- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-12-10 11:27:33+13:00
- Desc:
- Added images in ai and svg format, removed non pub med reference
- Permanent Source URI:
- https://models.cellml.org/workspace/michailova_mcculloch_2001/rawfile/ee82e0b2b161aed3ac08dd1c9690fc9a23646f9d/michailova_mcculloch_2001.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : michailova_model_2001.xml
CREATED : 30th May 2004
LAST MODIFIED : 27th April 2005
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th
January, 2002.
DESCRIPTION : This file contains a CellML description of Michailova and McCulloch's mathematical model of ATP and ADP buffering, transport of Ca and Mg, and regulation of ion pumps in ventricular myocytes.
CHANGES:
27/04/2005 - PJV - Removed undefined initial values.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="michailova_mcculloch_2001_version01" name="michailova_mcculloch_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling ATP and ADP Buffering, Ca<superscript>2+</superscript> and Mg<superscript>2+</superscript> Transport, and Ion Pump Regulation in Ventricular Myocytes</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Several mathematical models have been developed with the aim of investigating Ca<superscript>2+</superscript> signalling in cardiac muscle. Such models include:
</para>
<itemizedlist>
<listitem>
<para>
Keizer and Levine, RyR Adaptation and Ca<superscript>2+</superscript> Oscillations, 1996
</para>
</listitem>
<listitem>
<para>
Jafri, Rice, Winslow Ventricular Model, 1998
</para>
</listitem>
<listitem>
<para>
Hunter, McCulloch, ter Keurs Model of the Mechanical Properties of Cardiac Muscle, 1998
</para>
</listitem>
<listitem>
<para>
Nygren <emphasis>et al.</emphasis>, Human Atrial Cell Model, 1998
</para>
</listitem>
<listitem>
<para>
Winslow <emphasis>et al.</emphasis>, Canine Ventricular Cell Model, 1999
</para>
</listitem>
<listitem>
<para>
Rice <emphasis>et al.</emphasis>,Cooperative Mechanisms in Cardiac Muscle, 1999
</para>
</listitem>
</itemizedlist>
<para>
However, the ability of these models to predict how the binding and transport of Ca<superscript>2+</superscript> and Mg<superscript>2+</superscript> by the mobile buffers ATP and ADP, or how changes in the ratio of [ATP]:[ADP] might influence intracellular ion concentrations and alter the behaviour of ion pumps or currents, is limited.
</para>
<para>
In the 2001 study by Michailova and McCulloch described here, the authors further develop the cardiac myocyte model of Winslow <emphasis>et al.</emphasis>, 1999 by incorporating equations for Ca<superscript>2+</superscript> and Mg<superscript>2+</superscript> buffering and transport by ATP and ADP, in addition to equations which describe the ATP regulation of transmembrane ion transporters (see the figure below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Model Study of ATP and ADP Buffering, Transport of Ca<superscript>2+</superscript> and Mg<superscript>2+</superscript>, and Regulation of Ion Pumps in Ventricular Myocyte, Anushka Michailova and Andrew McCulloch, 2001, <emphasis>Biophysical Journal</emphasis>, 81, 614-629. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11463611&dopt=Abstract">PubMed ID: 11463611</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="michailova_mcculloch_2001.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the mechanisms involved in the model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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</component>
<component name="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate">
<variable units="dimensionless" public_interface="out" name="X_kr" initial_value="0.6935"/>
<variable units="dimensionless" name="K12"/>
<variable units="dimensionless" name="K21"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="X_kr_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> X_kr </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> K12 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> X_kr </ci>
</apply>
</apply>
<apply>
<times/>
<ci> K12 </ci>
<ci> X_kr </ci>
</apply>
</apply>
</apply>
<apply id="K12_calculation">
<eq/>
<ci> K12 </ci>
<apply>
<exp/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> -5.495 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.169 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="K21_calculation">
<eq/>
<ci> K21 </ci>
<apply>
<exp/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> -7.677 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0128 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_activating_delayed_rectifiyer_K_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ks"/>
<variable units="milliS_per_microF" name="g_Ks" initial_value="0.00271"/>
<variable units="millivolt" name="E_Ks"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="X_ks"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ks_calculation">
<eq/>
<ci> i_Ks </ci>
<apply>
<times/>
<ci> g_Ks </ci>
<apply>
<power/>
<ci> X_ks </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ks </ci>
</apply>
</apply>
</apply>
<apply id="E_Ks_calculation">
<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> Ko </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.01833 </cn>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.01833 </cn>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_activating_delayed_rectifiyer_K_current_X_ks_gate">
<variable units="dimensionless" public_interface="out" name="X_ks" initial_value="0.00014589"/>
<variable units="dimensionless" name="tau_X_ks"/>
