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Comparison of Simulated and Measured Calcium Sparks in Intact Skeletal Muscle Fibers of the Frog

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<!--  FILE :baylor_model_e_2002.xml

CREATED :  1st November 2002

LAST MODIFIED : 9th April 2003

AUTHOR :  Catherine Lloyd
          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 Baylor, Hollingworth and Chandler's 2002 model of the Ca2+-ATP binding reaction in skeletal myocytes.

CHANGES:  
  09/04/2003 - AAC - Added publication date information.  

-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" name="baylor_model_e_2002" cmeta:id="baylor_model_e_2002">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  
<articleinfo>
  
<title>Calcium Sparks in Skeletal Muscle Fibers</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 is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          
</para>
    
<para>
        This model describes One-step reaction between Ca2+ and troponin
    
</para>
  
</section>
  
<sect1 id="sec_structure">
<title>Model Structure</title>

<para>
The activation of Ca
<superscript>2+</superscript> sparks is an essential step in cardiac excitation-contraction coupling.  A Ca<superscript>2+</superscript> spark arises when sarcoplasmic reticulum (SR) Ca<superscript>2+</superscript>-release channels (ryanodine receptors, or RyRs) open, allowing Ca<superscript>2+</superscript> to diffuse out of the intracellular store, down its electrochemical gradient into the cytoplasm.  The increase in intracellular calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) is recognised as a Ca<superscript>2+</superscript> spark.  After release, Ca<superscript>2+</superscript> diffuses through the cytoplasm and binds to buffers such as troponin, ATP, parvalbumin and the SR Ca<superscript>2+</superscript> pump. 

</para>

<para>
In their 2002 paper, S.M. Baylor, S. Hollingworth and W.K. Chandler model Ca
<superscript>2+</superscript> sparks in frog intact skeletal muscle fibers.  The model calculates changes in the concentration of free Ca<superscript>2+</superscript> and of Ca<superscript>2+</superscript> bound to the buffers and to the Ca<superscript>2+</superscript> indicator fluo-3 (see <xref linkend="fig_reaction_diagram" /> below).   

</para>

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

<para>
<ulink url="http://www.jgp.org/cgi/content/abstract/120/3/349">Comparison of Simulated and Measured Calcium Sparks in Intact Skeletal Muscle Fibers of the Frog</ulink>, S.M. Baylor, S. Hollingworth and W.K. Chandler, 2002, <ulink url="http://www.jgp.org/">
            
<emphasis>Journal of General Physiology</emphasis>
          
</ulink>, 120, 349-368. (<ulink url="http://www.jgp.org/cgi/content/full/120/3/349">Full text</ulink> and <ulink url="http://www.jgp.org/cgi/reprint/120/3/349.pdf">PDF versions</ulink> of the article are available to subscribers on the Journal of General Physiology website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=12198091&amp;dopt=Abstract">PubMed ID: 12198091</ulink> 

</para>

<para>
The raw CellML descriptions of the model can be downloaded in various formats as described in 
<xref linkend="sec_download_this_model" />.
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  
<imageobject>
    
<objectinfo>
      
<title>reaction_diagram</title>
    
</objectinfo>

    
<imagedata fileref="../images/baylor_model_2002/reaction_diagram.gif" />
  
</imageobject>
</mediaobject>
<caption>Schematic diagrams of the Ca<superscript>2+</superscript> binding reactions for various buffers and indicators: <emphasis role="bold">A</emphasis>  The reaction of Ca<superscript>2+</superscript> with ATP in the presence of free Mg<superscript>2+</superscript><emphasis role="bold">B</emphasis>  Reaction of Ca<superscript>2+</superscript> with protein (Pr) and fluo-3 (Fluo), <emphasis role="bold">C</emphasis>  Competitive reaction of Ca<superscript>2+</superscript> and Mg<superscript>2+</superscript> with parvalbumin (Parv), <emphasis role="bold">D</emphasis>  Binding reaction of Ca<superscript>2+</superscript> binding and transport by the sarcoplasmic reticulum Ca<superscript>2+</superscript> pump (E), <emphasis role="bold">E</emphasis>  One-step reaction of Ca<superscript>2+</superscript> with Troponin (Trop), and <emphasis role="bold">F</emphasis>  Two-step reaction of Ca<superscript>2+</superscript> with Troponin (Trop).</caption>

</informalfigure>

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

  
    
  
<!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  
-->

   
<units name="micromolar">
      
<unit units="mole" prefix="micro" />
      
<unit units="litre" exponent="-1" />
   
</units>
   
   
<units name="molar">
      
<unit units="litre" exponent="-1" />
   
</units>
   
   
<units name="flux">
      
<unit units="micromolar" exponent="1" />
      
<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="molar" exponent="-1" />
      
<unit units="second" exponent="-1" />
   
</units>
   
  
<!--
    The "environment" component is used to declare variables that are used by
    all or most of the other components, in this case just "time".
  
