Location: Chang, Fujita, B, 1999 @ 0db46845f2af / chang_fujita_b_1999.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2009-05-25 01:21:33+12:00
Desc:
committing version01 of chang_fujita_b_1999
Permanent Source URI:
https://models.fieldml.org/workspace/255/rawfile/0db46845f2af27127c497c1d802ee36a65b7ce5d/chang_fujita_b_1999.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  chang_model_II_1999.xml

CREATED :  10th February 2003

LAST MODIFIED : 20th April 2005

AUTHOR :  Catherine Lloyd
          The 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 Chang and Fujita's 1999 numerical model of the renal distal tubule.

CHANGES:  
  09/04/2003 - AAC - Added publication date information.  
  20/04/2005 - PJV - Changed MathML id's
--><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="chang_fujita_1999_version02" name="chang_fujita_1999_version02">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>A numerical model of the renal distal tubule</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 CellML description of Chang and Fujita's 1999 numerical model of the renal distal tubule. It should be noted that the initial conditions used in this description represent those in the early distal tubule. For model representations of the late distal tublule, these initial values should be replaced with those listed in the original paper for the late distal tubule.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
ABSTRACT: A numerical model of the rat distal tubule was developed to simulate water and solute transport in this nephron segment. This model incorporates the following: 1) Na-Cl cotransporter, K-Cl cotransporter, Na channel, K channel, and Cl channel in the luminal membrane; 2) Na-K-ATPase, K channel, and Cl channel in the basolateral membrane; and 3) conductances for Na, K, and Cl in the paracellular pathway. Transport rates were calculated using kinetic equations. Axial heterogeneity was represented by partitioning the model into two subsegments with different sets of model parameters. Model equations derived from the principles of mass conservation and electrical neutrality were solved numerically. Values of the model parameters were adjusted to minimize a penalty function that was devised to quantify the difference between model predictions and experimental results. The developed model could simulate the water and solute transport of the distal tubule in the normal state, as well as in conditions including thiazide or amiloride application and various levels of sodium load and tubular flow rate.
</para>

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

<para>
<ulink url="http://ajprenal.physiology.org/cgi/content/abstract/276/6/F931">A numerical model of the renal distal tubule</ulink>, Hangil Chang and Toshiro Fujita, 1999, <ulink url="http://ajprenal.physiology.org/">
            <emphasis>American Journal of Physiology</emphasis>
          </ulink>, 276, F952-F959.  (<ulink url="http://ajprenal.physiology.org/cgi/reprint/276/6/F931.pdf">PDF</ulink> and <ulink url="http://ajprenal.physiology.org/cgi/content/full/276/6/F931">full text</ulink> versions of the article are available to subscribers on the journal website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10362782&amp;dopt=Abstract">PubMed ID: 10362782</ulink>
</para>



<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the model</title>
    </objectinfo>
    <imagedata fileref="chang_1999b.png"/>
  </imageobject>
</mediaobject>
<caption>Transport mechanisms of model tubule. In the luminal cell membrane, there are Na-Cl cotransporter, K-Cl cotransporter, Na channel, K channel, and Cl channel. In the basolateral cell membrane, there are Na-K-ATPase, K channel, and Cl channel. In the paracellular pathway, which faces luminal and basolateral compartments, there are conductances for sodium, potassium, and chloride. Axial heterogeneity of the distal tubule was represented by changing the model parameters in the early and the late parts of the model tubule.</caption>
</informalfigure>




</sect1>
</article>
</documentation>
  
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. 
  -->
  
  <units name="cm_per_s">
    <unit units="metre" prefix="centi"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="mmol_per_cm3">
    <unit units="mole" prefix="milli"/>
    <unit units="metre" prefix="centi" exponent="-3"/>
  </units>
  
  <units name="mmol_per_cm2_s">
    <unit units="mole" prefix="milli"/>
    <unit units="metre" prefix="centi" exponent="-2"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="C_per_mmol">
    <unit units="coulomb"/>
    <unit units="mole" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="K">
    <unit units="kelvin"/>
  </units>
  
