- Author:
- Dewan Sarwar <sarwarcse@gmail.com>
- Date:
- 2019-03-11 12:09:49+13:00
- Desc:
- added blood capillary flux model
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/584/rawfile/dcab0d9157ad4fb602c5084666c323fb3e30323a/DiFrancesco_Noble_1985.cellml
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<article>
<articleinfo>
<title>Di Francesco-Noble Purkinje Fibre Model 1985</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 model has been curated and unit-checked by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>During the years that followed the formulation of the McAllister-Noble-Tsien Purkinje fibre model in 1975 and the Beeler-Reuter mammalian ventricular model in 1977, many experiments were performed which provided a greater insight into the working of the ion channels in cardiac tissue. D. Di Francesco and D. Noble (1985) constructed a new model of cardiac electrical activity which sought to incorporate much of this new data (see the figure below).</para>
<para>The complete original paper reference is cited below:</para>
<para>
A Model of the Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes - Simulations of Ionic Currents and Concentration Changes, Di Francesco, D. and Noble, D.
<ulink url="http://www.pubs.royalsoc.ac.uk/proc_bio/proc_bio.html">
<emphasis>Phil. Trans. R. Soc. Lond.</emphasis>
</ulink>
, B307, 353-398. (The
<ulink url="http://links.jstor.org/sici?sici=0080-4622%2819850110%29307%3A1133%3C353%3AAMOCEA%3E2.0.CO%3B2-O">full text</ulink>
of the article is available to members on the JSTOR website.)
<ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=2578676&dopt=Abstract">PubMed ID: 2578676</ulink>
</para>
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<imageobject>
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<title>cell diagram of the DFN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
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<imagedata fileref="difrancesco_noble_1985.png" />
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<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the DFN model.</caption>
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<title>the cellml rendering of the DFN model</title>
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<caption>
The network defined in the CellML description of the Di Francesco-Noble model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the
<ulink url="${HTML_EXMPL_GRAPHICAL_NOTATION}">notation guide</ulink>
. For simplicity, not all the variables are shown.
</caption>
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<para>
The membrane physically contains the currents, exchangers and pumps, as indicated by the blue arrows in
<xref linkend="fig_cellml_rendering" />
. The currents act independently and are not connected to each other. Several of the channels encapsulate
<emphasis>and</emphasis>
contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.
</para>
<para>The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.</para>
</sect1>
</article>
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<component name="extracellular_potassium_concentration">
<variable cmeta:id="extracellular_potassium_concentration.i_fK" name="i_fK" public_interface="in" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.i_K1" name="i_K1" public_interface="in" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.i_p" name="i_p" public_interface="in" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.i_siK" name="i_siK" public_interface="in" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.i_K" name="i_K" public_interface="in" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.Kc" name="Kc" public_interface="out" units="millimolar" />
<variable cmeta:id="extracellular_potassium_concentration.Kb" name="Kb" units="millimolar" />
<variable cmeta:id="extracellular_potassium_concentration.i_to" name="i_to" public_interface="in" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.pf" name="pf" units="per_second" />
<variable cmeta:id="extracellular_potassium_concentration.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="extracellular_potassium_concentration.Ve" name="Ve" units="micrometre3" />
<variable cmeta:id="extracellular_potassium_concentration.i_mK" name="i_mK" public_interface="out" units="nanoA" />
<variable cmeta:id="extracellular_potassium_concentration.F" name="F" public_interface="in" units="coulomb_per_mole" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_mK</ci>
<apply>
<minus />
<apply>
<plus />
<ci>i_K1</ci>
<ci>i_K</ci>
<ci>i_fK</ci>
<ci>i_siK</ci>
<ci>i_to</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>i_p</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Kc</ci>
</apply>
<apply>
<plus />
<apply>
<times />
<apply>
<minus />
<ci>pf</ci>
</apply>
<apply>
<minus />
<ci>Kc</ci>
<ci>Kb</ci>
</apply>
