Location: Sachse, Glanzel, Seemann, 2003 @ e2c6a42568ae / sachse_glanzel_seemann_2003.cellml

Author:
Hanne <Hanne@hanne-nielsens-macbook.local>
Date:
2009-12-14 14:48:55+13:00
Desc:
Added images in ai and svg format
Permanent Source URI:
https://models.physiomeproject.org/workspace/sachse_glanzel_seemann_2003/rawfile/e2c6a42568aeab5dbac9e580f371cb0db0c5065a/sachse_glanzel_seemann_2003.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  sachse_model_2003_raw.xml

CREATED :  19th February 2004

LAST MODIFIED : 19th February 2004

AUTHOR :  Catherine Lloyd
          The Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
                10th August 2001, and the 16/01/2002 CellML Metadata 1.0
                Specification.

DESCRIPTION :  This file contains a CellML description of Sachse et al's mathematical model of cardiac electromechanics in human myocardium.

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="sachse_model_2003_CellMLrender.xml" cmeta:id="sachse_glanzel_seemann_2003_version01" name="sachse_glanzel_seemann_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modelling the Protein Interactions Involved in Cardiac Tension Development</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
           This model contains partial differentials and as such can not currently be solved by existing CellML tools.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Mathematical modelling of the protein interactions responsible for cardiac tension development can improve the understanding of the physiological and pathophysiological processes occuring in the heart.  The principal components of muscular tension development are the proteins actin, myosin, troponin and tropomyosin.  The tension is produced by cross-bridge cycling of actin and myosin using the hydrolyisis of adenosine triphosphate (ATP) as an energy source.  The cross-bridge cycle is initiated by the binding of intracellular calcium to troponin and the resulting configuration changes of tropomyosin. 
</para>

<para>
The first effort to mathematically model active tension development in muscle was published in 1938 by A. V. Hill.  Since then, several other models have been published, including the five models of <ulink url="${HTML_EXMPL_RICE_MODEL}">Rice <emphasis>et al.</emphasis>, 1999</ulink>.  Combining and extending existing models, Sachse <emphasis>et al.</emphasis> develop a hybrid model of protein interactions in cardiac tension development (see the figure below).  This model includes dependencies on intracellular calcium concentration, sarcomere stretch, and stretch velocity, as well as cooperativity mechanisms.   
</para>

<para>
The model has been described here in CellML (the raw CellML description of the Sachse <emphasis>et al.</emphasis> 2003 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).     
</para>

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

<para>
Modeling of Protein Interactions Involved in Cardiac Tension Development, F. B. Sachse, K. G. Glanzel, and G. Seemann, 2003, <emphasis>International Journal of Bifurcation and Chaos</emphasis>, 13, 3561-3578.  (A PDF version of the article is available to subscribers on the <emphasis>International Journal of Bifurcation and Chaos</emphasis> website.)  
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="sachse_2003.png"/>
  </imageobject>
</mediaobject>
<caption>State diagram of the model.  Two state variables quantify the calcium binding to troponin C (T).  Two further state variables describe the configuration of tropomyosin (TM).  Ten state variables represent the interaction of actin and myosin as well as the hydrolysis of adenosine triphosphate (ATP).  M and A represent myosin and actin respectively.  Transition between states is depicted by an arrow.</caption>
</informalfigure>

<para>
The authors suggest that this hybrid model of cardiac tension development provides an interface to other models of cardiac electromechanics.  The model can be coupled with models of cellular electrophysiology and passive mechanics of myocardium allowing the incorporation of mechano-electrical feedback mechanisms.  Results of simulations with the model can be used to elucidate cooperativity mechanisms, pathophysiological changes, and the metabolism of tension development.
</para>


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

  <units name="micromolar">
    <unit units="mole" prefix="micro"/>
    <unit units="litre" exponent="-1"/>
  </units>

  <units name="flux">
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     <unit units="second" exponent="-1"/>
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  </units>

