- Author:
- Tommy Yu <tommy.yu@auckland.ac.nz>
- Date:
- 2010-08-25 17:59:12+12:00
- Desc:
- e-notation fix
- Permanent Source URI:
- https://models.cellml.org/workspace/28f/rawfile/be649369a7c7c899abe548db0d188337e28c2686/Weinstein_1995_NHE3.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 27/05/2009 at 9:55:15 at a.m. using:
COR (0.9.31.1265)
Copyright 2002-2009 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.CellML.org/
-->
<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="weinstein_1995" name="weinstein_1995">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule</title>
<author>
<firstname>Jonna</firstname>
<surname>Terkildsen</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_status">
<title>Model Status</title>
<para>
This CellML model..........................................
</para>
</sect1>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The luminal membrane antiporter of the proximal tubule has been represented using the kinetic formulation of E. Heinz (1978. Mechanics and Engergetics of Biological Transport. Springer-Verlag, Berlin) with the assumption of equilibrium binding and 1:1 stoichiometry. Competitive binding and transport of NH+4 is included within this model. Ion affinities and permeation velocities were selected in a least-squares fit to the kinetic parameters determined experimentally in renal membrane vesicles (Aronson, P.S., M.A. Suhm, and J. Nee. 1983. Journal of Biological Chemistry. 258:6767-6771). The modifier role of internal H+ to enhance transport beyond the expected kinetics (Aronson, P.S., J. Nee, and M. A. Suhm. 1982. Nature. 299:161-163) is represented as a velocity effect of H+ binding to a single site. This kinetic formulation of the Na+/H+ antiporter was incorporated within a model of the rat proximal tubule (Weinstein, A. M. 1994. American Journal of Physiology. 267:F237-F248) as a replacement for the representation by linear nonequilibrium thermodynamics (NET). The membrane density of the antiporter was selected to yield agreement with the rate of tubular Na+ reabsorption. Simulation of 0.5 cm of tubule predicts that the activity of the Na+/H+ antiporter is the most important force for active secretion of ammonia. Model calculations of metabolic acid-base disturbances are performed and comparison is made among antiporter representations (kinetic model, kinetic model without internal modifier, and NET formulation). It is found that the ability to sharply turn off Na+/H+ exchange in cellular alkalosis substantially eliminates the cell volume increase associated with high HCO3- conditions. In the tubule model, diminished Na+/H+ exchange in alkalosis blunts the axial decrease in luminal HCO3- and thus diminishes paracellular reabsorption of Cl-. In this way, the kinetics of the Na+/H+ antiporter could act to enhance distal delivery of Na+, Cl-, and HCO3- in acute metabolic alkalosis.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule, A.M. Weinstein, 1995,
<emphasis>The Journal of General Physiology</emphasis>, 105, 617-641. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/7658195">PubMed ID: 7658195</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="weinstein_1995.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of the Na+/H+ antiporter. The carrier may either be empty, X, or bound to one of three ions, Na+, H+, or NH+4, designated XA, XB, or XC. Binding is rapid, and defined by equilibrium constants Ka, Kb, and K~. The carrier or carrier-ion complex may face either the external (') or internal (") membrane surface. Tramlocation of the loaded carrier occurs according to rate coefficients Pa, Pb, and Pc. There is no translocation of empty carrier.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="mmol">
<unit units="mole" prefix="milli"/>
</units>
<units name="umol">
<unit units="mole" prefix="micro"/>
</units>
<units name="nmol">
<unit units="mole" prefix="nano"/>
</units>
<units name="mM">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="M">
<unit units="mole"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="cm">
<unit units="metre" prefix="centi"/>
</units>
<units name="cm2">
<unit units="metre" prefix="centi" exponent="2"/>
</units>
<units name="mM_per_s">
<unit units="mM"/>
<unit units="second" exponent="-1"/>
</units>
<units name="per_s">
<unit units="second" exponent="-1"/>
</units>
<units name="mmol_per_s_per_cm2">
<unit units="mmol"/>
<unit units="second" exponent="-1"/>
<unit units="cm2" exponent="-1"/>
</units>
<units name="nmol_per_s_per_cm2">
<unit units="nmol"/>
<unit units="second" exponent="-1"/>
<unit units="cm2" exponent="-1"/>
</units>
<component name="environment">
