolar_per_second" public_interface="in"/>
<variable name="J_tr" units="millimolar_per_second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>beta_i</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>CMDN_tot</ci>
<ci>K_mCMDN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mCMDN</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>EGTA_tot</ci>
<ci>K_mEGTA</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mEGTA</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_SS</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>CMDN_tot</ci>
<ci>K_mCMDN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mCMDN</ci>
<ci>Ca_ss</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_JSR</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>CSQN_tot</ci>
<ci>K_mCSQN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>K_mCSQN</ci>
<ci>Ca_JSR</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>beta_i</ci>
<apply>
<minus/>
<ci>J_xfer</ci>
<apply>
<plus/>
<ci>J_up</ci>
<ci>J_trpn</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>i_B_Ca</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<ci>i_Ca_P</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_myo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_B_Na</ci>
<apply>
<times/>
<ci>i_NaCa</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>i_NaK</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>i_f_Na</ci>
</apply>
</apply>
<apply>
<times/>
<ci>V_myo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_ss</ci>
<ci>i_B_K</ci>
<ci>i_t</ci>
<ci>i_K1</ci>
<ci>i_f_K</ci>
<apply>
<times/>
<ci>i_NaK</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>V_myo</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_ss</ci>
</apply>
<apply>
<times/>
<ci>beta_SS</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_rel</ci>
<ci>V_JSR</ci>
</apply>
<ci>V_SS</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>J_xfer</ci>
<ci>V_myo</ci>
</apply>
<ci>V_SS</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>i_Ca_L</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_SS</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_JSR</ci>
</apply>
<apply>
<times/>
<ci>beta_JSR</ci>
<apply>
<minus/>
<ci>J_tr</ci>
<ci>J_rel</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_NSR</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_up</ci>
<ci>V_myo</ci>
</apply>
<ci>V_NSR</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>J_tr</ci>
<ci>V_JSR</ci>
</apply>
<ci>V_NSR</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="standard_ionic_concentrations">
<variable name="Na_o" units="millimolar" initial_value="140" public_interface="out"/>
<variable name="Ca_o" units="millimolar" initial_value="1.2" public_interface="out"/>
<variable name="K_o" units="millimolar" initial_value="5.4" public_interface="out"/>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h_gate"/>
<component_ref component="sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_11_gate"/>
<component_ref component="L_type_Ca_channel_f_12_gate"/>
<component_ref component="L_type_Ca_channel_Ca_inact_gate"/>
</component_ref>
<component_ref component="Ca_independent_transient_outward_K_current">
<component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_slow_gate"/>
</component_ref>
<component_ref component="steady_state_outward_K_current">
<component_ref component="steady_state_outward_K_current_r_ss_gate"/>
<component_ref component="steady_state_outward_K_current_s_ss_gate"/>
</component_ref>
<component_ref component="inward_rectifier"/>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
<component_ref component="background_currents"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sarcolemmal_calcium_pump_current"/>
<component_ref component="Na_Ca_ion_exchanger_current"/>
<component_ref component="SR_Ca_release_channel"/>
<component_ref component="SERCA2a_pump"/>
<component_ref component="intracellular_and_SR_Ca_fluxes"/>
<component_ref component="intracellular_ion_concentrations"/>
<component_ref component="standard_ionic_concentrations"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h_gate"/>
<component_ref component="sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_11_gate"/>
<component_ref component="L_type_Ca_channel_f_12_gate"/>
<component_ref component="L_type_Ca_channel_Ca_inact_gate"/>
</component_ref>
<component_ref component="Ca_independent_transient_outward_K_current">
<component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_slow_gate"/>
</component_ref>
<component_ref component="steady_state_outward_K_current">
<component_ref component="steady_state_outward_K_current_r_ss_gate"/>
<component_ref component="steady_state_outward_K_current_s_ss_gate"/>
</component_ref>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="L_type_Ca_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="steady_state_outward_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="inward_rectifier" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="hyperpolarisation_activated_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="background_currents" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_potassium_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sarcolemmal_calcium_pump_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Na_Ca_ion_exchanger_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="SR_Ca_release_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="SERCA2a_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="intracellular_and_SR_Ca_fluxes" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="L_type_Ca_channel"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Ca_L" variable_2="i_Ca_L"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Ca_independent_transient_outward_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_t" variable_2="i_t"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="steady_state_outward_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_ss" variable_2="i_ss"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="inward_rectifier"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="hyperpolarisation_activated_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_f" variable_2="i_f"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="background_currents"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_B" variable_2="i_B"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_potassium_pump"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sarcolemmal_calcium_pump_current"/>
<map_variables variable_1="i_Ca_P" variable_2="i_Ca_P"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Na_Ca_ion_exchanger_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="intracellular_ion_concentrations"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="sodium_current" component_2="intracellular_ion_concentrations"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
</connection>
<connection>
<map_components component_1="sodium_current" component_2="background_currents"/>
<map_variables variable_1="E_Na" variable_2="E_Na"/>
</connection>
<connection>
<map_components component_1="sodium_current" component_2="hyperpolarisation_activated_current"/>
<map_variables variable_1="E_Na" variable_2="E_Na"/>
</connection>
<connection>
<map_components component_1="sodium_current" component_2="standard_ionic_concentrations"/>
<map_variables variable_1="Na_o" variable_2="Na_o"/>
</connection>
<connection>
<map_components component_1="background_currents" component_2="standard_ionic_concentrations"/>
<map_variables variable_1="Ca_o" variable_2="Ca_o"/>
</connection>
<connection>
<map_components component_1="L_type_Ca_channel" component_2="intracellular_ion_concentrations"/>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#b6180be5-6086-486a-bdfb-a032cbf294a9">
<dc:creator rdf:resource="rdf:#8a4ae090-d825-41e4-9dea-095dc65a37e1"/>
<rdf:value>This version was created by Penny Noble of Oxford University and represents the EPICARDIAL CELL VARIANT. The model has been checked in COR, PCEnv and JSim and it runs in all three to recreate the published results. The units have been checked and are consistent. Thank you to Frank Sachse for his helpful feedback and careful code checking.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2ee4b150-2e99-4617-8c15-fb11b9a9cb12">
<dcterms:W3CDTF>2007-11-01T12:18:01+13:00</dcterms:W3CDTF>
</rdf:Description>
</rdf:RDF>
</model>
