- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2017-09-13 17:22:59+12:00
- Desc:
- update model with new version from Oleg Aslandi.
Correcting some typos and the file name.
- Permanent Source URI:
- https://models.cellml.org/workspace/4be/rawfile/c110576e05e42daf5c4fbba8f837622133fae822/Morgan atrial fibroblast 2016.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 08/09/2017 at 12:34:21 using:
COR (0.9.31.1409)
Copyright 2002-2017 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: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:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="morgan_atrial_fibroblast_2016" cmeta:id="morgan_atrial_fibroblast_2016" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Slow Conduction in the Border Zones of Patchy Fibrosis Stabilizes the Drivers for Atrial Fibrillation: Insights from Multi-Scale Human Atrial Modeling
</title>
<author>
<firstname>Oleg</firstname>
<surname>Aslanidi</surname>
<affiliation>
<shortaffil>King's College London</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML version of the model has been checked in both PCEnv and COR and it runs to recreate the published results. The units have been checked and they balance. We would like to thank the original model author Oleg Aslanidi for his help in the final stages of model curation.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: TBC
</para>
<para>
The original paper reference is cited below: http://journal.frontiersin.org/article/10.3389/fphys.2016.00474/full
</para>
<para>
http://journal.frontiersin.org/article/10.3389/fphys.2016.00474/full
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="morgan_2016.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the atrial cell model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:nodeID="n1"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_1 xml:lang="en">atrial cell</rdf:_1><rdf:_2 xml:lang="en">cardiac</rdf:_2><rdf:_3 xml:lang="en">electrophysiology</rdf:_3></rdf:Description><rdf:Description rdf:nodeID="n2"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">V</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">O</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Aslanidi</Family></rdf:Description><rdf:Description rdf:nodeID="n3"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Oleg Aslanidi</FN></rdf:Description><rdf:Description rdf:nodeID="n4"><maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">.1</maximumStepSize><pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">10000</pointDensity><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">5</endingValue></rdf:Description><rdf:Description rdf:nodeID="n5"><rdf:type><rdf:Description rdf:about="http://www.example.org/foo/bar/bazfoo"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n6"><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Oxford</Orgname><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Department of Physiology, Anatomy and Genetics</Orgunit></rdf:Description><rdf:Description rdf:nodeID="n7"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n8"/></Person></rdf:Description><rdf:Description rdf:nodeID="n9"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n10"/></Person></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n11"/></creator><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n12"/></created></rdf:Description><rdf:Description rdf:nodeID="n13"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n2"/></N></rdf:Description><rdf:Description rdf:nodeID="n11"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n14"/></N><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n15"/></EMAIL><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n6"/></ORG></rdf:Description><rdf:Description rdf:nodeID="n16"><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n3"/></creator><rdf:value xml:lang="en">
This is the CellML description of Morgan et al.'s mathematical
model of membrane voltage in atrial fibroblasts
</rdf:value></rdf:Description><rdf:Description rdf:nodeID="n14"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Oleg</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Aslanidi</Family></rdf:Description><rdf:Description rdf:nodeID="n15"><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type><rdf:value xml:lang="en">oleg.aslanidi@kcl.ac.uk</rdf:value></rdf:Description><rdf:Description rdf:nodeID="n17"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">19186122</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n18"/></JournalArticle></rdf:Description><rdf:Description rdf:nodeID="n19"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n20"/></Person></rdf:Description><rdf:Description rdf:about="#morgan_atrial_fibroblast_2016"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
The Morgan et al. 2016 Model of Atrial Fibroblasts
</title><cmeta:species xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:lang="en">Human</cmeta:species><cmeta:bio_entity xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:lang="en">atrial fibroblast</cmeta:bio_entity><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n17"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n21"/></reference><cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#"><rdf:Description rdf:nodeID="n16"/></cmeta:comment><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n22"/></simulation></rdf:Description><rdf:Description rdf:nodeID="n23"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">H</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Morgan</Family></rdf:Description><rdf:Description rdf:nodeID="n24"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Frontiers in Physiology</title></rdf:Description><rdf:Description rdf:nodeID="n25"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">J</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Li</Family></rdf:Description><rdf:Description rdf:nodeID="n8"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n23"/></N></rdf:Description><rdf:Description rdf:nodeID="n26"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n27"/></Person></rdf:Description><rdf:Description rdf:nodeID="n18"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
