- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-03-30 10:25:52+13:00
- Desc:
- Removed an unpaired <ulink> tag and also updated the documentation and fixed some broken RDF.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/faville_pullan_sanders_smith_2008/rawfile/39ae98d69a57ca800b4f232aab0a2d765e2ba67d/faville_pullan_sanders_smith_2008.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : faville_model_2008.xml
CREATED : 4th October 2007
LAST MODIFIED : 20th March 2008
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Richard Faville et al.'s 2008 biophysically based mathematical model of unitary potential activity in interstitial cells of Cajal.
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="faville_model_2008" name="faville_model_2008">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Biophysically Based Mathematical Model of Unitary Potential Activity in Interstitial Cells of Cajal</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model is known to run in both COR and PCEnv to replicate the published results. The units have been checked and are consistent. We'd like to acknowledge Richard Faville for his help in getting the CellML model to replicate his published model.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Unitary potential (UP) depolarizations are the basic intracellular events responsible for pacemaker activity in interstitial cells of Cajal (ICCs), and are generated at intracellular sites termed "pacemaker units". In this study, we present a mathematical model of the transmembrane ion flows and intracellular Ca(2+) dynamics from a single ICC pacemaker unit acting at near-resting membrane potential. This model quantitatively formalizes the framework of a novel ICC pacemaking mechanism that has recently been proposed. Model simulations produce spontaneously rhythmic UP depolarizations with an amplitude of approximately 3 mV at a frequency of 0.05 Hz. The model predicts that the main inward currents, carried by a Ca(2+)-inhibited nonselective cation conductance, are activated by depletion of sub-plasma-membrane [Ca(2+)] caused by sarcoendoplasmic reticulum calcium ATPase Ca(2+) sequestration. Furthermore, pacemaker activity predicted by our model persists under simulated voltage clamp and is independent of [IP(3)] oscillations. The model presented here provides a basis to quantitatively analyze UP depolarizations and the biophysical mechanisms underlying their production.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="faville_2008.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the pacemaker unit illustrating all the compartmental volumes and ionic conductances, together with their interactions.</caption>
</informalfigure>
<para>
The complete paper reference is cited below:
</para>
<para>
A Biophysically Based Mathematical Model of Unitary Potential Activity in Interstitial Cells of Cajal, R.A. Faville, A.J. Pullan, K.M. Sanders, and N.P. Smith, 2008, <emphasis>Biophysical Journal</emphasis>. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/18339738">PubMed ID: 18339738</ulink>
</para>
</sect1>
</article>
</documentation>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="per_micromolar">
<unit units="micromolar" exponent="-1"/>
</units>
<units name="per_micromolar2">
<unit units="micromolar" exponent="-2"/>
</units>
<units name="picofarad">
<unit units="farad" prefix="pico"/>
</units>
<units name="picosiemens">
<unit units="siemens" prefix="pico"/>
</units>
<units name="picoampere">
<unit units="ampere" prefix="pico"/>
</units>
<units name="femtoampere">
<unit units="ampere" prefix="femto"/>
</units>
<units name="micromolar_coulomb">
<unit units="micromolar"/>
<unit units="coulomb" exponent="-1"/>
</units>
<units name="femtocoulomb_per_zeptomole">
<unit units="coulomb" prefix="femto"/>
<unit units="mole" prefix="zepto" exponent="-1"/>
</units>
<units name="attojoule_per_zeptomole_kelvin">
<unit units="joule" prefix="atto"/>
<unit units="mole" prefix="zepto" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="per_second_squared">
<unit units="second" exponent="-2"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="Vm" initial_value="-70.1"/>
<variable units="picoampere" public_interface="out" name="I_iCa"/>
<variable units="picoampere" public_interface="out" name="I_iNa"/>
<variable units="picofarad" name="Cm" initial_value="20.0"/>
<variable units="picoampere" public_interface="in" name="I_Ca"/>
<variable units="picoampere" public_interface="in" name="I_Na"/>
<variable units="picoampere" public_interface="in" name="I_NSCC_Ca"/>
<variable units="picoampere" public_interface="in" name="I_PM"/>
<variable units="picoampere" public_interface="in" name="I_NSCC_Na"/>
<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> Vm </ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> I_iCa </ci>
<ci> I_iNa </ci>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> I_iCa </ci>
<apply>
<plus/>
<ci> I_Ca </ci>
<ci> I_NSCC_Ca </ci>
<ci> I_PM </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> I_iNa </ci>
<apply>
<plus/>
<ci> I_NSCC_Na </ci>
<ci> I_Na </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_Ca" name="I_Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_Ca">
<dc:title>I_Ca</dc:title>
<dcterms:alternative>calcium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_Ca"/>
<variable units="picosiemens" name="gCa" initial_value="0.01"/>
<variable units="millivolt" name="ECa"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="attojoule_per_zeptomole_kelvin" public_interface="in" name="R"/>
<variable units="femtocoulomb_per_zeptomole" public_interface="in" name="F"/>
