- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-05-26 22:26:05+12:00
- Desc:
- Added citation info and fixed metadata.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/stewart_aslanidi_noble_noble_boyett_zhang_2009/rawfile/b2fead7da30a1ba8797b179f15fbc8e7c71eb0b1/stewart_aslanidi_noble_noble_boyett_zhang_2009.cellml
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<!--
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COR (0.9.31.1027)
Copyright 2002-2008 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.CellML.org/
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<surname>Noble</surname>
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<title>Model Status</title>
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This CellML version of the model has been checked in COR and OpenCell. The units are consistent and the model runs to recreate the published results.
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In the paper described here, Philip Stewart and colleagues present a details of their newly developed model for the human Purkinje cell including validation against experimental data. Ionic mechanisms underlying the heterogeneity between
the Purkinje fibre and ventricular action potentials in humans and other species
were analysed. The newly developed Purkinje fibre cell model adds a new member
to the family of human cardiac cell models developed previously for the sino-atrial
node, atrial and ventricular cells, which can be incorporated into an anatomical
model of human heart with details of its electrophysiological heterogeneity and
anatomical complexity.
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The original paper reference is cited below:
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<para>
Mathematical models of the electrical action potential of Purkinje fibre cells, Philip Stewart, Oleg V. Aslanidi, Denis Noble, Penelope J. Noble, Mark R. Boyett, and Henggui Zhang, 2009, <emphasis>Philosophical Transactions of the Royal Society</emphasis>, 367, 2225-2255.
<ulink url="http://www.ncbi.nlm.nih.gov/pubmed/19414454">PubMed ID: 19414454</ulink>
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<caption>A schematic diagram describing the ion movement across the cell surface membrane and the sarcoplasmic reticulum, which are described by the Stewart et al. 2009 mathematical model of the human Purkinje fibres.</caption>
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<cn cellml:units="dimensionless">1.12</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xr2</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xr2</ci>
<ci>beta_xr2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xr2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>xr2_inf</ci>
<ci>Xr2</ci>
</apply>
<ci>tau_xr2</ci>
</apply>
</apply>
</math>
</component>
<component name="slow_time_dependent_potassium_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Ks"/>
<variable units="nanoS_per_picoF" name="g_Ks" initial_value="0.2352"/>
<variable units="millivolt" public_interface="in" name="E_Ks"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="Xs"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<apply>
<power/>
<ci>Xs</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ks</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_time_dependent_potassium_current_Xs_gate">
<variable units="dimensionless" public_interface="out" name="Xs" initial_value="0.0591727476586368"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="xs_inf"/>
<variable units="dimensionless" name="alpha_xs"/>
<variable units="dimensionless" name="beta_xs"/>
<variable units="millisecond" name="tau_xs"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>xs_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">14</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_xs</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1400</cn>
<apply>
<root/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_xs</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xs</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xs</ci>
<ci>beta_xs</ci>
</apply>
<cn cellml:units="millisecond">80</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xs</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>xs_inf</ci>
<ci>Xs</ci>
</apply>
<ci>tau_xs</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_Na"/>
<variable units="nanoS_per_picoF" name="g_Na" initial_value="130.5744"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<variable units="dimensionless" private_interface="in" name="j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Na</ci>
<apply>
<times/>
<ci>g_Na</ci>
<apply>
<power/>
<ci>m</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<ci>j</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0145683559378387"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="m_inf"/>
<variable units="dimensionless" name="alpha_m"/>
<variable units="dimensionless" name="beta_m"/>
<variable units="millisecond" name="tau_m"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>m_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">56.86</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">9.03</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<cn cellml:units="millivolt">200</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_m</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_m</ci>
<ci>beta_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>m_inf</ci>
<ci>m</ci>
</apply>
<ci>tau_m</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.227796287677146"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="h_inf"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<variable units="millisecond" name="tau_h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<cn cellml:units="millivolt">7.43</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_h</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.057</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">80</cn>
</apply>
</apply>
<cn cellml:units="millivolt">6.8</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond">2.7</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.079</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">310000</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.3485</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.77</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.13</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10.66</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">11.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_h</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_h</ci>
<ci>beta_h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>h_inf</ci>
<ci>h</ci>
</apply>
