Location: Rice, Winslow, Jafri, 1999 @ 8868a51f5a60 / rice_winslow_jafri_1999.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2009-06-17 15:44:01+12:00
Desc:
committing version03 of rice_winslow_jafri_1999
Permanent Source URI:
https://models.cellml.org/workspace/rice_winslow_jafri_1999/rawfile/8868a51f5a6000ff1dea379bd5297c70a9ed228e/rice_winslow_jafri_1999.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  RJW_model_1999_raw.xml

CREATED :  21st May 2007

LAST MODIFIED : 21st May 2007

AUTHOR :  Catherine Lloyd
          The Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.1 Specification.

DESCRIPTION :  This file contains a CellML description of Rice et al's 1999 model of the functional Ca2+ release unit.

CHANGES:  
 
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:pathway_editor="http://www.physiome.com/pathway_editor/1.0#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" pathway_editor:rendering_config_file="RJW_model_1999_CellMLrender.xml" cmeta:id="RJW_model_1999" name="rice_winslow_jafri_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modelling the Functional Ca2+ Release Unit</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Calcium-induced calcium release (CICR) in cardiac muscle displays both gradedness and high gain.  It is graded because release of Ca<superscript>2+</superscript> from the sarcoplasmic reticulum (SR) is proportional to the influx of trigger Ca<superscript>2+</superscript>, and high gain refers to the observation that Ca<superscript>2+</superscript> release from the SR is much greater than the trigger influx.  Inherent to such high-gain systems is positive feedback, which causes an all-or-nothing response rather than graded Ca<superscript>2+</superscript> release.  Such behaviour is predicted by all mathematical models in which sarcolemmal Ca<superscript>2+</superscript> influx and SR Ca<superscript>2+</superscript> release are directed into a single compartment, or common pool model.  
</para>

<para>
The previous (1998) model of cardiac calcium handling, (see <ulink url="${HTML_EXMPL_JRW_MODEL}">Jafri-Rice-Winslow Ventricular Model, 1998</ulink>) by the authors was an example of a common pool model.  While it was able to simulate frequency-dependent aspects of cardiac Ca<superscript>2+</superscript> cycling and high gain, it also displayed an all-or-none rather than a graded Ca<superscript>2+</superscript> release.  By contrast, their 1999 model (see the figure below) is based on functional release units (FRUs) formulated from one sarcolemmal dihydropyridine receptor (DHPR), eight ryanodine receptor (RyR) channels, and the volume (subspace) surrounding them.  It is assumed that a variable number of independent FRUs can be recruited to produce graded Ca<superscript>2+</superscript> release.  Voltage-gated DHPR channels open adjacent RyRs via a localised increase in [Ca<superscript>2+</superscript>].
</para>

<para>
Results obtained with the stochastic model suggest that high gain and gradedness can occur by the recruitment of independent FRUs without requiring spatial [Ca<superscript>2+</superscript>] gradients within a functional unit, or coupling between adjacent units.
</para>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/77/4/1871">Modeling Gain and Gradedness of Ca<superscript>2+</superscript> Release in the Functional Unit of the Cardiac Diadic Space</ulink> John J. Rice, Saleet Jafri and Raimond L. Winslow, 1999, <ulink url="http://www.biophysj.org/">
            <emphasis>Biophysical Journal</emphasis>
          </ulink>, 77, 1871-1884.  (<ulink url="http://www.biophysj.org/cgi/content/full/77/4/1871">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/77/4/1871.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10512809&amp;dopt=Abstract">PubMed ID: 10512809</ulink> 
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell_diagram</title>
    </objectinfo>
    <imagedata fileref="rice_1999.png"/>
  </imageobject>
</mediaobject>
<caption>A) Schematic diagram of the functional release unit model.  B) State diagram of the DHPR Channel.  C) State diagram of the RyR channel.</caption>
</informalfigure>

</sect1>
</article>
</documentation>


  
  
  
  <units name="millisecond">
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  </units>
  
  <units name="cm_per_millisecond">
    <unit units="metre" prefix="centi"/>
    <unit units="millisecond" exponent="-1"/>
  </units>
  
  <units name="millimolar">
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    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="micromolar">
    <unit units="mole" prefix="micro"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="micrometre">
    <unit units="metre" prefix="micro"/>
  </units>
  
  <units name="per_micromolar">
    <unit units="micromolar" exponent="-1"/>
  </units>
  
  <units name="flux">
    <unit units="micromolar"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="first_order_rate_constant">
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="second_order_rate_constant">
    <unit units="micromolar" exponent="-1"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="millivolt">
    <unit units="volt" prefix="milli"/>
  </units>
  
  <units name="microA_per_microF">
    <unit units="ampere" prefix="micro"/>
    <unit units="farad" prefix="micro" exponent="-1"/>
  </units>
  
  <units name="joule_per_mole_kelvin">
    <unit units="joule"/>
    <unit units="mole" exponent="-1"/>
    <unit units="kelvin" exponent="-1"/>
  </units>
  
  <units name="coulomb_per_mole">
    <unit units="coulomb"/>
    <unit units="mole" exponent="-1"/>
  </units>
  