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    <unit units="second" exponent="-1"/>
  </units>

  <units name="m_per_s">
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  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>
   
  <component cmeta:id="ATP" name="ATP">
    <rdf:RDF>
      <rdf:Description rdf:about="ATP">
        <dc:title>ATP</dc:title>
        <dcterms:alternative>adenosine triphosphate</dcterms:alternative>  
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        <dc:title>T</dc:title>
        <dcterms:alternative>troponin C</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
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  </component>
  
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    <rdf:RDF>
      <rdf:Description rdf:about="TCa">
        <dc:title>TCa</dc:title>
        <dcterms:alternative>troponin C-calcium complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
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    <variable units="second_order_rate_constant" name="kon" initial_value="40.0"/>
    <variable units="first_order_rate_constant" name="koff" initial_value="40.0"/>
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    <variable units="dimensionless" public_interface="in" name="lamda"/>
    <variable units="micromolar" public_interface="in" name="T"/>
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    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
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        <eq/> 
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          <partialdiff/> 
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            <ci>time</ci>
          </bvar> 
          <ci>TCa</ci> 
        </apply>
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          <minus/>
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            <times/>
            <ci> kon </ci>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <ci> S_A_M </ci>
              <apply>
                <power/>
                <ci> lamda </ci>
                <ci> TCa_lamda </ci>
              </apply>
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            <ci> T </ci>
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            <times/>
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            <ci> TCa </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="TMoff" name="TMoff">
    <rdf:RDF>
      <rdf:Description rdf:about="TMoff">
        <dc:title>TMoff</dc:title>
        <dcterms:alternative>inactive tropomyosin</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="TMoff" initial_value="1.0"/>
  </component>
  
  <component cmeta:id="TMon" name="TMon">
    <rdf:RDF>
      <rdf:Description rdf:about="TMon">
        <dc:title>TMon</dc:title>
        <dcterms:alternative>active tropomnyosin</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="TMon" initial_value="0.0"/>
    
    <variable units="first_order_rate_constant" name="kmon" initial_value="12.0"/>
    <variable units="first_order_rate_constant" name="kmoff" initial_value="35.0"/>
    <variable units="dimensionless" name="TMoncoop" initial_value="2.0"/>
    <variable units="dimensionless" name="TMonpow" initial_value="2.0"/>
    
    <variable units="dimensionless" public_interface="in" name="lamda"/>
    <variable units="micromolar" public_interface="in" name="TMoff"/>
    <variable units="micromolar" public_interface="in" name="TCa"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
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            <ci>time</ci>
          </bvar> 
          <ci>TMon</ci> 
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            <ci> TCa </ci>
            <apply>
              <power/> 
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
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                  </apply>
                  <ci> TMon </ci>
                </apply>
              </apply>
              <ci> TMonpow </ci>
            </apply>
            <ci> TMoff </ci>
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          <apply>
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            <ci> TMon </ci>
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      </apply>    
    </math>
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    <rdf:RDF>
      <rdf:Description rdf:about="M_ATP">
        <dc:title>M_ATP</dc:title>
        <dcterms:alternative>myosin ATP complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="M_ATP" initial_value="0.0385"/>
    
    <variable units="flux" public_interface="in" name="t2"/>
    <variable units="flux" public_interface="in" name="t3"/>
    <variable units="flux" public_interface="in" name="t14"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
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          <partialdiff/> 
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            <ci>time</ci>
          </bvar> 
          <ci>M_ATP</ci> 
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          <minus/>
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            <plus/>
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            <ci> t14 </ci>
          </apply>
          <ci> t3 </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="M_ADP_Pi" name="M_ADP_Pi">
    <rdf:RDF>
      <rdf:Description rdf:about="M_ADP_Pi">
        <dc:title>M_ADP_Pi</dc:title>
        <dcterms:alternative>myosin ADP inorganic phosphate complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="M_ADP_Pi" initial_value="0.3846"/>
    
