<?xml version="1.0"?>
<!--
This CellML file was generated on 20/12/2007 at 3:22:13 at PM using:
COR (0.9.31.769)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:base="" cmeta:id="Hinch_2004" name="Hinch">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is known to run in OpenCell and COR to reproduce the output shown in the publication.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Calcium (Ca2+)-induced Ca2+ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca2+ release. Existing local control models of Ca2+ release in which interactions between L-Type Ca2+ channels (LCCs) and ryanodine-sensitive Ca2+ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca2+ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca2+ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost.
</para>
<para>
The original publication reference is cited below:
</para>
<para>
A Simplified Local Control Model of Calcium-Induced Calcium Release in Cardiac Ventricular Myocytes, R. Hinch, J.R. Greenstein, A.J. Tanskanen, L. Xu, R.L. Winslow, 2004 <emphasis>Biophysical Journal</emphasis>, 87, 3723-3736, <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/15465866">PubMed ID: 15465866</ulink>
</para>
<informalfigure float="0" id="cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>state diagram</title>
</objectinfo>
<imagedata fileref="hinch_2004.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the currents and the ion exchanges described by the cardiac ventricular myocyte model.</caption>
</informalfigure>
<informalfigure float="0" id="markov_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>state diagram</title>
</objectinfo>
<imagedata fileref="hinch_2004b.png"/>
</imageobject>
</mediaobject>
<caption>The nine-state Markov model of the calcium release unit (CaRU). In state yij, the LCC is in the state i and the RyR is in the state j.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="per_ms">
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<units name="mM">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="mM_per_ms">
<unit units="mM"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="per_mM_ms">
<unit exponent="-1" units="mM"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="mM_per_mV_ms">
<unit units="mM"/>
<unit exponent="-1" prefix="milli" units="second"/>
<unit exponent="-1" prefix="milli" units="volt"/>
</units>
<units name="per_ms3">
<unit exponent="-3" prefix="milli" units="second"/>
</units>
<units name="um2">
<unit exponent="2" prefix="micro" units="meter"/>
</units>
<units name="um3">
<unit exponent="3" prefix="micro" units="meter"/>
</units>
<units name="um3_per_ms">
<unit exponent="3" prefix="micro" units="meter"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="um3_mM_per_ms">
<unit exponent="3" prefix="micro" units="meter"/>
<unit units="mM"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="mJ_per_mole_K">
<unit prefix="milli" units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="C_per_mole">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="ms"/>
</component>
<component name="cell_geometry">
<variable initial_value="25.84e3" name="V_myo" public_interface="out" units="um3"/>
<variable initial_value="2.098e3" name="V_SR" public_interface="out" units="um3"/>
<variable initial_value="1.534e4" name="A_cap" public_interface="out" units="um2"/>
</component>
<component name="membrane">
<variable cmeta:id="membrane_V" name="V" public_interface="out" units="mV"/>
<variable initial_value="8314.5" name="R" public_interface="out" units="mJ_per_mole_K"/>
<variable initial_value="295" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="96487" name="F" public_interface="out" units="C_per_mole"/>
<variable name="time" public_interface="in" units="ms"/>
<variable name="FVRT" public_interface="out" units="dimensionless"/>
<variable name="FVRT_Ca" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>FVRT</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>FVRT_Ca</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>FVRT</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V</ci>
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<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">0</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">0</cn>
</apply>
<apply>
<leq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">200</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">80</cn>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="CaRU">
<variable initial_value="0.065" name="g_D" private_interface="out" units="um3_per_ms"/>
<variable initial_value="0.02" name="J_R" private_interface="out" units="um3_per_ms"/>
