Location: Chang, Fujita, 2001 @ 3154891c06df / chang_fujita_2001renal_Na_H_exchanger_model.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2009-06-17 12:44:46+12:00
Desc:
committing version02 of chang_fujita_2001
Permanent Source URI:
https://models.cellml.org/workspace/chang_fujita_2001/rawfile/3154891c06dfcd5cdb61375c7e916e39fa7d41d0/chang_fujita_2001renal_Na_H_exchanger_model.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  renal_anion_exchanger_model_version02.xml

CREATED :  29th May 2007

LAST MODIFIED : 29th May 2007

AUTHOR :  Catherine Lloyd
          The 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 Chang and Fujita's 2001 mathematical model of an anion exchanger in the distal tubule of the rat: it is one component of an overall model of acid/base transport in a distal tubule.

CHANGES:  
  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="renal_anion_exchanger_model_version02" name="chang_fujita_2001_version03">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Mathematical Models of Ionic Transport in the Distal Tubule of the Rat</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 CellML model is a description of Chang and Fujita's 2001 mathematical model of an anion exchanger in the distal tubule of the rat: it is one component of an overall model of acid/base transport in a distal tubule.          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Acid-base transport in the rat distal tubule of the kidney has been extensively studied by a variety of different experimental methods.  These experiments have shown that in the early part of the distal tubule, H<superscript>+</superscript> is secreted into the tubular fluid via a Na/H exchanger embedded in the luminal membrane.  Closely linked with this process is the transport of HCO<subscript>3</subscript>
          <superscript>-</superscript> out of the cytosolic space into the basolateral space.  This probably occurs via an anion exchanger (see <xref linkend="fig_reaction_diagram2"/> below).  In the late distal tubule, distinct cell types called intercalated cells are present.  These cells are specifically involved in acid-base transport.  Type A cells secrete H<superscript>+</superscript> via a luminal H-ATPase, and they extrude HCO<subscript>3</subscript>
          <superscript>-</superscript> via a basolateral anion exchanger.  Type B cells have anion transporters on their opposite side, and they function to secrete HCO<subscript>3</subscript>
          <superscript>-</superscript> into the tubular fluid.    
</para>

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

<para>
<ulink url="http://ajprenal.physiology.org/cgi/content/abstract/281/2/F222">A numerical model of acid-base transport in rat distal tubule</ulink>, Hangil Chang and Toshiro Fujita, 2001, <ulink url="http://ajpcon.physiology.org/">
            <emphasis>American Journal of Physiology</emphasis>
          </ulink>, 281, F222-F243. (<ulink url="http://ajprenal.physiology.org/cgi/reprint/281/2/F222.pdf">PDF</ulink> and <ulink url="http://ajprenal.physiology.org/cgi/content/full/281/2/F222">text</ulink> versions of the article are available to Journal subscribers.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11457714&amp;dopt=Abstract">PubMed ID: 11457714</ulink>) 
</para>


<informalfigure float="0" id="fig_reaction_diagram2">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction_diagram2</title>
    </objectinfo>
    <imagedata fileref="chang_2001b.png"/>
  </imageobject>
</mediaobject>
<caption>State diagram of the anion exchanger.  In this model, the anion transporter (E) has a single binding site to which Cl<superscript>-</superscript> and HCO<subscript>3</subscript>
            <superscript>-</superscript> competitively bind.  Only the bound forms of the transporter are able to cross the membrane.  (Symbols with the asterisk (*) represent conformations facing the cytosol, symbols without indicate conformations facing the extracellular environment.)</caption>
</informalfigure>

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


  
  
  
   <units name="millimolar">
     <unit units="mole" prefix="milli"/>
     <unit units="litre" exponent="-1"/>
   </units>

   <units name="flux">
     <unit units="millimolar"/>
     <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="millimolar" exponent="-1"/>
     <unit units="second" exponent="-1"/>
   </units>
   
   <component name="environment">
      <variable units="second" public_interface="out" name="time"/>
   </component>
   
   <component name="E" cmeta:id="E">
     
    <variable units="millimolar" public_interface="out" name="E"/>
      
    <variable units="second_order_rate_constant" public_interface="in" name="k1"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k3"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k4"/>
    <variable units="millimolar" public_interface="in" name="ECl"/>
    <variable units="millimolar" public_interface="in" name="EHCO3"/>
    <variable units="millimolar" public_interface="in" name="HCO3"/>
    <variable units="millimolar" public_interface="in" name="Cl"/>
    <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> k2 </ci>
              <ci> ECl </ci>
            </apply>
            <apply>
              <times/>
              <ci> k4 </ci>
              <ci> EHCO3 </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> Cl </ci>
              <ci> E </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> HCO3 </ci>
              <ci> E </ci>
            </apply>
          </apply>
        </apply>  
      </apply> 
    </math> 
  </component>
  
  <component name="ECl" cmeta:id="ECl">
     
    <variable units="millimolar" public_interface="out" name="ECl"/>
      
    <variable units="second_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="k9"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k10"/>
    <variable units="millimolar" public_interface="in" name="ECl_"/>
    <variable units="millimolar" public_interface="in" name="E"/>
    <variable units="millimolar" public_interface="in" name="Cl"/>
    <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> ECl </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> Cl </ci>
              <ci> E </ci>
            </apply>
            <apply>
              <times/>
              <ci> k10 </ci>
              <ci> ECl_ </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> ECl </ci>
            </apply>
            <apply>
              <times/>
              <ci> k9 </ci>
              <ci> ECl </ci>
            </apply>
          </apply>
        </apply>  
      </apply> 
    </math> 
  </component>
  
  <component name="EHCO3" cmeta:id="EHCO3">
     
    <variable units="millimolar" public_interface="out" name="EHCO3"/>
      
    <variable units="first_order_rate_constant" public_interface="in" name="k11"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k12"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k3"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k4"/>
    <variable units="millimolar" public_interface="in" name="E"/>
    <variable units="millimolar" public_interface="in" name="EHCO3_"/>
    <variable units="millimolar" public_interface="in" name="HCO3"/>
    <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> EHCO3 </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> HCO3 </ci>
              <ci> E </ci>
            </apply>
            <apply>
              <times/>
              <ci> k12 </ci>
              <ci> EHCO3_ </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k4 </ci>
              <ci> EHCO3 </ci>
            </apply>
            <apply>
              <times/>
              <ci> k11 </ci>
              <ci> EHCO3 </ci>
            </apply>
          </apply>
        </apply>  
      </apply> 
    </math> 
  </component>
 
   <component name="E_" cmeta:id="E_">
     
    <variable units="millimolar" public_interface="out" name="E_"/>
      
    <variable units="second_order_rate_constant" public_interface="in" name="k5"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k6"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k7"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k8"/>
    <variable units="millimolar" public_interface="in" name="ECl_"/>
    <variable units="millimolar" public_interface="in" name="EHCO3_"/>
    <variable units="millimolar" public_interface="in" name="HCO3_"/>
    <variable units="millimolar" public_interface="in" name="Cl_"/>
    <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> k6 </ci>
              <ci> ECl_ </ci>
            </apply>
            <apply>
              <times/>
              <ci> k8 </ci>
              <ci> EHCO3_ </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k5 </ci>
              <ci> Cl_ </ci>
              <ci> E_ </ci>
            </apply>
            <apply>
              <times/>
              <ci> k7 </ci>
              <ci> HCO3_ </ci>
              <ci> E_ </ci>
            </apply>
          </apply>
        </apply>  
      </apply> 
    </math> 
  </component>
  
