Rendering of the source text

<?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> 

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                                 <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/>
                           <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_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>
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            <ci>beta_CMDN</ci>
            <apply>
               <power/>
               <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/>
                        <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>
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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>
            </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/>
            <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="extracellular_ion_concentrations">
      <variable initial_value="140" name="Na_o" public_interface="out" units="mM"/>
      <variable initial_value="1" name="Ca_o" public_interface="out" units="mM"/>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="intracellular_ion_concentrations"/>
         <component_ref component="extracellular_ion_concentrations"/>
         <component_ref component="cell_geometry"/>
         <component_ref component="CaRU">
            <component_ref component="CaRU_Transitions"/>
            <component_ref component="CaRU_states"/>
            <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="LCC_current"/>
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         <component_ref component="Na_Ca_Exchanger"/>
         <component_ref component="SERCA"/>
         <component_ref component="Sarcolemmal_Ca_pump"/>
         <component_ref component="Background_Ca_current"/>
         <component_ref component="SR_Ca_leak_current"/>
         <component_ref component="troponin_Ca_buffer"/>
         <component_ref component="calmodulin_Ca_buffer"/>
      </component_ref>
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      <component_ref component="CaRU">
         <component_ref component="CaRU_Transitions"/>
         <component_ref component="CaRU_states"/>
         <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="LCC_current"/>
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      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
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      <map_variables variable_1="time" variable_2="time"/>
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   <connection>
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      <map_variables variable_1="time" variable_2="time"/>
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      <map_variables variable_1="V_myo" variable_2="V_myo"/>
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   <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="CaRU" component_2="LCC_and_RyR_fluxes"/>
      <map_variables variable_1="g_D" variable_2="g_D"/>
      <map_variables variable_1="J_R" variable_2="J_R"/>
      <map_variables variable_1="J_L" variable_2="J_L"/>
      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="Ca_SR" variable_2="Ca_SR"/>
      <map_variables variable_1="Ca_o" variable_2="Ca_o"/>
      <map_variables variable_1="FVRT_Ca" variable_2="FVRT_Ca"/>
   </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="CaRU" component_2="CaRU_Transitions"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
   </connection>
   <connection>
      <map_components component_1="CaRU_Transitions" component_2="CaRU_states"/>
      <map_variables variable_1="alpha_p" variable_2="alpha_p"/>
      <map_variables variable_1="alpha_m" variable_2="alpha_m"/>
      <map_variables variable_1="beta_pcc" variable_2="beta_pcc"/>
      <map_variables variable_1="beta_poc" variable_2="beta_poc"/>
      <map_variables variable_1="beta_m" variable_2="beta_m"/>
   </connection>
   <connection>
      <map_components component_1="CaRU_Transitions" component_2="RyR_current"/>
      <map_variables variable_1="beta_pcc" variable_2="beta_pcc"/>
      <map_variables variable_1="beta_m" variable_2="beta_m"/>
   </connection>
   <connection>
      <map_components component_1="CaRU_Transitions" component_2="LCC_current"/>
      <map_variables variable_1="alpha_p" variable_2="alpha_p"/>
      <map_variables variable_1="alpha_m" variable_2="alpha_m"/>
   </connection>
   <connection>
      <map_components component_1="CaRU_states" component_2="RyR_current"/>
      <map_variables variable_1="y_oo" variable_2="y_oo"/>
      <map_variables variable_1="y_co" variable_2="y_co"/>
      <map_variables variable_1="y_oc" variable_2="y_oc"/>
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   <connection>
      <map_components component_1="CaRU_states" component_2="LCC_current"/>
      <map_variables variable_1="y_oo" variable_2="y_oo"/>
      <map_variables variable_1="y_oc" variable_2="y_oc"/>
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   <connection>
      <map_components component_1="LCC_and_RyR_fluxes" component_2="RyR_current"/>
      <map_variables variable_1="J_Roo" variable_2="J_Roo"/>
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      <map_variables variable_1="J_Loo" variable_2="J_Loo"/>
      <map_variables variable_1="J_Loc" variable_2="J_Loc"/>
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      <map_variables variable_1="z_1" variable_2="z_1"/>
      <map_variables variable_1="z_3" variable_2="z_3"/>
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      <map_variables variable_1="z_1" variable_2="z_1"/>
      <map_variables variable_1="z_2" variable_2="z_2"/>
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      <map_variables variable_1="C_oc" variable_2="C_oc"/>
      <map_variables variable_1="C_co" variable_2="C_co"/>
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      <map_variables variable_1="alpha_m" variable_2="alpha_m"/>
      <map_variables variable_1="beta_pcc" variable_2="beta_pcc"/>
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      <map_variables variable_1="epsilon_pco" variable_2="epsilon_pco"/>
      <map_variables variable_1="epsilon_pcc" variable_2="epsilon_pcc"/>
      <map_variables variable_1="epsilon_m" variable_2="epsilon_m"/>
      <map_variables variable_1="mu_poc" variable_2="mu_poc"/>
      <map_variables variable_1="mu_pcc" variable_2="mu_pcc"/>
      <map_variables variable_1="mu_moc" variable_2="mu_moc"/>
      <map_variables variable_1="mu_mcc" variable_2="mu_mcc"/>
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   <connection>
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      <map_variables variable_1="y_oc" variable_2="y_oc"/>
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      <map_variables variable_1="y_co" variable_2="y_co"/>
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      <map_variables variable_1="g_D" variable_2="g_D"/>
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      <map_variables variable_1="Ca_o" variable_2="Ca_o"/>
      <map_variables variable_1="Ca_SR" variable_2="Ca_SR"/>
      <map_variables variable_1="FVRT_Ca" variable_2="FVRT_Ca"/>
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   <connection>
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      <map_variables variable_1="V_myo" variable_2="V_myo"/>
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      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="Ca_SR" variable_2="Ca_SR"/>
      <map_variables variable_1="I_RyR" variable_2="I_RyR"/>
      <map_variables variable_1="I_LCC" variable_2="I_LCC"/>
   </connection>
   <connection>
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      <map_variables variable_1="Ca_o" variable_2="Ca_o"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_ion_concentrations" component_2="Na_Ca_Exchanger"/>
      <map_variables variable_1="Na_i" variable_2="Na_i"/>
      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="I_NaCa" variable_2="I_NaCa"/>
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   <connection>
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      <map_variables variable_1="Na_o" variable_2="Na_o"/>
      <map_variables variable_1="Ca_o" variable_2="Ca_o"/>
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      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
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      <map_variables variable_1="I_pCa" variable_2="I_pCa"/>
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      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="Ca_SR" variable_2="Ca_SR"/>
      <map_variables variable_1="I_SR" variable_2="I_SR"/>
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      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="TRPN" variable_2="TRPN"/>
      <map_variables variable_1="I_TRPN" variable_2="I_TRPN"/>
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      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="beta_CMDN" variable_2="beta_CMDN"/>
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      <map_variables variable_1="V_myo" variable_2="V_myo"/>
      <map_variables variable_1="V_SR" variable_2="V_SR"/>
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    <rdf:value>This model runs in both COR and PCEnv.</rdf:value>
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    <rdf:value>added cmeta:ids to some variables</rdf:value>
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    <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Biophysical Journal</dc:title>
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    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2004-12-01 00:00</dcterms:W3CDTF>
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    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Robert</vCard:Given>
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