    <variable units="flux" public_interface="in" name="t3"/>
    <variable units="flux" public_interface="in" name="t4"/>
    <variable units="flux" public_interface="in" name="t13"/>
    <variable units="second" public_interface="in" name="time"/>
    
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      <apply>
        <eq/> 
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            <ci>time</ci>
          </bvar> 
          <ci>M_ADP_Pi</ci> 
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          <minus/>
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            <plus/>
            <ci> t3 </ci>
            <ci> t13 </ci>
          </apply>
          <ci> t4 </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="A_M__ADP_Pi" name="A_M__ADP_Pi">
    <rdf:RDF>
      <rdf:Description rdf:about="A_M__ADP_Pi">
        <dc:title>A_M__ADP_Pi</dc:title>
        <dcterms:alternative>loosely bound actin-myosin ADP inorganic phosphate complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="A_M__ADP_Pi" initial_value="0.5769"/>
    
    <variable units="flux" public_interface="in" name="t5"/>
    <variable units="flux" public_interface="in" name="t4"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
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            <ci>time</ci>
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          <minus/>
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        </apply>
      </apply>    
    </math>
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  <component cmeta:id="A_M_ADP_Pi" name="A_M_ADP_Pi">
    <rdf:RDF>
      <rdf:Description rdf:about="A_M_ADP_Pi">
        <dc:title>A_M_ADP_Pi</dc:title>
        <dcterms:alternative>tightly bound actin-myosin ADP inorganic phosphate complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="A_M_ADP_Pi" initial_value="0.0"/>
    
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      <rdf:Description rdf:about="A_M__ADP">
        <dc:title>A_M__ADP</dc:title>
        <dcterms:alternative>active actin-myosin ADP complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
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      </apply>    
    </math>
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        <dc:title>A_M_ADP</dc:title>
        <dcterms:alternative>actin-myosin ADP complex</dcterms:alternative>  
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        <dc:title>A__M_ATP</dc:title>
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      <rdf:Description rdf:about="M">
        <dc:title>M</dc:title>
        <dcterms:alternative>myosin</dcterms:alternative>  
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            <ci> t12 </ci>
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  <component cmeta:id="M_ADP" name="M_ADP">
    <rdf:RDF>
      <rdf:Description rdf:about="M_ADP">
        <dc:title>M_ADP</dc:title>
        <dcterms:alternative>myosin-ADP complex</dcterms:alternative>  
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    <variable units="flux" public_interface="in" name="t10"/>
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            <ci>time</ci>
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      <rdf:Description rdf:about="S_A_M">
        <dc:title>S_A_M</dc:title>
        <dcterms:alternative>strongly actin-myosin complex</dcterms:alternative>       </rdf:Description>
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    <variable units="micromolar" public_interface="in" name="A_M"/>
    <variable units="micromolar" public_interface="in" name="A_M_ADP_Pi"/>
    <variable units="micromolar" public_interface="in" name="A_M__ADP"/>
    <variable units="micromolar" public_interface="in" name="A_M_ADP"/>
    
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          <ci> A_M_ADP_Pi </ci>
          <ci> A_M__ADP </ci>
          <ci> A_M_ADP </ci>
          <ci> A_M </ci>
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      </apply>    
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    <variable units="first_order_rate_constant" name="k1" initial_value="1000.0"/>
    <variable units="first_order_rate_constant" name="k_1" initial_value="10.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M"/>
    <variable units="micromolar" public_interface="in" name="A__M_ATP"/>
    <variable units="micromolar" public_interface="in" name="ATP"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t1</ci> 
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k1 </ci>
            <ci> ATP </ci>
            <ci> A_M </ci>
          </apply>
          <apply>
            <times/>
            <ci> k_1 </ci>
            <ci> A__M_ATP </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t2"> 
    <variable units="flux" public_interface="out" name="t2"/>
    