<variable units="dimensionless" name="X_ks_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="X_ks_diff_eq">
<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>
<apply id="X_ks_infinity_calculation">
<eq/>
<ci> X_ks_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.7 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 13.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_X_ks_calculation">
<eq/>
<ci> tau_X_ks </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0000719 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.148 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.000131 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0687 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_to1"/>
<variable units="milliS_per_microF" name="g_to1" initial_value="0.23815"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="X_to1"/>
<variable units="dimensionless" private_interface="in" name="Y_to1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_to1_calculation">
<eq/>
<ci> i_to1 </ci>
<apply>
<times/>
<ci> g_to1 </ci>
<ci> X_to1 </ci>
<ci> Y_to1 </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_X_to1_gate">
<variable units="dimensionless" public_interface="out" name="X_to1" initial_value="0.00003742"/>
<variable units="per_millisecond" name="alpha_X_to1"/>
<variable units="per_millisecond" name="beta_X_to1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dX_to1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> X_to1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_X_to1 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> X_to1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_X_to1 </ci>
<ci> X_to1 </ci>
</apply>
</apply>
</apply>
<apply id="alpha_X_to1_calculation">
<eq/>
<ci> alpha_X_to1 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.04561 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.03577 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_X_to1_calculation">
<eq/>
<ci> beta_X_to1 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0989 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.06237 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_potassium_current_Y_to1_gate">
<variable units="dimensionless" public_interface="out" name="Y_to1" initial_value="1.0"/>
<variable units="per_millisecond" name="alpha_Y_to1"/>
<variable units="per_millisecond" name="beta_Y_to1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dY_to1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Y_to1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_Y_to1 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Y_to1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_Y_to1 </ci>
<ci> Y_to1 </ci>
</apply>
</apply>
</apply>
<apply id="alpha_Y_to1_calculation">
<eq/>
<ci> alpha_Y_to1 </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.005415 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 33.5 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.051335 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 33.5 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_Y_to1_calculation">
<eq/>
<ci> beta_Y_to1 </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"> 5.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </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"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_K1"/>
<variable units="milliS_per_microF" name="g_K1" initial_value="2.8"/>
<variable units="millimolar" name="K_mK1" initial_value="13.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" private_interface="out" name="R"/>
<variable units="kelvin" public_interface="in" private_interface="out" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" private_interface="out" name="F"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E_K"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="dimensionless" private_interface="in" name="K1_infinity_V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<ci> K1_infinity_V </ci>
<apply>
<divide/>
<ci> Ko </ci>
<apply>
<plus/>
<ci> Ko </ci>
<ci> K_mK1 </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current_K1_gate">
<variable units="dimensionless" public_interface="out" name="K1_infinity_V"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_K1_calculation">
<eq/>
<ci> K1_infinity_V </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.5 </cn>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current">
<variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
<variable units="milliS_per_microF" name="g_Kp" initial_value="0.002216"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="Kp_V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Kp_calculation">
<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 units="dimensionless" public_interface="out" name="Kp_V"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Kp_V_calculation">
<eq/>
<ci> Kp_V </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </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="Na_Ca_exchanger">
<variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
<variable units="millimolar" name="K_mCa" initial_value="1.38"/>
<variable units="millimolar" name="K_mNa" initial_value="87.5"/>
<variable units="microA_per_microF" name="K_NaCa" initial_value="0.30"/>
<variable units="dimensionless" name="K_sat" initial_value="0.2"/>
<variable units="dimensionless" name="eta" initial_value="0.35"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 5000.0 </cn>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> K_mCa </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> K_sat </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<ci> eta </ci>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
