Views
A numerical model of the renal distal tubule
The CellML code.
<!-- FILE : chang_model_II_1999_updated.xml
CREATED : 17th February 2003
LAST MODIFIED : 17th February 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 1999 numerical model of the renal distal tubule.
CHANGES:
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="chang_fujita_1999_version03" name="chang_fujita_1999_version03">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Kinetic Model of the Thiazide-Sensitive Na-Cl Cotransporter</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 original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The thiazide-sensitive Na-Cl cotransporter (TSC) is a transmembrane protein, which is embedded in the luminal plasma membrane of the epithelial cells, which line the renal distal tubule. Na<superscript>+</superscript> and Ca<superscript>2+</superscript> transmembrane exchange mediated by TSC is blocked by the diuretic drug thiazide. The physiological importance of TSC in maintaining a sodium balance can be highlighted by the efficacy of thiazide in treating hypertension. In addition, genetic defects in TSC disrupt electrolyte metabolism in a condition known as Gitelman's syndrome.
</para>
<para>
Experimental studies have shown that thiazides have a high affinity to TSC, and that the drug-transporter binding can be inhibited or enhanced by the presence of chloride or sodium respectively. To describe the mechanisms underlying these observations, Fanestil <emphasis>et al.</emphasis> (1988, 1991) developed a mathematical model of TSC. In this model, TSC had two bindings sites, one that was selective for sodium and one which showed an affinity for both chloride and thiazide (competitive inhibition arises when both substances are present). Sodium binding increases the affinity of the second site for thiazide.
</para>
<para>
Direct measurement of sodium influx through TSC expressed in <emphasis>Xenopus laevis</emphasis> oocytes has shown that sodium influx is a saturable process. This is consistent with a carrier-mediated mechanism cotransporting sodium and chloride with a 1:1 stoichiometry.
</para>
<para>
In 1999, Hangil Chang and Toshiro Fujita published a numerical model of TSC that can predict the kinetics of thiazide binding and substrate transport of TSC (see <xref linkend="fig_reaction_diagram" /> below). Based on the previously published Fanestil <emphasis>et al.</emphasis> model, Chang and Fujita developed a state diagram in which the TSC has two binding sites, one for sodium and one for chloride. However, unlike the Fanestil model, thiazide binding is possible from both the intra- and extracellular sides of the plasma membrane. Model simulations supported experimental data, and Chang and Fujita concluded that known kinetic properties of TSC can be predicted by a model which is based on a state diagram.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://ajprenal.physiology.org/cgi/content/abstract/276/6/F952">A kinetic model of the thiazide-sensitive Na-Cl cotransporter</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/F952.pdf">PDF</ulink> and <ulink url="http://ajprenal.physiology.org/cgi/content/full/276/6/F952">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&db=PubMed&list_uids=10362783&dopt=Abstract">PubMed ID: 10362783</ulink>
</para>
<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model" />
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the model</title>
</objectinfo>
<imagedata fileref="../images/chang_model_1999/reaction_diagram.gif" />
</imageobject>
</mediaobject>
<caption>State diagram for the thiazide-sensitive Na-Cl cotransporter (TSC). Transporter (E) has binding sites for sodium (Na ) and chloride (Cl). Thiazide diuretics (D) compete with chloride for the same binding site. <emphasis>_i</emphasis> is used to indicate which symbols belong to the intracellular side.</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="J_per_mmol">
<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_Imp" />
<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="solute_concentrations">
<variable units="mmol_per_cm3" public_interface="out" name="C_m_Na" />
<variable units="mmol_per_cm3" public_interface="out" name="C_m_K" />
<variable units="mmol_per_cm3" public_interface="out" name="C_m_Cl" />
<variable units="mmol_per_cm3" public_interface="out" name="C_c_Na" />
<variable units="mmol_per_cm3" public_interface="out" name="C_c_K" />
<variable units="mmol_per_cm3" public_interface="out" name="C_c_Cl" />
<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_cm2_s" public_interface="in" name="J_mc_Na" />
<variable units="mmol_per_cm2_s" public_interface="in" name="J_ms_Na" />
<variable units="mmol_per_cm2_s" public_interface="in" name="J_sc_Na" />
<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="mmol_per_cm2_s" public_interface="in" name="J_sc_K" />