<ci>tau_h</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_j_gate">
<variable units="dimensionless" public_interface="out" name="j" initial_value="0.042752581290848"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="j_inf"/>
<variable units="per_millisecond" name="alpha_j"/>
<variable units="per_millisecond" name="beta_j"/>
<variable units="millisecond" name="tau_j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>j_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<cn cellml:units="millivolt">7.43</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_j</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millisecond">25428</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.2444</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">6.948e-6</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.04391</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37.78</cn>
</apply>
</apply>
<cn cellml:units="millivolt">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.311</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">79.23</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_j</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.02424</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.01052</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.1378</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40.14</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.6</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.057</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</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">32</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_j</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_j</ci>
<ci>beta_j</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>j</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>j_inf</ci>
<ci>j</ci>
</apply>
<ci>tau_j</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_b_Na"/>
<variable units="nanoS_per_picoF" name="g_bna" initial_value="0.00029"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_bna</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_CaL"/>
<variable units="litre_per_farad_second" name="g_CaL" initial_value="3.98e-5"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Ca_ss"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" public_interface="out" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f2"/>
<variable units="dimensionless" private_interface="in" name="fCass"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_CaL</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_CaL</ci>
<ci>d</ci>
<ci>f</ci>
<ci>f2</ci>
<ci>fCass</ci>
<cn cellml:units="dimensionless">4</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<apply>
<power/>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.25</cn>
<ci>Ca_ss</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>Ca_o</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.000135998943798924"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="d_inf"/>
<variable units="dimensionless" name="alpha_d"/>
<variable units="dimensionless" name="beta_d"/>
<variable units="millisecond" name="gamma_d"/>
<variable units="millisecond" name="tau_d"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>d_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">8</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">7.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">35</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_d</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">50</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_d</ci>
<ci>beta_d</ci>
</apply>
<ci>gamma_d</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_inf</ci>
<ci>d</ci>
</apply>
<ci>tau_d</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.522414966076568"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="f_inf"/>
<variable units="millisecond" name="tau_f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_inf</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">20</cn>
</apply>
<cn cellml:units="millivolt">7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1102.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">27</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">225</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">200</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">13</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">180</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">20</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_inf</ci>
<ci>f</ci>
</apply>
<ci>tau_f</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_f2_gate">
<variable units="dimensionless" public_interface="out" name="f2" initial_value="0.771494632989322"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="f2_inf"/>
<variable units="millisecond" name="tau_f2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f2_inf</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.67</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">7</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.33</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f2</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">562</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">27</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">240</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">31</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">80</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f2_inf</ci>
<ci>f2</ci>
</apply>
<ci>tau_f2</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_fCass_gate">
<variable units="dimensionless" public_interface="out" name="fCass" initial_value="0.977536882751221"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="fCass_inf"/>
<variable units="millisecond" name="tau_fCass"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>fCass_inf</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.6</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">0.05</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.4</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_fCass</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond">80</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">0.05</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">2</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCass</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>fCass_inf</ci>
<ci>fCass</ci>
</apply>
<ci>tau_fCass</ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_b_Ca"/>
<variable units="nanoS_per_picoF" name="g_bca" initial_value="0.000592"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Ca</ci>
<apply>
<times/>
<ci>g_bca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_to"/>