    <variable units="first_order_rate_constant" name="k2" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="A__M_ATP"/>
    <variable units="dimensionless" public_interface="in" name="v_factor"/>
    <variable units="dimensionless" public_interface="in" name="v_detach"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t2</ci> 
        <apply>
          <times/>
          <ci> k2 </ci>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <times/>
              <ci> v_factor </ci>
              <ci> v_detach </ci>
            </apply>
          </apply>
          <ci> A__M_ATP </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t3"> 
    <variable units="flux" public_interface="out" name="t3"/>
    
    <variable units="first_order_rate_constant" name="k3" initial_value="150.0"/>
    <variable units="first_order_rate_constant" name="k_3" initial_value="15.0"/>
    
    <variable units="micromolar" public_interface="in" name="M_ATP"/>
    <variable units="micromolar" public_interface="in" name="M_ADP_Pi"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t3</ci> 
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k3 </ci>
            <ci> M_ATP </ci>
          </apply>
          <apply>
            <times/>
            <ci> k_3 </ci>
            <ci> M_ADP_Pi </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t4"> 
    <variable units="flux" public_interface="out" name="t4"/>
    
    <variable units="first_order_rate_constant" name="k4" initial_value="1500.0"/>
    <variable units="first_order_rate_constant" name="k_4" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="M_ADP_Pi"/>
    <variable units="micromolar" public_interface="in" name="A_M__ADP_Pi"/>
    <variable units="dimensionless" public_interface="in" name="v_factor"/>
    <variable units="dimensionless" public_interface="in" name="v_detach"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t4</ci> 
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k4 </ci>
            <ci> M_ADP_Pi </ci>
          </apply>
          <apply>
            <times/>
            <ci> k_4 </ci>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <times/>
                <ci> v_factor </ci>
                <ci> v_detach </ci>
              </apply>
            </apply>
            <ci> A_M__ADP_Pi </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t5"> 
    <variable units="flux" public_interface="out" name="t5"/>
    
    <variable units="first_order_rate_constant" name="k5" initial_value="25.0"/>
    <variable units="first_order_rate_constant" name="k_5" initial_value="8.0"/>
    <variable units="dimensionless" name="k5_lamda" initial_value="1.0"/>
    <variable units="dimensionless" name="k5_xb" initial_value="1.5"/>
    
    <variable units="micromolar" public_interface="in" name="TMon"/>
    <variable units="micromolar" public_interface="in" name="A_M__ADP_Pi"/>
    <variable units="micromolar" public_interface="in" name="A_M_ADP_Pi"/>
    <variable units="dimensionless" public_interface="in" name="lamda"/>
    <variable units="micromolar" public_interface="in" name="S_A_M"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t5</ci> 
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k5 </ci>
            <ci> TMon </ci>
            <apply>
              <plus/>
              <apply>
                <times/>
                <ci> k5_lamda </ci>
                <ci> lamda </ci>
              </apply>
              <cn cellml:units="dimensionless"> 0.4 </cn>
            </apply>
            <apply>
              <power/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
                  <ci> k5_xb </ci>
                  <ci> S_A_M </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <ci> A_M__ADP_Pi </ci>
          </apply>
          <apply>
            <times/>
            <ci> k_5 </ci>
            <ci> A_M_ADP_Pi </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t6"> 
    <variable units="flux" public_interface="out" name="t6"/>
    
    <variable units="first_order_rate_constant" name="k6" initial_value="50.0"/>
    <variable units="first_order_rate_constant" name="k_6" initial_value="20.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M__ADP"/>
    <variable units="micromolar" public_interface="in" name="A_M_ADP_Pi"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
       <ci>t6</ci> 
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k6 </ci>
            <ci> A_M_ADP_Pi </ci>
          </apply>
          <apply>
            <times/>
            <ci> k_6 </ci>
            <ci> A_M__ADP </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t7"> 
    <variable units="flux" public_interface="out" name="t7"/>
    