  <units name="J_per_mmol_K">
    <unit units="joule"/>
    <unit units="mole" prefix="milli" exponent="-1"/>
    <unit units="kelvin" exponent="-1"/>
  </units>
  
  <units base_units="yes" name="mmHg"/>
  
  <units name="cm_per_s_mmHg">
    <unit units="metre" prefix="centi"/>
    <unit units="second" exponent="-1"/>
    <unit units="mmHg" exponent="-1"/>
  </units> 
  
  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>
  
  <component name="imported_variables">
    <variable units="mmol_per_cm3" private_interface="out" name="C_m_Na"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_m_K"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_m_Imp"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_c_Na"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_c_K"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_c_Cl"/>
    <variable units="mmol_per_cm3" private_interface="out" name="C_c_Imp"/>
    <variable units="volt" private_interface="out" name="psi_m"/>
    <variable units="volt" private_interface="out" name="psi_c"/>
  </component>
  
  <component name="constants">
    <variable units="J_per_mmol_K" public_interface="out" name="R" initial_value="8.314E-3"/>
    <variable units="K" public_interface="out" name="T" initial_value="310.0"/>
    <variable units="C_per_mmol" public_interface="out" name="F" initial_value="96.48"/>
    <variable units="mmol_per_cm3" public_interface="out" name="C_s_Na" initial_value="1.438E-1"/>
    <variable units="mmol_per_cm3" public_interface="out" name="C_s_K" initial_value="4.25E-3"/>
    <variable units="mmol_per_cm3" public_interface="out" name="C_s_Cl" initial_value="1.12E-1"/>
    <variable units="mmol_per_cm3" public_interface="out" name="C_s_Imp" initial_value="4.525E-2"/>
    <variable units="volt" public_interface="out" name="psi_s" initial_value="0.0"/>
  </component>
  
  <component name="mc_sodium_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_mc_Na"/>
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_mc_NaCl"/>
    
    <variable units="dimensionless" name="G_mc_Na"/>
    <variable units="cm_per_s" name="P_mc_Na" initial_value="3.27E-6"/>
    <variable units="mmol_per_cm2_s" name="K_mc_NaCl_max" initial_value="3.21E-5"/>
    <variable units="mmol_per_cm3" name="K_mc_Na_NaCl" initial_value="5.11E-2"/>
    <variable units="mmol_per_cm3" name="K_mc_Cl_NaCl" initial_value="1.92E-2"/>
     
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Na"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_Na"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_Cl"/>
    <variable units="volt" public_interface="in" name="psi_m"/>
    <variable units="volt" public_interface="in" name="psi_c"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_mc_Na_calculation">
        <eq/>
        <ci> J_mc_Na </ci>
        <apply>
          <plus/>
          <ci> J_mc_NaCl </ci>
          <ci> G_mc_Na </ci>
        </apply>
      </apply>
      
      <apply id="G_mc_Na_calculation">
        <eq/>
        <ci> G_mc_Na </ci>
        <apply>
          <times/> 
          <ci> P_mc_Na </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_m </ci>
                <ci> psi_c </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_m_Na </ci>
              <apply>
                <times/>
                <ci> C_c_Na </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <ci> F </ci>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_m </ci>
                      <ci> psi_c </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
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                  <apply>
                    <minus/>
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                    <ci> psi_c </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="J_mc_NaCl_calculation">
        <eq/>
        <ci> J_mc_NaCl </ci>
        <apply>
          <times/>
          <ci> K_mc_NaCl_max </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <ci> C_m_Na </ci>
                  <ci> K_mc_Na_NaCl </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> C_m_Cl </ci>
                  <ci> K_mc_Cl_NaCl </ci>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <ci> C_c_Na </ci>
                  <ci> K_mc_Na_NaCl </ci>
                </apply>
                <apply>
                  <divide/>
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                  <ci> K_mc_Cl_NaCl </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <apply>
                      <divide/>
                      <ci> C_m_Na </ci>
                      <ci> K_mc_Na_NaCl </ci>
                    </apply>
                    <apply>
                      <divide/>
                      <ci> C_m_Cl </ci>
                      <ci> K_mc_Cl_NaCl </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> C_c_Na </ci>
                    <ci> K_mc_Na_NaCl </ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> C_c_Cl </ci>
                    <ci> K_mc_Cl_NaCl </ci>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <apply>
                      <divide/>
                      <ci> C_c_Na </ci>
                      <ci> K_mc_Na_NaCl </ci>
                    </apply>
                    <apply>
                      <divide/>
                      <ci> C_c_Cl </ci>
                      <ci> K_mc_Cl_NaCl </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> C_m_Na </ci>
                    <ci> K_mc_Na_NaCl </ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> C_m_Cl </ci>
                    <ci> K_mc_Cl_NaCl </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="mc_potassium_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_mc_K"/>
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_mc_KCl"/>
    