  <component name="ECl_" cmeta:id="ECl_">
     
    <variable units="millimolar" public_interface="out" name="ECl_"/>
      
    <variable units="second_order_rate_constant" public_interface="in" name="k5"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k6"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k9"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k10"/>
    <variable units="millimolar" public_interface="in" name="ECl"/>
    <variable units="millimolar" public_interface="in" name="E_"/>
    <variable units="millimolar" public_interface="in" name="Cl_"/>
    <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> ECl_ </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k5 </ci>
              <ci> Cl_ </ci>
              <ci> E_ </ci>
            </apply>
            <apply>
              <times/>
              <ci> k9 </ci>
              <ci> ECl </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k6 </ci>
              <ci> ECl_ </ci>
            </apply>
            <apply>
              <times/>
              <ci> k10 </ci>
              <ci> ECl_ </ci>
            </apply>
          </apply>
        </apply>  
      </apply> 
    </math> 
  </component>
  
  <component name="EHCO3_" cmeta:id="EHCO3_">
     
    <variable units="millimolar" public_interface="out" name="EHCO3_"/>
      
    <variable units="first_order_rate_constant" public_interface="in" name="k11"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k12"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k7"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k8"/>
    <variable units="millimolar" public_interface="in" name="E_"/>
    <variable units="millimolar" public_interface="in" name="EHCO3"/>
    <variable units="millimolar" public_interface="in" name="HCO3_"/>
    <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> EHCO3_ </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k7 </ci>
              <ci> HCO3_ </ci>
              <ci> E_ </ci>
            </apply>
            <apply>
              <times/>
              <ci> k11 </ci>
              <ci> EHCO3 </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k8 </ci>
              <ci> EHCO3_ </ci>
            </apply>
            <apply>
              <times/>
              <ci> k12 </ci>
              <ci> EHCO3_ </ci>
            </apply>
          </apply>
        </apply>  
      </apply> 
    </math> 
  </component>
   
  <component name="J_Cl_influx" cmeta:id="J_Cl_influx">
    <variable units="flux" public_interface="out" name="J_Cl_influx"/>
     
    <variable units="millimolar" name="Ki_Cl" initial_value="0.528"/>
    <variable units="millimolar" name="Ki_HCO3" initial_value="0.423"/>
 
    <variable units="first_order_rate_constant" public_interface="in" name="k9"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k10"/>
    <variable units="millimolar" public_interface="in" name="ECl_"/>
    <variable units="millimolar" public_interface="in" name="ECl"/>
    <variable units="millimolar" public_interface="in" name="Cl_"/>
    <variable units="millimolar" public_interface="in" name="HCO3_"/>
    <variable units="second" public_interface="in" name="time"/> 
      
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
        <eq/>
            <ci>J_Cl_influx</ci>
            <apply>
          <times/>
               <apply>
            <minus/>
                 <apply>
              <times/>
                   <ci> k9 </ci>
                   <ci> ECl </ci>
                 </apply>
                 <apply>
              <times/>
                   <ci> k10 </ci>
                   <ci> ECl_ </ci>
                 </apply>
               </apply>
               <apply>
            <power/>
                  <apply>
              <plus/>
                     <cn cellml:units="dimensionless"> 1.0 </cn>
                     <apply>
                <divide/>
                        <ci> Cl_ </ci>
                        <ci> Ki_Cl </ci>
                     </apply>
                     <apply>
                <divide/>
                        <ci> HCO3_ </ci>
                        <ci> Ki_HCO3 </ci>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless"> -1.0 </cn>
               </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="k2" initial_value="7.87E6"/>
    <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="k4" initial_value="8.28E6"/>
    <variable units="second_order_rate_constant" public_interface="out" name="k5" initial_value="1.0E8"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k6" initial_value="7.87E6"/>
    <variable units="second_order_rate_constant" public_interface="out" name="k7" initial_value="1.0E8"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k8" initial_value="8.28E6"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k9" initial_value="5.14E5"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k10" initial_value="9.26E4"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k11" initial_value="3.24E5"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k12" initial_value="5.83E4"/>
    <variable units="millimolar" public_interface="out" name="Cl" initial_value="1.0"/>
    <variable units="millimolar" public_interface="out" name="HCO3" initial_value="1.0"/>
    <variable units="millimolar" public_interface="out" name="Cl_" initial_value="1.0"/>
    <variable units="millimolar" public_interface="out" name="HCO3_" initial_value="1.0"/>
   </component>
   
