- 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_2001_renal_anion_exchanger_model.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : renal_anion_exchanger_model.xml
CREATED : 23rd December 2002
LAST MODIFIED : 9th April 2003
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 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:
09/04/2003 - AAC - Added publication date information.
--><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_2001_version01" name="chang_fujita_2001_version01">
<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 (see <xref linkend="fig_reaction_diagram1"/> below). 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 (see <xref linkend="fig_reaction_diagram3"/> and <xref linkend="fig_reaction_diagram4"/> below), 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 features of acid-base transport described above are captured in the mathematical models of Hangil Chang and Toshiro Fujita (2001). Their models of transporters simulate the transport kinetics of the Na/H exchanger, anion exchanger and the H-ATPase. The raw CellML descriptions of the models 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://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&db=PubMed&list_uids=11457714&dopt=Abstract">PubMed ID: 11457714</ulink>)
</para>
<informalfigure float="0" id="fig_reaction_diagram1">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction_diagram1</title>
</objectinfo>
<imagedata fileref="Na_H_reaction_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>State diagram of the Na-H exchanger. In this model, the Na-H exchanger has a single binding site (E) to which Na<superscript>+</superscript>, H<superscript>+</superscript>, and NH<subscript>4</subscript>
<superscript>+</superscript> bind competitively. 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>
<informalfigure float="0" id="fig_reaction_diagram2">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction_diagram2</title>
</objectinfo>
<imagedata fileref="anion_exchanger_reaction_diagram.gif"/>
</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>
<informalfigure float="0" id="fig_reaction_diagram3">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction_diagram3</title>
</objectinfo>
<imagedata fileref="H_ATPase_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>Conceptual diagram of the H-ATPase. The transporter consists of two components: a transmembrane channel and an intracellular catalytic unit. Between these two components there is a buffer space known as the antechamber, in which hydrogen ions (H<subscript>a</subscript>) are in equilibrium with extracellular hydrogen ions (H) due to a large conductance of the transmembrane channel. Hydrogen ions are also moved between the antechamber and the cytosol via the catalytic unit. This ion transport is coupled to ATP hydrolysis/synthesis.</caption>
</informalfigure>
<informalfigure float="0" id="fig_reaction_diagram4">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction_diagram4</title>
</objectinfo>
<imagedata fileref="H_ATPase_reaction_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>State diagram of the catalytic unit of the H-ATPase. The catalytic unit (E) has two binding sites for H. Symbols with the asterisk (*) indicate conformations of the catalytic unit in which the binding sites face the cytosol, and symbols without the asterisk represent conformations in which the binding sites face the antechamber. Transition between the unloaded conformations is coupled with ATP synthesis/hydrolysis.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
We start the model definition with a definition of some named
sets of units for use throughout the model.
-->
<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>
<!--
The following component is defined for modelling convenience. It contains
all the universal variables, in this case, only time.
-->
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in the model.
-->
<component cmeta:id="E_e" name="E_e">
<variable units="millimolar" public_interface="out" name="E_e" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_E_e_rxn0"/>
<variable units="flux" public_interface="in" name="delta_E_e_rxn1"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
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</bvar>
<ci>E_e</ci>
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<ci>delta_E_e_rxn1</ci>
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<variable units="flux" public_interface="in" name="delta_E_i_rxn3"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci>delta_E_i_rxn3</ci>
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<variable units="flux" public_interface="in" name="delta_Cl_e_rxn0"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<ci>Cl_e</ci>
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<component cmeta:id="Cl_i" name="Cl_i">
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<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<diff/>
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<ci>Cl_i</ci>
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<ci>delta_Cl_i_rxn2</ci>
</apply>
</math>
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<component cmeta:id="ECl_e" name="ECl_e">
<variable units="millimolar" public_interface="out" name="ECl_e" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_ECl_e_rxn0"/>
<variable units="flux" public_interface="in" name="delta_ECl_e_rxn4"/>
<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_e</ci>
</apply>
<apply>
<plus/>
<ci>delta_ECl_e_rxn0</ci>
<ci>delta_ECl_e_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="J_Cl_influx" name="J_Cl_influx">
<variable units="flux" public_interface="out" name="J_Cl_influx" initial_value="1.0"/>
<variable units="millimolar" name="Ki_Cl" initial_value="0.528"/>
<variable units="millimolar" name="Ki_HCO3" initial_value="0.423"/>
<variable units="flux" public_interface="in" name="delta_ECl_i_rxn4"/>