    <variable units="dimensionless" name="G_mc_K"/>
    <variable units="mmol_per_cm2_s" name="K_mc_KCl_max" initial_value="6.31E-8"/>
    <variable units="mmol_per_cm3" name="K_mc_K_KCl" initial_value="5.30E-2"/>
    <variable units="mmol_per_cm3" name="K_mc_Cl_KCl" initial_value="2.13E-2"/>
    <variable units="cm_per_s" name="P_mc_K" initial_value="4.90E-7"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_K"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_K"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_Cl"/>
    <variable units="volt" public_interface="in" name="psi_m"/>
    <variable units="volt" public_interface="in" name="psi_c"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_mc_K_calculation">
        <eq/>
        <ci> J_mc_K </ci>
        <apply>
          <plus/>
          <ci> J_mc_KCl </ci>
          <ci> G_mc_K </ci>
        </apply>
      </apply>
      
      <apply id="G_mc_K_calculation">
        <eq/>
        <ci> G_mc_K </ci>
        <apply>
          <times/> 
          <ci> P_mc_K </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_m </ci>
                <ci> psi_c </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_m_K </ci>
              <apply>
                <times/>
                <ci> C_c_K </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <ci> F </ci>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_m </ci>
                      <ci> psi_c </ci>
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                  </apply>
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                      <apply>
                        <times/>
                        <ci> R </ci>
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                      </apply>
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                  </apply>
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                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="J_mc_KCl_calculation">
        <eq/>
        <ci> J_mc_KCl </ci>
        <apply>
          <times/>
          <ci> K_mc_KCl_max </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
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                <times/>
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                  <divide/>
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                  <ci> K_mc_K_KCl </ci>
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                <apply>
                  <divide/>
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                  <divide/>
                  <ci> C_c_K </ci>
                  <ci> K_mc_K_KCl </ci>
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                  <ci> C_c_Cl </ci>
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                  <apply>
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                    <ci> C_c_Cl </ci>
                    <ci> K_mc_Cl_KCl </ci>
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                  <apply>
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                      <ci> C_c_K </ci>
                      <ci> K_mc_K_KCl </ci>
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                      <ci> C_c_Cl </ci>
                      <ci> K_mc_Cl_KCl </ci>
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                </apply>
                <apply>
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                  <apply>
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                    <ci> C_m_K </ci>
                    <ci> K_mc_K_KCl </ci>
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                </apply>
                <apply>
                  <plus/>
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                  <apply>
                    <divide/>
                    <ci> C_m_Cl </ci>
                    <ci> K_mc_Cl_KCl </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="mc_chloride_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_mc_Cl"/>
    
    <variable units="dimensionless" name="G_mc_Cl"/>
    <variable units="cm_per_s" name="P_mc_Cl" initial_value="1.43E-6"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_mc_NaCl"/>
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_mc_KCl"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_Cl"/>
    <variable units="volt" public_interface="in" name="psi_m"/>
    <variable units="volt" public_interface="in" name="psi_c"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_mc_Cl_calculation">
        <eq/>
        <ci> J_mc_Cl </ci>
        <apply>
          <plus/>
          <ci> J_mc_NaCl </ci>
          <ci> J_mc_KCl </ci>
          <ci> G_mc_Cl </ci>
        </apply>
      </apply>
      
