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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.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_d_2002" cmeta:id="baylor_model_d_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 Four state reaction for Ca2+ binding and transport by the SR Ca2+ pump
    
</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>
   
   
<units name="third_order_rate_constant">
      
<unit units="molar" exponent="-2" />
      
<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_rxn3" />
      
<variable units="flux" public_interface="in" name="delta_Ca_rxn0" />
      
<variable units="flux" public_interface="in" name="delta_Ca_rxn2" />
      
<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>
               
<plus />
               
<ci>delta_Ca_rxn3</ci>
               
<ci>delta_Ca_rxn0</ci>
               
<ci>delta_Ca_rxn2</ci>
            
</apply>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="E" name="E">
      
<variable units="micromolar" public_interface="out" name="E" initial_value="240.0" />
      
<variable units="flux" public_interface="in" name="delta_E_rxn3" />
      
<variable units="flux" public_interface="in" name="delta_E_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>E</ci>
            
</apply>
            
<apply>
               
<plus />
               
<ci>delta_E_rxn3</ci>
               
<ci>delta_E_rxn0</ci>
            
</apply>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="CaE" name="CaE">
      
<variable units="micromolar" public_interface="out" name="CaE" />
      
<variable units="flux" public_interface="in" name="delta_CaE_rxn0" />
      
<variable units="flux" public_interface="in" name="delta_CaE_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>CaE</ci>
            
</apply>
            
<apply>
               
<plus />
               
<ci>delta_CaE_rxn0</ci>
               
<ci>delta_CaE_rxn1</ci>
            
</apply>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="Ca2E" name="Ca2E">
      
<variable units="micromolar" public_interface="out" name="Ca2E" initial_value="1.0" />
      
<variable units="flux" public_interface="in" name="delta_Ca2E_rxn2" />
      
<variable units="flux" public_interface="in" name="delta_Ca2E_rxn3" />
      
<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>Ca2E</ci>
            
</apply>
            
<apply>
               
<plus />
               
<ci>delta_Ca2E_rxn2</ci>
               
<ci>delta_Ca2E_rxn3</ci>
            
</apply>
         
</apply>
      
</math>
   
</component>
  
   
<component cmeta:id="CaE_" name="CaE_">
      
<variable units="micromolar" public_interface="out" name="CaE_" />
      
<variable units="flux" public_interface="in" name="delta_CaE__rxn1" />
      
<variable units="flux" public_interface="in" name="delta_CaE__rxn2" />
      
<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>
               
<plus />
               
<ci>delta_CaE__rxn1</ci>
               
<ci>delta_CaE__rxn2</ci>
            
</apply>
         
</apply>
      
</math>
   
</component>
   
   
<!--
    The following components describe the reactions of the model.
   
-->
  
   
<component name="reaction0">
      
<variable units="micromolar" public_interface="in" name="E" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="CaE" />
      
<variable units="flux" public_interface="out" name="delta_E_rxn0" />
      
<variable units="flux" public_interface="out" name="delta_Ca_rxn0" />
      
<variable units="flux" public_interface="out" name="delta_CaE_rxn0" />
      
<variable units="second_order_rate_constant" name="k0" initial_value="1.0E8" />
      
<variable units="first_order_rate_constant" name="k0_" initial_value="1000.0" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="E">
            
<role role="reactant" direction="forward" delta_variable="delta_E_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="CaE">
            
<role role="product" direction="forward" delta_variable="delta_CaE_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>E</ci>
                           
<ci>Ca</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k0_</ci>
                              
<ci>CaE</ci>
                           
</apply>
                        
</apply>
                     
</apply>
                  
</apply>
               
</math>
            
</role>
         
</variable_ref>
      
</reaction>
   
</component>
   
   
<component name="reaction1">
      
<variable units="micromolar" public_interface="in" name="CaE" />
      
<variable units="micromolar" public_interface="in" name="CaE_" />
      
<variable units="flux" public_interface="out" name="delta_CaE_rxn1" />
      
<variable units="flux" public_interface="out" name="delta_CaE__rxn1" />
      
<variable units="first_order_rate_constant" name="k1" initial_value="500.0" />
      
<variable units="first_order_rate_constant" name="k1_" initial_value="1200.0" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="CaE">
            
<role role="reactant" direction="forward" delta_variable="delta_CaE_rxn1" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="CaE_">
            
<role role="product" direction="forward" delta_variable="delta_CaE__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>CaE</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k1_</ci>
                              
<ci>CaE_</ci>
                           
</apply>
                        
</apply>
                     
</apply>
                  
</apply>
               
</math>
            
</role>
         
</variable_ref>
      
</reaction>
   
</component>
   
   
<component name="reaction2">
      
<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="flux" public_interface="out" name="delta_Ca_rxn2" />
      
<variable units="flux" public_interface="out" name="delta_CaE__rxn2" />
      
<variable units="flux" public_interface="out" name="delta_Ca2E_rxn2" />
      
<variable units="second_order_rate_constant" name="k2" initial_value="1.0E8" />
      
<variable units="first_order_rate_constant" name="k2_" initial_value="10.0" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="Ca">
            
<role role="reactant" direction="forward" delta_variable="delta_Ca_rxn2" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="CaE_">
            
<role role="reactant" direction="forward" delta_variable="delta_CaE__rxn2" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="Ca2E">
            
<role role="product" direction="forward" delta_variable="delta_Ca2E_rxn2" 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>k2</ci>
                           