</apply>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
<ci>i_mK</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>Ve</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current">
<variable cmeta:id="transient_outward_current.time" name="time" public_interface="in" private_interface="out" units="second" />
<variable cmeta:id="transient_outward_current.Km_to" name="Km_to" units="millimolar" />
<variable cmeta:id="transient_outward_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="transient_outward_current.Km_Ca" name="Km_Ca" units="millimolar" />
<variable cmeta:id="transient_outward_current.Kc" name="Kc" public_interface="in" units="millimolar" />
<variable cmeta:id="transient_outward_current.Cai" name="Cai" public_interface="in" units="millimolar" />
<variable cmeta:id="transient_outward_current.s" name="s" private_interface="in" units="dimensionless" />
<variable cmeta:id="transient_outward_current.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="transient_outward_current.RTONF" name="RTONF" public_interface="in" units="millivolt" />
<variable cmeta:id="transient_outward_current.g_to" name="g_to" units="microS_per_millimolar" />
<variable cmeta:id="transient_outward_current_i_to" name="i_to" public_interface="out" units="nanoA" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_to</ci>
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<ci>s</ci>
<ci>g_to</ci>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.2</cn>
<apply>
<divide />
<ci>Kc</ci>
<apply>
<plus />
<ci>Km_to</ci>
<ci>Kc</ci>
</apply>
</apply>
</apply>
<ci>Cai</ci>
</apply>
<apply>
<plus />
<ci>Km_Ca</ci>
<ci>Cai</ci>
</apply>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>Ki</ci>
<apply>
<exp />
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn>
<ci>V</ci>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
<apply>
<times />
<ci>Kc</ci>
<apply>
<exp />
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn>
</apply>
<ci>V</ci>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarising_activated_current">
<variable cmeta:id="hyperpolarising_activated_current_i_f" name="i_f" public_interface="out" units="nanoA" />
<variable cmeta:id="hyperpolarising_activated_current.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="hyperpolarising_activated_current.g_f_K" name="g_f_K" units="microS" />
<variable cmeta:id="hyperpolarising_activated_current.Km_f" name="Km_f" units="millimolar" />
<variable cmeta:id="hyperpolarising_activated_current.E_Na" name="E_Na" public_interface="out" units="millivolt" />
<variable cmeta:id="hyperpolarising_activated_current.Kc" name="Kc" public_interface="in" units="millimolar" />
<variable cmeta:id="hyperpolarising_activated_current.i_fK" name="i_fK" public_interface="out" units="nanoA" />
<variable cmeta:id="hyperpolarising_activated_current.RTONF" name="RTONF" public_interface="in" units="millivolt" />
<variable cmeta:id="hyperpolarising_activated_current.g_f_Na" name="g_f_Na" units="microS" />
<variable cmeta:id="hyperpolarising_activated_current.time" name="time" public_interface="in" private_interface="out" units="second" />
<variable cmeta:id="hyperpolarising_activated_current.i_fNa" name="i_fNa" public_interface="out" units="nanoA" />
<variable cmeta:id="hyperpolarising_activated_current.y" name="y" private_interface="in" units="dimensionless" />
<variable cmeta:id="hyperpolarising_activated_current.Nao" name="Nao" public_interface="in" units="millimolar" />
<variable cmeta:id="hyperpolarising_activated_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="hyperpolarising_activated_current.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="hyperpolarising_activated_current.E_K" name="E_K" public_interface="out" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E_Na</ci>
<apply>
<times />
<ci>RTONF</ci>
<apply>
<ln />
<apply>
<divide />
<ci>Nao</ci>
<ci>Nai</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>E_K</ci>
<apply>
<times />
<ci>RTONF</ci>
<apply>
<ln />
<apply>
<divide />
<ci>Kc</ci>
<ci>Ki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_fNa</ci>
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<ci>y</ci>
<ci>Kc</ci>
</apply>
<apply>
<plus />
<ci>Kc</ci>
<ci>Km_f</ci>
</apply>
</apply>
<ci>g_f_Na</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_fK</ci>
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<ci>y</ci>
<ci>Kc</ci>
</apply>
<apply>
<plus />
<ci>Kc</ci>
<ci>Km_f</ci>
</apply>
</apply>
<ci>g_f_K</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_f</ci>
<apply>
<plus />
<ci>i_fNa</ci>
<ci>i_fK</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable cmeta:id="sodium_potassium_pump.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="sodium_potassium_pump.I_p" name="I_p" units="nanoA" />
<variable cmeta:id="sodium_potassium_pump.i_p" name="i_p" public_interface="out" units="nanoA" />
