- Author:
- AnandR <a.rampadarath@auckland.ac.nz>
- Date:
- 2019-09-11 12:58:46+12:00
- Desc:
- Added .omex file
- Permanent Source URI:
- https://models.cellml.org/workspace/599/rawfile/62e2b7dada2321b97f9c2d6a4deaea19b3b36d6c/model/hinch_greenstein_tanskanen_xu_winslow_2004.cellml
<?xml version="1.0" encoding="UTF-8"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:semsim="http://www.bhi.washington.edu/SemSim#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="hinch_greenstein_tanskanen_xu_winslow_2004" cmeta:id="Hinch_2004">
<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>
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<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/1.1#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">0.00001</cn>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">0.00001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="troponin_Ca_buffer">
<variable cmeta:id="troponin_Ca_buffer.Ca_i" name="Ca_i" public_interface="in" units="mM" />
<variable cmeta:id="troponin_Ca_buffer.k_p_TRPN" initial_value="0.04e3" name="k_p_TRPN" units="per_mM_ms" />
<variable cmeta:id="troponin_Ca_buffer.B_TRPN" initial_value="70e-3" name="B_TRPN" units="mM" />
<variable cmeta:id="troponin_Ca_buffer.k_m_TRPN" initial_value="0.04" name="k_m_TRPN" units="per_ms" />
<variable cmeta:id="troponin_Ca_buffer.TRPN" name="TRPN" public_interface="in" units="mM" />
<variable cmeta:id="troponin_Ca_buffer.I_TRPN" 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="RyR_current">
<variable cmeta:id="RyR_current.y_co" name="y_co" public_interface="in" units="dimensionless" />
<variable cmeta:id="RyR_current.J_Roo" name="J_Roo" public_interface="in" units="um3_mM_per_ms" />
<variable cmeta:id="RyR_current.beta_pcc" name="beta_pcc" public_interface="in" units="per_ms" />
<variable cmeta:id="RyR_current.z_3" name="z_3" public_interface="in" units="dimensionless" />
<variable cmeta:id="RyR_current.J_R3" name="J_R3" public_interface="out" units="um3_mM_per_ms" />
<variable cmeta:id="RyR_current.y_oc" name="y_oc" public_interface="in" units="dimensionless" />
<variable cmeta:id="RyR_current.J_R1" name="J_R1" public_interface="out" units="um3_mM_per_ms" />
<variable cmeta:id="RyR_current.J_Rco" name="J_Rco" public_interface="in" units="um3_mM_per_ms" />
<variable cmeta:id="RyR_current.y_oo" name="y_oo" public_interface="in" units="dimensionless" />
<variable cmeta:id="RyR_current.z_1" name="z_1" public_interface="in" units="dimensionless" />
<variable cmeta:id="RyR_current_I_RyR" name="I_RyR" public_interface="out" units="mM_per_ms" />
<variable cmeta:id="RyR_current.N" name="N" public_interface="in" units="dimensionless" />
<variable cmeta:id="RyR_current.V_myo" name="V_myo" public_interface="in" units="um3" />
<variable cmeta:id="RyR_current.beta_m" name="beta_m" public_interface="in" units="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="SR_Ca_leak_current">
<variable cmeta:id="SR_Ca_leak_current.Ca_i" name="Ca_i" public_interface="in" units="mM" />
<variable cmeta:id="SR_Ca_leak_current.g_SRl" initial_value="1.8951e-5" name="g_SRl" units="per_ms" />
<variable cmeta:id="SR_Ca_leak_current.Ca_SR" name="Ca_SR" public_interface="in" units="mM" />
<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="LCC_current">
<variable cmeta:id="LCC_current.y_oo" name="y_oo" public_interface="in" units="dimensionless" />
<variable cmeta:id="LCC_current.J_Loo" name="J_Loo" public_interface="in" units="um3_mM_per_ms" />
<variable cmeta:id="LCC_current.N" name="N" public_interface="in" units="dimensionless" />
<variable cmeta:id="LCC_current_I_LCC" name="I_LCC" public_interface="out" units="mM_per_ms" />
<variable cmeta:id="LCC_current.alpha_p" name="alpha_p" public_interface="in" units="per_ms" />
<variable cmeta:id="LCC_current.z_2" name="z_2" public_interface="in" units="dimensionless" />
<variable cmeta:id="LCC_current.J_Loc" name="J_Loc" public_interface="in" units="um3_mM_per_ms" />
<variable cmeta:id="LCC_current.alpha_m" name="alpha_m" public_interface="in" units="per_ms" />
<variable cmeta:id="LCC_current.J_L2" name="J_L2" public_interface="out" units="um3_mM_per_ms" />
<variable cmeta:id="LCC_current.z_1" name="z_1" public_interface="in" units="dimensionless" />
<variable cmeta:id="LCC_current.V_myo" name="V_myo" public_interface="in" units="um3" />
<variable cmeta:id="LCC_current.y_oc" name="y_oc" public_interface="in" units="dimensionless" />
<variable cmeta:id="LCC_current.J_L1" name="J_L1" public_interface="out" units="um3_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="SERCA">