<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="mmol_per_cm2_s" public_interface="in" name="J_sc_Cl" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="C_m_Na_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_m_Na </ci>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci> J_mc_Na </ci>
<ci> J_ms_Na </ci>
</apply>
</apply>
</apply>
<apply id="C_s_Na_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_s_Na </ci>
</apply>
<apply>
<minus />
<ci> J_ms_Na </ci>
<ci> J_sc_Na </ci>
</apply>
</apply>
<apply id="C_c_Na_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_c_Na </ci>
</apply>
<apply>
<plus />
<ci> J_mc_Na </ci>
<ci> J_sc_Na </ci>
</apply>
</apply>
<apply id="C_m_K_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_m_K </ci>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci> J_mc_K </ci>
<ci> J_ms_K </ci>
</apply>
</apply>
</apply>
<apply id="C_s_K_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_s_K </ci>
</apply>
<apply>
<minus />
<ci> J_ms_K </ci>
<ci> J_sc_K </ci>
</apply>
</apply>
<apply id="C_c_K_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_c_K </ci>
</apply>
<apply>
<plus />
<ci> J_mc_K </ci>
<ci> J_sc_K </ci>
</apply>
</apply>
<apply id="C_m_Cl_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_m_Cl </ci>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci> J_mc_Cl </ci>
<ci> J_ms_Cl </ci>
</apply>
</apply>
</apply>
<apply id="C_s_Cl_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_s_Cl </ci>
</apply>
<apply>
<minus />
<ci> J_ms_Cl </ci>
<ci> J_sc_Cl </ci>
</apply>
</apply>
<apply id="C_c_Cl_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_c_Cl </ci>
</apply>
<apply>
<plus />
<ci> J_mc_Cl </ci>
<ci> J_sc_Cl </ci>
</apply>
</apply>
</math>
</component>
<component name="constants">
<variable units="J_per_mmol" public_interface="out" name="RT" initial_value="2.579" />
<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_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="J_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" public_interface="in" name="RT" />
<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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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 />
<ci> F </ci>
<ci> RT </ci>
</apply>
</apply>
<apply>
<minus />
<ci> psi_m </ci>
<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> J_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 />
<ci> C_c_Cl </ci>
<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="J_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" public_interface="in" name="RT" />
<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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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 />
<ci> F </ci>
<ci> RT </ci>
</apply>
</apply>
<apply>
<minus />
<ci> psi_m </ci>
<ci> psi_c </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="J_mc_KCl_calculation">
<eq />
<ci> J_mc_KCl </ci>
<apply>
<times />
<ci> J_mc_KCl_max </ci>
<apply>
<divide />
<apply>
<minus />
<apply>
<times />
CREATED : 17th February 2003
LAST MODIFIED : 17th February 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 1999 numerical model of the renal distal tubule.
CHANGES:
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="chang_fujita_1999_version03" name="chang_fujita_1999_version03">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Kinetic Model of the Thiazide-Sensitive Na-Cl Cotransporter</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 original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The thiazide-sensitive Na-Cl cotransporter (TSC) is a transmembrane protein, which is embedded in the luminal plasma membrane of the epithelial cells, which line the renal distal tubule. Na<superscript>+</superscript> and Ca<superscript>2+</superscript> transmembrane exchange mediated by TSC is blocked by the diuretic drug thiazide. The physiological importance of TSC in maintaining a sodium balance can be highlighted by the efficacy of thiazide in treating hypertension. In addition, genetic defects in TSC disrupt electrolyte metabolism in a condition known as Gitelman's syndrome.
</para>
<para>
Experimental studies have shown that thiazides have a high affinity to TSC, and that the drug-transporter binding can be inhibited or enhanced by the presence of chloride or sodium respectively. To describe the mechanisms underlying these observations, Fanestil <emphasis>et al.</emphasis> (1988, 1991) developed a mathematical model of TSC. In this model, TSC had two bindings sites, one that was selective for sodium and one which showed an affinity for both chloride and thiazide (competitive inhibition arises when both substances are present). Sodium binding increases the affinity of the second site for thiazide.
</para>
<para>
Direct measurement of sodium influx through TSC expressed in <emphasis>Xenopus laevis</emphasis> oocytes has shown that sodium influx is a saturable process. This is consistent with a carrier-mediated mechanism cotransporting sodium and chloride with a 1:1 stoichiometry.
