- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-12 13:55:11+13:00
- Desc:
- Added annotations to shiferaw_watanabe_gafinkel_weiss_karma_2003.cellml model
- Permanent Source URI:
- http://models.cellml.org/workspace/shiferaw_watanabe_garfinkel_weiss_karma_2003/rawfile/1a49ddac9d9ae581ab9b66445978742091d990ac/shiferaw_watanabe_garfinkel_weiss_karma_2003.cellml
<?xml version="1.0"?>
<!-- FILE : shiferaw_model_2003.xml
CREATED : 8th January 2004
LAST MODIFIED : 8th January 2004
AUTHOR : Catherine Lloyd
Bioengineering Instute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Shiferaw et al.'s 2003 mathematical model of intracellular calcium cycling in ventricular myocytes.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xml:base="file:///H:/shiferaw_watanabe_garfinkel_weiss_karma_2003/shiferaw_watanabe_garfinkel_weiss_karma_2003.cellml" cmeta:id="shiferaw_watanabe_garfinkel_weiss_karma_2003_version01" name="shiferaw_watanabe_garfinkel_weiss_karma_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Intracellular Calcium Cycling 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>
Cardiac myocyte contraction is stimulated by a rise in the concentration of intracellular calcium ([Ca<superscript>2+</superscript>]<subscript>i</subscript>), which in turn is due to the coordinated release of calcium from the sarcoplasmic reticulum (SR) via ryanodine receptors (RyR). These receptors are close to the L-type calcium channels in the cell surface membrane, and when the cell is depolarised, the calcium that enters the cell through the L-type channels is confined within a microdomain (the dyadic junction). The RyR then sense this increase in [Ca<superscript>2+</superscript>]<subscript>i</subscript> and respond by opening and releasing more calcium from the SR in a process known as calcium-induced calcium releases (CICR). The cell's contractile elements are activated by this increase in [Ca<superscript>2+</superscript>]<subscript>i</subscript> and the cell contracts. A calcium-activated uptake pump then pumps calcium back into the SR. This interaction between membrane potential and intracellular calcium cycling forms the basis of excitation-contraction (EC) coupling. The calcium system is driven by an action potential waveform that is itself dependent on the dynamics of the calcium system.
</para>
<para>
There have been several efforts to mathematically model intracellular calcium dynamics, such as:
</para>
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_RJW_MODEL}">Modelling the Functional Ca<superscript>2+</superscript> Release Unit, 1999, Rice <emphasis>et al.</emphasis>, 1999</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_STERN_MODEL}">Model of Ryanodine Receptor Gating in Cardiac Muscle, 1999, Stern <emphasis>et al.</emphasis>
</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_SOBIE_MODEL}">Sobie <emphasis>et al.</emphasis> Mechanism of Cardiac Ca<superscript>2+</superscript> Spark Termination, 2002</ulink>
</para>
</listitem>
</itemizedlist>
<para>
which focus on the detailed calcium dynamics within the dyadic junction. Several authors have developed models of calcium cycling at the whole cell level, including:
</para>
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_LR_II_MODEL}">Luo-Rudy Ventricular Model II (dynamic), 1994</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_JRW_MODEL}">Jafri-Rice-Winslow Ventricular Model, 1998</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_SNYDER_MODEL}">Snyder <emphasis>et al.</emphasis>, Cardiocyte Ca<superscript>2+</superscript> Dynamics, 2000</ulink>
</para>
</listitem>
</itemizedlist>
<para>However, some of these models are lacking in physiological detail; for example, some ignore intracellular calcium compartmentation, or they overlook the fact that calcium release from the SR is in fact the summation of several discrete events.
