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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_d_2002_version02.xml

CREATED :  23rd May 2007

LAST MODIFIED : 23rd May 2007

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

CHANGES:  
 
-->
<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#" cmeta:id="baylor_model_d_2002_version02" name="baylor_model_f_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>
  
  
<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>
  
    
  
   
<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="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>
   
  
   
<component name="environment">
      
<variable units="second" public_interface="out" name="time" />
   
</component>
   
   
   
<component name="Ca" cmeta:id="Ca">
      
<variable units="micromolar" public_interface="out" name="Ca" initial_value="0.05" />
     
      
<variable units="second_order_rate_constant" public_interface="in" name="k1" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k1_" />
      
<variable units="second_order_rate_constant" public_interface="in" name="k3" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k3_" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k4" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k4_" />
      
<variable units="micromolar" public_interface="in" name="E" />
      
<variable units="micromolar" public_interface="in" name="CaE" />
      
<variable units="micromolar" public_interface="in" name="Ca2E_" />
      
<variable units="micromolar" public_interface="in" name="CaE_" />
      
<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>
          
<apply>
          
<minus />
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k1_ </ci>
                
<ci> CaE </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k3_ </ci>
                
<ci> Ca2E_ </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k4 </ci>
                
<ci> Ca2E_ </ci>
              
</apply>
            
</apply>
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k1 </ci>
                
<ci> Ca </ci>
                
<ci> E </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k3 </ci>
                
<ci> Ca </ci>
                
<ci> CaE_ </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k4_ </ci>
                
<cn cellml:units="dimensionless"> 2.0 </cn>
                
<ci> Ca </ci>
                
<ci> E </ci>
              
</apply>
            
</apply>
          
</apply>
        
</apply>
      
</math>
   
</component>
  
   
<component name="E" cmeta:id="E">
      
<variable units="micromolar" public_interface="out" name="E" initial_value="240.0" />
      
      
<variable units="second_order_rate_constant" public_interface="in" name="k1" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k1_" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k4" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k4_" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="CaE" />
      
<variable units="micromolar" public_interface="in" name="Ca2E_" />
      
<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> E </ci> 
          
</apply>
          
<apply>
          
<minus />
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k1_ </ci>
                
<ci> CaE </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k4 </ci>
                
<ci> Ca2E_ </ci>
              
</apply>
            
</apply>
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k1 </ci>
                
<ci> Ca </ci>
                
<ci> E </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k4_ </ci>
                
<cn cellml:units="dimensionless"> 2.0 </cn>
                
<ci> Ca </ci>
                
<ci> E </ci>
              
</apply>
            
</apply>
          
</apply>
        
</apply>
      
</math>
   
</component>
  
   
<component name="CaE" cmeta:id="CaE">
      
<variable units="micromolar" public_interface="out" name="CaE" />
      
      
<variable units="second_order_rate_constant" public_interface="in" name="k1" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k1_" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k2" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k2_" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="E" />
      
<variable units="micromolar" public_interface="in" name="CaE_" />
      
<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> CaE </ci> 
          
</apply>
          
<apply>
          
<minus />
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k1 </ci>
                
<ci> Ca </ci>
                
<ci> E </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k2_ </ci>
                
<ci> CaE_ </ci>
              
</apply>
            
</apply>
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k1_ </ci>
                
<ci> CaE </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k2 </ci>
                
<ci> CaE </ci>
              
</apply>
            
</apply>
          
</apply>
        
</apply>
      
</math>
   
</component>
  
   
<component name="Ca2E_" cmeta:id="Ca2E_">
      
<variable units="micromolar" public_interface="out" name="Ca2E_" initial_value="1.0" />
      
      
<variable units="second_order_rate_constant" public_interface="in" name="k3" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k3_" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k4" />
      
<variable units="first_order_rate_constant" public_interface="in" name="k4_" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="CaE_" />
      
<variable units="micromolar" public_interface="in" name="E" />
      
<variable units="second" public_interface="in" name="time" />
      
      
<math xmlns="http://www.w3.org/1998/Math/MathML">
        
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<ci> CaE_ </ci>
                
<ci> Ca </ci>
              
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<apply>
              
<times />
                
<ci> k4_ </ci>
                
<ci> E </ci>
              
</apply>
            
</apply>
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k3_ </ci>
                
<ci> Ca2E_ </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k4 </ci>
                
<cn cellml:units="dimensionless"> 2.0 </cn>
                
<ci> Ca </ci>
                
<ci> Ca2E_ </ci>
              
</apply>
            
</apply>
          
</apply>
        
</apply>
      
</math>
   
</component>
  
   
<component name="CaE_" cmeta:id="CaE_">
      
<variable units="micromolar" public_interface="out" name="CaE_" />
      
      
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<variable units="first_order_rate_constant" public_interface="in" name="k2_" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="CaE" />
      
<variable units="micromolar" public_interface="in" name="Ca2E_" />
      
<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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<diff /> 
            