<variable cmeta:id="sodium_potassium_pump.K_mK" name="K_mK" units="millimolar" />
<variable cmeta:id="sodium_potassium_pump.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="sodium_potassium_pump.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="sodium_potassium_pump.Kc" name="Kc" public_interface="in" units="millimolar" />
<variable cmeta:id="sodium_potassium_pump.K_mNa" name="K_mNa" units="millimolar" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_p</ci>
<apply>
<divide />
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<ci>I_p</ci>
<ci>Kc</ci>
</apply>
<apply>
<plus />
<ci>K_mK</ci>
<ci>Kc</ci>
</apply>
</apply>
<ci>Nai</ci>
</apply>
<apply>
<plus />
<ci>K_mNa</ci>
<ci>Nai</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_potassium_current">
<variable cmeta:id="time_dependent_potassium_current.I_K" name="I_K" units="nanoA" />
<variable cmeta:id="time_dependent_potassium_current.i_K" name="i_K" public_interface="out" units="nanoA" />
<variable cmeta:id="time_dependent_potassium_current.Kc" name="Kc" public_interface="in" units="millimolar" />
<variable cmeta:id="time_dependent_potassium_current.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="time_dependent_potassium_current.x" name="x" private_interface="in" units="dimensionless" />
<variable cmeta:id="time_dependent_potassium_current.i_K_max" name="i_K_max" units="nanoA" />
<variable cmeta:id="time_dependent_potassium_current.RTONF" name="RTONF" public_interface="in" units="millivolt" />
<variable cmeta:id="time_dependent_potassium_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="time_dependent_potassium_current.time" name="time" public_interface="in" private_interface="out" units="second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>I_K</ci>
<apply>
<divide />
<apply>
<times />
<ci>i_K_max</ci>
<apply>
<minus />
<ci>Ki</ci>
<apply>
<times />
<ci>Kc</ci>
<apply>
<exp />
<apply>
<divide />
<apply>
<minus />
<ci>V</ci>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">140</cn>
</apply>
</apply>
<apply>
<eq />
<ci>i_K</ci>
<apply>
<times />
<ci>x</ci>
<ci>I_K</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable cmeta:id="fast_sodium_current_m_gate.m" name="m" public_interface="out" units="dimensionless" />
<variable cmeta:id="fast_sodium_current_m_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="fast_sodium_current_m_gate.beta_m" name="beta_m" units="per_second" />
<variable cmeta:id="fast_sodium_current_m_gate.delta_m" name="delta_m" units="millivolt" />
<variable cmeta:id="fast_sodium_current_m_gate.E0_m" name="E0_m" units="millivolt" />
<variable cmeta:id="fast_sodium_current_m_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="fast_sodium_current_m_gate.alpha_m" name="alpha_m" units="per_second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E0_m</ci>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">41</cn>
</apply>
</apply>
<apply>
<eq />
<ci>alpha_m</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2000</cn>
<apply>
<lt />
<apply>
<abs />
<ci>E0_m</ci>
</apply>
<ci>delta_m</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">200</cn>
<ci>E0_m</ci>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
</apply>
<ci>E0_m</ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq />
<ci>beta_m</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">8000</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.056</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">66</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_m</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>m</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_m</ci>
<ci>m</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable cmeta:id="calcium_background_current.Cao" name="Cao" public_interface="in" units="millimolar" />
<variable cmeta:id="calcium_background_current.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="calcium_background_current.RTONF" name="RTONF" public_interface="in" units="millivolt" />
<variable cmeta:id="calcium_background_current.E_Ca" name="E_Ca" public_interface="out" units="millivolt" />
<variable cmeta:id="calcium_background_current.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="calcium_background_current.g_Cab" name="g_Cab" units="microS" />
<variable cmeta:id="calcium_background_current.Cai" name="Cai" public_interface="in" units="millimolar" />
<variable cmeta:id="calcium_background_current.i_Ca_b" name="i_Ca_b" public_interface="out" units="nanoA" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E_Ca</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn>
<ci>RTONF</ci>
<apply>
<ln />
<apply>
<divide />
<ci>Cao</ci>
<ci>Cai</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_Ca_b</ci>
<apply>
<times />
<ci>g_Cab</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_potassium_concentration">