<variable units="microA_per_microF" name="I_NaK"/>
<variable units="dimensionless" public_interface="in" name="S_MgATP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> S_MgATP </ci>
<ci> I_NaK </ci>
</apply>
</apply>
</math>
</component>
<component name="sarcolemmal_calcium_pump">
<variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
<variable units="microA_per_microF" name="I_p_Ca"/>
<variable units="dimensionless" public_interface="in" name="S_MgATP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_Ca_calculation">
<eq/>
<ci> i_p_Ca </ci>
<apply>
<times/>
<ci> S_MgATP </ci>
<ci> I_p_Ca </ci>
</apply>
</apply>
</math>
</component>
<component name="SERCA_pump">
<variable units="millimolar_per_millisecond" public_interface="out" name="J_up"/>
<variable units="microA_per_microF" name="j_up"/>
<variable units="dimensionless" public_interface="in" name="S_MgATP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_up_calculation">
<eq/>
<ci> J_up </ci>
<apply>
<times/>
<ci> S_MgATP </ci>
<ci> j_up </ci>
</apply>
</apply>
</math>
</component>
<component name="S_MgATP">
<variable units="dimensionless" public_interface="out" name="S_MgATP"/>
<variable units="millimolar" name="MgATP_i0"/>
<variable units="millimolar" public_interface="in" name="MgATP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="S_MgATP_calculation">
<eq/>
<ci> S_MgATP </ci>
<apply>
<divide/>
<ci> MgATP_i </ci>
<ci> MgATP_i0 </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
<variable units="milliS_per_microF" name="g_Cab" initial_value="0.0003842"/>
<variable units="millivolt" name="E_Ca"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_b_calculation">
<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 units="microA_per_microF" public_interface="out" name="i_Na_b"/>
<variable units="milliS_per_microF" name="g_Nab" initial_value="0.0031"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_b_calculation">
<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 units="microA_per_microF" public_interface="out" name="i_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_Ca_K"/>
<variable units="cm_per_second" name="P_Ca" initial_value="0.0003125"/>
<variable units="cm_per_second" name="P_K" initial_value="0.000000579"/>
<variable units="cm_per_second" name="p_k"/>
<variable units="microA_per_microF" name="i_Ca_half" initial_value="-0.265"/>
<variable units="microA_per_microF" name="i_Ca_max"/>
<variable units="dimensionless" name="O" initial_value="0.0"/>
<variable units="dimensionless" name="O_Ca" initial_value="0.0"/>
<variable units="per_millisecond" name="alpha"/>
<variable units="per_millisecond" name="beta"/>
<variable units="per_millisecond" name="gamma"/>
<variable units="per_millisecond" name="alpha_a"/>
<variable units="per_millisecond" name="beta_b"/>
<variable units="dimensionless" name="a" initial_value="2.0"/>
<variable units="dimensionless" name="b" initial_value="2.0"/>
<variable units="per_millisecond" name="g" initial_value="2.0"/>
<variable units="per_millisecond" name="f" initial_value="0.3"/>
<variable units="per_millisecond" name="g_" initial_value="7.0"/>
<variable units="per_millisecond" name="f_" initial_value="0.005"/>
<variable units="per_millisecond" name="omega" initial_value="0.01"/>
<variable units="dimensionless" name="C0" initial_value="0.99802"/>
<variable units="dimensionless" name="C1" initial_value="0.0000019544"/>
<variable units="dimensionless" name="C2" initial_value="0.0"/>
<variable units="dimensionless" name="C3" initial_value="0.0"/>
<variable units="dimensionless" name="C4" initial_value="0.0"/>
<variable units="dimensionless" name="C_Ca0" initial_value="0.0019734"/>
<variable units="dimensionless" name="C_Ca1" initial_value="0.0"/>
<variable units="dimensionless" name="C_Ca2" initial_value="0.0"/>
<variable units="dimensionless" name="C_Ca3" initial_value="0.0"/>
<variable units="dimensionless" name="C_Ca4" initial_value="0.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="microF_per_cm2" public_interface="in" name="C_sc"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_calculation">
<eq/>
<ci> i_Ca </ci>
<apply>
<times/>
<ci> i_Ca_max </ci>
<ci> y </ci>
<apply>
<plus/>
<ci> O </ci>
<ci> O_Ca </ci>
</apply>
</apply>
</apply>
<apply id="i_Ca_K_calculation">
<eq/>
<ci> i_Ca_K </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> p_k </ci>
<ci> C_sc </ci>
</apply>
<ci> y </ci>
<apply>
<plus/>
<ci> O </ci>
<ci> O_Ca </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </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> Ko </ci>
</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"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="p_k_calculation">
<eq/>
<ci> p_k </ci>
<apply>
<divide/>
<ci> P_K </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> i_Ca_max </ci>
<ci> i_Ca_half </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_max_calculation">
<eq/>
<ci> i_Ca_max </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> P_Ca </ci>
<ci> C_sc </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.001 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </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> Cao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_calculation">
<eq/>
<ci> alpha </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.4 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 2.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_calculation">
<eq/>