<variable units="flux" public_interface="in" name="delta_ECl_e_rxn4"/>
<variable units="millimolar" public_interface="in" name="Cl_i"/>
<variable units="millimolar" public_interface="in" name="HCO3_i"/>
<variable units="second" public_interface="in" name="time"/>
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<ci>J_Cl_influx</ci>
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<ci>delta_ECl_e_rxn4</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Cl_i </ci>
<ci> Ki_Cl </ci>
</apply>
<apply>
<divide/>
<ci> HCO3_i </ci>
<ci> Ki_HCO3 </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</apply>
</math>
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<variable units="millimolar" public_interface="out" name="ECl_i" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_ECl_i_rxn2"/>
<variable units="flux" public_interface="in" name="delta_ECl_i_rxn4"/>
<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_i</ci>
</apply>
<apply>
<plus/>
<ci>delta_ECl_i_rxn2</ci>
<ci>delta_ECl_i_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="HCO3_e" name="HCO3_e">
<variable units="millimolar" public_interface="out" name="HCO3_e" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_HCO3_e_rxn1"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HCO3_e</ci>
</apply>
<ci>delta_HCO3_e_rxn1</ci>
</apply>
</math>
</component>
<component cmeta:id="EHCO3_e" name="EHCO3_e">
<variable units="millimolar" public_interface="out" name="EHCO3_e" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_EHCO3_e_rxn1"/>
<variable units="flux" public_interface="in" name="delta_EHCO3_e_rxn5"/>
<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_e</ci>
</apply>
<apply>
<plus/>
<ci>delta_EHCO3_e_rxn1</ci>
<ci>delta_EHCO3_e_rxn5</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="HCO3_i" name="HCO3_i">
<variable units="millimolar" public_interface="out" name="HCO3_i" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_HCO3_i_rxn3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HCO3_i</ci>
</apply>
<ci>delta_HCO3_i_rxn3</ci>
</apply>
</math>
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<variable units="flux" public_interface="in" name="delta_EHCO3_i_rxn3"/>
<variable units="flux" public_interface="in" name="delta_EHCO3_i_rxn5"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci>delta_EHCO3_i_rxn5</ci>
</apply>
</apply>
</math>
</component>
<!--
The following components represent the reaction steps of the model.
-->
<component name="reaction0">
<variable units="millimolar" public_interface="in" name="ECl_e"/>
<variable units="millimolar" public_interface="in" name="Cl_e"/>
<variable units="millimolar" public_interface="in" name="E_e"/>
<variable units="flux" public_interface="out" name="delta_ECl_e_rxn0"/>
<variable units="flux" public_interface="out" name="delta_Cl_e_rxn0"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<apply>
<plus/>
<apply>
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<ci>k0</ci>
<ci>ECl_e</ci>
<ci>Cl_e</ci>
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<apply>
<minus/>
<apply>
<times/>
<ci>k0_</ci>
<ci>E_e</ci>
</apply>
</apply>
</apply>
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</math>
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<variable units="millimolar" public_interface="in" name="EHCO3_e"/>
<variable units="flux" public_interface="out" name="delta_E_e_rxn1"/>
<variable units="flux" public_interface="out" name="delta_HCO3_e_rxn1"/>
<variable units="flux" public_interface="out" name="delta_EHCO3_e_rxn1"/>
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<variable_ref variable="HCO3_e">
<role stoichiometry="1" direction="forward" delta_variable="delta_HCO3_e_rxn1" role="reactant"/>
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<variable_ref variable="EHCO3_e">
<role stoichiometry="1" direction="forward" delta_variable="delta_EHCO3_e_rxn1" role="product"/>
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<apply>
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<ci>k1</ci>
<ci>E_e</ci>
<ci>HCO3_e</ci>
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<apply>
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<apply>
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<ci>EHCO3_e</ci>
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<component name="reaction2">
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<variable units="millimolar" public_interface="in" name="Cl_i"/>
<variable units="millimolar" public_interface="in" name="ECl_i"/>
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<reaction reversible="yes">
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<variable_ref variable="Cl_i">
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<ci>E_i</ci>
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<apply>
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<apply>
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<ci>ECl_i</ci>
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</apply>
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<variable units="millimolar" public_interface="in" name="HCO3_i"/>
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<variable units="flux" name="rate"/>
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<component name="reaction4">
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<variable units="millimolar" public_interface="in" name="ECl_i"/>
<variable units="flux" public_interface="out" name="delta_ECl_e_rxn4"/>
<variable units="flux" public_interface="out" name="delta_ECl_i_rxn4"/>
<variable units="first_order_rate_constant" name="k4" initial_value="514000.0"/>
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Chang and Fujita's 2001 mathematical model of an anion exchanger in the
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The University of Auckland, Bioengineering Institute
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