<variable cmeta:id="intracellular_potassium_concentration.Vi" name="Vi" public_interface="in" units="micrometre3" />
<variable cmeta:id="intracellular_potassium_concentration.i_mK" name="i_mK" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_potassium_concentration.F" name="F" public_interface="in" units="coulomb_per_mole" />
<variable cmeta:id="intracellular_potassium_concentration.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="intracellular_potassium_concentration.Ki" name="Ki" public_interface="out" units="millimolar" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Ki</ci>
</apply>
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
</apply>
<ci>i_mK</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable cmeta:id="sodium_background_current.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="sodium_background_current.E_Na" name="E_Na" public_interface="in" units="millivolt" />
<variable cmeta:id="sodium_background_current.i_Na_b" name="i_Na_b" public_interface="out" units="nanoA" />
<variable cmeta:id="sodium_background_current.g_Nab" name="g_Nab" units="microS" />
<variable cmeta:id="sodium_background_current.time" name="time" public_interface="in" units="second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_Na_b</ci>
<apply>
<times />
<ci>g_Nab</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_f_gate">
<variable cmeta:id="second_inward_current_f_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="second_inward_current_f_gate.f" name="f" public_interface="out" units="dimensionless" />
<variable cmeta:id="second_inward_current_f_gate.beta_f" name="beta_f" units="per_second" />
<variable cmeta:id="second_inward_current_f_gate.alpha_f" name="alpha_f" units="per_second" />
<variable cmeta:id="second_inward_current_f_gate.delta_f" name="delta_f" units="millivolt" />
<variable cmeta:id="second_inward_current_f_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="second_inward_current_f_gate.E0_f" name="E0_f" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E0_f</ci>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
</apply>
</apply>
<apply>
<eq />
<ci>alpha_f</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">25</cn>
<apply>
<lt />
<apply>
<abs />
<ci>E0_f</ci>
</apply>
<ci>delta_f</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">6.25</cn>
<ci>E0_f</ci>
</apply>
<apply>
<minus />
<apply>
<exp />
<apply>
<divide />
<ci>E0_f</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq />
<ci>beta_f</ci>
<apply>
<divide />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">50</cn>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_f</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>f</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_f</ci>
<ci>f</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_calcium_concentration">
<variable cmeta:id="intracellular_calcium_concentration.i_siCa" name="i_siCa" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_calcium_concentration.Ca_up" name="Ca_up" units="millimolar" />
<variable cmeta:id="intracellular_calcium_concentration.V_up" name="V_up" units="micrometre3" />
<variable cmeta:id="intracellular_calcium_concentration.Cai" name="Cai" public_interface="out" units="millimolar" />
<variable cmeta:id="intracellular_calcium_concentration.tau_rep" name="tau_rep" units="second" />
<variable cmeta:id="intracellular_calcium_concentration.tau_rel" name="tau_rel" units="second" />
<variable cmeta:id="intracellular_calcium_concentration.V_rel" name="V_rel" units="micrometre3" />
<variable cmeta:id="intracellular_calcium_concentration.Ca_up_max" name="Ca_up_max" units="millimolar" />
<variable cmeta:id="intracellular_calcium_concentration.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="intracellular_calcium_concentration.i_NaCa" name="i_NaCa" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_calcium_concentration.Ca_rel" name="Ca_rel" units="millimolar" />
<variable cmeta:id="intracellular_calcium_concentration.i_tr" name="i_tr" units="nanoA" />
<variable cmeta:id="intracellular_calcium_concentration.Vi" name="Vi" public_interface="in" units="micrometre3" />
<variable cmeta:id="intracellular_calcium_concentration.n_NaCa" name="n_NaCa" public_interface="in" units="dimensionless" />
<variable cmeta:id="intracellular_calcium_concentration.i_Ca_b" name="i_Ca_b" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_calcium_concentration.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="intracellular_calcium_concentration.F" name="F" public_interface="in" units="coulomb_per_mole" />
<variable cmeta:id="intracellular_calcium_concentration.rCa" name="rCa" units="dimensionless" />
<variable cmeta:id="intracellular_calcium_concentration.alpha_p" name="alpha_p" units="per_second" />
<variable cmeta:id="intracellular_calcium_concentration.beta_p" name="beta_p" units="per_second" />
