- Author:
- Tommy Yu <tommy.yu@auckland.ac.nz>
- Date:
- 2010-08-25 18:36:35+12:00
- Desc:
- xml:base fix
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/nygren_fiset_firek_clark_lindblad_clark_giles_1998/rawfile/2768515a81a686e53fe7793385f3be23737957ff/nygren_fiset_firek_clark_lindblad_clark_giles_1998.cellml
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<!--
This CellML file was generated on 16/01/2008 at 16:52:25 using:
COR (0.9.31.857)
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 cellular model
http://www.CellML.org/
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<article>
<articleinfo>
<title>Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
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<title>Model Status</title>
<para>
This CellML model runs in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent.
</para>
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We have developed a mathematical model of the human atria myocyte based on averaged voltage-clamp data recorded from isolated single myocytes. Our model consists of a Hodgkin-Huxley-type equivalent circuit for the sarcolemma, coupled with a fluid compartment model, which accounts for changes in ionic concentrations in the cytoplasm as well as in the sarcoplasmic reticulum. This formulation can reconstruct action potential data that are representative of recordings from a majority of human atrial cells in our laboratory and therefore provides a biophysically based account of the underlying ionic currents. This work is based in part on a previous model of the rabbit atrial myocyte published by our group and was motivated by differences in some of the repolarizing currents between human and rabbit atrium. We have therefore given particular attention to the sustained outward K+ current (I[sus]), which putatively has a prominent role in determining the duration of the human atrial action potential. Our results demonstrate that the action potential shape during the peak and plateau phases is determined primarily by transient outward K+ current, I(sus) and L-type Ca2+ current (I[Ca,L]) and that the role of I(sus) in the human atrial action potential can be modulated by the baseline sizes of I(Ca,L), I(sus) and the rapid delayed rectifier K+ current. As a result, our simulations suggest that the functional role of I(sus) can depend on the physiological/disease state of the cell.</para>
<para>
The original paper reference is cited below:
</para>
<para>
Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization, Nygren A, Fiset C, Firek L, Clark JW, Lindblad DS, Clark RB and Giles WR, 1998,<emphasis>Circulation Research</emphasis>, 82, 63-81. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/9440706">PubMed ID: 9440706</ulink>
</para>
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<caption>A fluid compartment model of the human atrial cell, including intracellular, cleft and extracellular spaces.</caption>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.002</cn>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_L1_gate">
<variable initial_value="0.9986" name="f_L_1" public_interface="out" units="dimensionless"/>
<variable name="f_L_infinity" public_interface="out" units="dimensionless"/>
<variable name="tau_f_L1" units="second"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_L_1</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_L_infinity</ci>
<ci>f_L_1</ci>
</apply>
<ci>tau_f_L1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>f_L_infinity</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>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">27.4</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">7.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.161</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">14.4</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.01</cn>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_L2_gate">
<variable initial_value="0.9986" name="f_L_2" public_interface="out" units="dimensionless"/>
<variable name="tau_f_L2" units="second"/>
<variable name="f_L_infinity" public_interface="in" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f_L_2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_L_infinity</ci>
<ci>f_L_2</ci>
</apply>
<ci>tau_f_L2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L2</ci>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">1.3323</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">14.2</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.0626</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current">
<variable name="i_t" public_interface="out" units="picoA"/>
<variable name="E_K" public_interface="out" units="millivolt"/>
<variable initial_value="7.5" name="g_t" units="nanoS"/>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="K_c" public_interface="in" units="millimolar"/>
<variable name="K_i" public_interface="in" units="millimolar"/>
<variable name="r" private_interface="in" units="dimensionless"/>
<variable name="s" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_t</ci>
<apply>
<times/>
<ci>g_t</ci>
<ci>r</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</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/>
<ci>K_c</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_r_gate">
<variable initial_value="0.0010678" name="r" public_interface="out" units="dimensionless"/>
<variable name="tau_r" units="second"/>
<variable name="r_infinity" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_infinity</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_infinity</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/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">1</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">11</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.0035</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">30</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.0015</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_independent_transient_outward_K_current_s_gate">
<variable initial_value="0.949" name="s" public_interface="out" units="dimensionless"/>
<variable name="tau_s" units="second"/>
<variable name="s_infinity" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_infinity</ci>
<ci>s</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>s_infinity</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>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40.5</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">11.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.4812</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">52.45</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">14.97</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.01414</cn>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_K_current">
<variable name="i_sus" public_interface="out" units="picoA"/>
<variable initial_value="2.75" name="g_sus" units="nanoS"/>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<variable name="r_sus" private_interface="in" units="dimensionless"/>
<variable name="s_sus" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_sus</ci>
<apply>
<times/>
<ci>g_sus</ci>
<ci>r_sus</ci>
<ci>s_sus</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_K_current_r_sus_gate">
<variable initial_value="0.00015949" name="r_sus" public_interface="out" units="dimensionless"/>
<variable name="tau_r_sus" units="second"/>
<variable name="r_sus_infinity" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r_sus</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_sus_infinity</ci>
<ci>r_sus</ci>
</apply>
<ci>tau_r_sus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_sus_infinity</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>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4.3</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r_sus</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.009</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">12</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.0005</cn>
</apply>
</apply>
</math>
</component>
<component name="sustained_outward_K_current_s_sus_gate">
<variable initial_value="0.9912" name="s_sus" public_interface="out" units="dimensionless"/>
<variable name="tau_s_sus" units="second"/>
<variable name="s_sus_infinity" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s_sus</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_sus_infinity</ci>
<ci>s_sus</ci>
</apply>
<ci>tau_s_sus</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>s_sus_infinity</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.6</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s_sus</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.047</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">60</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.3</cn>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents">
<variable name="i_Ks" public_interface="out" units="picoA"/>
<variable name="i_Kr" public_interface="out" units="picoA"/>
<variable initial_value="1" name="g_Ks" units="nanoS"/>
<variable initial_value="0.5" name="g_Kr" units="nanoS"/>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<variable name="p_a" private_interface="in" units="dimensionless"/>
<variable name="p_i" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<ci>n</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Kr</ci>
<apply>
<times/>
<ci>g_Kr</ci>
<ci>p_a</ci>
<ci>p_i</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents_n_gate">
<variable initial_value="0.0048357" name="n" public_interface="out" units="dimensionless"/>
<variable name="tau_n" units="second"/>
<variable name="n_infinity" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>n_infinity</ci>
<ci>n</ci>
</apply>
<ci>tau_n</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>n_infinity</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/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">19.9</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">12.7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.7</cn>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.4</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents_pa_gate">
<variable initial_value="0.0001" name="p_a" public_interface="out" units="dimensionless"/>
<variable name="tau_p_a" units="second"/>
<variable name="p_a_infinity" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p_a</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>p_a_infinity</ci>
<ci>p_a</ci>
</apply>
<ci>tau_p_a</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>p_a_infinity</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>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">15</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_p_a</ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.03118</cn>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.21718</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20.1376</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">22.1996</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_currents_pi_gate">
<variable name="p_i" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>p_i</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>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">55</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">24</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier">
<variable name="i_K1" public_interface="out" units="picoA"/>
<variable initial_value="3" name="g_K1" units="nanoS"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="K_c" public_interface="in" units="millimolar"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>K_c</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4457</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
<apply>
<plus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">3.6</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_currents">
<variable name="i_B_Na" public_interface="out" units="picoA"/>
<variable name="i_B_Ca" public_interface="out" units="picoA"/>
<variable initial_value="0.060599" name="g_B_Na" units="nanoS"/>
<variable initial_value="0.078681" name="g_B_Ca" units="nanoS"/>
<variable name="E_Ca" units="millivolt"/>
<variable name="E_Na" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="Ca_c" public_interface="in" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="V" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_B_Na</ci>
<apply>
<times/>
<ci>g_B_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_Ca</ci>
<apply>
<times/>
<ci>g_B_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_c</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable name="i_NaK" public_interface="out" units="picoA"/>
<variable initial_value="1" name="k_NaK_K" units="millimolar"/>
<variable initial_value="11" name="k_NaK_Na" units="millimolar"/>
<variable initial_value="70.8253" name="i_NaK_max" units="picoA"/>
<variable name="K_c" public_interface="in" units="millimolar"/>
<variable name="Na_i" public_interface="in" units="millimolar"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaK_max</ci>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<ci>K_c</ci>
<ci>k_NaK_K</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Na_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
</apply>
<apply>
<power/>
<ci>k_NaK_Na</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">150</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">200</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump_current">
<variable name="i_CaP" public_interface="out" units="picoA"/>
<variable initial_value="4" name="i_CaP_max" units="picoA"/>
<variable initial_value="0.0002" name="k_CaP" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_CaP</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_CaP_max</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_CaP</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_ion_exchanger_current">
<variable name="i_NaCa" public_interface="out" units="picoA"/>
<variable initial_value="0.0374842" name="k_NaCa" units="picoA_per_millimolar_4"/>
<variable initial_value="0.0003" name="d_NaCa" units="per_millimolar_4"/>
<variable initial_value="0.45" name="gamma" units="dimensionless"/>
<variable name="Na_i" public_interface="in" units="millimolar"/>
<variable name="Na_c" public_interface="in" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="Ca_c" public_interface="in" units="millimolar"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>Na_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_c</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_c</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>d_NaCa</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<power/>
<ci>Na_c</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_c</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable cmeta:id="intracellular_ion_concentrations_Na_i" initial_value="8.5547" name="Na_i" public_interface="out" units="millimolar"/>
<variable cmeta:id="intracellular_ion_concentrations_Ca_i" initial_value="6.729e-5" name="Ca_i" public_interface="out" units="millimolar"/>
<variable cmeta:id="intracellular_ion_concentrations_K_i" initial_value="129.435" name="K_i" public_interface="out" units="millimolar"/>
<variable initial_value="7.2495e-5" name="Ca_d" public_interface="out" units="millimolar"/>
<variable initial_value="-1.68" name="phi_Na_en" public_interface="out" units="picoA"/>
<variable initial_value="0.005884" name="Vol_i" public_interface="out" units="nanolitre"/>
<variable name="Vol_d" units="nanolitre"/>
<variable name="i_di" units="picoA"/>
<variable initial_value="0.01" name="tau_di" units="second"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="i_Na" public_interface="in" units="picoA"/>
<variable name="i_Ca_L" public_interface="in" units="picoA"/>
<variable name="i_B_Na" public_interface="in" units="picoA"/>
<variable name="i_NaCa" public_interface="in" units="picoA"/>
<variable name="i_NaK" public_interface="in" units="picoA"/>
<variable name="i_Ks" public_interface="in" units="picoA"/>
<variable name="i_Kr" public_interface="in" units="picoA"/>
<variable name="i_K1" public_interface="in" units="picoA"/>
<variable name="i_t" public_interface="in" units="picoA"/>
<variable name="i_sus" public_interface="in" units="picoA"/>
<variable name="i_CaP" public_interface="in" units="picoA"/>
<variable name="i_B_Ca" public_interface="in" units="picoA"/>
<variable name="i_up" public_interface="in" units="picoA"/>
<variable name="i_rel" public_interface="in" units="picoA"/>
<variable name="dOCdt" public_interface="in" units="per_second"/>
<variable name="dOTCdt" public_interface="in" units="per_second"/>
<variable name="dOTMgCdt" public_interface="in" units="per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Vol_d</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.02</cn>
<ci>Vol_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_B_Na</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<ci>phi_Na_en</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_i</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_t</ci>
<ci>i_sus</ci>
<ci>i_K1</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_i</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>i_di</ci>
</apply>
<ci>i_B_Ca</ci>
<ci>i_CaP</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<ci>i_up</ci>
</apply>
<ci>i_rel</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>Vol_i</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.08</cn>
<ci>dOTCdt</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.16</cn>
<ci>dOTMgCdt</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.045</cn>
<ci>dOCdt</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca_L</ci>
<ci>i_di</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>Vol_d</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_di</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_d</ci>
<ci>Ca_i</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>Vol_d</ci>
</apply>
<ci>tau_di</ci>
</apply>
</apply>
</math>
</component>
<component name="intracellular_Ca_buffering">
<variable initial_value="0.0275" name="O_C" units="dimensionless"/>
<variable name="dOCdt" public_interface="out" units="per_second"/>
<variable initial_value="0.0133" name="O_TC" units="dimensionless"/>
<variable name="dOTCdt" public_interface="out" units="per_second"/>
<variable initial_value="0.1961" name="O_TMgC" units="dimensionless"/>
<variable name="dOTMgCdt" public_interface="out" units="per_second"/>
<variable initial_value="0.7094" name="O_TMgMg" units="dimensionless"/>
<variable initial_value="2.5" name="Mg_i" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_C</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millimolar_second">200000</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>O_C</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">476</cn>