</para>
<para>
In the publication described here, Shiferaw <emphasis>et al.</emphasis> present a new model of EC coupling in ventricular myocytes (see <xref linkend="fig_cell_diagram"/> below). In contrast to the previously published models this one represents calcium release from the SR as a summation of elementary release events that correspond to calcium sparks. In addition, the model includes features that are absent in the earlier models, such as:
</para>
<itemizedlist>
<listitem>
<para>a description of intracellular sodium accumulation;</para>
</listitem>
<listitem>
<para>compartmentation of myoplasm into a submembrane space near the sarcolemma, and the rest of the myoplasm; and</para>
</listitem>
<listitem>
<para>a calcium diffusional delay between the network SR (NSR) and the junctional SR (JSR)</para>
</listitem>
</itemizedlist>
<para>
The model has been described here in CellML (the raw CellML description of the Shiferaw <emphasis>et al.</emphasis> 2003 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Model of Intracellular Calcium Cycling in Ventricular Myocytes, Y. Shiferaw, M. A. Wantanabe, A. Garfinkel, J. N. Weiss, and A. Karma, 2003, <emphasis>Biophysical Journal</emphasis>, 85, 3666-3686. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=14645059&dopt=Abstract">PubMed ID: 14645059</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="shiferaw_2003.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the intracellular compartments relevant to calcium cycling in ventricular myocytes.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<variable name="time" public_interface="out" units="second"/>
</component>
<component cmeta:id="id_00001" name="Ca_concentration_in_the_dyadic_space">
<variable name="cp" public_interface="out" units="micromolar"/>
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<variable cmeta:id="id_00023" name="i_Ca" public_interface="in" units="picoA"/>
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</math>
</component>
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<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f_infinity </ci>
</apply>
<ci> tau_f </ci>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00020" name="Na_Ca_exchanger">
<variable cmeta:id="id_00021" name="I_NaCa" public_interface="out" units="picoA"/>
<variable cmeta:id="id_00022" initial_value="2E4" name="K_NaCa" units="flux"/>
<variable initial_value="87.5" name="K_mNa" units="millimolar"/>
<variable initial_value="1.38" name="K_mCa" units="millimolar"/>
<variable initial_value="0.1" name="K_sat" units="dimensionless"/>
<variable initial_value="0.35" name="eta" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="joule_per_mole_kelvin"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="Nai" public_interface="in" units="millimolar"/>
<variable name="Nao" public_interface="in" units="millimolar"/>
<variable name="cs" public_interface="in" units="micromolar"/>
<variable name="Cao" public_interface="in" units="millimolar"/>
<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"> 1.0 </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> cs </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="uptake_current">
<variable name="I_up" public_interface="out" units="picoA"/>
<variable initial_value="250.0" name="vup" units="flux"/>
<variable initial_value="0.5" name="cup" units="micromolar"/>
<variable name="ci" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="I_up_calculation">
<eq/>
<ci> I_up </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> vup </ci>
<apply>
<power/>
<ci> ci </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> ci </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> cup </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_buffering">
<variable name="beta_ci" public_interface="out" units="dimensionless"/>
<variable name="beta_cs" public_interface="out" units="dimensionless"/>
<variable name="I_trpn_i" public_interface="out" units="picoA"/>
<variable name="I_trpn_s" public_interface="out" units="picoA"/>
<variable name="CaTi" units="micromolar"/>
<variable name="CaTs" units="micromolar"/>
<variable initial_value="32.7" name="kT_on" units="second_order_rate_constant"/>
<variable initial_value="19.6" name="kT_off" units="first_order_rate_constant"/>
<variable initial_value="70.0" name="BT" units="micromolar"/>
<variable initial_value="47.0" name="BSR" units="micromolar"/>
<variable initial_value="24.0" name="BCd" units="micromolar"/>
<variable initial_value="0.6" name="KSR" units="micromolar"/>
<variable initial_value="7.0" name="KCd" units="micromolar"/>
<variable name="ci" public_interface="in" units="micromolar"/>
<variable name="cs" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CaTi_calculation">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaTi </ci>
</apply>
<ci> I_trpn_i </ci>
</apply>
<apply id="I_trpn_i_calculation">
<eq/>
<ci> I_trpn_i </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> kT_on </ci>
<ci> ci </ci>
<apply>
<minus/>
<ci> BT </ci>
<ci> CaTi </ci>
</apply>
</apply>
<apply>
<times/>
<ci> kT_off </ci>
<ci> CaTi </ci>
</apply>
</apply>