<variable cmeta:id="intracellular_calcium_concentration.i_rel" name="i_rel" units="nanoA" />
<variable cmeta:id="intracellular_calcium_concentration.K_mCa" name="K_mCa" units="millimolar" />
<variable cmeta:id="intracellular_calcium_concentration.p" name="p" units="dimensionless" />
<variable cmeta:id="intracellular_calcium_concentration.i_up" name="i_up" units="nanoA" />
<variable cmeta:id="intracellular_calcium_concentration.tau_up" name="tau_up" units="second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_up</ci>
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
<ci>tau_up</ci>
<ci>Ca_up_max</ci>
</apply>
</apply>
<ci>Cai</ci>
<apply>
<minus />
<ci>Ca_up_max</ci>
<ci>Ca_up</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_tr</ci>
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
<ci>tau_rep</ci>
</apply>
</apply>
<ci>p</ci>
<apply>
<minus />
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>alpha_p</ci>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">0.625</cn>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
</apply>
</apply>
<apply>
<minus />
<apply>
<exp />
<apply>
<divide />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_p</ci>
<apply>
<divide />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">5</cn>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_rel</ci>
<apply>
<divide />
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
<ci>tau_rel</ci>
</apply>
</apply>
<ci>Ca_rel</ci>
<apply>
<power />
<ci>Cai</ci>
<ci>rCa</ci>
</apply>
</apply>
<apply>
<plus />
<apply>
<power />
<ci>Cai</ci>
<ci>rCa</ci>
</apply>
<apply>
<power />
<ci>K_mCa</ci>
<ci>rCa</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>p</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_p</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>p</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_p</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
<apply>
<minus />
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>V_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>V_up</ci>
<apply>
<times />
<ci>Vi</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
<apply>
<minus />
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>V_rel</ci>
<apply>
<times />
<ci>Vi</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.02</cn>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Cai</ci>
</apply>
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
</apply>
<apply>
<plus />
<apply>
<minus />
<apply>
<minus />
<apply>
<plus />
<ci>i_siCa</ci>
<ci>i_Ca_b</ci>
</apply>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
<apply>
<minus />
<ci>n_NaCa</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>i_rel</ci>
</apply>
<ci>i_up</ci>
</apply>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable cmeta:id="fast_sodium_current.E_mh" name="E_mh" units="millivolt" />
<variable cmeta:id="fast_sodium_current.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="fast_sodium_current.RTONF" name="RTONF" public_interface="in" units="millivolt" />
<variable cmeta:id="fast_sodium_current.Nao" name="Nao" public_interface="in" units="millimolar" />
<variable cmeta:id="fast_sodium_current.i_Na" name="i_Na" public_interface="out" units="nanoA" />
<variable cmeta:id="fast_sodium_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable cmeta:id="fast_sodium_current.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="fast_sodium_current.h" name="h" private_interface="in" units="dimensionless" />
<variable cmeta:id="fast_sodium_current.Kc" name="Kc" public_interface="in" units="millimolar" />
<variable cmeta:id="fast_sodium_current.g_Na" name="g_Na" units="microS" />
<variable cmeta:id="fast_sodium_current.m" name="m" private_interface="in" units="dimensionless" />
<variable cmeta:id="fast_sodium_current.time" name="time" public_interface="in" private_interface="out" units="second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E_mh</ci>
<apply>
<times />
<ci>RTONF</ci>
<apply>
<ln />
<apply>
<divide />
<apply>
<plus />
<ci>Nao</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn>
<ci>Kc</ci>
</apply>
</apply>
<apply>
<plus />
<ci>Nai</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn>
<ci>Ki</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>i_Na</ci>
<apply>
<times />
<ci>g_Na</ci>
<apply>
<power />
<ci>m</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<apply>
<minus />
<ci>V</ci>
<ci>E_mh</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_sodium_concentration">
<variable cmeta:id="intracellular_sodium_concentration.V_e_ratio" name="V_e_ratio" units="dimensionless" />
<variable cmeta:id="intracellular_sodium_concentration.i_siNa" name="i_siNa" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_sodium_concentration.F" name="F" public_interface="in" units="coulomb_per_mole" />