<variable initial_value="9.13e-4" name="J_L" private_interface="out" units="um3_per_ms"/>
<variable name="V_myo" private_interface="out" public_interface="in" units="um3"/>
<variable initial_value="50000" name="N" private_interface="out" units="dimensionless"/>
<variable name="V" private_interface="out" public_interface="in" units="mV"/>
<variable name="Ca_i" private_interface="out" public_interface="in" units="mM"/>
<variable name="Ca_o" private_interface="out" public_interface="in" units="mM"/>
<variable name="Ca_SR" private_interface="out" public_interface="in" units="mM"/>
<variable name="time" private_interface="out" public_interface="in" units="ms"/>
<variable name="FVRT_Ca" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="I_RyR" private_interface="in" public_interface="out" units="mM_per_ms"/>
<variable name="I_LCC" private_interface="in" public_interface="out" units="mM_per_ms"/>
</component>
<component name="CaRU_Transitions">
<variable name="V" public_interface="in" units="mV"/>
<variable name="C_oc" public_interface="in" units="mM"/>
<variable name="C_co" public_interface="in" units="mM"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable initial_value="-2" name="V_L" units="mV"/>
<variable initial_value="7" name="del_VL" units="mV"/>
<variable initial_value="2.35" name="phi_L" units="dimensionless"/>
<variable initial_value="1" name="t_L" units="ms"/>
<variable initial_value="650" name="tau_L" units="ms"/>
<variable name="t_R" units="ms"/>
<variable initial_value="2.43" name="tau_R" units="ms"/>
<variable initial_value="0.05" name="phi_R" units="dimensionless"/>
<variable initial_value="0.012" name="theta_R" units="dimensionless"/>
<variable initial_value="41e-3" name="K_RyR" units="mM"/>
<variable initial_value="0.22e-3" name="K_L" units="mM"/>
<variable initial_value="0.0625" name="a" units="dimensionless"/>
<variable initial_value="14" name="b" units="dimensionless"/>
<variable initial_value="0.01" name="c" units="dimensionless"/>
<variable initial_value="100" name="d" units="dimensionless"/>
<variable name="expVL" units="dimensionless"/>
<variable name="alpha_p" public_interface="out" units="per_ms"/>
<variable name="alpha_m" public_interface="out" units="per_ms"/>
<variable name="beta_poc" public_interface="out" units="per_ms"/>
<variable name="beta_pcc" public_interface="out" units="per_ms"/>
<variable name="beta_m" public_interface="out" units="per_ms"/>
<variable name="epsilon_pco" public_interface="out" units="per_ms"/>
<variable name="epsilon_pcc" public_interface="out" units="per_ms"/>
<variable name="epsilon_m" public_interface="out" units="per_ms"/>
<variable name="mu_poc" public_interface="out" units="per_ms"/>
<variable name="mu_pcc" public_interface="out" units="per_ms"/>
<variable name="mu_moc" public_interface="out" units="per_ms"/>
<variable name="mu_mcc" public_interface="out" units="per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>expVL</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_L</ci>
</apply>
<ci>del_VL</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>t_R</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.17</cn>
<ci>t_L</ci>
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</apply>
<apply>
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<ci>alpha_p</ci>
<apply>
<divide/>
<ci>expVL</ci>
<apply>
<times/>
<ci>t_L</ci>
<apply>
<plus/>
<ci>expVL</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<ci>phi_L</ci>
<ci>t_L</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_poc</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>t_R</ci>
<apply>
<plus/>
<apply>
<power/>
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_pcc</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>t_R</ci>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<divide/>
<ci>phi_R</ci>
<ci>t_R</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>epsilon_pco</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>C_co</ci>
<apply>
<plus/>
<ci>expVL</ci>
<ci>a</ci>
</apply>
</apply>
<apply>
<times/>
<ci>tau_L</ci>
<ci>K_L</ci>
<apply>
<plus/>
<ci>expVL</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>epsilon_pcc</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>expVL</ci>
<ci>a</ci>
</apply>
</apply>
<apply>
<times/>
<ci>tau_L</ci>
<ci>K_L</ci>
<apply>
<plus/>
<ci>expVL</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>epsilon_m</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>b</ci>
<apply>
<plus/>
<ci>expVL</ci>
<ci>a</ci>
</apply>
</apply>
<apply>
<times/>
<ci>tau_L</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>b</ci>
<ci>expVL</ci>
</apply>