</apply>
<apply id="beta_ci_calculation">
<eq/>
<ci> beta_ci </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> BSR </ci>
<ci> KSR </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> ci </ci>
<ci> KSR </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> BCd </ci>
<ci> KCd </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> ci </ci>
<ci> KCd </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
<apply id="CaTs_calculation">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaTs </ci>
</apply>
<ci> I_trpn_s </ci>
</apply>
<apply id="I_trpn_s_calculation">
<eq/>
<ci> I_trpn_s </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> kT_on </ci>
<ci> cs </ci>
<apply>
<minus/>
<ci> BT </ci>
<ci> CaTs </ci>
</apply>
</apply>
<apply>
<times/>
<ci> kT_off </ci>
<ci> CaTs </ci>
</apply>
</apply>
</apply>
<apply id="beta_cs_calculation">
<eq/>
<ci> beta_cs </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> BSR </ci>
<ci> KSR </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> cs </ci>
<ci> KSR </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> BCd </ci>
<ci> KCd </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> cs </ci>
<ci> KCd </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00024" name="Ca_concentration_in_the_submembrane_space">
<variable name="cs" public_interface="out" units="micromolar"/>
<variable initial_value="0.0001" name="vi" units="microlitre"/>
<variable initial_value="0.00001" name="vs" units="microlitre"/>
<variable name="taus" public_interface="in" units="millisecond"/>
<variable name="beta_cs" public_interface="in" units="dimensionless"/>
<variable name="ci" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_00025" name="I_Ca" public_interface="in" units="picoA"/>
<variable cmeta:id="id_00026" name="I_NaCa" public_interface="in" units="picoA"/>
<variable name="I_r" public_interface="in" units="picoA"/>
<variable name="I_trpn_s" public_interface="in" units="picoA"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dcs_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> cs </ci>
</apply>
<apply>
<times/>
<ci> beta_cs </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> vi </ci>
<ci> vs </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci> I_r </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> cs </ci>
<ci> ci </ci>
</apply>
<ci> taus </ci>
</apply>
<ci> I_Ca </ci>
</apply>
</apply>
<ci> I_NaCa </ci>
</apply>
</apply>
<ci> I_trpn_s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_concentration_in_the_cytosol">
<variable name="ci" public_interface="out" units="micromolar"/>
<variable name="taus" public_interface="in" units="millisecond"/>
<variable name="beta_ci" public_interface="in" units="dimensionless"/>
<variable name="cs" public_interface="in" units="micromolar"/>
<variable name="I_up" public_interface="in" units="picoA"/>
<variable name="I_trpn_i" public_interface="in" units="picoA"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dci_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ci </ci>
</apply>
<apply>
<times/>
<ci> beta_ci </ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> cs </ci>
<ci> ci </ci>
</apply>
<ci> taus </ci>
</apply>
<apply>
<plus/>
<ci> I_up </ci>
<ci> I_trpn_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="total_Ca_concentration_in_the_SR">
<variable name="cj" public_interface="out" units="micromolar"/>
<variable name="I_up" public_interface="in" units="picoA"/>
<variable name="I_r" public_interface="in" units="picoA"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dcj_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> cj </ci>
</apply>
<apply>
<minus/>
<ci> I_up </ci>
<ci> I_r </ci>
</apply>
</apply>
</math>
</component>
<component name="average_Ca_concentration_in_unrecruited_JSR_compartments">
<variable name="cj_" public_interface="out" units="micromolar"/>
<variable initial_value="50.0" name="taua" units="millisecond"/>
<variable name="cj" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dcj__dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> cj_ </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> cj </ci>
<ci> cj_ </ci>
</apply>
<ci> taua </ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_flux_out_of_the_SR">
<variable name="I_r" public_interface="out" units="picoA"/>
<variable name="N" units="sparks"/>
<variable initial_value="20.0" name="taur" units="millisecond"/>
<variable initial_value="1.5E4" name="g" units="sparks_per_micromolar"/>
<variable name="Q" units="micromolar"/>
<variable name="s" units="micromolar"/>
<variable name="A" units="dimensionless"/>
<variable initial_value="11.3" name="u" units="first_order_rate_constant"/>
<variable name="I_Ca" public_interface="in" units="picoA"/>
<variable name="cj_" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="I_r_calculation">
<eq/>
<ci> I_r </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> g </ci>
<ci> I_Ca </ci>
<ci> Q </ci>
<apply>
<divide/>
<ci> I_r </ci>
<ci> taur </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="N_calculation">
<eq/>
<ci> N </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> g </ci>