  <units name="micro_litre">
    <unit units="litre" prefix="micro"/>
  </units>
  
  
  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>
  
  <component name="sarcolemma">
    <variable units="millivolt" public_interface="out" name="V" initial_value="-84.624"/>
    <variable units="joule_per_mole_kelvin" public_interface="out" name="R" initial_value="8.314"/>
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    <variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96500.0"/>
    <variable units="millimolar" public_interface="out" name="Ca_o" initial_value="1.8"/>
  </component>
  
  <component name="subspace">
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    <variable units="flux" public_interface="out" name="J_RyR"/>
    <variable units="micromolar" public_interface="out" name="Ca_SS"/>
   
    <variable units="flux" name="J_DHPR"/>
    <variable units="dimensionless" name="DHPR_open"/>
    <variable units="dimensionless" name="RyR_open"/>
    <variable units="microA_per_microF" name="I_DHPR"/>
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    <variable units="micromolar" name="B_SR" initial_value="47.0"/>
    <variable units="micromolar" name="K_BSR" initial_value="0.87"/>
    <variable units="micromolar" name="B_SL" initial_value="1124.0"/>
    <variable units="micromolar" name="K_BSL" initial_value="8.7"/>
    <variable units="cm_per_millisecond" name="P_Ca" initial_value="1.51E-11"/>
    <variable units="flux" name="J_xfer"/>
    <variable units="millisecond" name="tau_xfer" initial_value="0.0007"/>
    <variable units="micromolar" name="Ca_myo" initial_value="0.1"/>
    <variable units="dimensionless" name="i" initial_value="0.0"/>
    <variable units="micro_litre" name="V_myo" initial_value="0.1"/>
    
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    <variable units="millimolar" public_interface="in" name="O"/>
    <variable units="millimolar" public_interface="in" name="O_Ca"/>
    <variable units="millimolar" public_interface="in" name="P_O3"/>
    <variable units="millimolar" public_interface="in" name="P_O4"/>
    <variable units="micromolar" public_interface="in" name="Ca_JSR"/>
    
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            <ci> tau_xfer </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="1d" cmeta:id="1d">  
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        <eq/>
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              <ci> Ca_JSR </ci>
              <ci> Ca_SS </ci>
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            </apply>
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    </math> 
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="1f" cmeta:id="1f">  
      <apply id="calcium_subspace_diff_eq">
        <eq/>
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          <bvar>
            <ci> time </ci>
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                <ci> V_myo </ci>
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                  <ci> K_BSR </ci>
                  <ci> Ca_SS </ci>
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          <cn cellml:units="dimensionless"> -1.0 </cn>
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    </math>
  </component>
  
  <component name="sarcoplasmic_reticulum">
    <variable units="micromolar" public_interface="out" name="Ca_JSR"/>
    
    <variable units="micro_litre" name="V_JSR" initial_value="2.03E-12"/>
    <variable units="millimolar" name="beta_JSR"/>
    <variable units="millimolar" name="CSQN_tot" initial_value="15.0"/>
    <variable units="millimolar" name="K_CSQN" initial_value="0.8"/>
    <variable units="flux" name="J_tr"/>
    <variable units="millisecond" name="tau_tr" initial_value="0.005"/>
    <variable units="micromolar" name="Ca_NSR" initial_value="800.0"/>
      
    <variable units="flux" public_interface="in" name="J_RyR"/>
    <variable units="micro_litre" public_interface="in" name="V_SS"/>
    <variable units="millisecond" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="2" cmeta:id="2">
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          <bvar>
            <ci> time </ci>
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          <ci> Ca_JSR </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="2b" cmeta:id="2b">     
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            <ci> tau_tr </ci>
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            <ci> Ca_NSR </ci>
            <ci> Ca_JSR </ci>
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    <component cmeta:id="C0" name="C0">
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      <variable units="dimensionless" public_interface="in" name="C1"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca0"/>
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      <variable units="first_order_rate_constant" public_interface="in" name="beta"/>
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                  <ci> C0 </ci>
                  <ci> gamma </ci>
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      <variable units="dimensionless" public_interface="in" name="C2"/>
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      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
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   <component cmeta:id="C2" name="C2">
      <variable units="dimensionless" public_interface="out" name="C2"/>
      
      <variable units="dimensionless" public_interface="in" name="C1"/>
      <variable units="dimensionless" public_interface="in" name="C3"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca2"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="5">
         <apply>
        <eq/>
            <ci> C2 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C1 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> alpha </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C3 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> beta </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca2 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <apply>
                  <power/>
                      <ci> b </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> beta </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> alpha </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C2 </ci>
                  <ci> gamma </ci>
                  <apply>
                <power/>
                    <ci> a </ci>
                    <cn cellml:units="dimensionless"> 2.0 </cn>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component cmeta:id="C3" name="C3">
      <variable units="dimensionless" public_interface="out" name="C3"/>
      
      <variable units="dimensionless" public_interface="in" name="C2"/>
      <variable units="dimensionless" public_interface="in" name="C4"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca3"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="6">
         <apply>
        <eq/>
            <ci> C3 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> alpha </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C4 </ci>
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci> beta </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca3 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <apply>
                  <power/>
                      <ci> b </ci>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C3 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> beta </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C3 </ci>
                  <ci> alpha </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C3 </ci>
                  <ci> gamma </ci>
                  <apply>
                <power/>
                    <ci> a </ci>
                    <cn cellml:units="dimensionless"> 3.0 </cn>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>
      