<ci> beta </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.05 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 2.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 13.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_a_calculation">
<eq/>
<ci> alpha_a </ci>
<apply>
<times/>
<ci> alpha </ci>
<ci> a </ci>
</apply>
</apply>
<apply id="beta_b_calculation">
<eq/>
<ci> beta_b </ci>
<apply>
<divide/>
<ci> beta </ci>
<ci> b </ci>
</apply>
</apply>
<apply id="gamma_calculation">
<eq/>
<ci> gamma </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.10375 </cn>
<ci> Ca_ss </ci>
</apply>
</apply>
<apply id="C0_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C0 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<ci> C1 </ci>
</apply>
<apply>
<times/>
<ci> omega </ci>
<ci> C_Ca0 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha </ci>
</apply>
<ci> gamma </ci>
</apply>
<ci> C0 </ci>
</apply>
</apply>
</apply>
<apply id="C1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C1 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha </ci>
<ci> C0 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta </ci>
<ci> C2 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<ci> b </ci>
</apply>
<ci> C_Ca1 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> beta </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> a </ci>
</apply>
</apply>
<ci> C1 </ci>
</apply>
</apply>
</apply>
<apply id="C2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C2 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha </ci>
<ci> C1 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta </ci>
<ci> C3 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> C_Ca2 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> C2 </ci>
</apply>
</apply>
</apply>
<apply id="C3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C3 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha </ci>
<ci> C2 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta </ci>
<ci> C4 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<ci> C_Ca3 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> alpha </ci>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<ci> C3 </ci>
</apply>
</apply>
</apply>
<apply id="C4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C4 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha </ci>
<ci> C3 </ci>
</apply>
<apply>
<times/>
<ci> g </ci>
<ci> O </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
<ci> C_Ca4 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> f </ci>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<ci> C4 </ci>
</apply>
</apply>
</apply>
<apply id="O_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> O </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> f </ci>
<ci> C4 </ci>
</apply>
<apply>
<times/>
<ci> g </ci>
<ci> O </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca0_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca0 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<ci> C_Ca1 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> C_Ca0 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
</apply>
<ci> omega </ci>
</apply>
<ci> C_Ca0 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca1 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca0 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca2 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> a </ci>
<ci> C1 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_b </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
</apply>
<apply>
<divide/>
<ci> omega </ci>
<ci> b </ci>
</apply>
</apply>
<ci> C_Ca1 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca2 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca1 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca3 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> C2 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
</apply>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca2 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca3 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca2 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca4 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> C3 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> alpha_a </ci>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca3 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca4 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_a </ci>
<ci> C_Ca3 </ci>
</apply>
<apply>
<times/>
<ci> g_ </ci>
<ci> O_Ca </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> C4 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> f_ </ci>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca4 </ci>
</apply>
</apply>
</apply>
<apply id="O_Ca_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> O_Ca </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> f_ </ci>
<ci> C_Ca4 </ci>
</apply>
<apply>
<times/>
<ci> g_ </ci>
<ci> O_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.7959"/>
<variable units="dimensionless" name="y_infinity"/>
<variable units="dimensionless" name="tau_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="y_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> y_infinity </ci>
<ci> y </ci>
</apply>
<ci> tau_y </ci>
</apply>
</apply>
<apply id="y_infinity_calculation">
<eq/>
<ci> y_infinity </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.8 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 12.5 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.2 </cn>
</apply>
</apply>
<apply id="tau_y_calculation">
<eq/>