</title><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n28"/></issued><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n29"/></creator><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">96</volume><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">798</first_page><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">817</last_page><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n24"/></Journal></rdf:Description><rdf:Description rdf:nodeID="n28"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2016</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n30"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">H</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Aslanidi</Family></rdf:Description><rdf:Description rdf:nodeID="n29"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type><rdf:_5><rdf:Description rdf:nodeID="n9"/></rdf:_5><rdf:_4><rdf:Description rdf:nodeID="n26"/></rdf:_4><rdf:_1><rdf:Description rdf:nodeID="n31"/></rdf:_1><rdf:_2><rdf:Description rdf:nodeID="n19"/></rdf:_2><rdf:_3><rdf:Description rdf:nodeID="n7"/></rdf:_3></rdf:Description><rdf:Description rdf:nodeID="n21"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n32"/></subject></rdf:Description><rdf:Description rdf:nodeID="n20"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n33"/></N></rdf:Description><rdf:Description rdf:nodeID="n27"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n25"/></N></rdf:Description><rdf:Description rdf:nodeID="n31"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n13"/></Person></rdf:Description><rdf:Description rdf:nodeID="n32"><rdf:value><rdf:Description rdf:nodeID="n1"/></rdf:value><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type></rdf:Description><rdf:Description rdf:nodeID="n34"><rdf:first><rdf:Description rdf:nodeID="n4"/></rdf:first><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest></rdf:Description><rdf:Description rdf:nodeID="n22"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n34"/></boundIntervals></rdf:Description><rdf:Description rdf:nodeID="n10"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n30"/></N></rdf:Description><rdf:Description rdf:nodeID="n33"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">R</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">M</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Boyett</Family></rdf:Description><rdf:Description rdf:nodeID="n12"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2009-09-28</W3CDTF></rdf:Description></rdf:RDF> <units xmlns="http://www.cellml.org/cellml/1.0#" name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="per_millisecond">
<unit units="millisecond" exponent="-1"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="picoA_per_picoF">
<unit units="ampere" prefix="pico"/>
<unit units="picoF" exponent="-1"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="nanoS_per_picoF">
<unit units="siemens" prefix="nano"/>
<unit units="picoF" exponent="-1"/>
</units>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="environment">
<variable name="time" units="millisecond" public_interface="out"/>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="membrane">
<variable name="V" units="millivolt" initial_value="-80" public_interface="out"/>
<variable name="RToF" units="millivolt" initial_value="26.54" public_interface="out"/>
<variable name="K_c" units="millimolar" initial_value="5.4" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="139" public_interface="out"/>
<variable name="Na_c" units="millimolar" initial_value="140" public_interface="out"/>
<variable name="Na_i" units="millimolar" initial_value="11.2" public_interface="out"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="i_ns" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_to" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_K1" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_Kur" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_b_Na" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_NaK" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_Stim" units="picoA_per_picoF"/>
<variable name="stim_start" units="millisecond" initial_value="100"/>
<variable name="stim_end" units="millisecond" initial_value="10000"/>
<variable name="stim_period" units="millisecond" initial_value="5000"/>
<variable name="stim_duration" units="millisecond" initial_value="2"/>
<variable name="stim_amplitude" units="picoA_per_picoF" initial_value="-100"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Stim</ci>
<piecewise>
<piece>
<ci>stim_amplitude</ci>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<ci>stim_start</ci>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>stim_end</ci>
</apply>
<apply>
<leq/>
<apply>
<minus/>
<apply>
<minus/>
<ci>time</ci>
<ci>stim_start</ci>
</apply>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
<ci>stim_start</ci>
</apply>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_duration</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="picoA_per_picoF">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_ns</ci>
<ci>i_Kur</ci>
<ci>i_to</ci>
<ci>i_K1</ci>
<ci>i_b_Na</ci>
<ci>i_NaK</ci>
<ci>i_Stim</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="non_specific_current">
<variable name="i_ns" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_ns" units="nanoS_per_picoF" initial_value="0.018"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_ns</ci>
