<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 30/10/2007 at 17:49:22 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>Ionic mechanism of electrical alternans</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is known to run in OpenCell and COR to recreate the published results. The units have been checked and they are consistent.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Although alternans of action potential duration (APD) is a robust feature of the rapidly paced canine ventricle, currently available ionic models of cardiac myocytes do not recreate this phenomenon. To address this problem, we developed a new ionic model using formulations of currents based on previous models and recent experimental data. Compared with existing models, the inward rectifier K(+) current (I(K1)) was decreased at depolarized potentials, the maximum conductance and rectification of the rapid component of the delayed rectifier K(+) current (I(Kr)) were increased, and I(Kr) activation kinetics were slowed. The slow component of the delayed rectifier K(+) current (I(Ks)) was increased in magnitude and activation shifted to less positive voltages, and the L-type Ca(2+) current (I(Ca)) was modified to produce a smaller, more rapidly inactivating current. Finally, a simplified form of intracellular calcium dynamics was adopted. In this model, APD alternans occurred at cycle lengths = 150-210 ms, with a maximum alternans amplitude of 39 ms. APD alternans was suppressed by decreasing I(Ca) magnitude or calcium-induced inactivation and by increasing the magnitude of I(K1), I(Kr), or I(Ks). These results establish an ionic basis for APD alternans, which should facilitate the development of pharmacological approaches to eliminating alternans.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Ionic mechanism of electrical alternans, Jeffrey J. Fox, Jennifer L. McHarg, and Robert F. Gilmour Jr, 2002,
<emphasis>American Journal of Physiology: Heart and Circulatory Physiology</emphasis>, 282, H516-H530.
<ulink url="http://www.ncbi.nlm.nih.gov/pubmed/11788399">PubMed ID: 11788399</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="fox_2001.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane and the calcium fluxes between the cytoplasm and the sarcoplasmic reticulum that are captured in the Fox <emphasis>et al.</emphasis> canine ventricular cell model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<variable name="X_kr_inf" units="dimensionless"/>
<variable name="tau_X_kr" units="millisecond"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>X_kr_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2.182</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.1819</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_X_kr</ci>
<apply>
<plus/>
<cn cellml:units="millisecond">43</cn>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">5.495</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.1691</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">7.677</cn>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0128</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X_kr</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>X_kr_inf</ci>
<ci>X_kr</ci>
</apply>
<ci>tau_X_kr</ci>
</apply>
</apply>
</math>
</component>
<component name="slow_activating_delayed_rectifiyer_K_current">
<variable name="i_Ks" units="microA_per_microF" public_interface="out"/>
<variable name="g_Ks" units="milliS_per_microF" initial_value="0.0245"/>
<variable name="E_Ks" units="millivolt"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="K_o" units="millimolar" public_interface="in"/>
<variable name="K_i" 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="joule_per_mole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_millimole" public_interface="in"/>
<variable name="X_ks" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ks</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>K_o</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01833</cn>
<ci>Na_o</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>K_i</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01833</cn>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<apply>
<power/>
<ci>X_ks</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_activating_delayed_rectifiyer_K_current_X_ks_gate">
<variable name="X_ks" units="dimensionless" initial_value="0.0001" public_interface="out"/>
<variable name="tau_X_ks" units="millisecond"/>
<variable name="X_ks_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>X_ks_infinity</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">16</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">13.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_X_ks</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0000719</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.148</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.000131</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0687</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X_ks</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>X_ks_infinity</ci>
<ci>X_ks</ci>
</apply>
<ci>tau_X_ks</ci>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current">
<variable name="i_to" units="microA_per_microF" public_interface="out"/>
<variable name="g_to" units="milliS_per_microF" initial_value="0.23815"/>
<variable name="time" units="millisecond" 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="X_to" units="dimensionless" private_interface="in"/>
<variable name="Y_to" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<ci>X_to</ci>