<ci>a</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_poc</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<power/>
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>c</ci>
<apply>
<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>tau_R</ci>
<apply>
<plus/>
<apply>
<power/>
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_pcc</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>c</ci>
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<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>tau_R</ci>
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<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_moc</ci>
<apply>
<divide/>
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<times/>
<ci>theta_R</ci>
<ci>d</ci>
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<plus/>
<apply>
<power/>
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>c</ci>
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<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>tau_R</ci>
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<plus/>
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<times/>
<ci>d</ci>
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<power/>
<ci>C_oc</ci>
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<times/>
<ci>c</ci>
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<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_mcc</ci>
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<divide/>
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<times/>
<ci>theta_R</ci>
<ci>d</ci>
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<plus/>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>c</ci>
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<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>tau_R</ci>
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<plus/>
<apply>
<times/>
<ci>d</ci>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>c</ci>
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<power/>
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="DS_Calcium_Concentrations">
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="Ca_SR" public_interface="in" units="mM"/>
<variable name="Ca_o" public_interface="in" units="mM"/>
<variable name="FVRT_Ca" public_interface="in" units="dimensionless"/>
<variable name="g_D" public_interface="in" units="um3_per_ms"/>
<variable name="J_R" public_interface="in" units="um3_per_ms"/>
<variable name="J_L" public_interface="in" units="um3_per_ms"/>
<variable name="C_cc" public_interface="out" units="mM"/>
<variable name="C_oc" public_interface="out" units="mM"/>
<variable name="C_co" public_interface="out" units="mM"/>
<variable name="C_oo" public_interface="out" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_cc</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<eq/>
<ci>C_co</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_SR</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C_oc</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_o</ci>
<ci>FVRT_Ca</ci>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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<apply>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
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<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<apply>
<abs/>
<ci>FVRT_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.000000001</cn>
</apply>
</piece>
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<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_o</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>C_oo</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_SR</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_o</ci>
<ci>FVRT_Ca</ci>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<apply>
<abs/>
<ci>FVRT_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.000000001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ca_i</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_SR</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>Ca_o</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="LCC_and_RyR_fluxes">
<variable name="g_D" public_interface="in" units="um3_per_ms"/>
<variable name="J_R" public_interface="in" units="um3_per_ms"/>
<variable name="J_L" public_interface="in" units="um3_per_ms"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="Ca_SR" public_interface="in" units="mM"/>
<variable name="Ca_o" public_interface="in" units="mM"/>
<variable name="FVRT_Ca" public_interface="in" units="dimensionless"/>
<variable name="J_Loo" public_interface="out" units="um3_mM_per_ms"/>
<variable name="J_Loc" public_interface="out" units="um3_mM_per_ms"/>
