- Author:
- Dewan Sarwar <dsar941@UoA.auckland.ac.nz>
- Date:
- 2020-06-25 21:17:52+12:00
- Desc:
- annotations changed for mackenzie model
- Permanent Source URI:
- https://models.cellml.org/workspace/267/rawfile/92367a08b2bb9612257ef3f32b6823adf5e0d53b/SEDML/luo_rudy_1991_13.cellml
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<title>Luo-Rudy Mammalian Ventricular Model I 1991</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
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<section id="sec_status">
<title>Model Status</title>
<para>This model has been curated and unit checked and is known to replicate the published results in OpenCell and COR.</para>
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>In 1991, Ching-hsing Luo and Yoram Rudy published a mathematical model of the ventricular cardiac action potential. This original model is the first of the two Luo-Rudy models, and it has subsequently come to be known as the Luo-Rudy I model. It is a significant update of the Beeler-Reuter mammalian ventricular model (1977) (see the figure below), and like the the Beeler-Reuter model, the Luo-Rudy I model uses Hodgkin-Huxley type equations to calculate ionic currents.</para>
<para>The complete original paper reference is cited below:</para>
<para>
A Model of the Ventricular Cardiac Action Potential - Depolarisation, Repolarisation and Their Interaction, Ching-hsing Luo and Yoram Rudy, 1991
<emphasis>Circulation Research</emphasis>
, 68, 1501-1526.
<ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=1709839&dopt=Abstract">PubMed ID: 1709839</ulink>
</para>
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<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the LR-I model.</caption>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">32</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>j</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_j</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>j</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_j</ci>
<ci>j</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current" cmeta:id="id_00028">
<variable cmeta:id="id_00030" name="i_si" public_interface="out" units="microA_per_cm2" />
<variable cmeta:id="id_00031" name="E_si" units="millivolt" />
<variable cmeta:id="slow_inward_current.time" name="time" public_interface="in" private_interface="out" units="millisecond" />
<variable cmeta:id="slow_inward_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="id_00029" name="Cai" public_interface="in" units="millimolar" />
<variable cmeta:id="slow_inward_current.d" name="d" private_interface="in" units="dimensionless" />
<variable cmeta:id="slow_inward_current.f" name="f" private_interface="in" units="dimensionless" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E_si</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">7.7</cn>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">13.0287</cn>
<apply>
<ln />
<apply>
<divide />
<ci>Cai</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_si</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="milliS_per_cm2">0.09</cn>
<ci>d</ci>
<ci>f</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_si</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_d_gate" cmeta:id="id_00026">
<variable cmeta:id="slow_inward_current_d_gate.d" initial_value="0.00302126301779861" name="d" public_interface="out" units="dimensionless" />
<variable cmeta:id="slow_inward_current_d_gate.alpha_d" name="alpha_d" units="per_millisecond" />
<variable cmeta:id="slow_inward_current_d_gate.beta_d" name="beta_d" units="per_millisecond" />
<variable cmeta:id="slow_inward_current_d_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="slow_inward_current_d_gate.time" name="time" public_interface="in" units="millisecond" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_d</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.095</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.01</cn>
</apply>
<apply>
<minus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.072</cn>
</apply>
<apply>
<minus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_d</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.07</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.017</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">44</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.05</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">44</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_d</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>d</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_d</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_f_gate" cmeta:id="id_00027">
<variable cmeta:id="slow_inward_current_f_gate.f" initial_value="0.999967936476325" name="f" public_interface="out" units="dimensionless" />
<variable cmeta:id="slow_inward_current_f_gate.alpha_f" name="alpha_f" units="per_millisecond" />
<variable cmeta:id="slow_inward_current_f_gate.beta_f" name="beta_f" units="per_millisecond" />
<variable cmeta:id="slow_inward_current_f_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="slow_inward_current_f_gate.time" name="time" public_interface="in" units="millisecond" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_f</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.012</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.008</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">28</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.15</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">28</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_f</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.0065</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.02</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_f</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>f</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_f</ci>