<bvar>
            
<ci>time</ci>
          
</bvar> 
            
<ci> CaE_ </ci> 
          
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<minus />
            
<apply>
            
<plus />
              
<apply>
              
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<ci> k3_ </ci>
                
<ci> Ca2E_ </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k2 </ci>
                
<ci> CaE </ci>
              
</apply>
            
</apply>
            
<apply>
            
<plus />
              
<apply>
              
<times />
                
<ci> k2_ </ci>
                
<ci> CaE_ </ci>
              
</apply>
              
<apply>
              
<times />
                
<ci> k3 </ci>
                
<ci> Ca </ci>
                
<ci> CaE_ </ci>
              
</apply>
            
</apply>
          
</apply>
        
</apply>
      
</math>
   
</component>
   
   
<component name="reaction_constants">
      
<variable units="second_order_rate_constant" public_interface="out" name="k1" initial_value="1.0E8" />
      
<variable units="first_order_rate_constant" public_interface="out" name="k1_" initial_value="1000.0" />
      
<variable units="first_order_rate_constant" public_interface="out" name="k2" initial_value="500.0" />
      
<variable units="first_order_rate_constant" public_interface="out" name="k2_" initial_value="1200.0" />
      
<variable units="second_order_rate_constant" public_interface="out" name="k3" initial_value="1.0E8" />
      
<variable units="first_order_rate_constant" public_interface="out" name="k3_" initial_value="10.0" />
      
<variable units="first_order_rate_constant" public_interface="out" name="k4" initial_value="20.0" />
      
<variable units="first_order_rate_constant" public_interface="out" name="k4_" initial_value="0.0" />
   
</component>
  
   
   
<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="E" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
   
   
<connection>
      
<map_components component_2="environment" component_1="CaE" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
  
   
<connection>
      
<map_components component_2="environment" component_1="Ca2E_" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>
  
   
<connection>
      
<map_components component_2="environment" component_1="CaE_" />
      
<map_variables variable_2="time" variable_1="time" />
   
</connection>

   
<connection>
      
<map_components component_2="E" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="E" variable_1="E" />
   
</connection>

   
<connection>
      
<map_components component_2="CaE" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="CaE" variable_1="CaE" />
   
</connection>

   
<connection>
      
<map_components component_2="CaE_" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="CaE_" variable_1="CaE_" />
   
</connection>

   
<connection>
      
<map_components component_2="Ca2E_" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="Ca2E_" variable_1="Ca2E_" />
   
</connection>

   
<connection>
      
<map_components component_2="E" component_1="Ca2E_" />
      
<map_variables variable_2="Ca2E_" variable_1="Ca2E_" />
      
<map_variables variable_2="E" variable_1="E" />
   
</connection>

   
<connection>
      
<map_components component_2="E" component_1="CaE" />
      
<map_variables variable_2="CaE" variable_1="CaE" />
      
<map_variables variable_2="E" variable_1="E" />
   
</connection>

   
<connection>
      
<map_components component_2="CaE" component_1="CaE_" />
      
<map_variables variable_2="CaE_" variable_1="CaE_" />
      
<map_variables variable_2="CaE" variable_1="CaE" />
   
</connection>

   
<connection>
      
<map_components component_2="Ca2E_" component_1="CaE_" />
      
<map_variables variable_2="CaE_" variable_1="CaE_" />
      
<map_variables variable_2="Ca2E_" variable_1="Ca2E_" />
   
</connection>

   
<connection>
      
<map_components component_2="reaction_constants" component_1="Ca" />
      
<map_variables variable_2="k1" variable_1="k1" />
      
<map_variables variable_2="k1_" variable_1="k1_" />
      
<map_variables variable_2="k3" variable_1="k3" />
      
<map_variables variable_2="k3_" variable_1="k3_" />
      
<map_variables variable_2="k4" variable_1="k4" />
      
<map_variables variable_2="k4_" variable_1="k4_" />
   
</connection>

   
<connection>
      
<map_components component_2="reaction_constants" component_1="E" />
      
<map_variables variable_2="k1" variable_1="k1" />
      
<map_variables variable_2="k1_" variable_1="k1_" />
      
<map_variables variable_2="k4" variable_1="k4" />
      
<map_variables variable_2="k4_" variable_1="k4_" />
   
</connection>

   
<connection>
      
<map_components component_2="reaction_constants" component_1="CaE" />
      
<map_variables variable_2="k1" variable_1="k1" />
      
<map_variables variable_2="k1_" variable_1="k1_" />
      
<map_variables variable_2="k2" variable_1="k2" />
      
<map_variables variable_2="k2_" variable_1="k2_" />
   
</connection>

   
<connection>
      
<map_components component_2="reaction_constants" component_1="Ca2E_" />
      
<map_variables variable_2="k3" variable_1="k3" />
      
<map_variables variable_2="k3_" variable_1="k3_" />
      
<map_variables variable_2="k4" variable_1="k4" />
      
<map_variables variable_2="k4_" variable_1="k4_" />
   
</connection>

   
<connection>
      
<map_components component_2="reaction_constants" component_1="CaE_" />
      
<map_variables variable_2="k3" variable_1="k3" />
      
<map_variables variable_2="k3_" variable_1="k3_" />
      
<map_variables variable_2="k2" variable_1="k2" />
      
<map_variables variable_2="k2_" variable_1="k2_" />
   
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