   <component cmeta:id="C4" name="C4">
      <variable units="dimensionless" public_interface="out" name="C4"/>
      
      <variable units="dimensionless" public_interface="in" name="C3"/>
      <variable units="dimensionless" public_interface="in" name="O"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca4"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      <variable units="first_order_rate_constant" public_interface="in" name="f"/>
      <variable units="first_order_rate_constant" public_interface="in" name="g"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="7">
         <apply>
        <eq/>
            <ci> C4 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C3 </ci>
                  <ci> alpha </ci>
                </apply>
                <apply>
              <times/>
                  <ci> O </ci>
                  <ci> g </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca4 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <apply>
                  <power/>
                      <ci> b </ci>
                      <cn cellml:units="dimensionless"> 4.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C4 </ci>
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci> beta </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C4 </ci>
                  <ci> f </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C4 </ci>
                  <ci> gamma </ci>
                  <apply>
                <power/>
                    <ci> a </ci>
                    <cn cellml:units="dimensionless"> 4.0 </cn>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>

   <component cmeta:id="O" name="O">
      <variable units="dimensionless" public_interface="out" name="O"/>
      
      <variable units="dimensionless" public_interface="in" name="C4"/>
      <variable units="first_order_rate_constant" public_interface="in" name="f"/>
      <variable units="first_order_rate_constant" public_interface="in" name="g"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="8">
         <apply>
        <eq/>
            <ci> O </ci>
            <apply>
          <minus/>
              <apply>
            <times/>
                <ci> C4 </ci>
                <ci> f </ci>
              </apply>
              <apply>
            <times/>
                <ci> O </ci>
                <ci> g </ci>
              </apply>
            </apply>
         </apply>
      </math>
   </component>

   <component cmeta:id="C_Ca0" name="C_Ca0">
      <variable units="dimensionless" public_interface="out" name="C_Ca0"/>
      
      <variable units="dimensionless" public_interface="in" name="C0"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca1"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="9">
         <apply>
        <eq/>
            <ci> C_Ca0 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C0 </ci>
                  <ci> gamma </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca1 </ci>
                  <ci> beta_ </ci>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca0 </ci>
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca0 </ci>
                  <ci> omega </ci>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>

   <component cmeta:id="C_Ca1" name="C_Ca1">
      <variable units="dimensionless" public_interface="out" name="C_Ca1"/>
      
      <variable units="dimensionless" public_interface="in" name="C_Ca0"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca2"/>
      <variable units="dimensionless" public_interface="in" name="C1"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="10">
         <apply>
        <eq/>
            <ci> C_Ca1 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca0 </ci>
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C1 </ci>
                  <ci> gamma </ci>
                  <ci> a </ci>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca1 </ci>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca1 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca1 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <ci> b </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component cmeta:id="C_Ca2" name="C_Ca2">
      <variable units="dimensionless" public_interface="out" name="C_Ca2"/>
      
      <variable units="dimensionless" public_interface="in" name="C_Ca1"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca3"/>
      <variable units="dimensionless" public_interface="in" name="C2"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="11">
         <apply>
        <eq/>
            <ci> C_Ca2 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca1 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca3 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C2 </ci>
                  <ci> gamma </ci>
                  <apply>
                <power/>
                    <ci> a </ci>
                    <cn cellml:units="dimensionless"> 2.0 </cn>
                  </apply>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca2 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <apply>
                  <power/>
                      <ci> b </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component cmeta:id="C_Ca3" name="C_Ca3">
      <variable units="dimensionless" public_interface="out" name="C_Ca3"/>
      
      <variable units="dimensionless" public_interface="in" name="C_Ca2"/>
      <variable units="dimensionless" public_interface="in" name="C_Ca4"/>
      <variable units="dimensionless" public_interface="in" name="C3"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="12">
         <apply>
        <eq/>
            <ci> C_Ca3 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca2 </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca4 </ci>
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C3 </ci>
                  <ci> gamma </ci>
                  <apply>
                <power/>
                    <ci> a </ci>
                    <cn cellml:units="dimensionless"> 3.0 </cn>
                  </apply>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca3 </ci>
                  <cn cellml:units="dimensionless"> 3.0 </cn>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca3 </ci>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca3 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <apply>
                  <power/>
                      <ci> b </ci>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>
      
   <component cmeta:id="C_Ca4" name="C_Ca4">
      <variable units="dimensionless" public_interface="out" name="C_Ca4"/>
      