<ci>f</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current" cmeta:id="id_00007">
<variable cmeta:id="id_00034" name="i_K" public_interface="out" units="microA_per_cm2" />
<variable cmeta:id="id_00033" name="g_K" units="milliS_per_cm2" />
<variable cmeta:id="id_00032" name="E_K" units="millivolt" />
<variable cmeta:id="time_dependent_potassium_current.PR_NaK" initial_value="0.01833" name="PR_NaK" units="dimensionless" />
<variable cmeta:id="time_dependent_potassium_current.time" name="time" public_interface="in" private_interface="out" units="millisecond" />
<variable cmeta:id="time_dependent_potassium_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="time_dependent_potassium_current.R" name="R" public_interface="in" units="joule_per_kilomole_kelvin" />
<variable cmeta:id="time_dependent_potassium_current.T" name="T" public_interface="in" units="kelvin" />
<variable cmeta:id="time_dependent_potassium_current.F" name="F" public_interface="in" units="coulomb_per_mole" />
<variable cmeta:id="id_00035" name="Ko" public_interface="in" units="millimolar" />
<variable cmeta:id="id_00036" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="id_00037" name="Nao" public_interface="in" units="millimolar" />
<variable cmeta:id="id_00038" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="time_dependent_potassium_current.X" name="X" private_interface="in" units="dimensionless" />
<variable cmeta:id="time_dependent_potassium_current.Xi" name="Xi" private_interface="in" units="dimensionless" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>g_K</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="milliS_per_cm2">0.282</cn>
<apply>
<root />
<apply>
<divide />
<ci>Ko</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">5.4</cn>
</apply>
</apply>
</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 />
<apply>
<plus />
<ci>Ko</ci>
<apply>
<times />
<ci>PR_NaK</ci>
<ci>Nao</ci>
</apply>
</apply>
<apply>
<plus />
<ci>Ki</ci>
<apply>
<times />
<ci>PR_NaK</ci>
<ci>Nai</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_K</ci>
<apply>
<times />
<ci>g_K</ci>
<ci>X</ci>
<ci>Xi</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current_X_gate" cmeta:id="id_00008">
<variable cmeta:id="time_dependent_potassium_current_X_gate.X" initial_value="0.0417603108167287" name="X" public_interface="out" units="dimensionless" />
<variable cmeta:id="time_dependent_potassium_current_X_gate.alpha_X" name="alpha_X" units="per_millisecond" />
<variable cmeta:id="time_dependent_potassium_current_X_gate.beta_X" name="beta_X" units="per_millisecond" />
<variable cmeta:id="time_dependent_potassium_current_X_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="time_dependent_potassium_current_X_gate.time" name="time" public_interface="in" units="millisecond" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_X</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.0005</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.083</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.057</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_X</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.0013</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.06</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.04</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>X</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_X</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>X</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_X</ci>
<ci>X</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current_Xi_gate" cmeta:id="id_00009">
<variable cmeta:id="time_dependent_potassium_current_Xi_gate.Xi" name="Xi" public_interface="out" units="dimensionless" />
<variable cmeta:id="time_dependent_potassium_current_Xi_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="time_dependent_potassium_current_Xi_gate.time" name="time" public_interface="in" units="millisecond" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>Xi</ci>
<piecewise>
<piece>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">2.837</cn>
<apply>
<minus />
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.04</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">77</cn>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<times />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">77</cn>
</apply>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.04</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">35</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt />
<ci>V</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">100</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="time_independent_potassium_current" cmeta:id="id_00010">
<variable cmeta:id="id_00039" name="i_K1" public_interface="out" units="microA_per_cm2" />
<variable cmeta:id="id_00040" name="E_K1" public_interface="out" private_interface="out" units="millivolt" />
<variable cmeta:id="id_00041" name="g_K1" units="milliS_per_cm2" />
<variable cmeta:id="time_independent_potassium_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="time_independent_potassium_current.Ko" name="Ko" public_interface="in" units="millimolar" />
<variable cmeta:id="time_independent_potassium_current.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="time_independent_potassium_current.R" name="R" public_interface="in" units="joule_per_kilomole_kelvin" />
<variable cmeta:id="time_independent_potassium_current.T" name="T" public_interface="in" units="kelvin" />
<variable cmeta:id="time_independent_potassium_current.F" name="F" public_interface="in" units="coulomb_per_mole" />
<variable cmeta:id="id_00047" name="K1_infinity" private_interface="in" units="dimensionless" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>g_K1</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="milliS_per_cm2">0.6047</cn>
<apply>
<root />
<apply>
<divide />
<ci>Ko</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">5.4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>E_K1</ci>
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln />
<apply>
<divide />
<ci>Ko</ci>
<ci>Ki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_K1</ci>
<apply>
<times />
<ci>g_K1</ci>
<ci>K1_infinity</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_K1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current_K1_gate" cmeta:id="id_00011">
<variable cmeta:id="time_independent_potassium_current_K1_gate.K1_infinity" name="K1_infinity" public_interface="out" units="dimensionless" />
<variable cmeta:id="time_independent_potassium_current_K1_gate.alpha_K1" name="alpha_K1" units="per_millisecond" />
<variable cmeta:id="time_independent_potassium_current_K1_gate.beta_K1" name="beta_K1" units="per_millisecond" />
<variable cmeta:id="time_independent_potassium_current_K1_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="id_00042" name="E_K1" public_interface="in" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_K1</ci>
<apply>
<divide />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">1.02</cn>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2385</cn>
<apply>
<minus />
<apply>
<minus />
<ci>V</ci>
<ci>E_K1</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">59.215</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_K1</ci>
<apply>
<divide />
<apply>
<plus />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.49124</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.08032</cn>
<apply>
<minus />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5.476</cn>
</apply>
<ci>E_K1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">1</cn>
<apply>
<exp />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.06175</cn>
<apply>
<minus />
<ci>V</ci>
<apply>
<plus />
<ci>E_K1</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">594.31</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.5143</cn>
</apply>
<apply>
<plus />
<apply>
<minus />
<ci>V</ci>
<ci>E_K1</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4.753</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>K1_infinity</ci>
<apply>
<divide />
<ci>alpha_K1</ci>
<apply>
<plus />
<ci>alpha_K1</ci>
<ci>beta_K1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current" cmeta:id="id_00022">
<variable cmeta:id="id_00023" name="i_Kp" public_interface="out" units="microA_per_cm2" />
<variable cmeta:id="id_00043" name="E_Kp" units="millivolt" />
<variable cmeta:id="id_00044" initial_value="0.0183" name="g_Kp" units="milliS_per_cm2" />
<variable cmeta:id="plateau_potassium_current.Kp" name="Kp" units="dimensionless" />
<variable cmeta:id="plateau_potassium_current.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="id_00046" name="E_K1" public_interface="in" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E_Kp</ci>
<ci>E_K1</ci>
</apply>
<apply>
<eq />
<ci>Kp</ci>
<apply>
<divide />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">7.488</cn>
<ci>V</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5.98</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_Kp</ci>
<apply>
<times />
<ci>g_Kp</ci>
<ci>Kp</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_Kp</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_current" cmeta:id="id_00018">
<variable cmeta:id="id_00019" name="i_b" public_interface="out" units="microA_per_cm2" />
<variable cmeta:id="id_00020" initial_value="-59.87" name="E_b" units="millivolt" />
<variable cmeta:id="id_00021" initial_value="0.03921" name="g_b" units="milliS_per_cm2" />
<variable cmeta:id="background_current.V" name="V" public_interface="in" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_b</ci>
<apply>
<times />
<ci>g_b</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_b</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ionic_concentrations">
<variable cmeta:id="id_00014" initial_value="140" name="Nao" public_interface="out" units="millimolar" />
<variable cmeta:id="id_00015" initial_value="18" name="Nai" public_interface="out" units="millimolar" />
<variable cmeta:id="id_00016" initial_value="145" name="Ki" public_interface="out" units="millimolar" />
<variable cmeta:id="id_00017" initial_value="5.4" name="Ko" public_interface="out" units="millimolar" />
</component>
<component name="intracellular_calcium_concentration" cmeta:id="id_00012">
<variable cmeta:id="id_00013" initial_value="0.00017948816388306" name="Cai" public_interface="out" units="millimolar" />
<variable cmeta:id="intracellular_calcium_concentration.time" name="time" public_interface="in" units="millisecond" />
<variable cmeta:id="id_00045" name="i_si" public_interface="in" units="microA_per_cm2" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Cai</ci>
</apply>
<apply>
<plus />
<apply>
<times />
<apply>
<divide />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_1000_centimetre">0.0001</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="coulomb_per_mole">1</cn>
</apply>
<ci>i_si</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.07</cn>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.0001</cn>
<ci>Cai</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<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_j_gate" />
<component_ref component="fast_sodium_current_h_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate" />
<component_ref component="time_dependent_potassium_current_Xi_gate" />
</component_ref>
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate" />
<component_ref component="slow_inward_current_f_gate" />
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate" />
</component_ref>
</group>
<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_j_gate" />
<component_ref component="fast_sodium_current_h_gate" />
</component_ref>
<component_ref component="plateau_potassium_current" />