<ci>Y_to</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_X_to_gate">
<variable name="X_to" units="dimensionless" initial_value="0.00003742" public_interface="out"/>
<variable name="alpha_X_to" units="per_millisecond"/>
<variable name="beta_X_to" units="per_millisecond"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_X_to</ci>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.04516</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.03577</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_X_to</ci>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.0989</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.06237</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>X_to</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_X_to</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>X_to</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_X_to</ci>
<ci>X_to</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_Y_to_gate">
<variable name="Y_to" units="dimensionless" initial_value="1" public_interface="out"/>
<variable name="alpha_Y_to" units="per_millisecond"/>
<variable name="beta_Y_to" units="per_millisecond"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_Y_to</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.005415</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.051335</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_Y_to</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.005415</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.051335</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Y_to</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_Y_to</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Y_to</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_Y_to</ci>
<ci>Y_to</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current">
<variable name="i_Kp" units="microA_per_microF" public_interface="out"/>
<variable name="g_Kp" units="milliS_per_microF" initial_value="0.002216"/>
<variable name="time" units="millisecond" 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="Kp_V" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Kp</ci>
<apply>
<times/>
<ci>g_Kp</ci>
<ci>Kp_V</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current_Kp_gate">
<variable name="Kp_V" units="dimensionless" public_interface="out"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Kp_V</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">7.488</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5.98</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable name="i_NaK" units="microA_per_microF" public_interface="out"/>
<variable name="i_NaK_max" units="microA_per_microF" initial_value="0.693"/>
<variable name="f_NaK" units="dimensionless"/>
<variable name="K_mNai" units="millimolar" initial_value="10"/>
<variable name="K_mKo" units="millimolar" initial_value="1.5"/>
<variable name="sigma" units="dimensionless"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_millimole" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_o" units="millimolar" public_interface="in"/>
<variable name="K_o" units="millimolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_NaK</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<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>
</apply>
<apply>
<eq/>
<ci>sigma</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<cn cellml:units="dimensionless">7</cn>
</apply>
<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>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaK_max</ci>
<ci>f_NaK</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>K_mNai</ci>
<ci>Na_i</ci>
</apply>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_mKo</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_exchanger">
<variable name="i_NaCa" units="microA_per_microF" public_interface="out"/>
<variable name="K_mCa" units="micromolar" initial_value="1380"/>
<variable name="K_mNa" units="millimolar" initial_value="87.5"/>
<variable name="K_NaCa" units="microA_per_microF" initial_value="1500"/>
<variable name="K_sat" units="dimensionless" initial_value="0.2"/>
<variable name="eta" units="dimensionless" initial_value="0.35"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_millimole" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_o" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<variable name="Ca_o" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>K_NaCa</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci>K_mNa</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>K_mCa</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>eta</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>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>eta</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>eta</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>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump">
<variable name="i_p_Ca" units="microA_per_microF" public_interface="out"/>
<variable name="K_mpCa" units="micromolar" initial_value="0.05"/>
<variable name="i_pCa_max" units="microA_per_microF" initial_value="0.05"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_Ca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_pCa_max</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>K_mpCa</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable name="i_Ca_b" units="microA_per_microF" public_interface="out"/>
<variable name="g_Cab" units="milliS_per_microF" initial_value="0.0003842"/>