<variable cmeta:id="SERCA.K_SERCA" initial_value="0.5e-3" name="K_SERCA" units="mM" />
<variable cmeta:id="SERCA.g_SERCA" initial_value="0.45e-3" name="g_SERCA" units="mM_per_ms" />
<variable cmeta:id="SERCA.Ca_i" name="Ca_i" public_interface="in" units="mM" />
<variable cmeta:id="SERCA_I_SERCA" name="I_SERCA" public_interface="out" units="mM_per_ms" />
<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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus />
<apply>
<power />
<ci>K_SERCA</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power />
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CaRU_states">
<variable cmeta:id="CaRU_states.denom" name="denom" units="per_ms3" />
<variable cmeta:id="CaRU_states.beta_pcc" name="beta_pcc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_states.y_co" name="y_co" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_oc" name="y_oc" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_ic" name="y_ic" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_oi" name="y_oi" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.alpha_m" name="alpha_m" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_states.beta_m" name="beta_m" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_states.alpha_p" name="alpha_p" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_states.beta_poc" name="beta_poc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_states.y_cc" name="y_cc" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_ii" name="y_ii" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_oo" name="y_oo" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_ci" name="y_ci" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_states.y_io" name="y_io" 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/1.1#" 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_Transitions">
<variable cmeta:id="CaRU_Transitions.C_oc" name="C_oc" public_interface="in" units="mM" />
<variable cmeta:id="CaRU_Transitions.phi_R" initial_value="0.05" name="phi_R" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.V" name="V" public_interface="in" units="mV" />
<variable cmeta:id="CaRU_Transitions.tau_R" initial_value="2.43" name="tau_R" units="ms" />
<variable cmeta:id="CaRU_Transitions.theta_R" initial_value="0.012" name="theta_R" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.K_L" initial_value="0.22e-3" name="K_L" units="mM" />
<variable cmeta:id="CaRU_Transitions.phi_L" initial_value="2.35" name="phi_L" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.beta_pcc" name="beta_pcc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.d" initial_value="100" name="d" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.c" initial_value="0.01" name="c" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.b" initial_value="14" name="b" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.a" initial_value="0.0625" name="a" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.epsilon_pcc" name="epsilon_pcc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.mu_pcc" name="mu_pcc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.beta_m" name="beta_m" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.tau_L" initial_value="650" name="tau_L" units="ms" />
<variable cmeta:id="CaRU_Transitions.V_L" initial_value="-2" name="V_L" units="mV" />
<variable cmeta:id="CaRU_Transitions.epsilon_pco" name="epsilon_pco" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.expVL" name="expVL" units="dimensionless" />
<variable cmeta:id="CaRU_Transitions.mu_moc" name="mu_moc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.mu_poc" name="mu_poc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.del_VL" initial_value="7" name="del_VL" units="mV" />
<variable cmeta:id="CaRU_Transitions.C_co" name="C_co" public_interface="in" units="mM" />
<variable cmeta:id="CaRU_Transitions.Ca_i" name="Ca_i" public_interface="in" units="mM" />
<variable cmeta:id="CaRU_Transitions.mu_mcc" name="mu_mcc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.alpha_p" name="alpha_p" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.alpha_m" name="alpha_m" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.beta_poc" name="beta_poc" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.t_R" name="t_R" units="ms" />
<variable cmeta:id="CaRU_Transitions.epsilon_m" name="epsilon_m" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_Transitions.t_L" initial_value="1" name="t_L" units="ms" />
<variable cmeta:id="CaRU_Transitions.K_RyR" initial_value="41e-3" name="K_RyR" units="mM" />