<ci>Ca</ci>
                           
<ci>CaE_</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k2_</ci>
                              
<ci>Ca2E</ci>
                           
</apply>
                        
</apply>
                     
</apply>
                  
</apply>
               
</math>
            
</role>
         
</variable_ref>
      
</reaction>
   
</component>
  
   
<component name="reaction3">
      
<variable units="micromolar" public_interface="in" name="Ca2E" />
      
<variable units="micromolar" public_interface="in" name="Ca" />
      
<variable units="micromolar" public_interface="in" name="E" />
      
<variable units="flux" public_interface="out" name="delta_Ca2E_rxn3" />
      
<variable units="flux" public_interface="out" name="delta_Ca_rxn3" />
      
<variable units="flux" public_interface="out" name="delta_E_rxn3" />
      
<variable units="first_order_rate_constant" name="k3" initial_value="20.0" />
      
<variable units="third_order_rate_constant" name="k3_" initial_value="0.0" />
      
<variable units="flux" name="rate" />
      
<reaction reversible="yes">
         
<variable_ref variable="Ca2E">
            
<role role="reactant" direction="forward" delta_variable="delta_Ca2E_rxn3" stoichiometry="1" />
         
</variable_ref>
         
<variable_ref variable="Ca">
            
<role role="product" direction="forward" delta_variable="delta_Ca_rxn3" stoichiometry="2" />
         
</variable_ref>
         
<variable_ref variable="E">
            
<role role="product" direction="forward" delta_variable="delta_E_rxn3" 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>k3</ci>
                           
<ci>Ca2E</ci>
                        
</apply>
                        
<apply>
                           
<minus />
                           
<apply>
                              
<times />
                              
<ci>k3_</ci>
                              
<apply>
                                 
<power />
                                 
<ci>Ca</ci>
                                 
<cn cellml:units="dimensionless">2.0</cn>
                              
</apply>
                              
<ci>E</ci>
                           
</apply>
                        
</apply>
                     
</apply>
                  
</apply>
               
</math>
            
</role>
         
</variable_ref>
      
</reaction>
   
</component>
  
   
<connection>
      
<map_components component_2="reaction3" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="delta_Ca_rxn3" variable_1="delta_Ca_rxn3" />
   
</connection>
  
   
<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="reaction2" component_1="Ca" />
      
<map_variables variable_2="Ca" variable_1="Ca" />
      
<map_variables variable_2="delta_Ca_rxn2" variable_1="delta_Ca_rxn2" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction3" component_1="E" />
      
<map_variables variable_2="E" variable_1="E" />
      
<map_variables variable_2="delta_E_rxn3" variable_1="delta_E_rxn3" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction0" component_1="E" />
      
<map_variables variable_2="E" variable_1="E" />
      
<map_variables variable_2="delta_E_rxn0" variable_1="delta_E_rxn0" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction0" component_1="CaE" />
      
<map_variables variable_2="CaE" variable_1="CaE" />
      
<map_variables variable_2="delta_CaE_rxn0" variable_1="delta_CaE_rxn0" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction1" component_1="CaE" />
      
<map_variables variable_2="CaE" variable_1="CaE" />
      
<map_variables variable_2="delta_CaE_rxn1" variable_1="delta_CaE_rxn1" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction2" component_1="Ca2E" />
      
<map_variables variable_2="Ca2E" variable_1="Ca2E" />
      
<map_variables variable_2="delta_Ca2E_rxn2" variable_1="delta_Ca2E_rxn2" />
   
</connection>
  
   
<connection>
      
<map_components component_2="reaction3" component_1="Ca2E" />
      
<map_variables variable_2="Ca2E" variable_1="Ca2E" />
      
<map_variables variable_2="delta_Ca2E_rxn3" variable_1="delta_Ca2E_rxn3" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction1" component_1="CaE_" />
      
<map_variables variable_2="CaE_" variable_1="CaE_" />
      
<map_variables variable_2="delta_CaE__rxn1" variable_1="delta_CaE__rxn1" />
   
</connection>
   
   
<connection>
      
<map_components component_2="reaction2" component_1="CaE_" />
      
<map_variables variable_2="CaE_" variable_1="CaE_" />
      
<map_variables variable_2="delta_CaE__rxn2" variable_1="delta_CaE__rxn2" />
   
</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="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>
<rdf:RDF>
  
<rdf:Bag rdf:about="rdf:#650c30d8-1b78-483a-908a-58880d5e9959">
    
<rdf:li>skeletal muscle</rdf:li>
    
<rdf:li>calcium dynamics</rdf:li>
  
</rdf:Bag>
  
<rdf:Seq rdf:about="rdf:#9e677ce9-8bf3-41f4-8f68-2f6d1dbeb2fd">
    
<rdf:li rdf:resource="rdf:#e931e770-69d3-49e6-ad21-164770d54a59" />
    
<rdf:li rdf:resource="rdf:#70e2e61b-1ac3-41b0-9e1a-c949b4437618" />
    
<rdf:li rdf:resource="rdf:#36de3241-cc7f-4808-858e-02ca16bc9854" />
  
</rdf:Seq>
  
<rdf:Description rdf:about="">
    
<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
    
<cmeta:comment rdf:resource="rdf:#70570ac0-d14f-4133-afbb-d3a618ff54b2" />
    
<dcterms:created rdf:resource="rdf:#7fbc766d-6b76-470b-83be-f79e1d69515c" />
    
<dc:creator rdf:resource="rdf:#ef50eb46-a188-45b4-b309-c2d0f1fa095c" />
    
<cmeta:modification rdf:resource="rdf:#cc25e295-f094-49d9-a008-9aea4647942b" />
  
</rdf:Description>
  
<rdf:Description rdf:about="rdf:#7fbc766d-6b76-470b-83be-f79e1d69515c">
    
<dcterms:W3CDTF>2002-11-01</dcterms: