- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-05-25 01:23:16+12:00
- Desc:
- committing version02 of chang_fujita_b_1999
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/chang_fujita_b_1999/rawfile/40d6469ac3f6a07f4632f8cf614abefe7ec4c188/chang_fujita_b_1999.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- 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="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_version03" name="chang_fujita_1999_version03">
<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 orginal paper for the late distal tubule. The model from the original paper has been modified slightly to include differential equations defining the change in solute concentrations over time. These equations were added to facilitate the use of the CellML code in CMISS.
</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&db=PubMed&list_uids=10362782&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="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/>
<apply>
<divide/>
<ci> C_m_K </ci>
<ci> K_mc_K_KCl </ci>
</apply>
<apply>
<divide/>
<ci> C_m_Cl </ci>
<ci> K_mc_Cl_KCl </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> C_c_K </ci>
<ci> K_mc_K_KCl </ci>
</apply>
<apply>
<divide/>
<ci> C_c_Cl </ci>
<ci> K_mc_Cl_KCl </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<apply>
<divide/>
<ci> C_m_K </ci>
<ci> K_mc_K_KCl </ci>
</apply>
<apply>
<divide/>
<ci> C_m_Cl </ci>
<ci> K_mc_Cl_KCl </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> C_c_K </ci>
<ci> K_mc_K_KCl </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> C_c_Cl </ci>
<ci> K_mc_Cl_KCl </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<apply>
<divide/>
<ci> C_c_K </ci>
<ci> K_mc_K_KCl </ci>
</apply>
<apply>
<divide/>
<ci> C_c_Cl </ci>
<ci> K_mc_Cl_KCl </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> C_m_K </ci>
<ci> K_mc_K_KCl </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<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" 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_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>
<ci> RT </ci>
</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>
</apply>
<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/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<ci> F </ci>
</apply>
<ci> RT </ci>
</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" public_interface="out" 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" public_interface="out" 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" 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_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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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" public_interface="out" 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" 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_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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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" 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_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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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" 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_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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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" 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_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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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>
<ci> RT </ci>
</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="osmolarities">
<variable units="mmol_per_cm3" public_interface="out" name="Osm_m"/>
<variable units="mmol_per_cm3" public_interface="out" name="Osm_c"/>
<variable units="mmol_per_cm3" public_interface="out" name="Osm_s"/>
<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"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_c_Na"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_c_Cl"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_c_K"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_c_Imp"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_s_Na"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_s_Cl"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_s_K"/>
<variable units="mmol_per_cm3" public_interface="in" name="C_s_Imp"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="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>
<apply id="Osm_c_calculation">
<eq/>
<ci> Osm_c </ci>
<apply>
<plus/>
<ci> C_c_Na </ci>
<ci> C_c_K </ci>
<ci> C_c_Cl </ci>
<ci> C_c_Imp </ci>
</apply>
</apply>
<apply id="Osm_s_calculation">
<eq/>
<ci> Osm_s </ci>
<apply>
<plus/>
<ci> C_s_Na </ci>
<ci> C_s_K </ci>
<ci> C_s_Cl </ci>
<ci> C_s_Imp </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" public_interface="in" name="Osm_m"/>
<variable units="mmol_per_cm3" public_interface="in" name="Osm_c"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="J_per_mmol" public_interface="in" name="RT"/>
<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> RT </ci>
<apply>
<minus/>
<ci> Osm_m </ci>
<ci> Osm_c </ci>
</apply>
</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" public_interface="in" name="Osm_m"/>
<variable units="mmol_per_cm3" public_interface="in" name="Osm_s"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="J_per_mmol" public_interface="in" name="RT"/>
<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> RT </ci>
<apply>
<minus/>
<ci> Osm_m </ci>
<ci> Osm_s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sc_transepithelial_volume_flux">
<variable units="cm_per_s" name="J_sc_v"/>
<variable units="cm_per_s_mmHg" name="L_sc_v" initial_value="5.22E-7"/>
<variable units="mmol_per_cm3" public_interface="in" name="Osm_s"/>
<variable units="mmol_per_cm3" public_interface="in" name="Osm_c"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="J_per_mmol" public_interface="in" name="RT"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_sc_v_calculation">
<eq/>
<ci> J_sc_v </ci>
<apply>
<times/>
<ci> L_sc_v </ci>
<ci> RT </ci>
<apply>
<minus/>
<ci> Osm_s </ci>
<ci> Osm_c </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="total_transepithelial_volume_flux">
<variable units="cm_per_s" name="J_v"/>
<variable units="cm_per_s" public_interface="in" name="J_mc_v"/>
<variable units="cm_per_s" public_interface="in" name="J_ms_v"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_v_calculation">
<eq/>
<ci> J_v </ci>
<apply>
<plus/>
<ci> J_mc_v </ci>
<ci> J_ms_v </ci>
</apply>
</apply>
</math>
</component>
<group>
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<vCard:N rdf:resource="rdf:#675a277e-e91c-4dfb-a6e5-fa3133847503"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7b8eacdf-c2d6-42ea-b7f9-cb663bbf73b8">
<dcterms:W3CDTF>1999-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#20d1b786-7957-4457-bda5-1d4df2f79cf6">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b28db5be-4a73-4d50-9675-5137f4a8235f">
<dcterms:modified rdf:resource="rdf:#697dc2eb-2e74-46d0-8a2d-f226062e9021"/>
<rdf:value>The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology.
The model runs in the PCEnv simulator but gives a flat output.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a907b383-1dcf-427b-a3cf-f75cada2346e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9413f374-026c-4147-b850-de6e1c16827a">
<dc:creator rdf:resource="rdf:#1dc4bf73-201d-4503-b8fc-2eeb36898c2c"/>
<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 orginal paper for the late distal tubule. The model from the original paper has been modified slightly to include differential equations defining the change in solute concentrations over time. These equations were added to facilitate the use of the CellML code in CMISS.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1dc4bf73-201d-4503-b8fc-2eeb36898c2c">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
</rdf:RDF>
</model>