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate" />
<component_ref component="time_dependent_potassium_current_Xi_gate" />
</component_ref>
<component_ref component="background_current" />
<component_ref component="intracellular_calcium_concentration" />
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate" />
<component_ref component="slow_inward_current_f_gate" />
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate" />
</component_ref>
<component_ref component="ionic_concentrations" />
</component_ref>
</group>
<connection>
<map_components component_1="environment" component_2="slow_inward_current" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="time_dependent_potassium_current_X_gate" component_2="time_dependent_potassium_current" />
<map_variables variable_1="X" variable_2="X" />
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="i_si" variable_2="i_si" />
</connection>
<connection>
<map_components component_1="membrane" component_2="background_current" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="membrane" component_2="time_dependent_potassium_current" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="R" variable_2="R" />
</connection>
<connection>
<map_components component_1="fast_sodium_current_m_gate" component_2="fast_sodium_current" />
<map_variables variable_1="m" variable_2="m" />
</connection>
<connection>
<map_components component_1="fast_sodium_current_h_gate" component_2="fast_sodium_current" />
<map_variables variable_1="h" variable_2="h" />
</connection>
<connection>
<map_components component_1="time_independent_potassium_current_K1_gate" component_2="time_independent_potassium_current" />
<map_variables variable_1="K1_infinity" variable_2="K1_infinity" />
</connection>
<connection>
<map_components component_1="membrane" component_2="fast_sodium_current" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="R" variable_2="R" />
</connection>
<connection>
<map_components component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_Xi_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="membrane" component_2="slow_inward_current" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="ionic_concentrations" component_2="fast_sodium_current" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="Nai" variable_2="Nai" />
</connection>
<connection>
<map_components component_1="membrane" component_2="time_independent_potassium_current" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="R" variable_2="R" />
</connection>
<connection>
<map_components component_1="intracellular_calcium_concentration" component_2="slow_inward_current" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="membrane" />
<map_variables variable_1="i_Na" variable_2="i_Na" />
</connection>
<connection>
<map_components component_1="ionic_concentrations" component_2="time_dependent_potassium_current" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="Nai" variable_2="Nai" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="slow_inward_current_d_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="time_dependent_potassium_current" component_2="membrane" />
<map_variables variable_1="i_K" variable_2="i_K" />
</connection>
<connection>
<map_components component_1="environment" component_2="membrane" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_j_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="time_independent_potassium_current" component_2="time_independent_potassium_current_K1_gate" />
<map_variables variable_1="E_K1" variable_2="E_K1" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="environment" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="slow_inward_current_d_gate" component_2="slow_inward_current" />
<map_variables variable_1="d" variable_2="d" />
</connection>
<connection>
<map_components component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_X_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="time_independent_potassium_current" component_2="plateau_potassium_current" />
<map_variables variable_1="E_K1" variable_2="E_K1" />
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="slow_inward_current_f_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="plateau_potassium_current" component_2="membrane" />
<map_variables variable_1="i_Kp" variable_2="i_Kp" />
</connection>
<connection>
<map_components component_1="environment" component_2="fast_sodium_current" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="slow_inward_current_f_gate" component_2="slow_inward_current" />
<map_variables variable_1="f" variable_2="f" />
</connection>
<connection>
<map_components component_1="time_dependent_potassium_current_Xi_gate" component_2="time_dependent_potassium_current" />
<map_variables variable_1="Xi" variable_2="Xi" />
</connection>
<connection>
<map_components component_1="time_independent_potassium_current" component_2="membrane" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
</connection>
<connection>
<map_components component_1="background_current" component_2="membrane" />
<map_variables variable_1="i_b" variable_2="i_b" />
</connection>
<connection>
<map_components component_1="environment" component_2="time_dependent_potassium_current" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="ionic_concentrations" component_2="time_independent_potassium_current" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="fast_sodium_current_j_gate" component_2="fast_sodium_current" />
<map_variables variable_1="j" variable_2="j" />
</connection>
<connection>
<map_components component_1="slow_inward_current" component_2="membrane" />
<map_variables variable_1="i_si" variable_2="i_si" />
</connection>
<connection>
<map_components component_1="membrane" component_2="plateau_potassium_current" />
<map_variables variable_1="V" variable_2="V" />
</connection>
</model>