<variable units="nanoS_per_picoF" name="g_to" initial_value="0.08184"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="dimensionless" private_interface="in" name="s"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<ci>r</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_s_gate">
<variable units="dimensionless" public_interface="out" name="s" initial_value="0.857244799993594"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="s_inf"/>
<variable units="millisecond" name="tau_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s_inf</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">27</cn>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">85</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">25</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">320</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">42</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_inf</ci>
<ci>s</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="0.00081180715479983"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" name="r_inf"/>
<variable units="millisecond" name="tau_r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">20</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">10.45</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">1800</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">7.3</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_inf</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_sus"/>
<variable units="nanoS_per_picoF" name="g_sus" initial_value="0.0227"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" name="a"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_sus</ci>
<apply>
<times/>
<ci>g_sus</ci>
<ci>a</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>a</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_NaK"/>
<variable units="picoA_per_picoF" name="P_NaK" initial_value="2.724"/>
<variable units="millimolar" name="K_mk" initial_value="1"/>
<variable units="millimolar" name="K_mNa" initial_value="40"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>P_NaK</ci>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_mk</ci>
</apply>
</apply>
<ci>Na_i</ci>
</apply>
<apply>
<plus/>
<ci>Na_i</ci>
<ci>K_mNa</ci>
</apply>
</apply>
<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">0.0353</cn>
<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>
</apply>
</math>
</component>
<component name="sodium_calcium_exchanger_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_NaCa"/>
<variable units="picoA_per_picoF" name="K_NaCa" initial_value="1000"/>
<variable units="dimensionless" name="K_sat" initial_value="0.1"/>
<variable units="dimensionless" name="alpha" initial_value="2.5"/>
<variable units="dimensionless" name="gamma" initial_value="0.35"/>
<variable units="millimolar" name="Km_Ca" initial_value="1.38"/>
<variable units="millimolar" name="Km_Nai" initial_value="87.5"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<ci>alpha</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci>Km_Nai</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>Km_Ca</ci>
<ci>Ca_o</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_sat</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_p_Ca"/>
<variable units="picoA_per_picoF" name="g_pCa" initial_value="0.1238"/>
<variable units="millimolar" name="K_pCa" initial_value="0.0005"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_Ca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pCa</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>K_pCa</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_pump_current">
<variable units="picoA_per_picoF" public_interface="out" name="i_p_K"/>
<variable units="nanoS_per_picoF" name="g_pK" initial_value="0.0146"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_K</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pK</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5.98</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_dynamics">
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="0.000171796816765762"/>
<variable units="millimolar" public_interface="out" name="Ca_o" initial_value="2"/>
<variable units="millimolar" name="Ca_SR" initial_value="3.26782829783572"/>
<variable units="millimolar" public_interface="out" name="Ca_ss" initial_value="0.00067021664481563"/>
<variable units="millimolar_per_millisecond" name="i_rel"/>
<variable units="millimolar_per_millisecond" name="i_up"/>
<variable units="millimolar_per_millisecond" name="i_leak"/>
<variable units="millimolar_per_millisecond" name="i_xfer"/>
<variable units="dimensionless" name="O"/>
<variable units="dimensionless" name="R_prime" initial_value="0.82150415298243"/>
<variable units="per_millimolar2_per_millisecond" name="k1"/>
<variable units="per_millimolar_per_millisecond" name="k2"/>
<variable units="per_millimolar2_per_millisecond" name="k1_prime" initial_value="0.15"/>
<variable units="per_millimolar_per_millisecond" name="k2_prime" initial_value="0.045"/>
<variable units="per_millisecond" name="k3" initial_value="0.06"/>
<variable units="per_millisecond" name="k4" initial_value="0.005"/>
<variable units="millimolar" name="EC" initial_value="1.5"/>
<variable units="dimensionless" name="max_sr" initial_value="2.5"/>
<variable units="dimensionless" name="min_sr" initial_value="1"/>
<variable units="dimensionless" name="kcasr"/>
<variable units="per_millisecond" name="V_rel" initial_value="0.102"/>
<variable units="per_millisecond" name="V_xfer" initial_value="0.0038"/>
<variable units="millimolar" name="K_up" initial_value="0.00025"/>
<variable units="per_millisecond" name="V_leak" initial_value="0.00036"/>
<variable units="millimolar_per_millisecond" name="Vmax_up" initial_value="0.006375"/>
<variable units="dimensionless" name="Ca_i_bufc"/>
<variable units="dimensionless" name="Ca_sr_bufsr"/>
<variable units="dimensionless" name="Ca_ss_bufss"/>
<variable units="millimolar" name="Buf_c" initial_value="0.2"/>
<variable units="millimolar" name="K_buf_c" initial_value="0.001"/>
<variable units="millimolar" name="Buf_sr" initial_value="10"/>
<variable units="millimolar" name="K_buf_sr" initial_value="0.3"/>
<variable units="millimolar" name="Buf_ss" initial_value="0.4"/>
<variable units="millimolar" name="K_buf_ss" initial_value="0.00025"/>
<variable units="micrometre3" name="V_sr" initial_value="0.001094"/>
<variable units="micrometre3" name="V_ss" initial_value="5.468e-5"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="micrometre3" public_interface="in" name="V_c"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="dimensionless" public_interface="in" name="d"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF" public_interface="in" name="Cm"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_CaL"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_p_Ca"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_b_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<ci>V_rel</ci>
