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Differential Regulation of ER Ca2+ Uptake and Release Rates Accounts for Multiple Modes of Ca2+-induced Ca2+ Release

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<!--  FILE :  albrecht_model_2002.xml

CREATED :  21st March 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 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Albrecht et al's
2002 model of differential regulation of ER Ca2+ uptake and release rates.

CHANGES:  
  18/07/2002 - CML - Added more metadata.
  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#" cmeta:id="albrecht_colegrove_friel_2002_version01" name="albrecht_colegrove_friel_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Differential Regulation of ER Ca2+ Uptake and Release Rates Accounts for Multiple Modes of Ca2+-induced Ca2+ Release</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 is consistently represented within the CellML but contains sets of algebraic equations that prevent the model from being solved in currently available software - 03/08.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Calcium is an important signalling ion, and changes in Ca<superscript>2+</superscript> concentration ([Ca<superscript>2+</superscript>]) regulate diverse processes in many cellular compartments.  In excitable cells, depolarisation-induced Ca<superscript>2+</superscript> entry increases [Ca<superscript>2+</superscript>]<subscript>i</subscript>, leading to secondary changes in [Ca<superscript>2+</superscript>] within organelles such as mitochondria and ER that regulate specific Ca<superscript>2+</superscript>-sensitive targets within these organelles.  Although mitochondria accumulate Ca<superscript>2+</superscript> in response to depolarisation-evoked [Ca<superscript>2+</superscript>]<subscript>i</subscript> elevations (see <ulink url="${HTML_EXMPL_COLEGROVE_MODEL}">The Colegrove <emphasis>et al</emphasis> Model Of Mitochondrial Ca<superscript>2+</superscript> Uptake And Release, 2000</ulink>), the ER is also an important component in Ca<superscript>2+</superscript> signalling in virtually all non-muscle cells, and it has been described as either a Ca<superscript>2+</superscript> source or sink.  Different modes of net ER Ca<superscript>2+</superscript> transport are expected to have very different effects on cytoplasmic and intraluminal Ca<superscript>2+</superscript> signals and on the processes they regulate (see <ulink url="${HTML_EXMPL_ALBRECHT_MODEL1}">The Albrecht <emphasis>et al</emphasis> Model Of Multiple Modes of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> Release in Sympathetic Neurons, 2001</ulink>).   
</para>

<para>
In a follow up study to their 2001 paper, Meredith A. Albrecht, Stephen L. Colegrove and David D. Friel have examined how differential regulation of ER Ca<superscript>2+</superscript> uptake and release rates accounts for multiple modes of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> release.  Three different macroscopic Ca<superscript>2+</superscript> fluxes were modelled: J<subscript>SERCA</subscript>, the rate of Ca<superscript>2+</superscript> uptake via SR Ca-ATPases; J<subscript>ICa</subscript>, the total cytoplasmic Ca<superscript>2+</superscript> flux when SR Ca-ATPases are inhibited; and J<subscript>pm</subscript>, the rate of Ca<superscript>2+</superscript> extrusion across the plasma membrane.  One additional flux J<subscript>release</subscript> was calculated from the difference between J<subscript>ICa</subscript> and J<subscript>pm</subscript> (see <xref linkend="fig_cell_diagram" /> below).  This mathematical model has been translated into a CellML description which 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>
<ulink url="http://www.jgp.org/cgi/content/abstract/119/3/211">Differential Regulation of ER Ca<superscript>2+</superscript> Uptake and Release Rates Accounts for Multiple Modes of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> Release</ulink>, Meredith A. Albrecht, Stephen L. Colegrove and David D. Friel, 2002, <ulink url="http://www.jgp.org/">
            <emphasis>The Journal Of General Physiology</emphasis>
          </ulink>, 119, 211-233.  (<ulink url="http://www.jgp.org/cgi/content/full/119/3/211">Full text</ulink> and <ulink url="http://www.jgp.org/cgi/reprint/119/3/211.pdf">PDF</ulink> versions of the article are available for Journal Members on the JGP website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11865019&amp;dopt=Abstract">PubMed ID: 11865019</ulink>  
</para>


<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell schematic for the model</title>
    </objectinfo>
    <imagedata fileref="../images/albrecht_model_2001/cell_diagram.gif" />
  </imageobject>
</mediaobject>
<caption>Schematic of the model indicating Ca<superscript>2+</superscript> compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca<superscript>2+</superscript> ion movement between the compartments.</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="per_second">
    <unit units="second" exponent="-1" />
  </units>
  
  <units name="millivolt">
    <unit units="volt" prefix="milli" />
  </units>
  
  <units name="millimolar">
    <unit units="mole" prefix="micro" />
    <unit units="litre" exponent="-1" />
  </units>
  
  <units name="micromolar">
    <unit units="mole" prefix="micro" />
    <unit units="litre" exponent="-1" />
  </units>
  
  <units name="nanomolar">
    <unit units="mole" prefix="nano" />
    <unit units="litre" exponent="-1" />
  </units>
  
  <units name="nanomolar_per_second">
    <unit units="nanomolar" />
    <unit units="second" exponent="-1" />
  </units>
  
  <units name="micromolar_per_second">
    <unit units="micromolar" />
    <unit units="second" exponent="-1" />
  </units>
  
  <units name="micro_litre">
    <unit units="litre" prefix="micro" />
  </units>
  
  <units name="coulomb_per_millimole">
    <unit units="coulomb" />
    <unit units="mole" prefix="milli" exponent="-1" />
  </units>
  
  <units name="picoA">
    <unit units="ampere" prefix="pico" />
  </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>
  
  <component name="cytoplasmic_calcium">
    <variable units="nanomolar" public_interface="out" name="Ca_i" />
    
    <variable units="nanomolar_per_second" name="J_i" />
    
    <variable units="nanomolar_per_second" public_interface="in" name="J_ER" />
    <variable units="nanomolar_per_second" public_interface="in" name="J_pm" />
    <variable units="second" public_interface="in" name="time" />
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Ca_i_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Ca_i </ci>
        </apply>
        <apply>
          <minus />
          <ci> J_i </ci>
        </apply>
      </apply>
      
      <apply id="J_i_calculation">
        <eq />
        <ci> J_i </ci>
        <apply>
          <plus />
          <ci> J_pm </ci>
          <ci> J_ER </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="intraluminal_calcium">
    <variable units="nanomolar" public_interface="out" name="Ca_ER" />
    
    <variable units="micro_litre" name="v_ER" />
    <variable units="dimensionless" name="k_ER" />
    <variable units="nanomolar" name="Ca_ER_init" />
   
    <variable units="nanomolar" public_interface="in" name="Ca_i" />
    <variable units="micro_litre" public_interface="in" name="v_i" />
    <variable units="dimensionless" public_interface="in" name="k_i" />
    <variable units="nanomolar_per_second" public_interface="in" name="J_ER" />
    <variable units="per_second" public_interface="in" name="P_ER" />
    <variable units="nanomolar_per_second" public_interface="in" name="J_SERCA" />
    <variable units="second" public_interface="in" name="time" />
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Ca_ER_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Ca_ER </ci>
        </apply>
        <apply>
          <times />
          <ci> J_ER </ci>
          <apply>
            <divide />
            <apply>
              <times />
              <ci> v_i </ci>
              <ci> k_i </ci>
            </apply>
            <apply>
              <times />
              <ci> v_ER </ci>
              <ci> k_ER </ci>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="Ca_ER_init_calculation">
        <eq />
        <ci> Ca_ER_init </ci>
        <apply>
          <plus />
          <ci> Ca_i </ci>
          <apply>
            <divide />
            <apply>
              <times />
              <ci> J_SERCA </ci>
              <ci> Ca_i </ci>
            </apply>
            <apply>
              <times />
              <ci> P_ER </ci>
              <apply>
                <divide />
                <ci> Ca_i </ci>
                <ci> v_i </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="total_cytoplasmic_Ca_flux">
    <variable units="nanomolar_per_second" public_interface="out" name="J_ICa" />
    <variable units="micro_litre" public_interface="out" name="v_i" />
    <variable units="dimensionless" public_interface="out" name="k_i" />
   
    <variable units="coulomb_per_millimole" name="F" initial_value="96.5" />
    <variable units="picoA" name="I_Ca" />
   
    <variable units="second" public_interface="in" name="time" />
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ICa_calculation">
        <eq />
        <ci> J_ICa </ci>
        <apply>
          <divide />
          <ci> I_Ca </ci>
          <apply>
            <times />
            <cn cellml:units="dimensionless"> 2.0 </cn>
            <ci> F </ci>
            <ci> v_i </ci>
            <ci> k_i </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="Ca_extrusion_across_the_plasma_membrane">
    <variable units="nanomolar_per_second" public_interface="out" name="J_pm" />
  
    <variable units="nanomolar_per_second" name="J_extru" />
    <variable units="per_second" name="k_leak_pm" initial_value="0.00000015" />
    <variable units="nanomolar_per_second" name="Vmax_extru" initial_value="25.0" />
    <variable units="nanomolar" name="EC50_extru" initial_value="386.0" />
    <variable units="dimensionless" name="n_extru" initial_value="2.4" />
    <variable units="millimolar" name="Ca_o" initial_value="2.0" />
    