-->
   
   
<component name="environment">
      
<variable units="second" public_interface="out" name="time" />
   
</component>
   
   
<!--
    The following components describe all the reactants and products involved in
    the reactions. 
   
--> 
   
   
<component cmeta:id="Ca" name="Ca">
      
<variable units="micromolar" public_interface="out" name="Ca" initial_value="0.05" />
      
<variable units="flux" public_interface="in" name="delta_Ca_rxn0" />
      
<variable units="second" public_interface="in" name="time" />
      
<math xmlns="http://www.w3.org/1998/Math/MathML">
         
<apply>
            
<eq />
            
<apply>
               
<diff />
               
<bvar>
                  
<ci>time</ci>
               
</bvar>
               
<ci>Ca</ci>
            
</apply>
            
<ci>delta_Ca_rxn0</ci>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="Trop" name="Trop">
      
<variable units="micromolar" public_interface="out" name="Trop" initial_value="360.0" />
      
<variable units="flux" public_interface="in" name="delta_Trop_rxn0" />
      
<variable units="second" public_interface="in" name="time" />
      
<math xmlns="http://www.w3.org/1998/Math/MathML">
         
<apply>
            
<eq />
            
<apply>
               
<diff />
               
<bvar>
                  
<ci>time</ci>
               
</bvar>
               
<ci>Trop</ci>
            
</apply>
            
<ci>delta_Trop_rxn0</ci>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="CaTrop" name="CaTrop">
      
<variable units="micromolar" public_interface="out" name="CaTrop" />
      
<variable units="flux" public_interface="in" name="delta_CaTrop_rxn0" />
      
<variable units="second" public_interface="in" name="time" />
      
<math xmlns="http://www.w3.org/1998/Math/MathML">
         
<apply>
            
<eq />
            
<apply>
               
<diff />
               
<bvar>
                  
<ci>time</ci>
               
</bvar>
               
<ci>CaTrop</ci>
            
</apply>
            
<ci>delta_CaTrop_rxn0</ci>
         
</apply>
      
</math>
   
</component>
   
   
<!--
    The following components describe the reactions of the model.
   
-->
   
   
<component name="reaction0">
      
<variable units="micromolar" public_interface="in" name="Trop" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="CaTrop" />
      
<variable units="flux" public_interface="out" name="delta_Trop_rxn0" />
      
<variable units="flux" public_interface="out" name="delta_Ca_rxn0" />
      
<variable units="flux" public_interface="out" name="delta_CaTrop_rxn0" />
      
<variable units="second_order_rate_constant" name="k0" initial_value="1.017E8" />
      
<variable units="first_order_rate_constant" name="k0_" initial_value="132.0" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="Trop">
            
<role role="reactant" direction="forward" delta_variable="delta_Trop_rxn0" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="Ca">
            
<role role="reactant" direction="forward" delta_variable="delta_Ca_rxn0" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="CaTrop">
            
<role role="product" direction="forward" delta_variable="delta_CaTrop_rxn0" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="rate">
            
<role role="rate">
               
<math xmlns="http://www.w3.org/1998/Math/MathML">
                  
<apply>
                     
<eq />
                     
<ci>rate</ci>
                     
<apply>
                        
<plus />
                        
<apply>
                           
<times />
                           
<ci>k0</ci>
                           
<ci>Trop</ci>
                           
<ci>Ca</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k0_</ci>
                              
<ci>CaTrop</ci>
                           
</apply>
                        
</apply>
                     
</apply>
                  
</apply>
               
</math>
            
</role>
         
</variable_ref>
      
</reaction>
   
</component>
   
   
<connection>
      
<map_components component_2="reaction0" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="delta_Ca_rxn0" variable_1="delta_Ca_rxn0" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction0" component_1="Trop" />
      
<map_variables variable_2="Trop" variable_1="Trop" />
      
<map_variables variable_2="delta_Trop_rxn0" variable_1="delta_Trop_rxn0" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction0" component_1="CaTrop" />
      
<map_variables variable_2="CaTrop" variable_1="CaTrop" />
      
<map_variables variable_2="delta_CaTrop_rxn0" variable_1="delta_CaTrop_rxn0" />
   
</connection>
   
   
<connection>
      
<map_components component_2="environment" component_1="Ca" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
   
   
<connection>
      
<map_components component_2="environment" component_1="Trop" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
   
   
<connection>
      
<map_components component_2="environment" component_1="CaTrop" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
<rdf:RDF>
  