<variable cmeta:id="intracellular_sodium_concentration.i_Na_b" name="i_Na_b" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_sodium_concentration.n_NaCa" name="n_NaCa" public_interface="in" units="dimensionless" />
<variable cmeta:id="intracellular_sodium_concentration.i_NaCa" name="i_NaCa" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_sodium_concentration.length" name="length" units="micrometre" />
<variable cmeta:id="intracellular_sodium_concentration.i_p" name="i_p" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_sodium_concentration.Vi" name="Vi" public_interface="out" units="micrometre3" />
<variable cmeta:id="intracellular_sodium_concentration.Nai" name="Nai" public_interface="out" units="millimolar" />
<variable cmeta:id="intracellular_sodium_concentration.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="intracellular_sodium_concentration.i_fNa" name="i_fNa" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_sodium_concentration.V_Cell" name="V_Cell" units="micrometre3" />
<variable cmeta:id="intracellular_sodium_concentration.i_Na" name="i_Na" public_interface="in" units="nanoA" />
<variable cmeta:id="intracellular_sodium_concentration.radius" name="radius" units="micrometre" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>V_Cell</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.141592654</cn>
<apply>
<power />
<ci>radius</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<ci>length</ci>
</apply>
</apply>
<apply>
<eq />
<ci>Vi</ci>
<apply>
<times />
<ci>V_Cell</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>V_e_ratio</ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>Nai</ci>
</apply>
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
</apply>
<apply>
<plus />
<ci>i_Na</ci>
<ci>i_Na_b</ci>
<ci>i_fNa</ci>
<ci>i_siNa</ci>
<apply>
<times />
<ci>i_p</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<apply>
<divide />
<apply>
<times />
<ci>i_NaCa</ci>
<ci>n_NaCa</ci>
</apply>
<apply>
<minus />
<ci>n_NaCa</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
<ci>Vi</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second" />
</component>
<component name="membrane">
<variable cmeta:id="membrane.T" name="T" public_interface="out" units="kelvin" />
<variable cmeta:id="membrane.R" name="R" public_interface="out" units="joule_per_kilomole_kelvin" />
<variable cmeta:id="membrane.RTONF" name="RTONF" public_interface="out" units="millivolt" />
<variable cmeta:id="membrane.i_to" name="i_to" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.i_NaCa" name="i_NaCa" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.i_si" name="i_si" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="membrane.i_p" name="i_p" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.F" name="F" public_interface="out" units="coulomb_per_mole" />
<variable cmeta:id="membrane.i_f" name="i_f" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.C" name="C" units="microF" />
<variable cmeta:id="membrane.i_K1" name="i_K1" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.i_K" name="i_K" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.i_Na_b" name="i_Na_b" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.i_Ca_b" name="i_Ca_b" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane.i_Na" name="i_Na" public_interface="in" units="nanoA" />
<variable cmeta:id="membrane_V" name="V" public_interface="out" units="millivolt" />
<variable cmeta:id="membrane.i_pulse" name="i_pulse" units="nanoA" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>RTONF</ci>
<apply>
<divide />
<apply>
<times />
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<divide />
<apply>
<minus />
<apply>
<plus />
<ci>i_f</ci>
<ci>i_K</ci>
<ci>i_K1</ci>
<ci>i_to</ci>
<ci>i_Na_b</ci>
<ci>i_Ca_b</ci>
<ci>i_p</ci>
<ci>i_NaCa</ci>
<ci>i_Na</ci>
<ci>i_si</ci>
<ci>i_pulse</ci>
</apply>
</apply>
<ci>C</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarising_activated_current_y_gate">
<variable cmeta:id="hyperpolarising_activated_current_y_gate.y" name="y" public_interface="out" units="dimensionless" />
<variable cmeta:id="hyperpolarising_activated_current_y_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="hyperpolarising_activated_current_y_gate.E0_y" name="E0_y" units="millivolt" />
<variable cmeta:id="hyperpolarising_activated_current_y_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="hyperpolarising_activated_current_y_gate.delta_y" name="delta_y" units="millivolt" />
<variable cmeta:id="hyperpolarising_activated_current_y_gate.alpha_y" name="alpha_y" units="per_second" />
<variable cmeta:id="hyperpolarising_activated_current_y_gate.beta_y" name="beta_y" units="per_second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_y</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">0.05</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.067</cn>
</apply>
<apply>
<minus />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">52</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>E0_y</ci>