<ci> tau_y </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 20.0 </cn>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 600.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 9.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="RyR_channel">
<variable units="millimolar_per_millisecond" public_interface="out" name="J_rel"/>
<variable units="per_millisecond" name="v1" initial_value="1.8"/>
<variable units="millimolar4_per_millisecond" name="k_a_plus" initial_value="12150000000.0"/>
<variable units="per_millisecond" name="k_a_minus" initial_value="0.576"/>
<variable units="millimolar3_per_millisecond" name="k_b_plus" initial_value="4050000.0"/>
<variable units="per_millisecond" name="k_b_minus" initial_value="1.930"/>
<variable units="per_millisecond" name="k_c_plus" initial_value="0.100"/>
<variable units="per_millisecond" name="k_c_minus" initial_value="0.0008"/>
<variable units="dimensionless" name="P_O1" initial_value="0.0006027"/>
<variable units="dimensionless" name="P_O2" initial_value="0.000000002882"/>
<variable units="dimensionless" name="P_C1" initial_value="0.4929"/>
<variable units="dimensionless" name="P_C2" initial_value="0.5056"/>
<variable units="dimensionless" name="n" initial_value="4.0"/>
<variable units="dimensionless" name="m" initial_value="3.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="P_C1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C1 </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> k_a_plus </ci>
</apply>
<apply>
<power/>
<ci> Ca_ss </ci>
<ci> n </ci>
</apply>
<ci> P_C1 </ci>
</apply>
<apply>
<times/>
<ci> k_a_minus </ci>
<ci> P_O1 </ci>
</apply>
</apply>
</apply>
<apply id="P_O1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_O1 </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> k_a_plus </ci>
<apply>
<power/>
<ci> Ca_ss </ci>
<ci> n </ci>
</apply>
<ci> P_C1 </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_a_minus </ci>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_b_plus </ci>
<apply>
<power/>
<ci> Ca_ss </ci>
<ci> m </ci>
</apply>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_c_plus </ci>
<ci> P_O1 </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k_b_minus </ci>
<ci> P_O2 </ci>
</apply>
<apply>
<times/>
<ci> k_c_minus </ci>
<ci> P_C2 </ci>
</apply>
</apply>
</apply>
<apply id="P_O2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_O2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_b_plus </ci>
<apply>
<power/>
<ci> Ca_ss </ci>
<ci> m </ci>
</apply>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_b_minus </ci>
<ci> P_O2 </ci>
</apply>
</apply>
</apply>
<apply id="P_C2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_c_plus </ci>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_c_minus </ci>
<ci> P_C2 </ci>
</apply>
</apply>
</apply>
<apply id="J_rel_calculation">
<eq/>
<ci> J_rel </ci>
<apply>
<times/>
<ci> v1 </ci>
<apply>
<plus/>
<ci> P_O1 </ci>
<ci> P_O2 </ci>
</apply>
<apply>
<minus/>
<ci> Ca_JSR </ci>
<ci> Ca_ss </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_Ca_fluxes">
<variable units="millimolar_per_millisecond" public_interface="out" name="J_tr"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="J_xfer"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="J_trpn"/>
<variable units="millisecond" name="tau_tr" initial_value="0.5747"/>
<variable units="millisecond" name="tau_xfer" initial_value="26.7"/>
<variable units="millimolar" name="HTRPNCa" initial_value="0.13664"/>
<variable units="millimolar" name="LTRPNCa" initial_value="0.0055443"/>
<variable units="millimolar_per_millisecond" name="J_HTRPNCa"/>
<variable units="millimolar_per_millisecond" name="J_LTRPNCa"/>
<variable units="millimolar" name="HTRPN_tot" initial_value="0.140"/>
<variable units="millimolar" name="LTRPN_tot" initial_value="0.070"/>
<variable units="millimolar_per_millisecond" name="k_htrpn_plus" initial_value="20.0"/>
<variable units="per_millisecond" name="k_htrpn_minus" initial_value="0.0000066"/>
<variable units="millimolar_per_millisecond" name="k_ltrpn_plus" initial_value="40.0"/>
<variable units="per_millisecond" name="k_ltrpn_minus" initial_value="0.040"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_NSR"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_tr_calculation">
<eq/>
<ci> J_tr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Ca_JSR </ci>
</apply>
<ci> tau_tr </ci>
</apply>
</apply>
<apply id="J_xfer_calculation">
<eq/>
<ci> J_xfer </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_ss </ci>
<ci> Ca_i </ci>
</apply>
<ci> tau_xfer </ci>
</apply>
</apply>
<apply id="J_trpn_calculation">
<eq/>
<ci> J_trpn </ci>
<apply>
<plus/>
<ci> J_HTRPNCa </ci>
<ci> J_LTRPNCa </ci>
</apply>
</apply>
<apply id="J_HTRPNCa_calculation">
<eq/>
<ci> J_HTRPNCa </ci>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> HTRPNCa </ci>
</apply>
</apply>
<apply id="HTRPNCa_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> HTRPNCa </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_htrpn_plus </ci>
<ci> Ca_i </ci>
<apply>
<minus/>
<ci> HTRPN_tot </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_htrpn_minus </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
</apply>
<apply id="J_LTRPNCa_calculation">
<eq/>
<ci> J_LTRPNCa </ci>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> LTRPNCa </ci>
</apply>
</apply>
<apply id="LTRPNCa_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> LTRPNCa </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_ltrpn_plus </ci>
<ci> Ca_i </ci>
<apply>
<minus/>