<variable name="E_Ca" units="millivolt"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_millimole" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<variable name="Ca_o" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_o</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_b</ci>
<apply>
<times/>
<ci>g_Cab</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable name="i_Na_b" units="microA_per_microF" public_interface="out"/>
<variable name="g_Nab" units="milliS_per_microF" initial_value="0.0031"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="E_Na" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Na_b</ci>
<apply>
<times/>
<ci>g_Nab</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current">
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="i_Ca" units="microA_per_microF" public_interface="out"/>
<variable name="i_CaK" units="microA_per_microF" public_interface="out"/>
<variable name="P_Ca" units="cm_per_millisecond" initial_value="0.0000226"/>
<variable name="P_CaK" units="cm_per_millisecond" initial_value="0.000000579"/>
<variable name="i_Ca_half" units="microA_per_microF" initial_value="-0.265"/>
<variable name="i_Ca_max" units="microA_per_microF"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="C_sc" units="microF_per_cm2" initial_value="1" public_interface="out"/>
<variable name="Ca_o" units="micromolar" public_interface="in"/>
<variable name="K_o" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_millimole" public_interface="in"/>
<variable name="f" units="dimensionless" public_interface="out" private_interface="in"/>
<variable name="d" units="dimensionless" public_interface="out" private_interface="in"/>
<variable name="f_Ca" units="dimensionless" public_interface="out" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca</ci>
<apply>
<times/>
<ci>i_Ca_max</ci>
<ci>f</ci>
<ci>d</ci>
<ci>f_Ca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_max</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>P_Ca</ci>
<ci>C_sc</ci>
</apply>
<cn cellml:units="uM_mM">4</cn>
<ci>V</ci>
<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/>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<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">0.341</cn>
<ci>Ca_o</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_CaK</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>P_CaK</ci>
<ci>C_sc</ci>
</apply>
<ci>f</ci>
<ci>d</ci>
<ci>f_Ca</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>i_Ca_max</ci>
<ci>i_Ca_half</ci>
</apply>
</apply>
</apply>
<cn cellml:units="nM_mM">1000</cn>
<ci>V</ci>
<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/>
<ci>K_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>K_o</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>V</ci>
<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_f_gate">
<variable name="f" units="dimensionless" initial_value="0.983" public_interface="out"/>
<variable name="f_infinity" units="dimensionless"/>
<variable name="tau_f" units="millisecond"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_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">12.5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f</ci>
<apply>
<plus/>
<cn cellml:units="millisecond">30</cn>
<apply>
<divide/>
<cn cellml:units="millisecond">200</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">9.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_infinity</ci>
<ci>f</ci>
</apply>
<ci>tau_f</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_d_gate">
<variable name="d" units="dimensionless" initial_value="0.0001" public_interface="out"/>
<variable name="d_infinity" units="dimensionless"/>
<variable name="tau_d" units="millisecond"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="E0_m" units="millivolt"/>
<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">10</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">6.24</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E0_m</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.25</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.01</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">0.07</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.07</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.05</cn>
</apply>
<ci>E0_m</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.05</cn>
<ci>E0_m</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</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_current_f_Ca_gate">
<variable name="f_Ca" units="dimensionless" initial_value="0.942" public_interface="out"/>
<variable name="tau_f_Ca" units="millisecond"/>
<variable name="f_Ca_infinity" units="dimensionless"/>
<variable name="K_mfCa" units="micromolar" initial_value="0.18"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="Ca_i" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_Ca_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>K_mfCa</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_Ca</ci>
<cn cellml:units="millisecond">30</cn>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_Ca</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_Ca_infinity</ci>
<ci>f_Ca</ci>
</apply>
<ci>tau_f_Ca</ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_dynamics">
<variable name="Ca_i" units="micromolar" initial_value="0.0472" public_interface="out"/>
<variable name="beta_i" units="dimensionless"/>
<variable name="K_mCMDN" units="micromolar" initial_value="2"/>
<variable name="CMDN_tot" units="micromolar" initial_value="10"/>
<variable name="V_myo" units="microlitre" initial_value="0.00002584"/>
<variable name="F" units="coulomb_per_millimole" public_interface="in"/>
<variable name="C_sc" units="microF_per_cm2" public_interface="in"/>
<variable name="A_Cap" units="cm2" initial_value="0.0001534"/>