<ci>O</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_ss</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<ci>Vmax_up</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<power/>
<ci>K_up</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_leak</ci>
<apply>
<times/>
<ci>V_leak</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_xfer</ci>
<apply>
<times/>
<ci>V_xfer</ci>
<apply>
<minus/>
<ci>Ca_ss</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>O</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k1</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>R_prime</ci>
</apply>
<apply>
<plus/>
<ci>k3</ci>
<apply>
<times/>
<ci>k1</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>R_prime</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2</ci>
</apply>
<ci>Ca_ss</ci>
<ci>R_prime</ci>
</apply>
<apply>
<times/>
<ci>k4</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>R_prime</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k1</ci>
<apply>
<divide/>
<ci>k1_prime</ci>
<ci>kcasr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k2</ci>
<apply>
<times/>
<ci>k2_prime</ci>
<ci>kcasr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>kcasr</ci>
<apply>
<minus/>
<ci>max_sr</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>max_sr</ci>
<ci>min_sr</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>EC</ci>
<ci>Ca_SR</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ca_i_bufc</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_c</ci>
<ci>K_buf_c</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>K_buf_c</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ca_sr_bufsr</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_sr</ci>
<ci>K_buf_sr</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_SR</ci>
<ci>K_buf_sr</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ca_ss_bufss</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_ss</ci>
<ci>K_buf_ss</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_ss</ci>
<ci>K_buf_ss</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>Ca_i_bufc</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>i_leak</ci>
<ci>i_up</ci>
</apply>
<ci>V_sr</ci>
</apply>
<ci>V_c</ci>
</apply>
<ci>i_xfer</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_b_Ca</ci>
<ci>i_p_Ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_SR</ci>
</apply>
<apply>
<times/>
<ci>Ca_sr_bufsr</ci>
<apply>
<minus/>
<ci>i_up</ci>
<apply>
<plus/>
<ci>i_rel</ci>
<ci>i_leak</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_ss</ci>
</apply>
<apply>
<times/>
<ci>Ca_ss_bufss</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<ci>i_CaL</ci>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_ss</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i_rel</ci>
<ci>V_sr</ci>
</apply>
<ci>V_ss</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i_xfer</ci>
<ci>V_c</ci>
</apply>
<ci>V_ss</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_dynamics">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="8.60640226508088"/>
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="140"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF" public_interface="in" name="Cm"/>
<variable units="micrometre3" public_interface="in" name="V_c"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_b_Na"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_f_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_b_Na</ci>
<ci>i_f_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component>
<component name="potassium_dynamics">
<variable units="millimolar" public_interface="out" name="K_i" initial_value="136.930478505585"/>
<variable units="millimolar" public_interface="out" name="K_o" initial_value="5.4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF" public_interface="in" name="Cm"/>
<variable units="micrometre3" public_interface="in" name="V_c"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_K1"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_to"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_sus"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Kr"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_Ks"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_p_K"/>
<variable units="picoA_per_picoF" public_interface="in" name="i_f_K"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_K1</ci>
<ci>i_to</ci>
<ci>i_f_K</ci>
<ci>i_sus</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
<ci>i_p_K</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_f2_gate"/>
<component_ref component="L_type_Ca_current_fCass_gate"/>
</component_ref>
<component_ref component="inward_rectifier_potassium_current"/>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref component="rapid_time_dependent_potassium_current_Xr2_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs_gate"/>
</component_ref>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="hyperpolarization_activated_current">
<component_ref component="hyperpolarization_activated_current_y_gate"/>
</component_ref>
<component_ref component="sustained_outward_current"/>
<component_ref component="sodium_potassium_pump_current"/>
<component_ref component="sodium_calcium_exchanger_current"/>
<component_ref component="calcium_pump_current"/>
<component_ref component="potassium_pump_current"/>
<component_ref component="calcium_dynamics"/>
<component_ref component="sodium_dynamics"/>
<component_ref component="potassium_dynamics"/>
<component_ref component="reversal_potentials"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_f2_gate"/>
<component_ref component="L_type_Ca_current_fCass_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref component="rapid_time_dependent_potassium_current_Xr2_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs_gate"/>
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="hyperpolarization_activated_current">
<component_ref component="hyperpolarization_activated_current_y_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="reversal_potentials"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="hyperpolarization_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="inward_rectifier_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_calcium_exchanger_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="potassium_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="reversal_potentials" component_1="membrane"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
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Mathematical models of the electrical action potential of Purkinje fibre cells
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