<variable name="J_Rco" public_interface="out" units="um3_mM_per_ms"/>
<variable name="J_Roo" public_interface="out" units="um3_mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_Rco</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>J_R</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_Roo</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<ci>J_R</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>Ca_SR</ci>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<apply>
<abs/>
<ci>FVRT_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>J_R</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>Ca_SR</ci>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>J_Loc</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_L</ci>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
<ci>Ca_i</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<apply>
<abs/>
<ci>FVRT_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_L</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
<ci>Ca_i</ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>J_Loo</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_L</ci>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
<ci>Ca_SR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<ci>FVRT_Ca</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<ci>FVRT_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<apply>
<abs/>
<ci>FVRT_Ca</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>J_L</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
<ci>Ca_SR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>J_R</ci>
<ci>g_D</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>J_L</ci>
<ci>g_D</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="CaRU_states">
<variable name="alpha_p" public_interface="in" units="per_ms"/>
<variable name="alpha_m" public_interface="in" units="per_ms"/>
<variable name="beta_pcc" public_interface="in" units="per_ms"/>
<variable name="beta_poc" public_interface="in" units="per_ms"/>
<variable name="beta_m" public_interface="in" units="per_ms"/>
<variable name="denom" units="per_ms3"/>
<variable name="y_oc" public_interface="out" units="dimensionless"/>
<variable name="y_co" public_interface="out" units="dimensionless"/>
<variable name="y_oo" public_interface="out" units="dimensionless"/>
<variable name="y_cc" public_interface="out" units="dimensionless"/>
<variable name="y_ci" public_interface="out" units="dimensionless"/>
<variable name="y_oi" public_interface="out" units="dimensionless"/>
<variable name="y_ic" public_interface="out" units="dimensionless"/>
<variable name="y_io" public_interface="out" units="dimensionless"/>
<variable name="y_ii" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>denom</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<ci>alpha_m</ci>
<ci>beta_m</ci>
<ci>beta_poc</ci>
</apply>
<apply>
<plus/>
<ci>beta_m</ci>
<ci>beta_pcc</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha_p</ci>
<apply>
<plus/>
<ci>beta_m</ci>
<ci>beta_poc</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>y_oc</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_p</ci>
<ci>beta_m</ci>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
<ci>beta_m</ci>
<ci>beta_pcc</ci>
</apply>
</apply>
<ci>denom</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>y_co</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_m</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_pcc</ci>
<apply>
<plus/>
<ci>alpha_m</ci>
<ci>beta_m</ci>
<ci>beta_poc</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_poc</ci>
<ci>alpha_p</ci>
</apply>
</apply>
</apply>
<ci>denom</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>y_oo</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_p</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_poc</ci>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>beta_m</ci>
<ci>beta_pcc</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_pcc</ci>
<ci>alpha_m</ci>
</apply>
</apply>
</apply>
<ci>denom</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>y_cc</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_m</ci>
<ci>beta_m</ci>
<apply>
<plus/>
<ci>alpha_m</ci>
<ci>alpha_p</ci>
<ci>beta_m</ci>
<ci>beta_poc</ci>
</apply>
</apply>
<ci>denom</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>y_ci</ci>
<apply>
<divide/>
<ci>alpha_m</ci>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>y_oi</ci>
<apply>
<divide/>
<ci>alpha_p</ci>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>y_ic</ci>
<apply>
<divide/>
<ci>beta_m</ci>
<apply>
<plus/>
<ci>beta_pcc</ci>
<ci>beta_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>y_io</ci>
<apply>
<divide/>
<ci>beta_pcc</ci>
<apply>
<plus/>
<ci>beta_pcc</ci>
<ci>beta_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>y_ii</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>y_oc</ci>
</apply>
<ci>y_co</ci>
</apply>
<ci>y_oo</ci>
</apply>
<ci>y_cc</ci>
</apply>
<ci>y_ci</ci>
</apply>
<ci>y_ic</ci>
</apply>
<ci>y_oi</ci>
</apply>
<ci>y_io</ci>
</apply>
</apply>
</math>
</component>
<component name="CaRU_reduced_states">
<variable name="y_oc" public_interface="in" units="dimensionless"/>
<variable name="y_cc" public_interface="in" units="dimensionless"/>
<variable name="y_co" public_interface="in" units="dimensionless"/>
<variable name="alpha_p" public_interface="in" units="per_ms"/>
<variable name="alpha_m" public_interface="in" units="per_ms"/>
<variable name="beta_pcc" public_interface="in" units="per_ms"/>
<variable name="beta_m" public_interface="in" units="per_ms"/>
<variable name="epsilon_pco" public_interface="in" units="per_ms"/>
<variable name="epsilon_pcc" public_interface="in" units="per_ms"/>
<variable name="epsilon_m" public_interface="in" units="per_ms"/>
<variable name="mu_poc" public_interface="in" units="per_ms"/>
<variable name="mu_pcc" public_interface="in" units="per_ms"/>
<variable name="mu_moc" public_interface="in" units="per_ms"/>
<variable name="mu_mcc" public_interface="in" units="per_ms"/>
<variable name="r_1" public_interface="out" units="per_ms"/>
<variable name="r_2" public_interface="out" units="per_ms"/>
<variable name="r_3" public_interface="out" units="per_ms"/>
<variable name="r_4" public_interface="out" units="per_ms"/>
<variable name="r_5" public_interface="out" units="per_ms"/>
<variable name="r_6" public_interface="out" units="per_ms"/>
<variable name="r_7" public_interface="out" units="per_ms"/>
<variable name="r_8" public_interface="out" units="per_ms"/>
<variable initial_value="0.98859" name="z_1" public_interface="out" units="dimensionless"/>
<variable initial_value="0.0087302" name="z_2" public_interface="out" units="dimensionless"/>
<variable initial_value="0.0026566" name="z_3" public_interface="out" units="dimensionless"/>
<variable name="z_4" public_interface="out" units="dimensionless"/>
<variable name="time" public_interface="in" units="ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>y_oc</ci>
<ci>mu_poc</ci>
</apply>
<apply>
<times/>
<ci>y_cc</ci>
<ci>mu_pcc</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_2</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_p</ci>
<ci>mu_moc</ci>
</apply>
<apply>
<times/>
<ci>alpha_m</ci>
<ci>mu_mcc</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>beta_m</ci>
<ci>mu_pcc</ci>
</apply>
<apply>
<plus/>
<ci>beta_m</ci>
<ci>beta_pcc</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_4</ci>
<ci>mu_mcc</ci>
</apply>
<apply>
<eq/>
<ci>r_5</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>y_co</ci>
<ci>epsilon_pco</ci>
</apply>
<apply>
<times/>
<ci>y_cc</ci>
<ci>epsilon_pcc</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_6</ci>
<ci>epsilon_m</ci>
</apply>
<apply>
<eq/>
<ci>r_7</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_m</ci>
<ci>epsilon_pcc</ci>
</apply>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_8</ci>
<ci>epsilon_m</ci>
</apply>
<apply>
<eq/>
<ci>z_4</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>z_1</ci>
</apply>
<ci>z_2</ci>
</apply>
<ci>z_3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z_1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>r_1</ci>
<ci>r_5</ci>
</apply>
</apply>
<ci>z_1</ci>
</apply>
<apply>
<times/>
<ci>r_2</ci>
<ci>z_2</ci>
</apply>
<apply>
<times/>
<ci>r_6</ci>
<ci>z_3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z_2</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>r_1</ci>
<ci>z_1</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>r_2</ci>
<ci>r_7</ci>
</apply>
<ci>z_2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>r_8</ci>
<ci>z_4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z_3</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>r_5</ci>
<ci>z_1</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>r_6</ci>
<ci>r_3</ci>
</apply>
<ci>z_3</ci>
</apply>
</apply>
<apply>
<times/>
<ci>r_4</ci>
<ci>z_4</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="RyR_current">
<variable name="y_oo" public_interface="in" units="dimensionless"/>
<variable name="y_co" public_interface="in" units="dimensionless"/>
<variable name="y_oc" public_interface="in" units="dimensionless"/>
<variable name="beta_pcc" public_interface="in" units="per_ms"/>
<variable name="beta_m" public_interface="in" units="per_ms"/>