<apply>
<minus />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">52</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<eq />
<ci>beta_y</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2.5</cn>
<apply>
<lt />
<apply>
<abs />
<ci>E0_y</ci>
</apply>
<ci>delta_y</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">1</cn>
<ci>E0_y</ci>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.2</cn>
</apply>
<ci>E0_y</ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_y</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>y</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_y</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable cmeta:id="fast_sodium_current_h_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="fast_sodium_current_h_gate.beta_h" name="beta_h" units="per_second" />
<variable cmeta:id="fast_sodium_current_h_gate.alpha_h" name="alpha_h" units="per_second" />
<variable cmeta:id="fast_sodium_current_h_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="fast_sodium_current_h_gate.h" name="h" public_interface="out" units="dimensionless" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_h</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">20</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.125</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_h</ci>
<apply>
<divide />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2000</cn>
<apply>
<plus />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">320</cn>
<apply>
<exp />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
</apply>
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_h</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>h</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_h</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_independent_potassium_current">
<variable cmeta:id="time_independent_potassium_current.Kc" name="Kc" public_interface="in" units="millimolar" />
<variable cmeta:id="time_independent_potassium_current.Km_K1" name="Km_K1" units="millimolar" />
<variable cmeta:id="time_independent_potassium_current.g_K1" name="g_K1" units="microS" />
<variable cmeta:id="time_independent_potassium_current.E_K" name="E_K" public_interface="in" units="millivolt" />
<variable cmeta:id="time_independent_potassium_current_i_K1" name="i_K1" public_interface="out" units="nanoA" />
<variable cmeta:id="time_independent_potassium_current.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="time_independent_potassium_current.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="time_independent_potassium_current.RTONF" name="RTONF" public_interface="in" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>i_K1</ci>
<apply>
<divide />
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<ci>g_K1</ci>
<ci>Kc</ci>
</apply>
<apply>
<plus />
<ci>Kc</ci>
<ci>Km_K1</ci>
</apply>
</apply>
<apply>
<minus />
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
<ci>E_K</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<ci>RTONF</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_d_gate">
<variable cmeta:id="second_inward_current_d_gate.d" name="d" public_interface="out" units="dimensionless" />
<variable cmeta:id="second_inward_current_d_gate.beta_d" name="beta_d" units="per_second" />
<variable cmeta:id="second_inward_current_d_gate.delta_d" name="delta_d" units="millivolt" />
<variable cmeta:id="second_inward_current_d_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="second_inward_current_d_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="second_inward_current_d_gate.E0_d" name="E0_d" units="millivolt" />
<variable cmeta:id="second_inward_current_d_gate.alpha_d" name="alpha_d" units="per_second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>E0_d</ci>
<apply>
<minus />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">24</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
</apply>
</apply>
<apply>
<eq />
<ci>alpha_d</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">120</cn>
<apply>
<lt />
<apply>
<abs />
<ci>E0_d</ci>
</apply>
<ci>delta_d</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">30</cn>
<ci>E0_d</ci>
</apply>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<times />
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<ci>E0_d</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq />
<ci>beta_d</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">120</cn>
<apply>
<lt />
<apply>
<abs />
<ci>E0_d</ci>
</apply>
<ci>delta_d</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">12</cn>
<ci>E0_d</ci>
</apply>
<apply>
<minus />
<apply>
<exp />
<apply>
<divide />
<ci>E0_d</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_d</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>d</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_d</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="second_inward_current_f2_gate">