      <apply id="G_mc_Cl_calculation">
        <eq/>
        <ci> G_mc_Cl </ci>
        <apply>
          <times/> 
          <ci> P_mc_Cl </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> -1.0 </cn>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_m </ci>
                <ci> psi_c </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
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          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_m_Cl </ci>
              <apply>
                <times/>
                <ci> C_c_Cl </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless"> -1.0 </cn>
                          <ci> F </ci>
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                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_m </ci>
                      <ci> psi_c </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> -1.0 </cn>
                        <ci> F </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci> psi_m </ci>
                    <ci> psi_c </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="sc_sodium_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_a"/>
    
    <variable units="mmol_per_cm2_s" name="J_sc_Na"/>
    <variable units="mmol_per_cm2_s" name="J_a_max" initial_value="2.69E-6"/>
    <variable units="mmol_per_cm3" name="K_Na_ATPase" initial_value="1.20E-2"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_Na"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_sc_Na_calculation">
        <eq/>
        <ci> J_sc_Na </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> -3.0 </cn>
          <ci> J_a </ci>
        </apply>
      </apply>
      
      <apply id="J_a_calculation">
        <eq/>
        <ci> J_a </ci>
        <apply>
          <times/>
          <ci> J_a_max </ci>
          <apply>
            <divide/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> K_Na_ATPase </ci>
                  <ci> C_c_Na </ci>
                </apply>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="sc_potassium_flux">
    <variable units="mmol_per_cm2_s" name="J_sc_K"/>
    <variable units="dimensionless" name="G_sc_K"/>
    <variable units="cm_per_s" name="P_sc_K" initial_value="4.74E-4"/>
    
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_a"/>
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_s_K"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_K"/>
    <variable units="volt" public_interface="in" name="psi_s"/>
    <variable units="volt" public_interface="in" name="psi_c"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_sc_K_calculation">
        <eq/>
        <ci> J_sc_K </ci>
        <apply>
          <plus/>
          <apply>
            <times/>
            <cn cellml:units="dimensionless"> 2.0 </cn>
            <ci> J_a </ci>
          </apply>
          <ci> G_sc_K </ci>
        </apply>
      </apply>
      
      <apply id="G_sc_K_calculation">
        <eq/>
        <ci> G_sc_K </ci>
        <apply>
          <times/> 
          <ci> P_sc_K </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_s </ci>
                <ci> psi_c </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_s_K </ci>
              <apply>
                <times/>
                <ci> C_c_K </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <ci> F </ci>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_s </ci>
                      <ci> psi_c </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <apply>
                      <divide/>
                      <ci> F </ci>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci> psi_s </ci>
                    <ci> psi_c </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="sc_chloride_flux">
    <variable units="mmol_per_cm2_s" name="J_sc_Cl"/>
    <variable units="dimensionless" name="G_sc_Cl"/>
    <variable units="cm_per_s" name="P_sc_Cl" initial_value="9.16E-5"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_s_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_c_Cl"/>
    <variable units="volt" public_interface="in" name="psi_s"/>
    <variable units="volt" public_interface="in" name="psi_c"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_sc_Cl_calculation">
        <eq/>
        <ci> J_sc_Cl </ci>
        <ci> G_sc_Cl </ci>
      </apply>
      
      <apply id="G_sc_Cl_calculation">
        <eq/>
        <ci> G_sc_Cl </ci>
        <apply>
          <times/> 
          <ci> P_sc_Cl </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> -1.0 </cn>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_s </ci>
                <ci> psi_c </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_s_Cl </ci>
              <apply>
                <times/>
                <ci> C_c_Cl </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless"> -1.0 </cn>
                          <ci> F </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_s </ci>
                      <ci> psi_c </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> -1.0 </cn>
                        <ci> F </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci> psi_s </ci>
                    <ci> psi_c </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="ms_sodium_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_ms_Na"/>
    
