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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_c_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_c_2002" cmeta:id="baylor_model_c_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 Competitive reaction of Ca2+ and Mg2+ with parvalbumin
    
</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="Parv" name="Parv">
      
<variable units="micromolar" public_interface="out" name="Parv" initial_value="1500.0" />
      
<variable units="flux" public_interface="in" name="delta_Parv_rxn0" />
      
<variable units="flux" public_interface="in" name="delta_Parv_rxn1" />
      
<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>Parv</ci>
            
</apply>
            
<apply>
               
<plus />
               
<ci>delta_Parv_rxn0</ci>
               
<ci>delta_Parv_rxn1</ci>
            
</apply>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="CaParv" name="CaParv">
      
<variable units="micromolar" public_interface="out" name="CaParv" />
      
<variable units="flux" public_interface="in" name="delta_CaParv_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>CaParv</ci>
            
</apply>
            
<ci>delta_CaParv_rxn0</ci>
         
</apply>
      
</math>
   
</component>
   
   
<component cmeta:id="Mg" name="Mg">
      
<variable units="micromolar" public_interface="out" name="Mg" initial_value="1000.0" />
      
<variable units="flux" public_interface="in" name="delta_Mg_rxn1" />
      
<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>Mg</ci>
            
</apply>
            
<ci>delta_Mg_rxn1</ci>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="MgParv" name="MgParv">
      
<variable units="micromolar" public_interface="out" name="MgParv" />
      
<variable units="flux" public_interface="in" name="delta_MgParv_rxn1" />
      
<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>MgParv</ci>
            
</apply>
            
<ci>delta_MgParv_rxn1</ci>
         
</apply>
      
</math>
   
</component>
   
   
<!--
    The following components describe the reactions of the model.
   
-->
   
   
<component name="reaction0">
      
<variable units="micromolar" public_interface="in" name="Parv" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="CaParv" />
      
<variable units="flux" public_interface="out" name="delta_Parv_rxn0" />
      
<variable units="flux" public_interface="out" name="delta_Ca_rxn0" />
      
<variable units="flux" public_interface="out" name="delta_CaParv_rxn0" />
      
<variable units="second_order_rate_constant" name="k0" initial_value="4.79E7" />
      
<variable units="first_order_rate_constant" name="k0_" initial_value="0.574" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="Parv">
            
<role role="reactant" direction="forward" delta_variable="delta_Parv_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="CaParv">
            
<role role="product" direction="forward" delta_variable="delta_CaParv_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>Parv</ci>
                           
<ci>Ca</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k0_</ci>
                              
<ci>CaParv</ci>
                           
</apply>
                        
</apply>
                     
</apply>
                  
</apply>
               
</math>
            
</role>
         
</variable_ref>
      
</reaction>
   
</component>
   
   
<component name="reaction1">
      
<variable units="micromolar" public_interface="in" name="Parv" />
      
<variable units="micromolar" public_interface="in" name="Mg" />
      
<variable units="micromolar" public_interface="in" name="MgParv" />
      
<variable units="flux" public_interface="out" name="delta_Parv_rxn1" />
      
<variable units="flux" public_interface="out" name="delta_Mg_rxn1" />
      
<variable units="flux" public_interface="out" name="delta_MgParv_rxn1" />
      
<variable units="second_order_rate_constant" name="k1" initial_value="39700.0" />
      
<variable units="first_order_rate_constant" name="k1_" initial_value="3.45" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="Parv">
            
<role role="reactant" direction="forward" delta_variable="delta_Parv_rxn1" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="Mg">
            
<role role="reactant" direction="forward" delta_variable="delta_Mg_rxn1" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="MgParv">
            
<role role="product" direction="forward" delta_variable="delta_MgParv_rxn1" 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>k1</ci>
                           
<ci>Parv</ci>
                           
<ci>Mg</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k1_</ci>
                              
<ci>MgParv</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="Parv" />
      
<map_variables variable_2="Parv" variable_1="Parv" />
      
<map_variables variable_2="delta_Parv_rxn0" variable_1="delta_Parv_rxn0" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction1" component_1="Parv" />
      
<map_variables variable_2="Parv" variable_1="Parv" />
      
<map_variables variable_2="delta_Parv_rxn1" variable_1="delta_Parv_rxn1" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction0" component_1="CaParv" />
      
<map_variables variable_2="CaParv" variable_1="CaParv" />
      
<map_variables variable_2="delta_CaParv_rxn0" variable_1="delta_CaParv_rxn0" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction1" component_1="Mg" />
      
<map_variables variable_2="Mg" variable_1="Mg" />
      
<map_variables variable_2="delta_Mg_rxn1" variable_1="delta_Mg_rxn1" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction1" component_1="MgParv" />
      
<map_variables variable_2="MgParv" variable_1="MgParv" />
      
<map_variables variable_2="delta_MgParv_rxn1" variable_1="delta_MgParv_rxn1" />
   
</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="Parv" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
  
   
<connection>
      
<map_components component_2="environment" component_1="CaParv" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
  
   
<connection>
      
<map_components component_2="environment" component_1="Mg" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
  
   
<connection>
      
<map_components component_2="environment" component_1="MgParv" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
<rdf:RDF>
  
<rdf:Bag rdf:about="rdf:#96be9735-878e-4970-90f0-298e531db6f8">
    
<rdf:li>skeletal muscle</rdf:li>
    
<rdf:li>calcium dynamics</rdf:li>
  
</rdf:Bag>
  
<rdf:Seq rdf:about="rdf:#8dd5da60-b787-4e49-8ead-b46478630634">
    
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</rdf:Description>
  
<rdf:Description rdf:about="">
    
<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
    
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<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
  
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          Added publication date information.
        
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<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>
    
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<bqs:last_page>368</bqs:last_page>
  
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<rdf:value>This is the CellML description of Baylor, Hollingworth and Chandler's 2002 model of the Competitive reaction of Ca2+ and Mg2+ with parvalbumin in skeletal myocytes.</rdf:value>
  
</rdf:Description>
  
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<bqs:Pubmed_id>12198091</bqs:Pubmed_id>
    
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<rdf:value />
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#687af47c-e619-4508-9956-f9dbe69596f1">
    
<dc:title>Journal of General Physiology</dc:title>
  
</rdf:Description>
  
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<vCard:FN />
  
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<vCard:Given>S</vCard:Given>
    
<vCard:Family>Baylor</vCard:Family>
    
<vCard:Other>M</vCard:Other>
  
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<rdf:Description rdf:about="rdf:#c5477634-e566-475c-8b44-0d53e37e1dc8">
    
<dcterms:W3CDTF>2002-09-01</dcterms:W3CDTF>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#ad82ad7a-0397-4250-a447-14bcf0145036">
    
<vCard:Given>S</vCard:Given>
    
<vCard:Family>Hollingworth</vCard:Family>
  
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<vCard:N rdf:resource="rdf:#ad82ad7a-0397-4250-a447-14bcf0145036" />
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#3bd73410-7dd6-4880-b03c-c9505321b8ca">
    
<vCard:FN>Catherine Lloyd</vCard:FN>
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#83c2c6da-fedc-4347-ad90-6045698d26fa">
    
<dcterms:W3CDTF>2002-11-01</dcterms:W3CDTF>
  
</rdf:Description>
  
<rdf:Description rdf:about="#baylor_model_c_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>
    
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<cmeta:species>Frog</cmeta:species>
  
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<bqs:subject_type>keyword</bqs:subject_type>
    
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<vCard:N rdf:resource="rdf:#7cf6a82a-4e3b-4326-b06c-f6fd5b897e3a" />
  
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</model>