    <variable units="nanomolar_per_second" public_interface="in" name="J_ICa" />
    <variable units="dimensionless" public_interface="in" name="k_i" /> 
    <variable units="nanomolar" public_interface="in" name="Ca_i" />
    <variable units="second" public_interface="in" name="time" />
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_pm_calculation">
        <eq />
        <ci> J_pm </ci>
        <apply>
          <plus />
          <ci> J_extru </ci>
          <ci> J_ICa </ci>
        </apply>
      </apply>
      
      <apply id="J_extru_calculation">
        <eq />
        <ci> J_extru </ci>
        <apply>
          <times />
          <apply>
            <power />
            <ci> k_i </ci>
            <cn cellml:units="dimensionless"> -1.0 </cn>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci> k_leak_pm </ci>
              <apply>
                <minus />
                <ci> Ca_i </ci>
                <ci> Ca_o </ci>
              </apply>
            </apply>
            <apply>
              <divide />
              <ci> Vmax_extru </ci>
              <apply>
                <plus />
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <power />
                  <apply>
                    <divide />
                    <ci> EC50_extru </ci>
                    <ci> Ca_i </ci>
                  </apply>
                  <ci> n_extru </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
      
  <component name="Ca_uptake_by_SR_Ca_ATPase">        
    <variable units="nanomolar_per_second" public_interface="out" name="J_SERCA" />
    
    <variable units="nanomolar_per_second" name="Vmax_SERCA" initial_value="2146.0" />
    <variable units="micromolar" name="EC50_SERCA" initial_value="30.3" />
    <variable units="dimensionless" name="n_SERCA" initial_value="2.5" />
   
    <variable units="dimensionless" public_interface="in" name="k_i" />
    <variable units="nanomolar" public_interface="in" name="Ca_i" />
    <variable units="second" public_interface="in" name="time" />
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_SERCA_calculation">
        <eq />
        <ci> J_SERCA </ci>
        <apply>
          <divide />
          <ci> Vmax_SERCA </ci>
          <apply>
            <times />
            <ci> k_i </ci>
            <apply>
              <plus />
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <power />
                <apply>
                  <divide />
                  <ci> EC50_SERCA </ci>
                  <ci> Ca_i </ci>
                </apply>
                <ci> n_SERCA </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="ER_Ca_release">     
    <variable units="nanomolar_per_second" public_interface="out" name="J_ER" />       
    <variable units="per_second" public_interface="out" name="P_ER" />
    
    <variable units="per_second" name="P_basal" initial_value="0.009" />
    <variable units="per_second" name="Pmax_RyR" initial_value="0.05" />
    <variable units="nanomolar" name="EC50_RyR" initial_value="2641.0" />
    <variable units="dimensionless" name="n_RyR" initial_value="0.96" />
    <variable units="nanomolar_per_second" name="J_release" />
    
    <variable units="nanomolar_per_second" public_interface="in" name="J_SERCA" />
    <variable units="micro_litre" public_interface="in" name="v_i" />
    <variable units="dimensionless" public_interface="in" name="k_i" />        
    <variable units="nanomolar" public_interface="in" name="Ca_i" />
    <variable units="nanomolar" public_interface="in" name="Ca_ER" />         
    <variable units="second" public_interface="in" name="time" />        
            
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_release_calculation">
        <eq />
        <ci> J_release </ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci> P_ER </ci>
            <apply>
              <minus />
              <ci> Ca_i </ci>
              <ci> Ca_ER </ci> 
            </apply>
          </apply>
          <apply>
            <times />
            <ci> v_i </ci>
            <ci> k_i </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="J_ER_calculation">
        <eq />
        <ci> J_ER </ci>
        <apply>
          <plus />
          <ci> J_SERCA </ci>
          <ci> J_release </ci>
        </apply>
      </apply>
      
      <apply id="P_ER_v_i_calculation">
        <eq />
        <ci> P_ER </ci>
          <apply>
          <times />
          <ci> v_i </ci>
          <apply>
            <plus />
            <ci> P_basal </ci>
            <apply>
              <divide />
              <ci> Pmax_RyR </ci>
              <apply>
                <plus />
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <power />
                  <apply>
                    <divide />
                    <ci> EC50_RyR </ci>
                    <ci> Ca_i </ci>
                  </apply>
                  <ci> n_RyR </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <connection>
    <map_components component_2="environment" component_1="cytoplasmic_calcium" />
    <map_variables variable_2="time" variable_1="time" />
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="intraluminal_calcium" />
    <map_variables variable_2="time" variable_1="time" />
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="total_cytoplasmic_Ca_flux" />
    <map_variables variable_2="time" variable_1="time" />
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="Ca_extrusion_across_the_plasma_membrane" />
    <map_variables variable_2="time" variable_1="time" />
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="Ca_uptake_by_SR_Ca_ATPase" />
    <map_variables variable_2="time" variable_1="time" />
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="ER_Ca_release" />
    <map_variables variable_2="time" variable_1="time" />
  </connection>
  