      <variable units="dimensionless" public_interface="in" name="C_Ca3"/>
      <variable units="dimensionless" public_interface="in" name="O_Ca"/>
      <variable units="dimensionless" public_interface="in" name="C4"/>
      <variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="omega"/>
      <variable units="first_order_rate_constant" public_interface="in" name="gamma"/>
      <variable units="first_order_rate_constant" public_interface="in" name="a"/>
      <variable units="first_order_rate_constant" public_interface="in" name="b"/>
      <variable units="first_order_rate_constant" public_interface="in" name="f_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="g_"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="13">
         <apply>
        <eq/>
            <ci> C_Ca4 </ci>
            <apply>
          <minus/>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca3 </ci>
                  <ci> alpha_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> O_Ca </ci>
                  <ci> g_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C4 </ci>
                  <ci> gamma </ci>
                  <apply>
                <power/>
                    <ci> a </ci>
                    <cn cellml:units="dimensionless"> 4.0 </cn>
                  </apply>
                </apply>
              </apply>
              <apply>
            <plus/>
                <apply>
              <times/>
                  <ci> C_Ca4 </ci>
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci> beta_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca4 </ci>
                  <ci> f_ </ci>
                </apply>
                <apply>
              <times/>
                  <ci> C_Ca4 </ci>
                  <apply>
                <divide/>
                    <ci> omega </ci>
                    <apply>
                  <power/>
                      <ci> b </ci>
                      <cn cellml:units="dimensionless"> 4.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
         </apply>
      </math>
   </component>

   <component cmeta:id="O_Ca" name="O_Ca">
      <variable units="dimensionless" public_interface="out" name="O_Ca"/>
      
      <variable units="dimensionless" public_interface="in" name="C_Ca4"/>
      <variable units="first_order_rate_constant" public_interface="in" name="f_"/>
      <variable units="first_order_rate_constant" public_interface="in" name="g_"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="14">
         <apply>
        <eq/>
            <ci> O_Ca </ci>
            <apply>
          <minus/>
              <apply>
            <times/>
                <ci> C_Ca4 </ci>
                <ci> f_ </ci>
              </apply>
              <apply>
            <times/>
                <ci> O_Ca </ci>
                <ci> g_ </ci>
              </apply>
            </apply>
         </apply>
      </math>
   </component>
  
    <component cmeta:id="P_C1" name="P_C1">
      <variable units="dimensionless" public_interface="out" name="P_C1"/>
      
      <variable units="first_order_rate_constant" public_interface="in" name="k12"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k21"/>
      <variable units="dimensionless" public_interface="in" name="P_C2"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="15">
        <apply>
        <eq/>
          <ci> P_C1 </ci>
          <apply>
          <minus/>
            <apply>
            <times/>
              <ci> P_C2 </ci>
              <ci> k21 </ci>
            </apply>
            <apply>
            <times/>
              <ci> P_C1 </ci>
              <ci> k12 </ci>
            </apply>
          </apply>
        </apply>
      </math>
    </component>
  
    <component cmeta:id="P_C2" name="P_C2">
      <variable units="dimensionless" public_interface="out" name="P_C2"/>
      
      <variable units="first_order_rate_constant" public_interface="in" name="k12"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k21"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k23"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k32"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k25"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k52"/>
      <variable units="dimensionless" public_interface="in" name="P_C1"/>
      <variable units="dimensionless" public_interface="in" name="P_O3"/>
      <variable units="dimensionless" public_interface="in" name="P_C5"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="16">
        <apply>
        <eq/>
          <ci> P_C2 </ci>
          <apply>
          <minus/>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_C1 </ci>
                <ci> k12 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_O3 </ci>
                <ci> k32 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C5 </ci>
                <ci> k52 </ci>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_C2 </ci>
                <ci> k21 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C2 </ci>
                <ci> k23 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C2 </ci>
                <ci> k25 </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </math>
    </component>

    <component cmeta:id="P_O3" name="P_O3">
      <variable units="dimensionless" public_interface="out" name="P_O3"/>
      
      <variable units="first_order_rate_constant" public_interface="in" name="k23"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k32"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k34"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k43"/>
      <variable units="dimensionless" public_interface="in" name="P_C2"/>
      <variable units="dimensionless" public_interface="in" name="P_O4"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="17">
        <apply>
        <eq/>
          <ci> P_O3 </ci>
          <apply>
          <minus/>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_C2 </ci>
                <ci> k23 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_O4 </ci>
                <ci> k43 </ci>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_O3 </ci>
                <ci> k32 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_O3 </ci>
                <ci> k34 </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </math>
    </component>

    <component cmeta:id="P_O4" name="P_O4">
      <variable units="dimensionless" public_interface="out" name="P_O4"/>
      
      <variable units="first_order_rate_constant" public_interface="in" name="k45"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k54"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k34"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k43"/>
      <variable units="dimensionless" public_interface="in" name="P_C5"/>
      <variable units="dimensionless" public_interface="in" name="P_O3"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="18">
        <apply>
        <eq/>
          <ci> P_O4 </ci>
          <apply>
          <minus/>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_O3 </ci>
                <ci> k34 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C5 </ci>
                <ci> k54 </ci>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_O4 </ci>
                <ci> k43 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_O4 </ci>
                <ci> k45 </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </math>
    </component>

    <component cmeta:id="P_C5" name="P_C5">
      <variable units="dimensionless" public_interface="out" name="P_C5"/>
      