<ci>O_C</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dOCdt</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_C</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millimolar_second">78400</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>O_TC</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">392</cn>
<ci>O_TC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dOTCdt</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgC</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millimolar_second">200000</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>O_TMgC</ci>
</apply>
<ci>O_TMgMg</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">6.6</cn>
<ci>O_TMgC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dOTMgCdt</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_TMgMg</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millimolar_second">2000</cn>
<ci>Mg_i</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>O_TMgC</ci>
</apply>
<ci>O_TMgMg</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">666</cn>
<ci>O_TMgMg</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cleft_space_ion_concentrations">
<variable cmeta:id="cleft_space_ion_concentrations_Na_c" initial_value="130.011" name="Na_c" public_interface="out" units="millimolar"/>
<variable cmeta:id="cleft_space_ion_concentrations_Ca_c" initial_value="1.8147" name="Ca_c" public_interface="out" units="millimolar"/>
<variable cmeta:id="cleft_space_ion_concentrations_K_c" initial_value="5.3581" name="K_c" public_interface="out" units="millimolar"/>
<variable name="Vol_i" public_interface="in" units="nanolitre"/>
<variable name="Vol_c" units="nanolitre"/>
<variable initial_value="14.3" name="tau_Na" units="second"/>
<variable initial_value="10" name="tau_K" units="second"/>
<variable initial_value="24.7" name="tau_Ca" units="second"/>
<variable cmeta:id="cleft_space_ion_concentrations_Na_b" initial_value="130" name="Na_b" units="millimolar"/>
<variable cmeta:id="cleft_space_ion_concentrations_Ca_b" initial_value="1.8" name="Ca_b" units="millimolar"/>
<variable cmeta:id="cleft_space_ion_concentrations_K_b" initial_value="5.4" name="K_b" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="i_Na" public_interface="in" units="picoA"/>
<variable name="i_Ca_L" public_interface="in" units="picoA"/>
<variable name="i_B_Na" public_interface="in" units="picoA"/>
<variable name="i_NaCa" public_interface="in" units="picoA"/>
<variable name="i_NaK" public_interface="in" units="picoA"/>
<variable name="i_Ks" public_interface="in" units="picoA"/>
<variable name="i_Kr" public_interface="in" units="picoA"/>
<variable name="i_K1" public_interface="in" units="picoA"/>
<variable name="i_t" public_interface="in" units="picoA"/>
<variable name="i_sus" public_interface="in" units="picoA"/>
<variable name="i_CaP" public_interface="in" units="picoA"/>
<variable name="i_B_Ca" public_interface="in" units="picoA"/>
<variable name="phi_Na_en" public_interface="in" units="picoA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Vol_c</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.136</cn>
<ci>Vol_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Na_b</ci>
<ci>Na_c</ci>
</apply>
<ci>tau_Na</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_B_Na</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<ci>phi_Na_en</ci>
</apply>
<apply>
<times/>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>K_b</ci>
<ci>K_c</ci>
</apply>
<ci>tau_K</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_t</ci>
<ci>i_sus</ci>
<ci>i_K1</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_b</ci>
<ci>Ca_c</ci>
</apply>
<ci>tau_Ca</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca_L</ci>
<ci>i_B_Ca</ci>
<ci>i_CaP</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>Vol_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_handling_by_the_SR">
<variable cmeta:id="Ca_handling_by_the_SR_i_rel" name="i_rel" public_interface="out" units="picoA"/>
<variable cmeta:id="Ca_handling_by_the_SR_i_up" name="i_up" public_interface="out" units="picoA"/>
<variable name="i_tr" units="picoA"/>
<variable initial_value="2800" name="I_up_max" units="picoA"/>
<variable initial_value="0.0003" name="k_cyca" units="millimolar"/>
<variable initial_value="0.5" name="k_srca" units="millimolar"/>
<variable initial_value="0.4" name="k_xcs" units="dimensionless"/>
<variable initial_value="200000" name="alpha_rel" units="picoA_per_millimolar"/>
<variable initial_value="0.6465" name="Ca_rel" units="millimolar"/>
<variable initial_value="0.6646" name="Ca_up" units="millimolar"/>
<variable initial_value="0.0003969" name="Vol_up" units="nanolitre"/>
<variable initial_value="4.41e-5" name="Vol_rel" units="nanolitre"/>
<variable name="r_act" units="per_second"/>
<variable name="r_inact" units="per_second"/>
<variable initial_value="0.815" name="r_recov" units="per_second"/>
<variable initial_value="0.4369" name="O_Calse" units="dimensionless"/>
<variable initial_value="0.4284" name="F1" units="dimensionless"/>
<variable initial_value="0.0028" name="F2" units="dimensionless"/>
<variable initial_value="0.01" name="tau_tr" units="second"/>
<variable initial_value="0.0003" name="k_rel_i" units="millimolar"/>
<variable initial_value="0.003" name="k_rel_d" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="Ca_d" public_interface="in" units="millimolar"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>I_up_max</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>k_cyca</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k_xcs</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<ci>Ca_up</ci>
</apply>
<ci>k_srca</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_cyca</ci>
</apply>
<ci>k_cyca</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k_xcs</ci>
<apply>
<plus/>
<ci>Ca_up</ci>
<ci>k_srca</ci>
</apply>
</apply>
<ci>k_srca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_tr</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>Vol_rel</ci>
</apply>
<ci>tau_tr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<ci>alpha_rel</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>F2</ci>
<apply>
<plus/>