  <connection>
    <map_components component_2="Ca_extrusion_across_the_plasma_membrane" component_1="cytoplasmic_calcium" />
    <map_variables variable_2="Ca_i" variable_1="Ca_i" />
    <map_variables variable_2="J_pm" variable_1="J_pm" />
  </connection>
  
  <connection>
    <map_components component_2="Ca_uptake_by_SR_Ca_ATPase" component_1="cytoplasmic_calcium" />
    <map_variables variable_2="Ca_i" variable_1="Ca_i" />
  </connection>
  
  <connection>
    <map_components component_2="ER_Ca_release" component_1="cytoplasmic_calcium" />
    <map_variables variable_2="Ca_i" variable_1="Ca_i" />
    <map_variables variable_2="J_ER" variable_1="J_ER" />
  </connection>
  
  <connection>
    <map_components component_2="intraluminal_calcium" component_1="cytoplasmic_calcium" />
    <map_variables variable_2="Ca_i" variable_1="Ca_i" />
  </connection>
  
  <connection>
    <map_components component_2="ER_Ca_release" component_1="intraluminal_calcium" />
    <map_variables variable_2="Ca_ER" variable_1="Ca_ER" />
    <map_variables variable_2="J_ER" variable_1="J_ER" />
    <map_variables variable_2="P_ER" variable_1="P_ER" />
  </connection>
  
  <connection>
    <map_components component_2="Ca_uptake_by_SR_Ca_ATPase" component_1="intraluminal_calcium" />
    <map_variables variable_2="J_SERCA" variable_1="J_SERCA" />
  </connection>
  
  <connection>
    <map_components component_2="ER_Ca_release" component_1="Ca_uptake_by_SR_Ca_ATPase" />
    <map_variables variable_2="J_SERCA" variable_1="J_SERCA" />
  </connection>
  
  <connection>
    <map_components component_2="Ca_extrusion_across_the_plasma_membrane" component_1="total_cytoplasmic_Ca_flux" />
    <map_variables variable_2="J_ICa" variable_1="J_ICa" />
    <map_variables variable_2="k_i" variable_1="k_i" />
  </connection>
  
  <connection>
    <map_components component_2="intraluminal_calcium" component_1="total_cytoplasmic_Ca_flux" />
    <map_variables variable_2="v_i" variable_1="v_i" />
    <map_variables variable_2="k_i" variable_1="k_i" />
  </connection> 
  
  <connection>
    <map_components component_2="ER_Ca_release" component_1="total_cytoplasmic_Ca_flux" />
    <map_variables variable_2="v_i" variable_1="v_i" />
    <map_variables variable_2="k_i" variable_1="k_i" />
  </connection>
  
  <connection>
    <map_components component_2="Ca_uptake_by_SR_Ca_ATPase" component_1="total_cytoplasmic_Ca_flux" />
    <map_variables variable_2="k_i" variable_1="k_i" />
  </connection>


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    <rdf:li>neuron</rdf:li>
    <rdf:li>electrophysiology</rdf:li>
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  <rdf:Description rdf:about="rdf:#4123a23b-4e83-4774-ac22-0297aefc5717">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
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    <vCard:Given>David</vCard:Given>
    <vCard:Family>Friel</vCard:Family>
    <vCard:Other>D</vCard:Other>
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  <rdf:Description rdf:about="rdf:#a72eecbd-8b6e-4c2d-8769-359866ae4502">
    <dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e7b7917e-e364-4783-be5f-d12f990f553e">
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    <rdf:value>
          This is the CellML description of Albrecht et al's 2002 model of 
          differential regulation of ER Ca2+ uptake and rates.
        </rdf:value>
  </rdf:Description>
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    <dc:creator rdf:resource="rdf:#2722806d-d55e-48d3-96c4-7b05e49b76cd" />
    <dc:title>
            Differential Regulation of ER Ca2+ Uptake and Release Rates Accounts             for Multiple Modes of Ca2+-induced Ca2+ Release 
          </dc:title>
    <bqs:volume>119</bqs:volume>
    <bqs:first_page>211</bqs:first_page>
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   Â