      <variable units="first_order_rate_constant" public_interface="in" name="k45"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k54"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k56"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k65"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k25"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k52"/>
      <variable units="dimensionless" public_interface="in" name="P_C2"/>
      <variable units="dimensionless" public_interface="in" name="P_O4"/>
      <variable units="dimensionless" public_interface="in" name="P_C6"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="19">
        <apply>
        <eq/>
          <ci> P_C5 </ci>
          <apply>
          <minus/>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_C2 </ci>
                <ci> k25 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_O4 </ci>
                <ci> k45 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C6 </ci>
                <ci> k65 </ci>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <times/>
                <ci> P_C5 </ci>
                <ci> k52 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C5 </ci>
                <ci> k54 </ci>
              </apply>
              <apply>
              <times/>
                <ci> P_C5 </ci>
                <ci> k56 </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </math>
    </component>

    <component cmeta:id="P_C6" name="P_C6">
      <variable units="dimensionless" public_interface="out" name="P_C6"/>
      
      <variable units="first_order_rate_constant" public_interface="in" name="k56"/>
      <variable units="first_order_rate_constant" public_interface="in" name="k65"/>
      <variable units="dimensionless" public_interface="in" name="P_C5"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="20">
        <apply>
        <eq/>
          <ci> P_C6 </ci>
          <apply>
          <minus/>
            <apply>
            <times/>
              <ci> P_C6 </ci>
              <ci> k65 </ci>
            </apply>
            <apply>
            <times/>
              <ci> P_C5 </ci>
              <ci> k56 </ci>
            </apply>
          </apply>
        </apply>
      </math>
    </component>
   
   <component name="DHPR_transition_probabilities">
     <variable units="first_order_rate_constant" public_interface="out" name="alpha"/>
     <variable units="first_order_rate_constant" public_interface="out" name="gamma"/>
     <variable units="first_order_rate_constant" public_interface="out" name="beta"/>
     <variable units="first_order_rate_constant" public_interface="out" name="alpha_"/>
     <variable units="first_order_rate_constant" public_interface="out" name="beta_"/>
     <variable units="first_order_rate_constant" public_interface="out" name="omega" initial_value="10.0"/>
     <variable units="first_order_rate_constant" public_interface="out" name="a" initial_value="2.0"/>
     <variable units="first_order_rate_constant" public_interface="out" name="b" initial_value="2.0"/>
     <variable units="first_order_rate_constant" public_interface="out" name="f" initial_value="300.0"/>
     <variable units="first_order_rate_constant" public_interface="out" name="g" initial_value="2000.0"/>
     <variable units="first_order_rate_constant" public_interface="out" name="f_" initial_value="5.0"/>
     <variable units="first_order_rate_constant" public_interface="out" name="g_" initial_value="7000.0"/>
               
     <variable units="millivolt" public_interface="in" name="V"/>
     <variable units="micromolar" public_interface="in" name="Ca_SS"/>
    
     <math xmlns="http://www.w3.org/1998/Math/MathML" id="21" cmeta:id="21">
       <apply id="gamma_calculation">
        <eq/>
         <ci> gamma </ci>
         <apply>
          <times/>
           <ci> Ca_SS </ci>
           <cn cellml:units="second_order_rate_constant"> 0.1875 </cn>
         </apply>
       </apply>
     </math> 
     <math xmlns="http://www.w3.org/1998/Math/MathML" id="21a" cmeta:id="21a">   
      <apply id="alpha_calculation">
        <eq/>
        <ci> alpha </ci>
        <apply>
          <times/>
          <cn cellml:units="first_order_rate_constant"> 0.4 </cn>
          <apply>
            <exp/>
            <apply>
              <divide/>
              <apply>
                <plus/>
                <ci> V </ci>
                <cn cellml:units="millivolt"> 6.0 </cn>
              </apply>
              <cn cellml:units="millivolt"> 25.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math> 
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="21b" cmeta:id="21b">    
      <apply id="beta_calculation">
        <eq/>
        <ci> beta </ci>
        <apply>
          <times/>
          <cn cellml:units="first_order_rate_constant"> 0.05 </cn>
          <apply>
            <exp/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <apply>
                  <plus/>
                  <ci> V </ci>
                  <cn cellml:units="millivolt"> 6.0 </cn>
                </apply>
              </apply>
              <cn cellml:units="millivolt"> 29.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math> 
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="21c" cmeta:id="21c">    
      <apply id="alpha__calculation">
        <eq/>
        <ci> alpha_ </ci>
        <apply>
          <times/>
          <ci> alpha </ci>
          <ci> a </ci>
        </apply>
      </apply>
    </math> 
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="21d" cmeta:id="21d">    
      <apply id="beta__calculation">
        <eq/>
        <ci> beta_ </ci>
        <apply>
          <divide/>
          <ci> beta </ci>
          <ci> b </ci>
        </apply>
      </apply>
    </math>     
  </component>

  <component name="RyR_transition_probabilities">
     <variable units="first_order_rate_constant" public_interface="out" name="k12"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k21" initial_value="2.5E5"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k23"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k32" initial_value="9.6E3"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k34"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k43" initial_value="1.3E4"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k54"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k45" initial_value="66.67"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k25"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k52" initial_value="1.235"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k56"/>
     <variable units="first_order_rate_constant" public_interface="out" name="k65" initial_value="3.0E6"/>
     