   
  <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="ECl"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="EHCO3"/>
    <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="ECl_"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="EHCO3_"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>

   <connection>
      <map_components component_2="ECl" component_1="E"/>
      <map_variables variable_2="E" variable_1="E"/>
      <map_variables variable_2="ECl" variable_1="ECl"/>
   </connection>
   
   <connection>
      <map_components component_2="EHCO3" component_1="E"/>
      <map_variables variable_2="E" variable_1="E"/>
      <map_variables variable_2="EHCO3" variable_1="EHCO3"/>
   </connection>

   <connection>
      <map_components component_2="ECl_" component_1="E_"/>
      <map_variables variable_2="E_" variable_1="E_"/>
      <map_variables variable_2="ECl_" variable_1="ECl_"/>
   </connection>
   
   <connection>
      <map_components component_2="EHCO3_" component_1="E_"/>
      <map_variables variable_2="E_" variable_1="E_"/>
      <map_variables variable_2="EHCO3_" variable_1="EHCO3_"/>
   </connection>
   
   <connection>
      <map_components component_2="ECl_" component_1="ECl"/>
      <map_variables variable_2="ECl" variable_1="ECl"/>
      <map_variables variable_2="ECl_" variable_1="ECl_"/>
   </connection>

   <connection>
      <map_components component_2="EHCO3_" component_1="EHCO3"/>
      <map_variables variable_2="EHCO3" variable_1="EHCO3"/>
      <map_variables variable_2="EHCO3_" variable_1="EHCO3_"/>
   </connection>
   
   <connection>
      <map_components component_2="environment" component_1="J_Cl_influx"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>

   <connection>
      <map_components component_2="ECl" component_1="J_Cl_influx"/>
      <map_variables variable_2="ECl" variable_1="ECl"/>
   </connection>

   <connection>
      <map_components component_2="ECl_" component_1="J_Cl_influx"/>
      <map_variables variable_2="ECl_" variable_1="ECl_"/>
   </connection>

   <connection>
      <map_components component_2="J_Cl_influx" component_1="reaction_constants"/>
      <map_variables variable_2="HCO3_" variable_1="HCO3_"/>
      <map_variables variable_2="Cl_" variable_1="Cl_"/>
      <map_variables variable_2="k9" variable_1="k9"/>
      <map_variables variable_2="k10" variable_1="k10"/>
   </connection>
   
   <connection>
      <map_components component_2="reaction_constants" component_1="E"/>
      <map_variables variable_2="Cl" variable_1="Cl"/>
      <map_variables variable_2="HCO3" variable_1="HCO3"/>
      <map_variables variable_2="k1" variable_1="k1"/>
      <map_variables variable_2="k2" variable_1="k2"/>
      <map_variables variable_2="k3" variable_1="k3"/>
      <map_variables variable_2="k4" variable_1="k4"/>
   </connection>

   <connection>
      <map_components component_2="reaction_constants" component_1="ECl"/>
      <map_variables variable_2="Cl" variable_1="Cl"/>
      <map_variables variable_2="k1" variable_1="k1"/>
      <map_variables variable_2="k2" variable_1="k2"/>
      <map_variables variable_2="k9" variable_1="k9"/>
      <map_variables variable_2="k10" variable_1="k10"/>
   </connection>

   <connection>
      <map_components component_2="reaction_constants" component_1="EHCO3"/>
      <map_variables variable_2="HCO3" variable_1="HCO3"/>
      <map_variables variable_2="k11" variable_1="k11"/>
      <map_variables variable_2="k12" variable_1="k12"/>
      <map_variables variable_2="k3" variable_1="k3"/>
      <map_variables variable_2="k4" variable_1="k4"/>
   </connection>

   <connection>
      <map_components component_2="reaction_constants" component_1="E_"/>
      <map_variables variable_2="Cl_" variable_1="Cl_"/>
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        Chang and Fujita's 2001 mathematical model of an anion exchanger in the 
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