    <variable units="dimensionless" name="G_ms_Na"/>
    <variable units="cm_per_s" name="P_ms_Na" initial_value="4.80E-6"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Na"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_s_Na"/>
    <variable units="volt" public_interface="in" name="psi_m"/>
    <variable units="volt" public_interface="in" name="psi_s"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ms_Na_calculation">
        <eq/>
        <ci> J_ms_Na </ci>
        <ci> G_ms_Na </ci>
      </apply>
      
      <apply id="G_ms_Na_calculation">
        <eq/>
        <ci> G_ms_Na </ci>
        <apply>
          <times/> 
          <ci> P_ms_Na </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_m </ci>
                <ci> psi_s </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_m_Na </ci>
              <apply>
                <times/>
                <ci> C_s_Na </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <ci> F </ci>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_m </ci>
                      <ci> psi_s </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <apply>
                      <divide/>
                      <ci> F </ci>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci> psi_m </ci>
                    <ci> psi_s </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="ms_potassium_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_ms_K"/>
    
    <variable units="dimensionless" name="G_ms_K"/>
    <variable units="cm_per_s" name="P_ms_K" initial_value="4.80E-6"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_K"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_s_K"/>
    <variable units="volt" public_interface="in" name="psi_m"/>
    <variable units="volt" public_interface="in" name="psi_s"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ms_K_calculation">
        <eq/>
        <ci> J_ms_K </ci>
        <ci> G_ms_K </ci>
      </apply>
      
      <apply id="G_ms_K_calculation">
        <eq/>
        <ci> G_ms_K </ci>
        <apply>
          <times/> 
          <ci> P_ms_K </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_m </ci>
                <ci> psi_s </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_m_K </ci>
              <apply>
                <times/>
                <ci> C_s_K </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <ci> F </ci>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_m </ci>
                      <ci> psi_s </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <apply>
                      <divide/>
                      <ci> F </ci>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci> psi_m </ci>
                    <ci> psi_s </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
                
  <component name="ms_chloride_flux">
    <variable units="mmol_per_cm2_s" public_interface="out" name="J_ms_Cl"/>
    
    <variable units="dimensionless" name="G_ms_Cl"/>
    <variable units="cm_per_s" name="P_ms_Cl" initial_value="2.40E-6"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="C_per_mmol" public_interface="in" name="F"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_s_Cl"/>
    <variable units="volt" public_interface="in" name="psi_m"/>
    <variable units="volt" public_interface="in" name="psi_s"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ms_Cl_calculation">
        <eq/>
        <ci> J_ms_Cl </ci>
        <ci> G_ms_Cl </ci>
      </apply>
      
      <apply id="G_ms_Cl_calculation">
        <eq/>
        <ci> G_ms_Cl </ci>
        <apply>
          <times/> 
          <ci> P_ms_Cl </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> -1.0 </cn>
              <ci> F </ci>
              <apply>
                <minus/>
                <ci> psi_m </ci>
                <ci> psi_s </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <ci> C_m_Cl </ci>
              <apply>
                <times/>
                <ci> C_s_Cl </ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <apply>
                      <minus/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless"> -1.0 </cn>
                          <ci> F </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <minus/>
                      <ci> psi_m </ci>
                      <ci> psi_s </ci>
                    </apply>
                  </apply>
                </apply>
              </apply> 
            </apply>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> -1.0 </cn>
                        <ci> F </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci> psi_m </ci>
                    <ci> psi_s </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="total_transepithelial_sodium_flux">
    <variable units="mmol_per_cm2_s" name="J_Na"/>
    
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_mc_Na"/>
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_ms_Na"/>
    <variable units="second" public_interface="in" name="time"/>
     