<ci>F2</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>Ca_rel</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_Calse</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millimolar_second">480</cn>
<ci>Ca_rel</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>O_Calse</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">400</cn>
<ci>O_Calse</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>Vol_rel</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">31</cn>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O_Calse</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>Vol_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>r_recov</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>F1</ci>
</apply>
<ci>F2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>r_act</ci>
<ci>F1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>r_act</ci>
<ci>F1</ci>
</apply>
<apply>
<times/>
<ci>r_inact</ci>
<ci>F2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_act</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">203.8</cn>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel_i</ci>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_d</ci>
<apply>
<plus/>
<ci>Ca_d</ci>
<ci>k_rel_d</ci>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_inact</ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">33.96</cn>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">339.6</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel_i</ci>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h1_gate"/>
<component_ref component="sodium_current_h2_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_L_gate"/>
<component_ref component="L_type_Ca_channel_f_L1_gate"/>
<component_ref component="L_type_Ca_channel_f_L2_gate"/>
</component_ref>
<component_ref component="Ca_independent_transient_outward_K_current">
<component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
</component_ref>
<component_ref component="sustained_outward_K_current">
<component_ref component="sustained_outward_K_current_r_sus_gate"/>
<component_ref component="sustained_outward_K_current_s_sus_gate"/>
</component_ref>
<component_ref component="delayed_rectifier_K_currents">
<component_ref component="delayed_rectifier_K_currents_n_gate"/>
<component_ref component="delayed_rectifier_K_currents_pa_gate"/>
<component_ref component="delayed_rectifier_K_currents_pi_gate"/>
</component_ref>
<component_ref component="inward_rectifier"/>
<component_ref component="background_currents"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sarcolemmal_calcium_pump_current"/>
<component_ref component="Na_Ca_ion_exchanger_current"/>
<component_ref component="Ca_handling_by_the_SR"/>
<component_ref component="intracellular_ion_concentrations"/>
<component_ref component="intracellular_Ca_buffering"/>
<component_ref component="cleft_space_ion_concentrations"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h1_gate"/>
<component_ref component="sodium_current_h2_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_L_gate"/>
<component_ref component="L_type_Ca_channel_f_L1_gate"/>
<component_ref component="L_type_Ca_channel_f_L2_gate"/>
</component_ref>
<component_ref component="Ca_independent_transient_outward_K_current">
<component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
<component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
</component_ref>
<component_ref component="sustained_outward_K_current">
<component_ref component="sustained_outward_K_current_r_sus_gate"/>
<component_ref component="sustained_outward_K_current_s_sus_gate"/>
</component_ref>
<component_ref component="delayed_rectifier_K_currents">
<component_ref component="delayed_rectifier_K_currents_n_gate"/>
<component_ref component="delayed_rectifier_K_currents_pa_gate"/>
<component_ref component="delayed_rectifier_K_currents_pi_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="L_type_Ca_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_independent_transient_outward_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sustained_outward_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="delayed_rectifier_K_currents" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="inward_rectifier" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="background_currents" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_potassium_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sarcolemmal_calcium_pump_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Na_Ca_ion_exchanger_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_handling_by_the_SR" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="intracellular_Ca_buffering" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="cleft_space_ion_concentrations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="L_type_Ca_channel"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Ca_L" variable_2="i_Ca_L"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Ca_independent_transient_outward_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_t" variable_2="i_t"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sustained_outward_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_sus" variable_2="i_sus"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="inward_rectifier"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="delayed_rectifier_K_currents"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Kr" variable_2="i_Kr"/>
<map_variables variable_1="i_Ks" variable_2="i_Ks"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="background_currents"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_B_Na" variable_2="i_B_Na"/>
<map_variables variable_1="i_B_Ca" variable_2="i_B_Ca"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_potassium_pump"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
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<connection>
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<rdf:value>This model has been curated by Penny Noble and James Lawson and is known to run and produce the correct output in PCEnv and COR.</rdf:value>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Mathematical Model of an Adult Human Atrial Cell: The Role of K+ Currents in Repolarization</dc:title>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Circulation Research</dc:title>
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