<apply>
<times/>
<ci>g_ns</ci>
<ci>V</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="transient_outward_K_current">
<variable name="i_to" units="picoA_per_picoF" public_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="out"/>
<variable name="g_to" units="nanoS_per_picoF" initial_value="0.01652"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="RToF" units="millivolt" public_interface="in"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="oa" units="dimensionless" private_interface="in"/>
<variable name="oi" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_K</ci>
<apply>
<times/>
<ci>RToF</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>K_c</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<apply>
<power/>
<ci>oa</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>oi</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="transient_outward_K_current_oa_gate">
<variable name="oa" units="dimensionless" initial_value="0.2488" public_interface="out"/>
<variable name="alpha_oa" units="per_millisecond"/>
<variable name="beta_oa" units="per_millisecond"/>
<variable name="tau_oa" units="millisecond"/>
<variable name="oa_inf" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_oa</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.65</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">8.5</cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">59</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_oa</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.65</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">82</cn>
</apply>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>oa_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">20.47</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">17.54</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_oa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">15</cn>
<apply>
<plus/>
<ci>alpha_oa</ci>
<ci>beta_oa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>oa</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>oa_inf</ci>
<ci>oa</ci>
</apply>
<ci>tau_oa</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="transient_outward_K_current_oi_gate">
<variable name="oi" units="dimensionless" initial_value="0.1866" public_interface="out"/>
<variable name="alpha_oi" units="per_millisecond"/>
<variable name="beta_oi" units="per_millisecond"/>
<variable name="tau_oi" units="millisecond"/>
<variable name="oi_inf" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_oi</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">18.53</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">113.7</cn>
</apply>
<cn cellml:units="millivolt">10.95</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_oi</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">35.56</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">1.26</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">7.44</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>oi_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">43.1</cn>
</apply>
<cn cellml:units="millivolt">5.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_oi</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">15</cn>
<apply>
<plus/>
<ci>alpha_oi</ci>
<ci>beta_oi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>oi</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>oi_inf</ci>
<ci>oi</ci>
</apply>
<ci>tau_oi</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ultra_rapid_K_current">
<variable name="i_Kur" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_Kur" units="nanoS_per_picoF" initial_value="0.6"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="ua" units="dimensionless" private_interface="in"/>
<variable name="ui" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Kur</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>g_Kur</ci>
<cn cellml:units="dimensionless">0.005</cn>
</apply>
<apply>
<divide/>
<cn cellml:units="nanoS_per_picoF">0.05</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>ua</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>ui</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ultra_rapid_K_current_ua_gate">
<variable name="ua" units="dimensionless" initial_value="0.9933" public_interface="out"/>
<variable name="alpha_ua" units="per_millisecond"/>
<variable name="beta_ua" units="per_millisecond"/>
<variable name="tau_ua" units="millisecond"/>
<variable name="ua_inf" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_ua</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.65</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">8.5</cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">59</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_ua</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.65</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">82</cn>
</apply>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ua_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">33.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">9.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_ua</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_ua</ci>
<ci>beta_ua</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ua</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>ua_inf</ci>
<ci>ua</ci>
</apply>
<ci>tau_ua</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ultra_rapid_K_current_ui_gate">
<variable name="ui" units="dimensionless" initial_value="0.0999" public_interface="out"/>
<variable name="alpha_ui" units="per_millisecond"/>
<variable name="beta_ui" units="per_millisecond"/>
<variable name="tau_ui" units="millisecond"/>
<variable name="ui_inf" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_ui</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">21</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">185</cn>