    <variable units="first_order_rate_constant" name="k7" initial_value="30.0"/>
    <variable units="dimensionless" name="k7_base" initial_value="2.25"/>
    <variable units="dimensionless" name="k7_lamda" initial_value="1.25"/>
    <variable units="dimensionless" name="k7_force" initial_value="1.0"/>
    
    <variable units="dimensionless" public_interface="in" name="F"/>
    <variable units="micromolar" public_interface="in" name="A_M__ADP"/>
    <variable units="dimensionless" public_interface="in" name="lamda"/>
    <variable units="m_per_s" public_interface="in" name="v"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t7</ci> 
        <apply>
          <times/>
          <ci> k7 </ci>
          <ci> A_M__ADP </ci>
          <apply>
            <divide/>
            <apply>
              <plus/>
              <apply>
                <minus/>
                <ci> k7_base </ci>
                <apply>
                  <times/>
                  <ci> k7_lamda </ci>
                  <ci> lamda </ci>
                </apply>
              </apply>
              <ci> v </ci>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <times/>
                <ci> k7_force </ci>
                <ci> F </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t8"> 
    <variable units="flux" public_interface="out" name="t8"/>
    
    <variable units="first_order_rate_constant" name="k8" initial_value="200.0"/>
    <variable units="first_order_rate_constant" name="k_8" initial_value="5.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M_ADP"/>
    <variable units="micromolar" public_interface="in" name="A_M"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t8</ci> 
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k8 </ci>
            <ci> A_M_ADP </ci>
          </apply>
          <apply>
            <times/>
            <ci> k_8 </ci>
            <ci> A_M </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t9"> 
    <variable units="flux" public_interface="out" name="t9"/>
    
    <variable units="first_order_rate_constant" name="k9" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M"/>
    <variable units="dimensionless" public_interface="in" name="v_factor"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t9</ci> 
        <apply>
          <times/>
          <ci> k9 </ci>
          <ci> v_factor </ci>
          <ci> A_M </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t10"> 
    <variable units="flux" public_interface="out" name="t10"/>
    
    <variable units="first_order_rate_constant" name="k10" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M_ADP"/>
    <variable units="dimensionless" public_interface="in" name="v_factor"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t10</ci> 
        <apply>
          <times/>
          <ci> k10 </ci>
          <ci> v_factor </ci>
          <ci> A_M_ADP </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t11"> 
    <variable units="flux" public_interface="out" name="t11"/>
    
    <variable units="first_order_rate_constant" name="k11" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M__ADP"/>
    <variable units="dimensionless" public_interface="in" name="v_factor"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t11</ci> 
        <apply>
          <times/>
          <ci> k11 </ci>
          <ci> v_factor </ci>
          <ci> A_M__ADP </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t12"> 
    <variable units="flux" public_interface="out" name="t12"/>
    
    <variable units="first_order_rate_constant" name="k12" initial_value="50.0"/>
    
    <variable units="micromolar" public_interface="in" name="M_ADP"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t12</ci> 
        <apply>
          <times/>
          <ci> k12 </ci>
          <ci> M_ADP </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t13"> 
    <variable units="flux" public_interface="out" name="t13"/>
    
    <variable units="first_order_rate_constant" name="k13" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="A_M_ADP_Pi"/>
    <variable units="dimensionless" public_interface="in" name="v_factor"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t13</ci> 
        <apply>
          <times/>
          <ci> k13 </ci>
          <ci> v_factor </ci>
          <ci> A_M_ADP_Pi </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="t14"> 
    <variable units="flux" public_interface="out" name="t14"/>
    
    <variable units="first_order_rate_constant" name="k14" initial_value="1000.0"/>
    
    <variable units="micromolar" public_interface="in" name="ATP"/>
    <variable units="micromolar" public_interface="in" name="M"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>t14</ci> 
        <apply>
          <times/>
          <ci> k14 </ci>
          <ci> ATP </ci>
          <ci> M </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v_factor"> 
    <variable units="dimensionless" public_interface="out" name="v_factor"/>
    