     <variable units="micromolar" public_interface="in" name="Ca_SS"/>
    
     <math xmlns="http://www.w3.org/1998/Math/MathML" id="22" cmeta:id="22">
        <apply>
        <eq/>
          <ci> k12 </ci>
          <apply>
          <divide/>
            <apply>
            <times/>
              <cn cellml:units="dimensionless"> 3.0E6 </cn>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <power/>
                <cn cellml:units="micromolar"> 2.68 </cn>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </math> 
      <math xmlns="http://www.w3.org/1998/Math/MathML" id="22a" cmeta:id="22a">  
        <apply>
        <eq/>
          <ci> k23 </ci>
          <apply>
          <divide/>
            <apply>
            <times/>
              <cn cellml:units="dimensionless"> 3.0E7 </cn>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <power/>
                <cn cellml:units="micromolar"> 2.68 </cn>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </math> 
      <math xmlns="http://www.w3.org/1998/Math/MathML" id="22b" cmeta:id="22b">  
        <apply>
        <eq/>
          <ci> k34 </ci>
          <apply>
          <divide/>
            <apply>
            <times/>
              <cn cellml:units="dimensionless"> 3.0E6 </cn>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <power/>
                <cn cellml:units="micromolar"> 2.68 </cn>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </math> 
      <math xmlns="http://www.w3.org/1998/Math/MathML" id="22c" cmeta:id="22c">  
        <apply>
        <eq/>
          <ci> k54 </ci>
          <apply>
          <divide/>
            <apply>
            <times/>
              <cn cellml:units="dimensionless"> 198.0 </cn>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <power/>
                <cn cellml:units="micromolar"> 2.68 </cn>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </math> 
      <math xmlns="http://www.w3.org/1998/Math/MathML" id="22d" cmeta:id="22d">  
        <apply>
        <eq/>
          <ci> k25 </ci>
          <apply>
          <divide/>
            <apply>
            <times/>
              <cn cellml:units="dimensionless"> 3.0E5 </cn>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <power/>
                <cn cellml:units="micromolar"> 2.68 </cn>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </math> 
      <math xmlns="http://www.w3.org/1998/Math/MathML" id="22e" cmeta:id="22e">  
        <apply>
        <eq/>
          <ci> k56 </ci>
          <apply>
          <divide/>
            <apply>
            <times/>
              <cn cellml:units="dimensionless"> 3.0E6 </cn>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
            <apply>
            <plus/>
              <apply>
              <power/>
                <cn cellml:units="micromolar"> 2.68 </cn>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
              <power/>
                <ci> Ca_SS </ci>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </math>     
    </component>

   
   <connection>
      <map_components component_2="environment" component_1="subspace"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="environment" component_1="sarcoplasmic_reticulum"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
    <map_components component_2="sarcolemma" component_1="subspace"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
    <map_variables variable_2="Ca_o" variable_1="Ca_o"/>
  </connection>
  
  <connection>
    <map_components component_2="sarcoplasmic_reticulum" component_1="subspace"/>
    <map_variables variable_2="J_RyR" variable_1="J_RyR"/>
    <map_variables variable_2="V_SS" variable_1="V_SS"/>
    <map_variables variable_2="Ca_JSR" variable_1="Ca_JSR"/>
  </connection>
  
   <connection>
      <map_components component_2="sarcolemma" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   
   <connection>
      <map_components component_2="subspace" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="Ca_SS" variable_1="Ca_SS"/>
   </connection>
   
   <connection>
      <map_components component_2="C0" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha" variable_1="alpha"/>
      <map_variables variable_2="beta" variable_1="beta"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
   </connection>

   <connection>
      <map_components component_2="C1" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha" variable_1="alpha"/>
      <map_variables variable_2="beta" variable_1="beta"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
   </connection>

   <connection>
      <map_components component_2="C2" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha" variable_1="alpha"/>
      <map_variables variable_2="beta" variable_1="beta"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
   </connection>

   <connection>
      <map_components component_2="C3" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha" variable_1="alpha"/>
      <map_variables variable_2="beta" variable_1="beta"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
   </connection>
   
   <connection>
      <map_components component_2="C4" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha" variable_1="alpha"/>
      <map_variables variable_2="beta" variable_1="beta"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
      <map_variables variable_2="f" variable_1="f"/>
      <map_variables variable_2="g" variable_1="g"/>
   </connection>

   <connection>
      <map_components component_2="O" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="f" variable_1="f"/>
      <map_variables variable_2="g" variable_1="g"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca0" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha_" variable_1="alpha_"/>
      <map_variables variable_2="beta_" variable_1="beta_"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca1" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha_" variable_1="alpha_"/>
      <map_variables variable_2="beta_" variable_1="beta_"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca2" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha_" variable_1="alpha_"/>
      <map_variables variable_2="beta_" variable_1="beta_"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca3" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha_" variable_1="alpha_"/>
      <map_variables variable_2="beta_" variable_1="beta_"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
   </connection>
   
   <connection>
      <map_components component_2="C_Ca4" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="alpha_" variable_1="alpha_"/>
      <map_variables variable_2="beta_" variable_1="beta_"/>
      <map_variables variable_2="omega" variable_1="omega"/>
      <map_variables variable_2="gamma" variable_1="gamma"/>
      <map_variables variable_2="a" variable_1="a"/>
      <map_variables variable_2="b" variable_1="b"/>
      <map_variables variable_2="f_" variable_1="f_"/>
      <map_variables variable_2="g_" variable_1="g_"/>
   </connection>
   