<variable name="J_rel" units="micromolar_per_millisecond"/>
<variable name="J_leak" units="micromolar_per_millisecond"/>
<variable name="J_up" units="micromolar_per_millisecond"/>
<variable name="i_Ca" units="microA_per_microF" public_interface="in"/>
<variable name="i_Ca_b" units="microA_per_microF" public_interface="in"/>
<variable name="i_p_Ca" units="microA_per_microF" public_interface="in"/>
<variable name="i_NaCa" units="microA_per_microF" public_interface="in"/>
<variable name="Ca_SR" units="micromolar" initial_value="320"/>
<variable name="P_rel" units="per_millisecond" initial_value="6"/>
<variable name="P_leak" units="per_millisecond" initial_value="0.000001"/>
<variable name="K_mCSQN" units="micromolar" initial_value="600"/>
<variable name="CSQN_tot" units="micromolar" initial_value="10000"/>
<variable name="V_SR" units="microlitre" initial_value="0.000002"/>
<variable name="V_up" units="micromolar_per_millisecond" initial_value="0.1"/>
<variable name="K_mup" units="micromolar" initial_value="0.32"/>
<variable name="gamma" units="dimensionless"/>
<variable name="f_Ca" units="dimensionless" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="f" units="dimensionless" public_interface="in"/>
<variable name="d" units="dimensionless" public_interface="in"/>
<variable name="beta_SR" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_up</ci>
<apply>
<divide/>
<ci>V_up</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>K_mup</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<cn cellml:units="micromolar">2000</cn>
<ci>Ca_SR</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_rel</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_rel</ci>
<ci>f</ci>
<ci>d</ci>
<ci>f_Ca</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>gamma</ci>
<ci>Ca_SR</ci>
</apply>
<ci>Ca_i</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">1.65</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_leak</ci>
<apply>
<times/>
<ci>P_leak</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_SR</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_SR</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_SR</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>beta_SR</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_up</ci>
<ci>J_leak</ci>
</apply>
<ci>J_rel</ci>
</apply>
<ci>V_myo</ci>
</apply>
<ci>V_SR</ci>
</apply>
</apply>
<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>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>beta_i</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>J_rel</ci>
<ci>J_leak</ci>
</apply>
<ci>J_up</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>A_Cap</ci>
<ci>C_sc</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>V_myo</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca</ci>
<ci>i_Ca_b</ci>
<ci>i_p_Ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="standard_ionic_concentrations">
<variable name="Na_i" units="millimolar" initial_value="10" public_interface="out"/>
<variable name="Na_o" units="millimolar" initial_value="138" public_interface="out"/>
<variable name="Ca_o" units="micromolar" initial_value="2000" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="149.4" public_interface="out"/>
<variable name="K_o" units="millimolar" initial_value="4" public_interface="out"/>
</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="rapid_activating_delayed_rectifiyer_K_current">
<component_ref component="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate"/>
</component_ref>
<component_ref component="slow_activating_delayed_rectifiyer_K_current">
<component_ref component="slow_activating_delayed_rectifiyer_K_current_X_ks_gate"/>
</component_ref>
<component_ref component="transient_outward_potassium_current">
<component_ref component="transient_outward_potassium_current_X_to_gate"/>
<component_ref component="transient_outward_potassium_current_Y_to_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current">
<component_ref component="plateau_potassium_current_Kp_gate"/>
</component_ref>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sarcolemmal_calcium_pump"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_background_current"/>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_Ca_gate"/>
</component_ref>
<component_ref component="calcium_dynamics"/>
<component_ref component="standard_ionic_concentrations"/>
</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="rapid_activating_delayed_rectifiyer_K_current">
<component_ref component="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate"/>
</component_ref>
<component_ref component="slow_activating_delayed_rectifiyer_K_current">
<component_ref component="slow_activating_delayed_rectifiyer_K_current_X_ks_gate"/>
</component_ref>
<component_ref component="transient_outward_potassium_current">
<component_ref component="transient_outward_potassium_current_X_to_gate"/>
<component_ref component="transient_outward_potassium_current_Y_to_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current">
<component_ref component="plateau_potassium_current_Kp_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_f_gate"/>
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<rdf:value>Changed the connections between "calcium_dynamics" and the "L_type_Ca_current" gates. Because these gates are encapsulated by the parent L_type_Ca_current channel, the variables d, f, and f_Ca need to be passed via the parent component to calcium_dynamics component - and not directly as they were in version 1 of this model.</rdf:value>
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