<ci> I_Ca </ci>
<ci> A </ci>
</apply>
</apply>
</apply>
<apply id="Q_calculation">
<eq/>
<ci> Q </ci>
<piecewise>
<piece>
<cn cellml:units="micromolar"> 0.0 </cn>
<apply>
<and/>
<apply>
<lt/>
<ci> cj_ </ci>
<cn cellml:units="micromolar"> 50.0 </cn>
</apply>
<apply>
<gt/>
<ci> cj_ </ci>
<cn cellml:units="micromolar"> 0.0 </cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<minus/>
<ci> cj_ </ci>
<cn cellml:units="micromolar"> 50.0 </cn>
</apply>
<apply>
<and/>
<apply>
<lt/>
<ci> cj_ </ci>
<cn cellml:units="micromolar"> 115.0 </cn>
</apply>
<apply>
<geq/>
<ci> cj_ </ci>
<cn cellml:units="micromolar"> 50.0 </cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<plus/>
<apply>
<times/>
<ci> u </ci>
<ci> cj_ </ci>
</apply>
<ci> s </ci>
</apply>
<apply>
<geq/>
<ci> cj_ </ci>
<cn cellml:units="micromolar"> 115.0 </cn>
</apply>
</piece>
</piecewise>
</apply>
</math>
</component>
<component name="membrane">
<variable name="V" public_interface="out" units="millivolt"/>
<variable initial_value="-80.0" name="Vmin" units="millivolt"/>
<variable initial_value="30.0" name="Vmax" units="millivolt"/>
<variable name="m" units="dimensionless"/>
<variable name="x" units="dimensionless"/>
<variable initial_value="0.666667" name="a" units="dimensionless"/>
<variable name="T" units="second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_calculation">
<eq/>
<ci> V </ci>
<piecewise>
<piece>
<apply>
<plus/>
<ci> Vmin </ci>
<apply>
<times/>
<apply>
<minus/>
<ci> Vmax </ci>
<ci> Vmin </ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci> time </ci>
<apply>
<times/>
<ci> m </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<times/>
<ci> m </ci>
<ci> T </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.5 </cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<leq/>
<ci> time </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> m </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<ci> x </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci> time </ci>
<apply>
<times/>
<ci> m </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</piece>
<piece>
<ci> Vmin </ci>
<apply>
<and/>
<apply>
<lt/>
<ci> time </ci>
<apply>
<times/>
<apply>
<plus/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> T </ci>
</apply>
</apply>
<apply>
<gt/>
<ci> time </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> m </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<ci> x </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</piece>
</piecewise>
</apply>
<apply id="x_calculation">
<eq/>
<ci> x </ci>
<apply>
<divide/>
<ci> a </ci>
<apply>
<plus/>
<ci> a </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_Na_concentration">
<variable name="Nai" public_interface="out" units="millimolar"/>
<variable name="a" units="millimolar"/>
<variable name="b" units="dimensionless"/>
<variable name="T" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Nai_calculation">
<eq/>
<ci> Nai </ci>
<apply>
<divide/>
<ci> a </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> b </ci>
<apply>
<power/>
<ci> T </ci>
<cn cellml:units="dimensionless"> 0.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="physical_constants_and_ionic_concentrations">
<variable initial_value="140.0" name="Nao" public_interface="out" units="millimolar"/>
<variable initial_value="1.8" name="Cao" public_interface="out" units="millimolar"/>
<variable initial_value="8.314" name="R" public_interface="out" units="joule_per_mole_kelvin"/>
<variable initial_value="310.0" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="9.65E4" name="F" public_interface="out" units="coulomb_per_mole"/>
<variable initial_value="10.0" name="taus" public_interface="out" units="millisecond"/>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="Ca_concentration_in_the_dyadic_space"/>
<component_ref component="Ca_concentration_in_the_local_JSR"/>
<component_ref component="Ca_concentration_in_the_submembrane_space"/>
<component_ref component="Ca_concentration_in_the_cytosol"/>
<component_ref component="total_Ca_concentration_in_the_SR"/>
<component_ref component="average_Ca_concentration_in_unrecruited_JSR_compartments"/>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
</component_ref>
<component_ref component="release_current"/>
<component_ref component="transfer_current"/>
<component_ref component="uptake_current"/>
<component_ref component="diffusion_current"/>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="calcium_buffering"/>
<component_ref component="Ca_flux_out_of_the_SR"/>
<component_ref component="intracellular_Na_concentration"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="Ca_concentration_in_the_dyadic_space" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_concentration_in_the_local_JSR" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="release_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="diffusion_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="transfer_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="calcium_buffering" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="environment"/>
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