<rdf:Bag rdf:about="rdf:#f43042f7-ed63-4013-9bcc-ef1453069f90">
    
<rdf:li>skeletal muscle</rdf:li>
    
<rdf:li>calcium dynamics</rdf:li>
  
</rdf:Bag>
  
<rdf:Seq rdf:about="rdf:#d0bc12ce-8e6f-4520-85a7-4ff726c38560">
    
<rdf:li rdf:resource="rdf:#dce30931-658c-4485-90d2-7cb8c547941c" />
    
<rdf:li rdf:resource="rdf:#94bb7372-fb1c-4773-a495-dd6b025d39bb" />
    
<rdf:li rdf:resource="rdf:#0772522a-6274-49ab-b779-9a2d12a3e5b0" />
  
</rdf:Seq>
  
<rdf:Description rdf:about="rdf:#cffda8ca-8dea-4765-a365-09778e4e38bb">
    
<dc:title>Journal of General Physiology</dc:title>
  
</rdf:Description>
  
<rdf:Description rdf:about="">
    
<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
    
<cmeta:comment rdf:resource="rdf:#36cdb5bd-eea6-48c4-a80e-db1ecd1bc1ed" />
    
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</rdf:Description>
  
<rdf:Description rdf:about="rdf:#e17bec9a-5688-493e-822f-d7a510a836fa">
    
<dcterms:W3CDTF>2002-11-01</dcterms:W3CDTF>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#2bc6e78f-317e-47f2-9b81-d8643ba5835b">
    
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
    
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#dce30931-658c-4485-90d2-7cb8c547941c">
    
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<vCard:Given>S</vCard:Given>
    
<vCard:Family>Baylor</vCard:Family>
    
<vCard:Other>M</vCard:Other>
  
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<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#ad670f4b-1934-45e6-bdee-00e642ec6fd6">
    
<vCard:Given>S</vCard:Given>
    
<vCard:Family>Hollingworth</vCard:Family>
  
</rdf:Description>
  
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<rdf:value>
          Added publication date information.
        
</rdf:value>
    
<cmeta:modifier rdf:resource="rdf:#d66ecd20-fd34-4ac6-b1db-d0c29031e7bd" />
  
</rdf:Description>
  
<rdf:Description rdf:about="#baylor_model_e_2002">
    
<dc:title>
        Baylor, Hollingworth and Chandler's 2002 model of the Ca2+-ATP binding
        reaction in skeletal myocytes.
      
</dc:title>
    
<cmeta:bio_entity>Skeletal Myocyte</cmeta:bio_entity>
    
<cmeta:comment rdf:resource="rdf:#48f72bc6-833a-4d43-869d-3049642c2e33" />
    
<bqs:reference rdf:resource="rdf:#960bea5d-dae8-4ed3-b608-4a4e2295d3da" />
    
<bqs:reference rdf:resource="rdf:#fba1f9cc-63c7-4deb-849f-21b7dbfb009e" />
    
<cmeta:species>Frog</cmeta:species>
  
</rdf:Description>
  
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<rdf:value>This is the CellML description of Baylor, Hollingworth and Chandler's 2002 model of the One-step reaction between Ca2+ and troponin in skeletal myocytes.</rdf:value>
  
</rdf:Description>
  
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<rdf:Description rdf:about="rdf:#d9896731-e2f6-4ab1-88fc-22099de2b6aa">
    
<vCard:FN>Catherine Lloyd</vCard:FN>
  
</rdf:Description>
  
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
    
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#d6577908-d95e-4026-8961-4a0f0a6aaeaa">
    
<vCard:Given>Autumn</vCard:Given>
    
<vCard:Family>Cuellar</vCard:Family>
    
<vCard:Other>A</vCard:Other>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#628dac1f-7a5f-4510-a525-38e12fe10bef">
    
<vCard:Given>W</vCard:Given>
    
<vCard:Family>Chandler</vCard:Family>
    
<vCard:Other>K</vCard:Other>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#d5ad8b2e-db77-4775-9788-9d95c0501339">
    
<dc:creator rdf:resource="rdf:#d0bc12ce-8e6f-4520-85a7-4ff726c38560" />
    
<dc:title>Comparison of Simulated and Measured Calcium Sparks in Intact 
            Skeletal Muscle Fibers of the Frog
</dc:title>
    
<bqs:volume>120</bqs:volume>
    
<bqs:first_page>349</bqs:first_page>
    
<bqs:Journal rdf:resource="rdf:#cffda8ca-8dea-4765-a365-09778e4e38bb" />
    
<dcterms:issued rdf:resource="rdf:#a5027929-6741-4a8c-a74a-62a0695b43a6" />
    
<bqs:last_page>368</bqs:last_page>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#a5027929-6741-4a8c-a74a-62a0695b43a6">
    
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