<ci> LTRPN_tot </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_ltrpn_minus </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable units="millimolar" public_interface="out" name="Nai" initial_value="10.0"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="8.464E-5"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="159.48"/>
<variable units="millimolar" public_interface="out" name="Ca_ss" initial_value="1.315E-4"/>
<variable units="millimolar" public_interface="out" name="Ca_JSR" initial_value="0.2616"/>
<variable units="millimolar" public_interface="out" name="Ca_NSR" initial_value="0.2620"/>
<variable units="cm2" name="A_cap" initial_value="0.0001534"/>
<variable units="micro_litre" name="V_JSR" initial_value="0.00000016"/>
<variable units="micro_litre" name="V_NSR" initial_value="0.0000021"/>
<variable units="millimolar" name="K_mCMDN" initial_value="0.00238"/>
<variable units="millimolar" name="K_mCSQN" initial_value="0.8"/>
<variable units="millimolar" name="CMDN_tot" initial_value="0.05"/>
<variable units="millimolar" name="CSQN_tot" initial_value="15.0"/>
<variable units="millimolar" name="beta_i"/>
<variable units="millimolar" name="beta_SS"/>
<variable units="millimolar" name="beta_JSR"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microF_per_cm2" public_interface="in" name="C_sc"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kr"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ks"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_to1"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="J_up"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="J_rel"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="J_xfer"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="J_trpn"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="J_tr"/>
<variable units="micro_litre" public_interface="in" name="V_myo"/>
<variable units="micro_litre" public_interface="in" name="V_ss"/>
<variable units="per_millimolar_per_millisecond" public_interface="in" name="k_plus_CaATP"/>
<variable units="per_millisecond" public_interface="in" name="k_minus_CaATP"/>
<variable units="per_millimolar_per_millisecond" public_interface="in" name="k_plus_CaADP"/>
<variable units="per_millisecond" public_interface="in" name="k_minus_CaADP"/>
<variable units="millimolar" public_interface="in" name="CaADP_i"/>
<variable units="millimolar" public_interface="in" name="CaADP_ss"/>
<variable units="millimolar" public_interface="in" name="CaATP_ss"/>
<variable units="millimolar" public_interface="in" name="ATP_i"/>
<variable units="millimolar" public_interface="in" name="ADP_i"/>
<variable units="millimolar" public_interface="in" name="ADP_ss"/>
<variable units="millimolar" public_interface="in" name="ATP_ss"/>
<variable units="millimolar" public_interface="in" name="CaATP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_i </ci>
<apply>
<minus/>
<ci> J_xfer </ci>
<apply>
<plus/>
<ci> J_up </ci>
<ci> J_trpn </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<minus/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
</apply>
<ci> i_p_Ca </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> A_cap </ci>
<ci> C_sc </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_i </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_i </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Nai_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Na_b </ci>
<apply>
<times/>
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> A_cap </ci>
<ci> C_sc </ci>
</apply>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ki_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Ca_K </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_to1 </ci>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> -2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> A_cap </ci>
<ci> C_sc </ci>
</apply>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_i_calculation">
<eq/>
<ci> beta_i </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CMDN_tot </ci>
<ci> K_mCMDN </ci>
</apply>
<apply>
<plus/>
<ci> K_mCMDN </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_SS_calculation">
<eq/>
<ci> beta_SS </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CMDN_tot </ci>
<ci> K_mCMDN </ci>
</apply>
<apply>
<plus/>
<ci> K_mCMDN </ci>
<apply>
<power/>
<ci> Ca_ss </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_JSR_calculation">
<eq/>
<ci> beta_JSR </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CSQN_tot </ci>
<ci> K_mCSQN </ci>
</apply>
<apply>
<plus/>
<ci> K_mCSQN </ci>
<apply>
<power/>
<ci> Ca_JSR </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_SS </ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci> J_rel </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> J_xfer </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> i_Ca </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> A_cap </ci>
<ci> C_sc </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_ss </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_ss </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_ss </ci>
<apply>
<plus/>
<ci> ADP_ss </ci>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_ss </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_JSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_JSR </ci>
</apply>
<apply>
<times/>
<ci> beta_JSR </ci>
<apply>
<minus/>
<ci> J_tr </ci>
<ci> J_rel </ci>
</apply>
</apply>
</apply>
<apply id="Ca_NSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_NSR </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> J_up </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_NSR </ci>
</apply>
</apply>
<apply>
<times/>
<ci> J_tr </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_NSR </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_and_Mg_buffering_by_ATP">