<variable units="micromolar" public_interface="in" name="CO"/>
<variable units="micromolar" public_interface="in" name="CS1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> ECa </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> CO </ci>
<ci> CS1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> I_Ca </ci>
<apply>
<times/>
<ci> gCa </ci>
<apply>
<minus/>
<ci> Vm </ci>
<ci> ECa </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_NSCC_Ca" name="I_NSCC_Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_NSCC_Ca">
<dc:title>I_NSCC_Ca</dc:title>
<dcterms:alternative>non-selective calcium conductance</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_NSCC_Ca"/>
<variable units="picosiemens" name="gNSCC_Ca_" initial_value="0.12"/>
<variable units="picosiemens" name="gNSCC_Ca"/>
<variable units="dimensionless" public_interface="in" name="hNSCC"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<variable units="millivolt" public_interface="in" name="ENSCC"/>
<variable units="micromolar" public_interface="in" name="KNSCC"/>
<variable units="micromolar" public_interface="in" name="CS1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> gNSCC_Ca </ci>
<apply>
<times/>
<ci> gNSCC_Ca_ </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KNSCC </ci>
<ci> hNSCC </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KNSCC </ci>
<ci> hNSCC </ci>
</apply>
<apply>
<power/>
<ci> CS1 </ci>
<ci> hNSCC </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> I_NSCC_Ca </ci>
<apply>
<times/>
<ci> gNSCC_Ca </ci>
<apply>
<minus/>
<ci> Vm </ci>
<ci> ENSCC </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_NSCC_Na" name="I_NSCC_Na">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_NSCC_Na">
<dc:title>I_NSCC_Na</dc:title>
<dcterms:alternative>non-selective sodium conductance</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_NSCC_Na"/>
<variable units="picosiemens" name="gNSCC_Na_" initial_value="220.0"/>
<variable units="picosiemens" name="gNSCC_Na"/>
<variable units="dimensionless" public_interface="in" name="hNSCC"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<variable units="millivolt" public_interface="in" name="ENSCC"/>
<variable units="micromolar" public_interface="in" name="KNSCC"/>
<variable units="micromolar" public_interface="in" name="CS1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> gNSCC_Na </ci>
<apply>
<times/>
<ci> gNSCC_Na_ </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KNSCC </ci>
<ci> hNSCC </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KNSCC </ci>
<ci> hNSCC </ci>
</apply>
<apply>
<power/>
<ci> CS1 </ci>
<ci> hNSCC </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> I_NSCC_Na </ci>
<apply>
<times/>
<ci> gNSCC_Na </ci>
<apply>
<minus/>
<ci> Vm </ci>
<ci> ENSCC </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_PM" name="I_PM">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_PM">
<dc:title>I_PM</dc:title>
<dcterms:alternative>plasma membrane Ca2+-ATPase current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_PM"/>
<variable units="femtoampere" name="gPM" initial_value="420.0"/>
<variable units="micromolar" name="KPM" initial_value="1.0"/>
<variable units="micromolar" public_interface="in" name="CS1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> I_PM </ci>
<apply>
<times/>
<ci> gPM </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> CS1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KPM </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> CS1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="I_Na" name="I_Na">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_Na">
<dc:title>I_Na</dc:title>
<dcterms:alternative>sodium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="picoampere" public_interface="out" name="I_Na"/>
<variable units="femtoampere" name="gNa" initial_value="1.5E4"/>
<variable units="micromolar" name="KNa" initial_value="1.0E4"/>
<variable units="dimensionless" name="hNa" initial_value="4.0"/>
<variable units="micromolar" public_interface="in" name="NS1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> I_Na </ci>
<apply>
<times/>
<ci> gNa </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> NS1 </ci>
<ci> hNa </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KNa </ci>
<ci> hNa </ci>
</apply>
<apply>
<power/>
<ci> NS1 </ci>
<ci> hNa </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="JSERCA" name="JSERCA">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#JSERCA">
<dc:title>JSERCA</dc:title>
<dcterms:alternative>SERCA pump</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="flux" public_interface="out" name="JSERCA"/>
<variable units="first_order_rate_constant" name="VSERCA" initial_value="1.0E5"/>
<variable units="dimensionless" name="A2" initial_value="6E-4"/>
<variable units="per_micromolar" name="A4" initial_value="3.57"/>
<variable units="per_micromolar" name="A5" initial_value="2.7E-5"/>
<variable units="per_micromolar2" name="A6" initial_value="2.31E-5"/>
<variable units="micromolar" public_interface="in" name="CER"/>
<variable units="micromolar" public_interface="in" name="CS1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JSERCA </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> VSERCA </ci>
<apply>
<minus/>
<ci> CS1 </ci>
<apply>
<times/>
<ci> A2 </ci>
<ci> CER </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> A4 </ci>
<ci> CS1 </ci>
</apply>
<apply>
<times/>
<ci> A5 </ci>
<ci> CER </ci>
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<apply>
<times/>
<ci> A6 </ci>
<ci> CS1 </ci>
<ci> CER </ci>
</apply>
</apply>