<variable name="J_Roo" public_interface="in" units="um3_mM_per_ms"/>
<variable name="J_Rco" public_interface="in" units="um3_mM_per_ms"/>
<variable name="z_1" public_interface="in" units="dimensionless"/>
<variable name="z_3" public_interface="in" units="dimensionless"/>
<variable name="V_myo" public_interface="in" units="um3"/>
<variable name="N" public_interface="in" units="dimensionless"/>
<variable name="J_R1" public_interface="out" units="um3_mM_per_ms"/>
<variable name="J_R3" public_interface="out" units="um3_mM_per_ms"/>
<variable cmeta:id="RyR_current_I_RyR" name="I_RyR" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_R1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>y_oo</ci>
<ci>J_Roo</ci>
</apply>
<apply>
<times/>
<ci>J_Rco</ci>
<ci>y_co</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_R3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>J_Rco</ci>
<ci>beta_pcc</ci>
</apply>
<apply>
<plus/>
<ci>beta_m</ci>
<ci>beta_pcc</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_RyR</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>z_1</ci>
<ci>J_R1</ci>
</apply>
<apply>
<times/>
<ci>z_3</ci>
<ci>J_R3</ci>
</apply>
</apply>
<ci>N</ci>
</apply>
<ci>V_myo</ci>
</apply>
</apply>
</math>
</component>
<component name="LCC_current">
<variable name="y_oo" public_interface="in" units="dimensionless"/>
<variable name="y_oc" public_interface="in" units="dimensionless"/>
<variable name="alpha_p" public_interface="in" units="per_ms"/>
<variable name="alpha_m" public_interface="in" units="per_ms"/>
<variable name="J_Loo" public_interface="in" units="um3_mM_per_ms"/>
<variable name="J_Loc" public_interface="in" units="um3_mM_per_ms"/>
<variable name="z_1" public_interface="in" units="dimensionless"/>
<variable name="z_2" public_interface="in" units="dimensionless"/>
<variable name="V_myo" public_interface="in" units="um3"/>
<variable name="N" public_interface="in" units="dimensionless"/>
<variable name="J_L1" public_interface="out" units="um3_mM_per_ms"/>
<variable name="J_L2" public_interface="out" units="um3_mM_per_ms"/>
<variable cmeta:id="LCC_current_I_LCC" name="I_LCC" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_L1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>J_Loo</ci>
<ci>y_oo</ci>
</apply>
<apply>
<times/>
<ci>J_Loc</ci>
<ci>y_oc</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_L2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>J_Loc</ci>
<ci>alpha_p</ci>
</apply>
<apply>
<plus/>
<ci>alpha_p</ci>
<ci>alpha_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_LCC</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>z_1</ci>
<ci>J_L1</ci>
</apply>
<apply>
<times/>
<ci>z_2</ci>
<ci>J_L2</ci>
</apply>
</apply>
<ci>N</ci>
</apply>
<ci>V_myo</ci>
</apply>
</apply>
</math>
</component>
<component name="Na_Ca_Exchanger">
<variable name="FVRT" public_interface="in" units="dimensionless"/>
<variable initial_value="87.5" name="K_mNa" units="mM"/>
<variable initial_value="1.38" name="K_mCa" units="mM"/>
<variable initial_value="0.35" name="eta" units="dimensionless"/>
<variable initial_value="0.1" name="k_sat" units="dimensionless"/>
<variable initial_value="38.5e-3" name="g_NCX" units="mM_per_ms"/>
<variable name="Na_i" public_interface="in" units="mM"/>
<variable name="Na_o" public_interface="in" units="mM"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="Ca_o" public_interface="in" units="mM"/>
<variable cmeta:id="Na_Ca_Exchanger_I_NaCa" name="I_NaCa" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_NCX</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<ci>eta</ci>
<ci>FVRT</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>eta</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<ci>FVRT</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci>Na_o</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>K_mNa</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>Ca_o</ci>
<ci>K_mCa</ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>k_sat</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>eta</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<ci>FVRT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SERCA">
<variable initial_value="0.45e-3" name="g_SERCA" units="mM_per_ms"/>
<variable initial_value="0.5e-3" name="K_SERCA" units="mM"/>
<variable cmeta:id="SERCA_I_SERCA" name="I_SERCA" public_interface="out" units="mM_per_ms"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_SERCA</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_SERCA</ci>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_SERCA</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Sarcolemmal_Ca_pump">