</apply>
<cn cellml:units="millivolt">28</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_ui</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">158</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">16</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ui_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">99.45</cn>
</apply>
<cn cellml:units="millivolt">27.48</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_ui</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">5</cn>
<apply>
<plus/>
<ci>alpha_ui</ci>
<ci>beta_ui</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ui</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>ui_inf</ci>
<ci>ui</ci>
</apply>
<ci>tau_ui</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="inward_rectifier">
<variable name="i_K1" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_K1" units="nanoS_per_picoF" initial_value="0.03"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">86.75</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="background_currents">
<variable name="i_b_Na" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_b_Na" units="nanoS_per_picoF" initial_value="0.00607"/>
<variable name="E_Na" units="millivolt" public_interface="out"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="RToF" units="millivolt" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_c" units="millimolar" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Na</ci>
<apply>
<times/>
<ci>RToF</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>Na_c</ci>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_b_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="sodium_potassium_pump">
<variable name="i_NaK" units="picoA_per_picoF" public_interface="out"/>
<variable name="k_NaK_K" units="millimolar" initial_value="1"/>
<variable name="k_NaK_Na" units="millimolar" initial_value="11"/>
<variable name="i_NaK_max" units="picoA_per_picoF" initial_value="2.002"/>
<variable name="V_rev" units="millivolt" initial_value="-150"/>
<variable name="B" units="millivolt" initial_value="-200"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaK_max</ci>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<ci>K_c</ci>
<ci>k_NaK_K</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
<apply>
<power/>
<ci>k_NaK_Na</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>V_rev</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>B</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="transient_outward_K_current">
<component_ref component="transient_outward_K_current_oa_gate"/>
<component_ref component="transient_outward_K_current_oi_gate"/>
</component_ref>
<component_ref component="ultra_rapid_K_current">
<component_ref component="ultra_rapid_K_current_ua_gate"/>
<component_ref component="ultra_rapid_K_current_ui_gate"/>
</component_ref>
<component_ref component="non_specific_current"/>
<component_ref component="inward_rectifier"/>
<component_ref component="background_currents"/>
<component_ref component="sodium_potassium_pump"/>
</component_ref>
</group>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="encapsulation"/>
<component_ref component="transient_outward_K_current">
<component_ref component="transient_outward_K_current_oa_gate"/>
<component_ref component="transient_outward_K_current_oi_gate"/>
</component_ref>
<component_ref component="ultra_rapid_K_current">
<component_ref component="ultra_rapid_K_current_ua_gate"/>
<component_ref component="ultra_rapid_K_current_ui_gate"/>
</component_ref>
</group>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ultra_rapid_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="non_specific_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="inward_rectifier" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="background_currents" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_potassium_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="transient_outward_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="RToF" variable_2="RToF"/>
<map_variables variable_1="K_i" variable_2="K_i"/>
<map_variables variable_1="K_c" variable_2="K_c"/>
<map_variables variable_1="i_to" variable_2="i_to"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="ultra_rapid_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Kur" variable_2="i_Kur"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="non_specific_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_ns" variable_2="i_ns"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="inward_rectifier"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="background_currents"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
<map_variables variable_1="Na_c" variable_2="Na_c"/>
<map_variables variable_1="RToF" variable_2="RToF"/>
<map_variables variable_1="i_b_Na" variable_2="i_b_Na"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="sodium_potassium_pump"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
<map_variables variable_1="K_c" variable_2="K_c"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="ultra_rapid_K_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="transient_outward_K_current_oa_gate"/>
<map_variables variable_1="oa" variable_2="oa"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="transient_outward_K_current_oi_gate"/>
<map_variables variable_1="oi" variable_2="oi"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ultra_rapid_K_current" component_2="ultra_rapid_K_current_ua_gate"/>
<map_variables variable_1="ua" variable_2="ua"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ultra_rapid_K_current" component_2="ultra_rapid_K_current_ui_gate"/>
<map_variables variable_1="ui" variable_2="ui"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
</model>