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</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#JMCU">
<dc:title>JMCU</dc:title>
<dcterms:alternative>mitochondrial Ca2+ uniporter</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="flux" public_interface="out" name="JMCU"/>
<variable units="flux" name="VMCU" initial_value="800.0"/>
<variable units="micromolar" name="KMCU" initial_value="10.0"/>
<variable units="dimensionless" name="epsilon_INH"/>
<variable units="micromolar" name="KINH" initial_value="10.0"/>
<variable units="dimensionless" name="hINH" initial_value="4.0"/>
<variable units="micromolar" public_interface="in" name="CS2"/>
<variable units="micromolar" public_interface="in" name="CMT"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JMCU </ci>
<apply>
<times/>
<ci> VMCU </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> CS2 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KMCU </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> CS2 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> epsilon_INH </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> epsilon_INH </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KINH </ci>
<ci> hINH </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KINH </ci>
<ci> hINH </ci>
</apply>
<apply>
<power/>
<ci> CMT </ci>
<ci> hINH </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="JNCX" name="JNCX">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#JNCX">
<dc:title>JNCX</dc:title>
<dcterms:alternative>mitochondrial Na+/Ca2+ exchanger</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="flux" public_interface="out" name="JNCX"/>
<variable units="flux" name="VNCX" initial_value="0.5"/>
<variable units="micromolar" name="KNCX" initial_value="0.3"/>
<variable units="micromolar" public_interface="in" name="CMT"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JNCX </ci>
<apply>
<times/>
<ci> VNCX </ci>
<apply>
<divide/>
<ci> CMT </ci>
<apply>
<plus/>
<ci> CMT </ci>
<ci> KNCX </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#JS1S2">
<dc:title>JS1S2</dc:title>
<dcterms:alternative>inter-subspace Ca2+ flux</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="flux" public_interface="out" name="JS1S2"/>
<variable units="first_order_rate_constant" name="mu_S1S2" initial_value="0.04"/>
<variable units="micromolar" public_interface="in" name="CS1"/>
<variable units="micromolar" public_interface="in" name="CS2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JS1S2 </ci>
<apply>
<times/>
<ci> mu_S1S2 </ci>
<apply>
<minus/>
<ci> CS2 </ci>
<ci> CS1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#JIPR">
<dc:title>JIPR</dc:title>
<dcterms:alternative>IP3R Ca2+ flux</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="flux" public_interface="out" name="JIPR"/>
<variable units="first_order_rate_constant" name="kIPR" initial_value="2000.0"/>
<variable units="flux" name="k_1" initial_value="6.4"/>
<variable units="first_order_rate_constant" name="k1" initial_value="0.0"/>
<variable units="first_order_rate_constant" name="k2" initial_value="4.0"/>
<variable units="first_order_rate_constant" name="r2" initial_value="200.0"/>
<variable units="flux" name="r_2" initial_value="0.0"/>
<variable units="first_order_rate_constant" name="r4" initial_value="750.0"/>
<variable units="micromolar" name="R1" initial_value="36.0"/>
<variable units="micromolar" name="R3" initial_value="300.0"/>
<variable units="first_order_rate_constant" name="phi1"/>
<variable units="flux" name="phi_1"/>
<variable units="first_order_rate_constant" name="phi2"/>
<variable units="first_order_rate_constant" name="phi3" initial_value="0.306"/>
<variable units="dimensionless" name="H" initial_value="0.787"/>
<variable units="first_order_rate_constant" name="g_beta" initial_value="300.0"/>
<variable units="dimensionless" name="h_beta" initial_value="2.0"/>
<variable units="per_second_squared" name="g_alpha" initial_value="0.02"/>
<variable units="micromolar" name="K_beta" initial_value="2.0"/>
<variable units="per_second_squared" name="alpha_phi3"/>
<variable units="first_order_rate_constant" name="beta_phi3"/>
<variable units="micromolar" public_interface="in" name="CER"/>
<variable units="micromolar" public_interface="in" name="CS2"/>
<variable units="micromolar" public_interface="in" name="P"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> H </ci>
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<minus/>
<apply>
<times/>
<ci> phi3 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> H </ci>
</apply>
</apply>
<apply>
<times/>
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<divide/>
<apply>
<times/>
<ci> P </ci>
<ci> phi1 </ci>
<ci> phi2 </ci>
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<apply>
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<rdf:value>Fixed a couple of typos - the equation for JNCX and the initial value for delta_s.</rdf:value>
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Richard Faville et al.'s 2008 biophysically based mathematical model of unitary potential activity in interstitial cells of Cajal.
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<rdf:value>This CellML model is known to run in both COR and PCEnv to replicate the published results. The units have been checked and are consistent. We'd like to acknowledge Richard Faville for his help in getting the CellML model to replicate his published model.</rdf:value>
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<dc:title>A Biophysically Based Mathematical Model of Unitary Potential Activity in Interstitial Cells of Cajal</dc:title>
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