<variable initial_value="0.0035e-3" name="g_pCa" units="mM_per_ms"/>
<variable initial_value="0.5e-3" name="K_mpCa" units="mM"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable cmeta:id="Sarcolemmal_Ca_pump_I_pCa" name="I_pCa" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_pCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pCa</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>K_mpCa</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Background_Ca_current">
<variable name="V" public_interface="in" units="mV"/>
<variable name="R" public_interface="in" units="mJ_per_mole_K"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="C_per_mole"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="Ca_o" public_interface="in" units="mM"/>
<variable name="E_Ca" public_interface="out" units="mV"/>
<variable initial_value="2.6875e-8" name="g_CaB" units="mM_per_mV_ms"/>
<variable cmeta:id="Background_Ca_current_I_CaB" name="I_CaB" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_o</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_CaB</ci>
<apply>
<times/>
<ci>g_CaB</ci>
<apply>
<minus/>
<ci>E_Ca</ci>
<ci>V</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SR_Ca_leak_current">
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="Ca_SR" public_interface="in" units="mM"/>
<variable initial_value="1.8951e-5" name="g_SRl" units="per_ms"/>
<variable cmeta:id="SR_Ca_leak_current_I_SR" name="I_SR" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_SR</ci>
<apply>
<times/>
<ci>g_SRl</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="troponin_Ca_buffer">
<variable initial_value="0.04" name="k_m_TRPN" units="per_ms"/>
<variable initial_value="0.04e3" name="k_p_TRPN" units="per_mM_ms"/>
<variable initial_value="70e-3" name="B_TRPN" units="mM"/>
<variable name="TRPN" public_interface="in" units="mM"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="I_TRPN" public_interface="out" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_TRPN</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>k_m_TRPN</ci>
<apply>
<minus/>
<ci>B_TRPN</ci>
<ci>TRPN</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_p_TRPN</ci>
<ci>TRPN</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calmodulin_Ca_buffer">
<variable initial_value="2.382e-3" name="k_CMDN" units="mM"/>
<variable initial_value="50e-3" name="B_CMDN" units="mM"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="beta_CMDN" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>beta_CMDN</ci>
<apply>
<power/>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>k_CMDN</ci>
<ci>B_CMDN</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>k_CMDN</ci>
<ci>Ca_i</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable initial_value="10" name="Na_i" public_interface="out" units="mM"/>
<variable cmeta:id="intracellular_ion_concentrations_Ca_i" initial_value="0.0001" name="Ca_i" public_interface="out" units="mM"/>
<variable initial_value="700e-3" name="Ca_SR" public_interface="out" units="mM"/>
<variable initial_value="0.0636364" name="TRPN" public_interface="out" units="mM"/>
<variable name="time" public_interface="in" units="ms"/>
<variable name="V_myo" public_interface="in" units="um3"/>
<variable name="V_SR" public_interface="in" units="um3"/>
<variable name="beta_CMDN" public_interface="in" units="dimensionless"/>
<variable name="I_SERCA" public_interface="in" units="mM_per_ms"/>
<variable name="I_pCa" public_interface="in" units="mM_per_ms"/>
<variable name="I_CaB" public_interface="in" units="mM_per_ms"/>
<variable name="I_TRPN" public_interface="in" units="mM_per_ms"/>
<variable name="I_SR" public_interface="in" units="mM_per_ms"/>
<variable name="I_NaCa" public_interface="in" units="mM_per_ms"/>
<variable name="I_RyR" public_interface="in" units="mM_per_ms"/>
<variable name="I_LCC" public_interface="in" units="mM_per_ms"/>
<variable cmeta:id="intracellular_ion_concentrations_CaSR_plot" name="CaSR_plot" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TRPN</ci>
</apply>
<ci>I_TRPN</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>beta_CMDN</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>I_LCC</ci>
<ci>I_RyR</ci>
</apply>
<ci>I_SERCA</ci>
</apply>
<ci>I_SR</ci>
<ci>I_NaCa</ci>
</apply>
<ci>I_pCa</ci>
</apply>
<ci>I_CaB</ci>
<ci>I_TRPN</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_SR</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>V_myo</ci>
<ci>V_SR</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>I_RyR</ci>
</apply>
<ci>I_SERCA</ci>
</apply>
<ci>I_SR</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
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