<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/1.1#" cellml:units="dimensionless">1.17</cn>
<ci>t_L</ci>
</apply>
</apply>
<apply>
<eq />
<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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power />
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power />
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power />
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<times />
<ci>tau_R</ci>
<apply>
<plus />
<apply>
<power />
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power />
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>mu_moc</ci>
<apply>
<divide />
<apply>
<times />
<ci>theta_R</ci>
<ci>d</ci>
<apply>
<plus />
<apply>
<power />
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times />
<ci>tau_R</ci>
<apply>
<plus />
<apply>
<times />
<ci>d</ci>
<apply>
<power />
<ci>C_oc</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times />
<ci>c</ci>
<apply>
<power />
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>mu_mcc</ci>
<apply>
<divide />
<apply>
<times />
<ci>theta_R</ci>
<ci>d</ci>
<apply>
<plus />
<apply>
<power />
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" 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/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times />
<ci>tau_R</ci>
<apply>
<plus />
<apply>
<times />
<ci>d</ci>
<apply>
<power />
<ci>Ca_i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times />
<ci>c</ci>
<apply>
<power />
<ci>K_RyR</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable cmeta:id="intracellular_ion_concentrations.Ca_SR" initial_value="700e-3" name="Ca_SR" 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 cmeta:id="intracellular_ion_concentrations.beta_CMDN" name="beta_CMDN" public_interface="in" units="dimensionless" />
<variable cmeta:id="intracellular_ion_concentrations_CaSR_plot" name="CaSR_plot" units="mM" />
<variable cmeta:id="intracellular_ion_concentrations.I_CaB" name="I_CaB" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.I_NaCa" name="I_NaCa" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.Na_i" initial_value="10" name="Na_i" public_interface="out" units="mM" />
<variable cmeta:id="intracellular_ion_concentrations.time" name="time" public_interface="in" units="ms" />
<variable cmeta:id="intracellular_ion_concentrations.I_SR" name="I_SR" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.TRPN" initial_value="0.0636364" name="TRPN" public_interface="out" units="mM" />
<variable cmeta:id="intracellular_ion_concentrations.V_myo" name="V_myo" public_interface="in" units="um3" />
<variable cmeta:id="intracellular_ion_concentrations.I_TRPN" name="I_TRPN" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.I_SERCA" name="I_SERCA" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.I_pCa" name="I_pCa" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.V_SR" name="V_SR" public_interface="in" units="um3" />
<variable cmeta:id="intracellular_ion_concentrations.I_RyR" name="I_RyR" public_interface="in" units="mM_per_ms" />
<variable cmeta:id="intracellular_ion_concentrations.I_LCC" name="I_LCC" public_interface="in" units="mM_per_ms" />
<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 />
<ci>CaSR_plot</ci>
<apply>
<divide />
<apply>
<times />
<ci>Ca_SR</ci>
<ci>V_SR</ci>
</apply>
<ci>V_myo</ci>
</apply>
</apply>
</math>
</component>
<component name="DS_Calcium_Concentrations">
<variable cmeta:id="DS_Calcium_Concentrations.Ca_SR" name="Ca_SR" public_interface="in" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.J_R" name="J_R" public_interface="in" units="um3_per_ms" />
<variable cmeta:id="DS_Calcium_Concentrations.g_D" name="g_D" public_interface="in" units="um3_per_ms" />
<variable cmeta:id="DS_Calcium_Concentrations.C_oc" name="C_oc" public_interface="out" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.Ca_o" name="Ca_o" public_interface="in" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.C_cc" name="C_cc" public_interface="out" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.C_oo" name="C_oo" public_interface="out" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.FVRT_Ca" name="FVRT_Ca" public_interface="in" units="dimensionless" />
<variable cmeta:id="DS_Calcium_Concentrations.C_co" name="C_co" public_interface="out" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.Ca_i" name="Ca_i" public_interface="in" units="mM" />
<variable cmeta:id="DS_Calcium_Concentrations.J_L" name="J_L" public_interface="in" units="um3_per_ms" />
<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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" cellml:units="dimensionless">0.000000001</cn>