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_Na_calculation">
        <eq/>
        <ci> J_Na </ci>
        <apply>
          <plus/>
          <ci> J_mc_Na </ci>
          <ci> J_ms_Na </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="total_transepithelial_potassium_flux">
    <variable units="mmol_per_cm2_s" name="J_K"/>
    
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_mc_K"/>
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_ms_K"/>
    <variable units="second" public_interface="in" name="time"/>
     
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_K_calculation">
        <eq/>
        <ci> J_K </ci>
        <apply>
          <plus/>
          <ci> J_mc_K </ci>
          <ci> J_ms_K </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="total_transepithelial_chloride_flux">
    <variable units="mmol_per_cm2_s" name="J_Cl"/>
    
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_mc_Cl"/>
    <variable units="mmol_per_cm2_s" public_interface="in" name="J_ms_Cl"/>
    <variable units="second" public_interface="in" name="time"/>
     
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_Cl_calculation">
        <eq/>
        <ci> J_Cl </ci>
        <apply>
          <plus/>
          <ci> J_mc_Cl </ci>
          <ci> J_ms_Cl </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="mc_transepithelial_volume_flux">
    <variable units="cm_per_s" public_interface="out" name="J_mc_v"/>
   
    <variable units="cm_per_s_mmHg" name="L_mc_v" initial_value="5.22E-9"/>
    <variable units="mmol_per_cm3" name="Osm_m"/>
    <variable units="mmol_per_cm3" name="Osm_c"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Na"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_K"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Imp"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_mc_v_calculation">
        <eq/>
        <ci> J_mc_v </ci>
        <apply>
          <times/>
          <ci> L_mc_v </ci>
          <ci> R </ci>
          <ci> T </ci>
          <apply>
            <minus/>
            <ci> Osm_m </ci>
            <ci> Osm_c </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="mc_transepithelial_volume_flux_Osm_m_calculation">
        <eq/>
        <ci> Osm_m </ci>
        <apply>
          <plus/>
          <ci> C_m_Na </ci>
          <ci> C_m_K </ci>
          <ci> C_m_Cl </ci>
          <ci> C_m_Imp </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="ms_transepithelial_volume_flux">
    <variable units="cm_per_s" public_interface="out" name="J_ms_v"/>
    
    <variable units="cm_per_s_mmHg" name="L_ms_v" initial_value="0.0"/>
    <variable units="mmol_per_cm3" name="Osm_m"/>
    <variable units="mmol_per_cm3" name="Osm_s"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="J_per_mmol_K" public_interface="in" name="R"/>
    <variable units="K" public_interface="in" name="T"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Na"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Cl"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_K"/>
    <variable units="mmol_per_cm3" public_interface="in" name="C_m_Imp"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ms_v_calculation">
        <eq/>
        <ci> J_ms_v </ci>
        <apply>
          <times/>
          <ci> L_ms_v </ci>
          <ci> R </ci>
          <ci> T </ci>
          <apply>
            <minus/>
            <ci> Osm_m </ci>
            <ci> Osm_s </ci>
          </apply>
        </apply>
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    <dcterms:W3CDTF>1999-01-01</dcterms:W3CDTF>
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    <vCard:FN>Catherine Lloyd</vCard:FN>
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    <bqs:Pubmed_id>10362782</bqs:Pubmed_id>
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    <dcterms:W3CDTF>2005-04-20</dcterms:W3CDTF>
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    <vCard:FN>Catherine Lloyd</vCard:FN>
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          Made MathMl id's unique
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    <dc:title>
       A CellML description of Chang and Fujita's 1999 numerical model of the 
       renal distal tubule.  
      </dc:title>
    <cmeta:bio_entity>Renal Distal Tubule</cmeta:bio_entity>
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    <vCard:Given>Toshiro</vCard:Given>
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    <rdf:value>This is the CellML description of Chang and Fujita's 1999 numerical model of the renal distal tubule. It should be noted that the initial conditions used in this description represent those in the early distal tubule. For model representations of the late distal tublule, these initial values should be replaced with those listed in the original paper for the late distal tubule.</rdf:value>
  </rdf:Description>
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</model>