    <variable units="dimensionless" name="Nv" initial_value="10.0"/>
    <variable units="m_per_s" name="v50" initial_value="3.0"/>
    
    <variable units="m_per_s" public_interface="in" name="v"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>v_factor</ci> 
        <apply>
          <divide/>
          <apply>
            <power/>
            <ci> v </ci>
            <ci> Nv </ci>
          </apply>
          <apply>
            <plus/>
            <apply>
              <power/>
              <ci> v </ci>
              <ci> Nv </ci>
            </apply>
            <apply>
              <power/>
              <ci> v50 </ci>
              <ci> Nv </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="F"> 
    <variable units="dimensionless" public_interface="out" name="F"/>
    
    <variable units="dimensionless" name="Fmax" initial_value="0.498"/>
    <variable units="dimensionless" name="alpha"/>
    <variable units="micromolar" name="T_AM"/>
    
    <variable units="micromolar" public_interface="in" name="A_M"/>
    <variable units="micromolar" public_interface="in" name="A_M_ADP"/>
    <variable units="micromolar" public_interface="in" name="A_M__ADP"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>T_AM</ci> 
        <apply>
          <plus/>
          <ci> A_M </ci>
          <ci> A_M_ADP </ci>
          <ci> A_M__ADP </ci>
        </apply>
      </apply>  
      
      <apply>
        <eq/> 
        <ci>F</ci> 
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> alpha </ci>
            <ci> T_AM </ci>
          </apply>
          <ci> Fmax </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="parameters">
    <variable units="dimensionless" public_interface="out" name="v_detach" initial_value="10.0"/>
    <variable units="m_per_s" public_interface="out" name="v"/>
    <variable units="dimensionless" public_interface="out" name="lamda"/>
  </component>
  
  
  <connection>
    <map_components component_2="environment" component_1="M_ATP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="M_ADP_Pi"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A_M__ADP_Pi"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A_M_ADP_Pi"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A_M__ADP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A_M_ADP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A_M"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="A__M_ATP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="M"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="M_ADP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="TCa"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="TMon"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M" component_1="t1"/>
    <map_variables variable_2="t1" variable_1="t1"/>
    <map_variables variable_2="A_M" variable_1="A_M"/>
  </connection>
  
  <connection>
    <map_components component_2="A__M_ATP" component_1="t1"/>
    <map_variables variable_2="t1" variable_1="t1"/>
    <map_variables variable_2="A__M_ATP" variable_1="A__M_ATP"/>
  </connection>
  
  <connection>
    <map_components component_2="ATP" component_1="t1"/>
    <map_variables variable_2="ATP" variable_1="ATP"/>
  </connection>
  
  <connection>
    <map_components component_2="A__M_ATP" component_1="t2"/>
    <map_variables variable_2="A__M_ATP" variable_1="A__M_ATP"/>
    <map_variables variable_2="t2" variable_1="t2"/>
  </connection>
  
  <connection>
    <map_components component_2="M_ATP" component_1="t2"/>
    <map_variables variable_2="t2" variable_1="t2"/>
  </connection>
  
  <connection>
    <map_components component_2="v_factor" component_1="t2"/>
    <map_variables variable_2="v_factor" variable_1="v_factor"/>
  </connection>
  
  <connection>
    <map_components component_2="parameters" component_1="t2"/>
    <map_variables variable_2="v_detach" variable_1="v_detach"/>
  </connection>
  
  <connection>
    <map_components component_2="M_ATP" component_1="t3"/>
    <map_variables variable_2="M_ATP" variable_1="M_ATP"/>
    <map_variables variable_2="t3" variable_1="t3"/>
  </connection>
  
  <connection>
    <map_components component_2="M_ADP_Pi" component_1="t3"/>
    <map_variables variable_2="M_ADP_Pi" variable_1="M_ADP_Pi"/>
    <map_variables variable_2="t3" variable_1="t3"/>
  </connection>
  