   <connection>
      <map_components component_2="O_Ca" component_1="DHPR_transition_probabilities"/>
      <map_variables variable_2="f_" variable_1="f_"/>
      <map_variables variable_2="g_" variable_1="g_"/>
   </connection>
   
   <connection>
      <map_components component_2="subspace" component_1="O"/>
      <map_variables variable_2="O" variable_1="O"/>
   </connection>
   
   <connection>
      <map_components component_2="subspace" component_1="O_Ca"/>
      <map_variables variable_2="O_Ca" variable_1="O_Ca"/>
   </connection>
   
   <connection>
      <map_components component_2="subspace" component_1="P_O3"/>
      <map_variables variable_2="P_O3" variable_1="P_O3"/>
   </connection>
   
   <connection>
      <map_components component_2="subspace" component_1="P_O4"/>
      <map_variables variable_2="P_O4" variable_1="P_O4"/>
   </connection>

   <connection>
      <map_components component_2="C1" component_1="C0"/>
      <map_variables variable_2="C0" variable_1="C0"/>
      <map_variables variable_2="C1" variable_1="C1"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca0" component_1="C0"/>
      <map_variables variable_2="C0" variable_1="C0"/>
      <map_variables variable_2="C_Ca0" variable_1="C_Ca0"/>
   </connection>

   <connection>
      <map_components component_2="C1" component_1="C2"/>
      <map_variables variable_2="C2" variable_1="C2"/>
      <map_variables variable_2="C1" variable_1="C1"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca1" component_1="C1"/>
      <map_variables variable_2="C1" variable_1="C1"/>
      <map_variables variable_2="C_Ca1" variable_1="C_Ca1"/>
   </connection>

   <connection>
      <map_components component_2="C3" component_1="C2"/>
      <map_variables variable_2="C2" variable_1="C2"/>
      <map_variables variable_2="C3" variable_1="C3"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca2" component_1="C2"/>
      <map_variables variable_2="C2" variable_1="C2"/>
      <map_variables variable_2="C_Ca2" variable_1="C_Ca2"/>
   </connection>

   <connection>
      <map_components component_2="C3" component_1="C4"/>
      <map_variables variable_2="C4" variable_1="C4"/>
      <map_variables variable_2="C3" variable_1="C3"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca3" component_1="C3"/>
      <map_variables variable_2="C3" variable_1="C3"/>
      <map_variables variable_2="C_Ca3" variable_1="C_Ca3"/>
   </connection>

   <connection>
      <map_components component_2="O" component_1="C4"/>
      <map_variables variable_2="C4" variable_1="C4"/>
      <map_variables variable_2="O" variable_1="O"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca4" component_1="C4"/>
      <map_variables variable_2="C4" variable_1="C4"/>
      <map_variables variable_2="C_Ca4" variable_1="C_Ca4"/>
   </connection>
   
   <connection>
      <map_components component_2="C_Ca0" component_1="C_Ca1"/>
      <map_variables variable_2="C_Ca1" variable_1="C_Ca1"/>
      <map_variables variable_2="C_Ca0" variable_1="C_Ca0"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca2" component_1="C_Ca1"/>
      <map_variables variable_2="C_Ca1" variable_1="C_Ca1"/>
      <map_variables variable_2="C_Ca2" variable_1="C_Ca2"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca2" component_1="C_Ca3"/>
      <map_variables variable_2="C_Ca3" variable_1="C_Ca3"/>
      <map_variables variable_2="C_Ca2" variable_1="C_Ca2"/>
   </connection>
   
   <connection>
      <map_components component_2="C_Ca4" component_1="C_Ca3"/>
      <map_variables variable_2="C_Ca3" variable_1="C_Ca3"/>
      <map_variables variable_2="C_Ca4" variable_1="C_Ca4"/>
   </connection>

   <connection>
      <map_components component_2="C_Ca4" component_1="O_Ca"/>
      <map_variables variable_2="O_Ca" variable_1="O_Ca"/>
      <map_variables variable_2="C_Ca4" variable_1="C_Ca4"/>
   </connection>

   <connection>
      <map_components component_2="subspace" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="Ca_SS" variable_1="Ca_SS"/>
   </connection>
   
   <connection>
      <map_components component_2="P_C1" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="k12" variable_1="k12"/>
      <map_variables variable_2="k21" variable_1="k21"/>
   </connection>
   
   <connection>
      <map_components component_2="P_C2" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="k12" variable_1="k12"/>
      <map_variables variable_2="k21" variable_1="k21"/>
      <map_variables variable_2="k23" variable_1="k23"/>
      <map_variables variable_2="k32" variable_1="k32"/>
      <map_variables variable_2="k25" variable_1="k25"/>
      <map_variables variable_2="k52" variable_1="k52"/>
   </connection>

   <connection>
      <map_components component_2="P_O3" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="k23" variable_1="k23"/>
      <map_variables variable_2="k32" variable_1="k32"/>
      <map_variables variable_2="k34" variable_1="k34"/>
      <map_variables variable_2="k43" variable_1="k43"/>
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   <connection>
      <map_components component_2="P_O4" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="k45" variable_1="k45"/>
      <map_variables variable_2="k54" variable_1="k54"/>
      <map_variables variable_2="k34" variable_1="k34"/>
      <map_variables variable_2="k43" variable_1="k43"/>
   </connection>