<variable name="time" units="second" public_interface="out"/>
</component>
<component name="Concentrations">
<variable name="C_ext_Na" units="mM" initial_value="140" public_interface="out"/>
<variable name="C_ext_H" units="mM" initial_value="4.95e-2" public_interface="out"/>
<variable name="C_ext_NH4" units="mM" initial_value="0.2" public_interface="out"/>
<variable name="C_int_Na" units="mM" initial_value="19.6" public_interface="out"/>
<variable name="C_int_H" units="mM" initial_value="1e-3" public_interface="out"/>
<variable name="C_int_NH4" units="mM" initial_value="0.23" public_interface="out"/>
<variable name="time" units="second" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_ext_Na</ci>
</apply>
<cn cellml:units="mM_per_s">10</cn>
</apply>
</math>
</component>
<component name="NHE3_Parameters">
<variable name="XTxP0_NHE3_Na" units="nmol_per_s_per_cm2" initial_value="1.6e-3" public_interface="out"/>
<variable name="XTxP0_NHE3_H" units="nmol_per_s_per_cm2" initial_value="0.48e-3" public_interface="out"/>
<variable name="XTxP0_NHE3_NH4" units="nmol_per_s_per_cm2" initial_value="1.6e-3" public_interface="out"/>
<variable name="K_NHE3_Na" units="mM" initial_value="0.03e3" public_interface="out"/>
<variable name="K_NHE3_H" units="mM" initial_value="72e-6" public_interface="out"/>
<variable name="K_NHE3_NH4" units="mM" initial_value="0.027e3" public_interface="out"/>
</component>
<component name="NHE3">
<variable name="C_ext_Na" units="mM" public_interface="in"/>
<variable name="C_ext_H" units="mM" public_interface="in"/>
<variable name="C_ext_NH4" units="mM" public_interface="in"/>
<variable name="C_int_Na" units="mM" public_interface="in"/>
<variable name="C_int_H" units="mM" public_interface="in"/>
<variable name="C_int_NH4" units="mM" public_interface="in"/>
<variable name="XTxP0_NHE3_Na" units="nmol_per_s_per_cm2" public_interface="in"/>
<variable name="XTxP0_NHE3_H" units="nmol_per_s_per_cm2" public_interface="in"/>
<variable name="XTxP0_NHE3_NH4" units="nmol_per_s_per_cm2" public_interface="in"/>
<variable name="XTxP_NHE3_Na" units="nmol_per_s_per_cm2"/>
<variable name="XTxP_NHE3_H" units="nmol_per_s_per_cm2"/>
<variable name="XTxP_NHE3_NH4" units="nmol_per_s_per_cm2"/>
<variable name="K_NHE3_Na" units="mM" public_interface="in"/>
<variable name="K_NHE3_H" units="mM" public_interface="in"/>
<variable name="K_NHE3_NH4" units="mM" public_interface="in"/>
<variable name="alpha_ext_Na" units="dimensionless"/>
<variable name="beta_ext_H" units="dimensionless"/>
<variable name="gamma_ext_NH4" units="dimensionless"/>
<variable name="alpha_int_Na" units="dimensionless"/>
<variable name="beta_int_H" units="dimensionless"/>
<variable name="gamma_int_NH4" units="dimensionless"/>
<variable name="sum_NHE3" units="nmol_per_s_per_cm2"/>
<variable name="J_NHE3_Na" units="nmol_per_s_per_cm2" public_interface="out"/>
<variable name="J_NHE3_H" units="nmol_per_s_per_cm2" public_interface="out"/>
<variable name="J_NHE3_NH4" units="nmol_per_s_per_cm2" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_ext_Na</ci>
<apply>
<divide/>
<ci>C_ext_Na</ci>
<ci>K_NHE3_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_ext_H</ci>
<apply>
<divide/>
<ci>C_ext_H</ci>
<ci>K_NHE3_H</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_ext_NH4</ci>
<apply>
<divide/>
<ci>C_ext_NH4</ci>
<ci>K_NHE3_NH4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_int_Na</ci>
<apply>
<divide/>
<ci>C_int_Na</ci>
<ci>K_NHE3_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_int_H</ci>
<apply>
<divide/>
<ci>C_int_H</ci>
<ci>K_NHE3_H</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_int_NH4</ci>
<apply>
<divide/>
<ci>C_int_NH4</ci>
<ci>K_NHE3_NH4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>XTxP_NHE3_Na</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP0_NHE3_Na</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>C_int_H</ci>
</apply>
<apply>
<plus/>
<ci>C_int_H</ci>
<cn type="e-notation" cellml:units="mM">1 <sep/>
-6</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>XTxP_NHE3_H</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP0_NHE3_H</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>C_int_H</ci>
</apply>
<apply>
<plus/>
<ci>C_int_H</ci>
<cn type="e-notation" cellml:units="mM">1 <sep/>
-6</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>XTxP_NHE3_NH4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP0_NHE3_NH4</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>C_int_H</ci>
</apply>
<apply>
<plus/>
<ci>C_int_H</ci>
<cn type="e-notation" cellml:units="mM">1 <sep/>
-6</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sum_NHE3</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha_ext_Na</ci>