</apply>
</piece>
<otherwise>
<apply>
<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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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/1.1#" 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="cell_geometry">
<variable cmeta:id="cell_geometry.V_myo" initial_value="25.84e3" name="V_myo" public_interface="out" units="um3" />
<variable cmeta:id="cell_geometry.A_cap" initial_value="1.534e4" name="A_cap" public_interface="out" units="um2" />
<variable cmeta:id="cell_geometry.V_SR" initial_value="2.098e3" name="V_SR" public_interface="out" units="um3" />
</component>
<component name="CaRU_reduced_states">
<variable cmeta:id="CaRU_reduced_states.r_1" name="r_1" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.r_2" name="r_2" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.alpha_p" name="alpha_p" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.r_5" name="r_5" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.alpha_m" name="alpha_m" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.r_6" name="r_6" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.r_3" name="r_3" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.r_4" name="r_4" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.z_2" initial_value="0.0087302" name="z_2" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_reduced_states.beta_m" name="beta_m" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.z_1" initial_value="0.98859" name="z_1" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_reduced_states.r_7" name="r_7" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.y_co" name="y_co" public_interface="in" units="dimensionless" />
<variable cmeta:id="CaRU_reduced_states.r_8" name="r_8" public_interface="out" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.z_4" name="z_4" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_reduced_states.z_3" initial_value="0.0026566" name="z_3" public_interface="out" units="dimensionless" />
<variable cmeta:id="CaRU_reduced_states.epsilon_m" name="epsilon_m" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.time" name="time" public_interface="in" units="ms" />
<variable cmeta:id="CaRU_reduced_states.beta_pcc" name="beta_pcc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.mu_pcc" name="mu_pcc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.mu_mcc" name="mu_mcc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.y_oc" name="y_oc" public_interface="in" units="dimensionless" />
<variable cmeta:id="CaRU_reduced_states.mu_poc" name="mu_poc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.mu_moc" name="mu_moc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.epsilon_pcc" name="epsilon_pcc" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.epsilon_pco" name="epsilon_pco" public_interface="in" units="per_ms" />
<variable cmeta:id="CaRU_reduced_states.y_cc" name="y_cc" public_interface="in" units="dimensionless" />
<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/1.1#" 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>
<group>
<relationship_ref relationship="containment" />
<component_ref component="membrane">
<component_ref component="Background_Ca_current" />
<component_ref component="intracellular_ion_concentrations" />
<component_ref component="SERCA" />
<component_ref component="CaRU">
<component_ref component="CaRU_reduced_states" />
<component_ref component="DS_Calcium_Concentrations" />
<component_ref component="LCC_and_RyR_fluxes" />
<component_ref component="RyR_current" />
<component_ref component="CaRU_Transitions" />
<component_ref component="CaRU_states" />
<component_ref component="LCC_current" />
</component_ref>
<component_ref component="extracellular_ion_concentrations" />
<component_ref component="calmodulin_Ca_buffer" />
<component_ref component="Na_Ca_Exchanger" />
<component_ref component="troponin_Ca_buffer" />
<component_ref component="Sarcolemmal_Ca_pump" />
<component_ref component="cell_geometry" />
<component_ref component="SR_Ca_leak_current" />
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation" />
<component_ref component="CaRU">
<component_ref component="CaRU_reduced_states" />
<component_ref component="DS_Calcium_Concentrations" />
<component_ref component="LCC_and_RyR_fluxes" />
<component_ref component="RyR_current" />
<component_ref component="CaRU_Transitions" />
<component_ref component="CaRU_states" />
<component_ref component="LCC_current" />
</component_ref>
</group>
<connection>