<variable units="millimolar" public_interface="out" name="CaATP_ss" initial_value="0.25E-3"/>
<variable units="millimolar" public_interface="out" name="ATP_ss" initial_value="0.56"/>
<variable units="millimolar" public_interface="out" name="MgATP_i" initial_value="6.4395"/>
<variable units="per_millimolar_per_millisecond" public_interface="out" name="k_plus_CaATP" initial_value="225.0"/>
<variable units="per_millisecond" public_interface="out" name="k_minus_CaATP" initial_value="45.0"/>
<variable units="per_millimolar_per_millisecond" public_interface="out" name="k_plus_CaADP" initial_value="125.0"/>
<variable units="per_millisecond" public_interface="out" name="k_minus_CaADP" initial_value="193.5"/>
<variable units="millimolar" public_interface="out" name="CaADP_i" initial_value="0.11E-6"/>
<variable units="millimolar" public_interface="out" name="CaADP_ss" initial_value="0.13E-6"/>
<variable units="millimolar" public_interface="out" name="ATP_i" initial_value="0.56"/>
<variable units="millimolar" public_interface="out" name="ADP_i" initial_value="0.002"/>
<variable units="millimolar" public_interface="out" name="ADP_ss" initial_value="0.002"/>
<variable units="millimolar" public_interface="out" name="CaATP_i" initial_value="0.237E-3"/>
<variable units="millimolar" name="Mg_ss" initial_value="1.0"/>
<variable units="millimolar" name="Mg_i" initial_value="1.0"/>
<variable units="millimolar" name="MgADP_i" initial_value="0.298E-2"/>
<variable units="millimolar" name="MgADP_ss" initial_value="0.298E-2"/>
<variable units="millimolar" name="MgATP_ss" initial_value="6.4395"/>
<variable units="millimolar" name="ATP_tot" initial_value="7.0"/>
<variable units="per_millimolar_per_millisecond" name="k_plus_MgATP" initial_value="125.0"/>
<variable units="per_millisecond" name="k_minus_MgATP" initial_value="10.875"/>
<variable units="millimolar_per_millisecond" name="Jxfer_CaATP"/>
<variable units="millimolar_per_millisecond" name="Jxfer_MgATP"/>
<variable units="millimolar_per_millisecond" name="Jxfer_Mg"/>
<variable units="millisecond" name="tau_xfer_CaATP" initial_value="53.4"/>
<variable units="millisecond" name="tau_xfer_MgATP" initial_value="53.4"/>
<variable units="millisecond" name="tau_xfer_Mg" initial_value="26.7"/>
<variable units="millimolar" name="ADP_tot" initial_value="0.005"/>
<variable units="per_millimolar_per_millisecond" name="k_plus_MgADP" initial_value="125.0"/>
<variable units="per_millisecond" name="k_minus_MgADP" initial_value="84.5"/>
<variable units="millimolar_per_millisecond" name="Jxfer_CaADP"/>
<variable units="millimolar_per_millisecond" name="Jxfer_MgADP"/>
<variable units="millisecond" name="tau_xfer_CaADP" initial_value="53.4"/>
<variable units="millisecond" name="tau_xfer_MgADP" initial_value="53.4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Ca_ss"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="micro_litre" public_interface="in" name="V_myo"/>
<variable units="micro_litre" public_interface="in" name="V_ss"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_ss_calculation">
<eq/>
<ci> ATP_ss </ci>
<apply>
<minus/>
<ci> ATP_tot </ci>
<apply>
<plus/>
<ci> CaATP_ss </ci>
<ci> MgATP_ss </ci>
</apply>
</apply>
</apply>
<apply id="CaATP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaATP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_CaATP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="MgATP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgATP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_MgATP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="ATP_i_calculation">
<eq/>
<ci> ATP_i </ci>
<apply>
<minus/>
<ci> ATP_tot </ci>
<apply>
<plus/>
<ci> CaATP_i </ci>
<ci> MgATP_i </ci>
</apply>
</apply>
</apply>
<apply id="CaATP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaATP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_CaATP </ci>
<apply>
<times/>
<ci> k_plus_CaATP </ci>
<ci> Ca_i </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaATP </ci>
<ci> CaATP_i </ci>
</apply>
</apply>
</apply>
<apply id="MgATP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgATP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_MgATP </ci>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_i </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_i </ci>
</apply>
</apply>
</apply>
<apply id="Jxfer_CaATP_calculation">
<eq/>
<ci> Jxfer_CaATP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> CaATP_ss </ci>
<ci> CaATP_i </ci>
</apply>
<ci> tau_xfer_CaATP </ci>
</apply>
</apply>
<apply id="Jxfer_MgATP_calculation">
<eq/>
<ci> Jxfer_MgATP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> MgATP_ss </ci>
<ci> MgATP_i </ci>
</apply>
<ci> tau_xfer_MgATP </ci>
</apply>
</apply>
<apply id="ADP_ss_calculation">
<eq/>
<ci> ADP_ss </ci>
<apply>
<minus/>
<ci> ADP_tot </ci>
<apply>
<plus/>
<ci> CaADP_ss </ci>
<ci> MgADP_ss </ci>
</apply>
</apply>
</apply>
<apply id="CaADP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaADP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_ss </ci>
<ci> ADP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_CaADP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="MgADP_ss_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgADP_ss </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_ss </ci>
<ci> ADP_ss </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Jxfer_MgADP </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_ss </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="ADP_i_calculation">
<eq/>
<ci> ADP_i </ci>
<apply>