  <connection>
    <map_components component_2="M_ADP_Pi" component_1="t4"/>
    <map_variables variable_2="M_ADP_Pi" variable_1="M_ADP_Pi"/>
    <map_variables variable_2="t4" variable_1="t4"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M__ADP_Pi" component_1="t4"/>
    <map_variables variable_2="A_M__ADP_Pi" variable_1="A_M__ADP_Pi"/>
    <map_variables variable_2="t4" variable_1="t4"/>
  </connection>
  
  <connection>
    <map_components component_2="v_factor" component_1="t4"/>
    <map_variables variable_2="v_factor" variable_1="v_factor"/>
  </connection>
  
  <connection>
    <map_components component_2="parameters" component_1="t4"/>
    <map_variables variable_2="v_detach" variable_1="v_detach"/>
  </connection>
  
  <connection>
    <map_components component_2="parameters" component_1="t5"/>
    <map_variables variable_2="lamda" variable_1="lamda"/>
  </connection>
  
  <connection>
    <map_components component_2="TMon" component_1="t5"/>
    <map_variables variable_2="TMon" variable_1="TMon"/>
  </connection>
  
  <connection>
    <map_components component_2="S_A_M" component_1="t5"/>
    <map_variables variable_2="S_A_M" variable_1="S_A_M"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M__ADP_Pi" component_1="t5"/>
    <map_variables variable_2="A_M__ADP_Pi" variable_1="A_M__ADP_Pi"/>
    <map_variables variable_2="t5" variable_1="t5"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M_ADP_Pi" component_1="t5"/>
    <map_variables variable_2="A_M_ADP_Pi" variable_1="A_M_ADP_Pi"/>
    <map_variables variable_2="t5" variable_1="t5"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M_ADP_Pi" component_1="t6"/>
    <map_variables variable_2="A_M_ADP_Pi" variable_1="A_M_ADP_Pi"/>
    <map_variables variable_2="t6" variable_1="t6"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M__ADP" component_1="t6"/>
    <map_variables variable_2="A_M__ADP" variable_1="A_M__ADP"/>
    <map_variables variable_2="t6" variable_1="t6"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M__ADP" component_1="t7"/>
    <map_variables variable_2="A_M__ADP" variable_1="A_M__ADP"/>
    <map_variables variable_2="t7" variable_1="t7"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M_ADP" component_1="t7"/>
    <map_variables variable_2="t7" variable_1="t7"/>
  </connection>
  
  <connection>
    <map_components component_2="parameters" component_1="t7"/>
    <map_variables variable_2="v" variable_1="v"/>
    <map_variables variable_2="lamda" variable_1="lamda"/>
  </connection>
  
  <connection>
    <map_components component_2="F" component_1="t7"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M_ADP" component_1="t8"/>
    <map_variables variable_2="A_M_ADP" variable_1="A_M_ADP"/>
    <map_variables variable_2="t8" variable_1="t8"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M" component_1="t8"/>
    <map_variables variable_2="A_M" variable_1="A_M"/>
    <map_variables variable_2="t8" variable_1="t8"/>
  </connection>
  
  <connection>
    <map_components component_2="A_M" component_1="t9"/>
    <map_variables variable_2="A_M" variable_1="A_M"/>
    <map_variables variable_2="t9" variable_1="t9"/>
  </connection>
  
  <connection>
    <map_components component_2="M" component_1="t9"/>
    <map_variables variable_2="t9" variable_1="t9"/>
  </connection>
  
  <connection>
    <map_components component_2="v_factor" component_1="t9"/>
    <map_variables variable_2="v_factor" variable_1="v_factor"/>
  </connection>
  
  <connection>
    <map_components component_2="M_ADP" component_1="t10"/>
    <map_variables variable_2="t10" variable_1="t10"/>
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