<map_components component_1="Background_Ca_current" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_CaB" variable_2="I_CaB" />
</connection>
<connection>
<map_components component_1="CaRU_states" component_2="LCC_current" />
<map_variables variable_1="y_oc" variable_2="y_oc" />
<map_variables variable_1="y_oo" variable_2="y_oo" />
</connection>
<connection>
<map_components component_1="cell_geometry" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="V_SR" variable_2="V_SR" />
<map_variables variable_1="V_myo" variable_2="V_myo" />
</connection>
<connection>
<map_components component_1="CaRU_reduced_states" component_2="LCC_current" />
<map_variables variable_1="z_1" variable_2="z_1" />
<map_variables variable_1="z_2" variable_2="z_2" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="CaRU_Transitions" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="environment" component_2="membrane" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="environment" component_2="CaRU" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="LCC_and_RyR_fluxes" component_2="LCC_current" />
<map_variables variable_1="J_Loc" variable_2="J_Loc" />
<map_variables variable_1="J_Loo" variable_2="J_Loo" />
</connection>
<connection>
<map_components component_1="membrane" component_2="CaRU" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="FVRT_Ca" variable_2="FVRT_Ca" />
</connection>
<connection>
<map_components component_1="calmodulin_Ca_buffer" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="beta_CMDN" variable_2="beta_CMDN" />
</connection>
<connection>
<map_components component_1="CaRU_states" component_2="RyR_current" />
<map_variables variable_1="y_oc" variable_2="y_oc" />
<map_variables variable_1="y_co" variable_2="y_co" />
<map_variables variable_1="y_oo" variable_2="y_oo" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="LCC_and_RyR_fluxes" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="Ca_SR" variable_2="Ca_SR" />
<map_variables variable_1="J_R" variable_2="J_R" />
<map_variables variable_1="FVRT_Ca" variable_2="FVRT_Ca" />
<map_variables variable_1="Ca_o" variable_2="Ca_o" />
<map_variables variable_1="J_L" variable_2="J_L" />
<map_variables variable_1="g_D" variable_2="g_D" />
</connection>
<connection>
<map_components component_1="CaRU_states" component_2="CaRU_reduced_states" />
<map_variables variable_1="y_oc" variable_2="y_oc" />
<map_variables variable_1="y_cc" variable_2="y_cc" />
<map_variables variable_1="y_co" variable_2="y_co" />
</connection>
<connection>
<map_components component_1="membrane" component_2="Na_Ca_Exchanger" />
<map_variables variable_1="FVRT" variable_2="FVRT" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="DS_Calcium_Concentrations" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="Ca_SR" variable_2="Ca_SR" />
<map_variables variable_1="J_R" variable_2="J_R" />
<map_variables variable_1="FVRT_Ca" variable_2="FVRT_Ca" />
<map_variables variable_1="Ca_o" variable_2="Ca_o" />
<map_variables variable_1="J_L" variable_2="J_L" />
<map_variables variable_1="g_D" variable_2="g_D" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="LCC_current" />
<map_variables variable_1="N" variable_2="N" />
<map_variables variable_1="V_myo" variable_2="V_myo" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="Na_Ca_Exchanger" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="Na_i" variable_2="Na_i" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="Sarcolemmal_Ca_pump" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
</connection>
<connection>
<map_components component_1="RyR_current" component_2="CaRU" />
<map_variables variable_1="I_RyR" variable_2="I_RyR" />
</connection>
<connection>
<map_components component_1="SERCA" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_SERCA" variable_2="I_SERCA" />
</connection>
<connection>
<map_components component_1="cell_geometry" component_2="CaRU" />
<map_variables variable_1="V_myo" variable_2="V_myo" />
</connection>
<connection>
<map_components component_1="extracellular_ion_concentrations" component_2="CaRU" />
<map_variables variable_1="Ca_o" variable_2="Ca_o" />
</connection>
<connection>
<map_components component_1="LCC_and_RyR_fluxes" component_2="RyR_current" />
<map_variables variable_1="J_Rco" variable_2="J_Rco" />
<map_variables variable_1="J_Roo" variable_2="J_Roo" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="troponin_Ca_buffer" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="TRPN" variable_2="TRPN" />
</connection>
<connection>
