- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-07-08 05:16:38+12:00
- Desc:
- Removed redundant old versions of the model. Updated the documentation of the remaining four models and added meaningful names to the metadata.
- Permanent Source URI:
- http://models.cellml.org/workspace/pandit_clark_giles_demir_2001/rawfile/03f7147d47aa58c3fc524ab0e7340c6a67ee2e34/pandit_clark_giles_demir_2001_endocardial_cell.cellml
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<!--
This CellML file was generated on 05/11/2007 at 19:52:01 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 endocardial cell. The model has been checked in COR, OpenCell 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>
ABSTRACT: Mathematical models were developed to reconstruct the action potentials (AP) recorded in epicardial and endocardial myocytes isolated from the adult rat left ventricle. The main goal was to obtain additional insight into the ionic mechanisms responsible for the transmural AP heterogeneity. The simulation results support the hypothesis that the smaller density and the slower reactivation kinetics of the Ca(2+)-independent transient outward K(+) current (I(t)) in the endocardial myocytes can account for the longer action potential duration (APD), and more prominent rate dependence in that cell type. The larger density of the Na(+) current (I(Na)) in the endocardial myocytes results in a faster upstroke (dV/dt(max)). This, in addition to the smaller magnitude of I(t), is responsible for the larger peak overshoot of the simulated endocardial AP. The prolonged APD in the endocardial cell also leads to an enhanced amplitude of the sustained K(+) current (I(ss)), and a larger influx of Ca(2+) ions via the L-type Ca(2+) current (I(CaL)). The latter results in an increased sarcoplasmic reticulum (SR) load, which is mainly responsible for the higher peak systolic value of the Ca(2+) transient [Ca(2+)](i), and the resultant increase in the Na(+)-Ca(2+) exchanger (I(NaCa)) activity, associated with the simulated endocardial AP. In combination, these calculations provide novel, quantitative insights into the repolarization process and its naturally occurring transmural variations in the rat left ventricle.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A Mathematical Model of Action Potential Heterogeneity in Adult Rat Left Ventricular Myocytes, Sandeep V. Pandit, Robert B. Clark, Wayne R. Giles and Semahat S. Demir, 2001, <emphasis>Biophysical Journal</emphasis>, 81, 3029-3051. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/11720973">PubMed ID: 11720973</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
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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="g_t_endo" units="microS"/>
<variable name="a_endo" units="dimensionless" initial_value="0.583"/>
<variable name="b_endo" units="dimensionless" initial_value="0.417"/>
<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>g_t_endo</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.4647</cn>
<ci>g_t</ci>
</apply>
</apply>
<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_endo</ci>
<ci>r</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a_endo</ci>
<ci>s</ci>
</apply>
<apply>
<times/>
<ci>b_endo</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_endo" 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_endo</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">0.55</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">25</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second">0.049</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_endo</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_endo" 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_endo</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="second">3.3</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">0.049</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_endo</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="millimolar4_per_second" initial_value="12.15e12"/>
<variable name="k_a_minus" units="per_second" initial_value="576"/>
<variable name="k_b_plus" units="millimolar3_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/>
<ci>Ca_ss</ci>
<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/>
<ci>Ca_ss</ci>
<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/>
<ci>Ca_ss</ci>
<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/>
<ci>Ca_ss</ci>
<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="0.000000056"/>
<variable name="V_NSR" units="micro_litre" initial_value="0.000000504"/>
<variable name="V_SS" units="micro_litre" initial_value="0.0000000012"/>
<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="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"/>
<map_variables variable_1="i_Ca_L" variable_2="i_Ca_L"/>
<map_variables variable_1="Ca_ss" variable_2="Ca_ss"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="intracellular_ion_concentrations"/>
<map_variables variable_1="i_t" variable_2="i_t"/>
<map_variables variable_1="K_i" variable_2="K_i"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="steady_state_outward_K_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="inward_rectifier"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="hyperpolarisation_activated_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="background_currents"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="standard_ionic_concentrations"/>
<map_variables variable_1="K_o" variable_2="K_o"/>
</connection>
<connection>
<map_components component_1="steady_state_outward_K_current" component_2="intracellular_ion_concentrations"/>
<map_variables variable_1="i_ss" variable_2="i_ss"/>
</connection>
<connection>
<map_components component_1="inward_rectifier" component_2="intracellular_ion_concentrations"/>
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