<minus/>
<ci> ADP_tot </ci>
<apply>
<plus/>
<ci> CaADP_i </ci>
<ci> MgADP_i </ci>
</apply>
</apply>
</apply>
<apply id="CaADP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaADP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_CaADP </ci>
<apply>
<times/>
<ci> k_plus_CaADP </ci>
<ci> Ca_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_CaADP </ci>
<ci> CaADP_i </ci>
</apply>
</apply>
</apply>
<apply id="MgADP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> MgADP_i </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_MgADP </ci>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_i </ci>
</apply>
</apply>
</apply>
<apply id="Jxfer_CaADP_calculation">
<eq/>
<ci> Jxfer_CaADP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> CaADP_ss </ci>
<ci> CaADP_i </ci>
</apply>
<ci> tau_xfer_CaADP </ci>
</apply>
</apply>
<apply id="Jxfer_MgADP_calculation">
<eq/>
<ci> Jxfer_MgADP </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> MgADP_ss </ci>
<ci> MgADP_i </ci>
</apply>
<ci> tau_xfer_MgADP </ci>
</apply>
</apply>
<apply id="Mg_ss_calculation">
<eq/>
<ci> Mg_ss </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_ss </ci>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_ss </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_ss </ci>
<ci> ATP_ss </ci>
</apply>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_ss </ci>
<ci> ADP_ss </ci>
</apply>
<apply>
<times/>
<ci> Jxfer_Mg </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_ss </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Mg_i_calculation">
<eq/>
<ci> Mg_i </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> Jxfer_Mg </ci>
<apply>
<times/>
<ci> k_minus_MgATP </ci>
<ci> MgATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_minus_MgADP </ci>
<ci> MgADP_i </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_MgATP </ci>
<ci> Mg_i </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<times/>
<ci> k_plus_MgADP </ci>
<ci> Mg_i </ci>
<ci> ADP_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Jxfer_Mg_calculation">
<eq/>
<ci> Jxfer_Mg </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Mg_ss </ci>
<ci> Mg_i </ci>
</apply>
<ci> tau_xfer_Mg </ci>
</apply>
</apply>
</math>
</component>
<component name="standard_ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Nao" initial_value="138.0"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="2.0"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="4.0"/>
</component>
<component name="model_parameters">
<variable units="micro_litre" public_interface="out" name="V_myo" initial_value="0.00002584"/>
<variable units="micro_litre" public_interface="out" name="V_ss" initial_value="0.0000000012"/>
</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_to1_gate"/>
<component_ref component="transient_outward_potassium_current_Y_to1_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_y_gate"/>
</component_ref>
<component_ref component="RyR_channel"/>
<component_ref component="SERCA_pump"/>
<component_ref component="intracellular_Ca_fluxes"/>
<component_ref component="intracellular_ion_concentrations"/>
<component_ref component="standard_ionic_concentrations"/>
<component_ref component="Ca_and_Mg_buffering_by_ATP"/>
</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_to1_gate"/>
<component_ref component="transient_outward_potassium_current_Y_to1_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_y_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="Ca_and_Mg_buffering_by_ATP"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_activating_delayed_rectifiyer_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_activating_delayed_rectifiyer_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_outward_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="RyR_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_Ca_fluxes"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_ion_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="rapid_activating_delayed_rectifiyer_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="slow_activating_delayed_rectifiyer_K_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="transient_outward_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_to1" variable_1="i_to1"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
</connection>
<connection>
<map_components component_2="sarcolemmal_calcium_pump" component_1="membrane"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca" variable_1="i_Ca"/>
<map_variables variable_2="i_Ca_K" variable_1="i_Ca_K"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="C_sc" variable_1="C_sc"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="C_sc" variable_1="C_sc"/>
</connection>
<connection>
<map_components component_2="intracellular_ion_concentrations" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
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Model study of ATP and ADP buffering, transport of Ca2+ and Mg2+, and regulation of ion pumps in ventricular myocyte
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This is the CellML description of Michailova and McCulloch's mathematical model of ATP and ADP buffering, transport of Ca and Mg, and regulation of ion pumps in ventricular myocytes.
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The University of Auckland, Bioengineering Institute
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Michailova and McCulloch's mathematical model of ATP and ADP buffering, transport of Ca and Mg, and regulation of ion pumps in ventricular myocytes.
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