<map_components component_1="environment" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="Na_Ca_Exchanger" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_NaCa" variable_2="I_NaCa" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="calmodulin_Ca_buffer" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="RyR_current" />
<map_variables variable_1="N" variable_2="N" />
<map_variables variable_1="V_myo" variable_2="V_myo" />
</connection>
<connection>
<map_components component_1="extracellular_ion_concentrations" component_2="Na_Ca_Exchanger" />
<map_variables variable_1="Ca_o" variable_2="Ca_o" />
<map_variables variable_1="Na_o" variable_2="Na_o" />
</connection>
<connection>
<map_components component_1="LCC_current" component_2="CaRU" />
<map_variables variable_1="I_LCC" variable_2="I_LCC" />
</connection>
<connection>
<map_components component_1="CaRU_Transitions" component_2="LCC_current" />
<map_variables variable_1="alpha_m" variable_2="alpha_m" />
<map_variables variable_1="alpha_p" variable_2="alpha_p" />
</connection>
<connection>
<map_components component_1="SR_Ca_leak_current" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_SR" variable_2="I_SR" />
</connection>
<connection>
<map_components component_1="CaRU_Transitions" component_2="CaRU_reduced_states" />
<map_variables variable_1="mu_moc" variable_2="mu_moc" />
<map_variables variable_1="epsilon_pcc" variable_2="epsilon_pcc" />
<map_variables variable_1="alpha_m" variable_2="alpha_m" />
<map_variables variable_1="mu_mcc" variable_2="mu_mcc" />
<map_variables variable_1="mu_pcc" variable_2="mu_pcc" />
<map_variables variable_1="epsilon_pco" variable_2="epsilon_pco" />
<map_variables variable_1="alpha_p" variable_2="alpha_p" />
<map_variables variable_1="epsilon_m" variable_2="epsilon_m" />
<map_variables variable_1="beta_m" variable_2="beta_m" />
<map_variables variable_1="mu_poc" variable_2="mu_poc" />
<map_variables variable_1="beta_pcc" variable_2="beta_pcc" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="SERCA" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
</connection>
<connection>
<map_components component_1="CaRU_Transitions" component_2="RyR_current" />
<map_variables variable_1="beta_m" variable_2="beta_m" />
<map_variables variable_1="beta_pcc" variable_2="beta_pcc" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="SR_Ca_leak_current" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="Ca_SR" variable_2="Ca_SR" />
</connection>
<connection>
<map_components component_1="troponin_Ca_buffer" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_TRPN" variable_2="I_TRPN" />
</connection>
<connection>
<map_components component_1="CaRU_Transitions" component_2="CaRU_states" />
<map_variables variable_1="alpha_m" variable_2="alpha_m" />
<map_variables variable_1="alpha_p" variable_2="alpha_p" />
<map_variables variable_1="beta_poc" variable_2="beta_poc" />
<map_variables variable_1="beta_m" variable_2="beta_m" />
<map_variables variable_1="beta_pcc" variable_2="beta_pcc" />
</connection>
<connection>
<map_components component_1="CaRU_reduced_states" component_2="RyR_current" />
<map_variables variable_1="z_1" variable_2="z_1" />
<map_variables variable_1="z_3" variable_2="z_3" />
</connection>
<connection>
<map_components component_1="Sarcolemmal_Ca_pump" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_pCa" variable_2="I_pCa" />
</connection>
<connection>
<map_components component_1="extracellular_ion_concentrations" component_2="Background_Ca_current" />
<map_variables variable_1="Ca_o" variable_2="Ca_o" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="intracellular_ion_concentrations" />
<map_variables variable_1="I_LCC" variable_2="I_LCC" />
<map_variables variable_1="I_RyR" variable_2="I_RyR" />
</connection>
<connection>
<map_components component_1="CaRU" component_2="CaRU_reduced_states" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="CaRU" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
<map_variables variable_1="Ca_SR" variable_2="Ca_SR" />
</connection>
<connection>
<map_components component_1="membrane" component_2="Background_Ca_current" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="R" variable_2="R" />
</connection>
<connection>
<map_components component_1="intracellular_ion_concentrations" component_2="Background_Ca_current" />
<map_variables variable_1="Ca_i" variable_2="Ca_i" />
</connection>
<connection>
<map_components component_1="DS_Calcium_Concentrations" component_2="CaRU_Transitions" />
<map_variables variable_1="C_co" variable_2="C_co" />
<map_variables variable_1="C_oc" variable_2="C_oc" />
</connection>
</model>