<ci>beta_ext_H</ci>
<ci>gamma_ext_NH4</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>XTxP_NHE3_Na</ci>
<ci>alpha_int_Na</ci>
</apply>
<apply>
<times/>
<ci>XTxP_NHE3_H</ci>
<ci>beta_int_H</ci>
</apply>
<apply>
<times/>
<ci>XTxP_NHE3_NH4</ci>
<ci>gamma_int_NH4</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha_int_Na</ci>
<ci>beta_int_H</ci>
<ci>gamma_int_NH4</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>XTxP_NHE3_Na</ci>
<ci>alpha_ext_Na</ci>
</apply>
<apply>
<times/>
<ci>XTxP_NHE3_H</ci>
<ci>beta_ext_H</ci>
</apply>
<apply>
<times/>
<ci>XTxP_NHE3_NH4</ci>
<ci>gamma_ext_NH4</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_NHE3_Na</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP_NHE3_Na</ci>
<ci>XTxP_NHE3_H</ci>
</apply>
<ci>sum_NHE3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_ext_Na</ci>
<ci>beta_int_H</ci>
</apply>
<apply>
<times/>
<ci>alpha_int_Na</ci>
<ci>beta_ext_H</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP_NHE3_Na</ci>
<ci>XTxP_NHE3_NH4</ci>
</apply>
<ci>sum_NHE3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_ext_Na</ci>
<ci>gamma_int_NH4</ci>
</apply>
<apply>
<times/>
<ci>alpha_int_Na</ci>
<ci>gamma_ext_NH4</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_NHE3_H</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP_NHE3_Na</ci>
<ci>XTxP_NHE3_H</ci>
</apply>
<ci>sum_NHE3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_int_Na</ci>
<ci>beta_ext_H</ci>
</apply>
<apply>
<times/>
<ci>alpha_ext_Na</ci>
<ci>beta_int_H</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP_NHE3_H</ci>
<ci>XTxP_NHE3_NH4</ci>
</apply>
<ci>sum_NHE3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_ext_H</ci>
<ci>gamma_int_NH4</ci>
</apply>
<apply>
<times/>
<ci>beta_int_H</ci>
<ci>gamma_ext_NH4</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_NHE3_NH4</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP_NHE3_Na</ci>
<ci>XTxP_NHE3_NH4</ci>
</apply>
<ci>sum_NHE3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_int_Na</ci>
<ci>gamma_ext_NH4</ci>
</apply>
<apply>
<times/>
<ci>alpha_ext_Na</ci>
<ci>gamma_int_NH4</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>XTxP_NHE3_H</ci>
<ci>XTxP_NHE3_NH4</ci>
</apply>
<ci>sum_NHE3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>gamma_ext_NH4</ci>
<ci>beta_int_H</ci>
</apply>
<apply>
<times/>
<ci>beta_ext_H</ci>
<ci>gamma_int_NH4</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="NHE3_Parameters" component_2="NHE3"/>
<map_variables variable_1="K_NHE3_Na" variable_2="K_NHE3_Na"/>
<map_variables variable_1="K_NHE3_H" variable_2="K_NHE3_H"/>
<map_variables variable_1="K_NHE3_NH4" variable_2="K_NHE3_NH4"/>
<map_variables variable_1="XTxP0_NHE3_Na" variable_2="XTxP0_NHE3_Na"/>
<map_variables variable_1="XTxP0_NHE3_H" variable_2="XTxP0_NHE3_H"/>
<map_variables variable_1="XTxP0_NHE3_NH4" variable_2="XTxP0_NHE3_NH4"/>
</connection>
<connection>
<map_components component_1="Concentrations" component_2="NHE3"/>
<map_variables variable_1="C_ext_Na" variable_2="C_ext_Na"/>
<map_variables variable_1="C_ext_H" variable_2="C_ext_H"/>
<map_variables variable_1="C_ext_NH4" variable_2="C_ext_NH4"/>
<map_variables variable_1="C_int_Na" variable_2="C_int_Na"/>
<map_variables variable_1="C_int_H" variable_2="C_int_H"/>
<map_variables variable_1="C_int_NH4" variable_2="C_int_NH4"/>
</connection>
<connection>
<map_components component_1="Concentrations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description rdf:about="">
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Terkildsen</vCard:Family>
<vCard:Given>Jonna</vCard:Given>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>j.terkildsen@auckland.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>Auckland Bioengineering Institute</vCard:Orgname>
</vCard:ORG>
</dc:creator>
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2009-05-27</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#weinstein_1995">
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>Na/H antiporter</rdf:li>
<rdf:li>ion transport</rdf:li>
<rdf:li>kidney</rdf:li>
<rdf:li>proximal tubule</rdf:li>
<rdf:li>renal</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>7658195</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Weinstein</vCard:Family>
<vCard:Given>A</vCard:Given>
<vCard:Other>M</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule
</dc:title>
<bqs:Journal rdf:parseType="Resource">
<dc:title>The Journal of General Physiology</dc:title>
</bqs:Journal>
<bqs:volume>105</bqs:volume>
<bqs:first_page>617</bqs:first_page>
<bqs:last_page>641</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
</model>