</para>
<para>
In 1999, Hangil Chang and Toshiro Fujita published a numerical model of TSC that can predict the kinetics of thiazide binding and substrate transport of TSC (see <xref linkend="fig_reaction_diagram" /> below). Based on the previously published Fanestil <emphasis>et al.</emphasis> model, Chang and Fujita developed a state diagram in which the TSC has two binding sites, one for sodium and one for chloride. However, unlike the Fanestil model, thiazide binding is possible from both the intra- and extracellular sides of the plasma membrane. Model simulations supported experimental data, and Chang and Fujita concluded that known kinetic properties of TSC can be predicted by a model which is based on a state diagram.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://ajprenal.physiology.org/cgi/content/abstract/276/6/F952">A kinetic model of the thiazide-sensitive Na-Cl cotransporter</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/F952.pdf">PDF</ulink> and <ulink url="http://ajprenal.physiology.org/cgi/content/full/276/6/F952">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&db=PubMed&list_uids=10362783&dopt=Abstract">PubMed ID: 10362783</ulink>
</para>
<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model" />
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the model</title>
</objectinfo>
<imagedata fileref="../images/chang_model_1999/reaction_diagram.gif" />
</imageobject>
</mediaobject>
<caption>State diagram for the thiazide-sensitive Na-Cl cotransporter (TSC). Transporter (E) has binding sites for sodium (Na ) and chloride (Cl). Thiazide diuretics (D) compete with chloride for the same binding site. <emphasis>_i</emphasis> is used to indicate which symbols belong to the intracellular side.</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="J_per_mmol">
<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_Imp" />
<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="solute_concentrations">
<variable units="mmol_per_cm3" public_interface="out" name="C_m_Na" />
<variable units="mmol_per_cm3" public_interface="out" name="C_m_K" />
<variable units="mmol_per_cm3" public_interface="out" name="C_m_Cl" />
<variable units="mmol_per_cm3" public_interface="out" name="C_c_Na" />
<variable units="mmol_per_cm3" public_interface="out" name="C_c_K" />
<variable units="mmol_per_cm3" public_interface="out" name="C_c_Cl" />
<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_cm2_s" public_interface="in" name="J_mc_Na" />
<variable units="mmol_per_cm2_s" public_interface="in" name="J_ms_Na" />
<variable units="mmol_per_cm2_s" public_interface="in" name="J_sc_Na" />
<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="mmol_per_cm2_s" public_interface="in" name="J_sc_K" />
<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="mmol_per_cm2_s" public_interface="in" name="J_sc_Cl" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="C_m_Na_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_m_Na </ci>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci> J_mc_Na </ci>
<ci> J_ms_Na </ci>
</apply>
</apply>
</apply>
<apply id="C_s_Na_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_s_Na </ci>
</apply>
<apply>
<minus />
<ci> J_ms_Na </ci>
<ci> J_sc_Na </ci>
</apply>
</apply>
<apply id="C_c_Na_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_c_Na </ci>
</apply>
<apply>
<plus />
<ci> J_mc_Na </ci>
<ci> J_sc_Na </ci>
</apply>
</apply>
<apply id="C_m_K_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_m_K </ci>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci> J_mc_K </ci>
<ci> J_ms_K </ci>
</apply>
</apply>
</apply>
<apply id="C_s_K_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_s_K </ci>
</apply>
<apply>
<minus />
<ci> J_ms_K </ci>
<ci> J_sc_K </ci>
</apply>
</apply>
<apply id="C_c_K_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_c_K </ci>
</apply>
<apply>
<plus />
<ci> J_mc_K </ci>
<ci> J_sc_K </ci>
</apply>
</apply>
<apply id="C_m_Cl_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_m_Cl </ci>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci> J_mc_Cl </ci>
<ci> J_ms_Cl </ci>
</apply>
</apply>
</apply>
<apply id="C_s_Cl_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_s_Cl </ci>
</apply>
<apply>
<minus />
<ci> J_ms_Cl </ci>
<ci> J_sc_Cl </ci>
</apply>
</apply>
<apply id="C_c_Cl_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> C_c_Cl </ci>
</apply>
<apply>
<plus />
<ci> J_mc_Cl </ci>
<ci> J_sc_Cl </ci>
</apply>
</apply>
</math>
</component>
<component name="constants">
<variable units="J_per_mmol" public_interface="out" name="RT" initial_value="2.579" />
<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_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="J_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" public_interface="in" name="RT" />
<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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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 />
<ci> F </ci>
<ci> RT </ci>
</apply>
</apply>
<apply>
<minus />
<ci> psi_m </ci>
<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> J_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 />
<ci> C_c_Cl </ci>
<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="J_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" public_interface="in" name="RT" />
<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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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 />
<ci> F </ci>
<ci> RT </ci>
</apply>
</apply>
<apply>
<minus />
<ci> psi_m </ci>
<ci> psi_c </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="J_mc_KCl_calculation">
<eq />
<ci> J_mc_KCl </ci>
<apply>
<times />
<ci> J_mc_KCl_max </ci>
<apply>
<divide />
<apply>
<minus />
<apply>
<times />