   <connection>
      <map_components component_2="P_C5" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="k45" variable_1="k45"/>
      <map_variables variable_2="k54" variable_1="k54"/>
      <map_variables variable_2="k56" variable_1="k56"/>
      <map_variables variable_2="k65" variable_1="k65"/>
      <map_variables variable_2="k25" variable_1="k25"/>
      <map_variables variable_2="k52" variable_1="k52"/>
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   <connection>
      <map_components component_2="P_C6" component_1="RyR_transition_probabilities"/>
      <map_variables variable_2="k56" variable_1="k56"/>
      <map_variables variable_2="k65" variable_1="k65"/>
   </connection>
 
   <connection>
      <map_components component_2="P_C2" component_1="P_C1"/>
      <map_variables variable_2="P_C1" variable_1="P_C1"/>
      <map_variables variable_2="P_C2" variable_1="P_C2"/>
   </connection>

   <connection>
      <map_components component_2="P_C2" component_1="P_C5"/>
      <map_variables variable_2="P_C5" variable_1="P_C5"/>
      <map_variables variable_2="P_C2" variable_1="P_C2"/>
   </connection>

   <connection>
      <map_components component_2="P_C2" component_1="P_O3"/>
      <map_variables variable_2="P_O3" variable_1="P_O3"/>
      <map_variables variable_2="P_C2" variable_1="P_C2"/>
   </connection>

   <connection>
      <map_components component_2="P_O4" component_1="P_O3"/>
      <map_variables variable_2="P_O3" variable_1="P_O3"/>
      <map_variables variable_2="P_O4" variable_1="P_O4"/>
   </connection>
   
   <connection>
      <map_components component_2="P_C5" component_1="P_O4"/>
      <map_variables variable_2="P_O4" variable_1="P_O4"/>
      <map_variables variable_2="P_C5" variable_1="P_C5"/>
   </connection>
   
   <connection>
      <map_components component_2="P_C6" component_1="P_C5"/>
      <map_variables variable_2="P_C5" variable_1="P_C5"/>
      <map_variables variable_2="P_C6" variable_1="P_C6"/>
   </connection>


<rdf:RDF>
  <rdf:Bag rdf:about="rdf:#b5d4b8c4-18d2-4a7f-80c2-1f6df7774835">
    <rdf:li>diadic space</rdf:li>
    <rdf:li>calcium dynamics</rdf:li>
    <rdf:li>cardiac myocyte</rdf:li>
    <rdf:li>Cardiac Myocyte</rdf:li>
    <rdf:li>electrophysiology</rdf:li>
    <rdf:li>gradedness</rdf:li>
    <rdf:li>gain</rdf:li>
    <rdf:li>cardiac</rdf:li>
  </rdf:Bag>
  <rdf:Seq rdf:about="rdf:#11a98bc9-f637-40e5-8cce-7106df54dfe4">
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    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
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    <dcterms:modified rdf:resource="rdf:#19b02008-7f70-449c-8ed3-f47d47e5c2d7"/>
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          Fixed "J_RyR_calculation".
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    <vCard:Given>Catherine</vCard:Given>
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    <dcterms:W3CDTF>2003-09-11</dcterms:W3CDTF>
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  </rdf:Description>
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    <vCard:Given>John</vCard:Given>
    <vCard:Family>Rice</vCard:Family>
    <vCard:Other>Jeremy</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#9772032b-01ec-4ca9-b444-6d1a4a26cec9">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
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        The Rice et al. 1999 model of the functional Ca2+ release unit. 
      </dc:title>
    <cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity>
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    <dc:title>Biophysical Journal</dc:title>
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    <dcterms:modified rdf:resource="rdf:#2f2167f4-f292-444d-a268-571429df2d7c"/>
    <rdf:value>The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology. &#13;
&#13;
The model does not run in the PCEnv simulator because it is underconstrained.  Not sure why or what is missing.  It may be that all the channel states sum to 1 (probabilities of being open or closed) and therefore maybe one should be calculated by subtracting the sum of all the other channel states from 1?   </rdf:value>
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    <vCard:Given>M</vCard:Given>
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    <rdf:value>This is the CellML description of Rice et al's model of the functional           Ca2+ release unit.</rdf:value>
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    <bqs:subject_type>keyword</bqs:subject_type>
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    <dc:title>Modeling Gain and Gradedness of Ca2+ Release in the Functional Unit              of the Cardiac Diadic Space</dc:title>
    <bqs:volume>77</bqs:volume>
    <bqs:first_page>1871</bqs:first_page>
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    <bqs:last_page>1884</bqs:last_page>
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    <dcterms:W3CDTF>2002-06-29</dcterms:W3CDTF>
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  <rdf:Description rdf:about="rdf:#3202a509-90a8-4d3c-88ce-37af279bfb9d">
    <vCard:FN>Catherine Lloyd</vCard:FN>
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    <dcterms:W3CDTF>2007-06-05T10:02:36+12:00</dcterms:W3CDTF>
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