<variable cmeta:id="second_inward_current_f2_gate.V" name="V" public_interface="in" units="millivolt" />
<variable cmeta:id="second_inward_current_f2_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="second_inward_current_f2_gate.Cai" name="Cai" public_interface="in" units="millimolar" />
<variable cmeta:id="second_inward_current_f2_gate.alpha_f2" name="alpha_f2" units="per_second" />
<variable cmeta:id="second_inward_current_f2_gate.f2" name="f2" public_interface="out" units="dimensionless" />
<variable cmeta:id="second_inward_current_f2_gate.K_mf2" name="K_mf2" units="millimolar" />
<variable cmeta:id="second_inward_current_f2_gate.beta_f2" name="beta_f2" units="per_second" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>f2</ci>
</apply>
<apply>
<minus />
<ci>alpha_f2</ci>
<apply>
<times />
<ci>f2</ci>
<apply>
<plus />
<ci>alpha_f2</ci>
<ci>beta_f2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_f2</ci>
<apply>
<divide />
<apply>
<times />
<ci>Cai</ci>
<ci>alpha_f2</ci>
</apply>
<ci>K_mf2</ci>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_s_gate">
<variable cmeta:id="transient_outward_current_s_gate.beta_s" name="beta_s" units="per_second" />
<variable cmeta:id="transient_outward_current_s_gate.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="transient_outward_current_s_gate.s" name="s" public_interface="out" units="dimensionless" />
<variable cmeta:id="transient_outward_current_s_gate.alpha_s" name="alpha_s" units="per_second" />
<variable cmeta:id="transient_outward_current_s_gate.V" name="V" public_interface="in" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<ci>alpha_s</ci>
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">0.033</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<minus />
<ci>V</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>beta_s</ci>
<apply>
<divide />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">33</cn>
<apply>
<plus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp />
<apply>
<divide />
<apply>
<minus />
<apply>
<plus />
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<minus />
<apply>
<times />
<ci>alpha_s</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>s</ci>
</apply>
</apply>
<apply>
<times />
<ci>beta_s</ci>
<ci>s</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation" />
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate" />
</component_ref>
<component_ref component="second_inward_current">
<component_ref component="second_inward_current_d_gate" />
<component_ref component="second_inward_current_f2_gate" />
<component_ref component="second_inward_current_f_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate" />
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate" />
<component_ref component="fast_sodium_current_h_gate" />
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate" />
</component_ref>
</group>
<group>
<relationship_ref relationship="containment" />
<component_ref component="membrane">
<component_ref component="calcium_background_current" />
<component_ref component="Na_Ca_exchanger" />
<component_ref component="sodium_background_current" />
<component_ref component="intracellular_calcium_concentration" />
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate" />
</component_ref>
<component_ref component="extracellular_calcium_concentration" />
<component_ref component="second_inward_current">
<component_ref component="second_inward_current_d_gate" />
<component_ref component="second_inward_current_f2_gate" />
<component_ref component="second_inward_current_f_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate" />
</component_ref>
<component_ref component="extracellular_sodium_concentration" />
<component_ref component="time_independent_potassium_current" />
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate" />
<component_ref component="fast_sodium_current_h_gate" />
</component_ref>
<component_ref component="extracellular_potassium_concentration" />
<component_ref component="intracellular_sodium_concentration" />
<component_ref component="sodium_potassium_pump" />
<component_ref component="intracellular_potassium_concentration" />
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate" />
</component_ref>
</component_ref>
</group>
<connection>
<map_components component_1="environment" component_2="second_inward_current" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="calcium_background_current" component_2="membrane" />
<map_variables variable_1="i_Ca_b" variable_2="i_Ca_b" />
</connection>
<connection>
<map_components component_1="hyperpolarising_activated_current_y_gate" component_2="hyperpolarising_activated_current" />
<map_variables variable_1="y" variable_2="y" />
</connection>
<connection>
<map_components component_1="extracellular_potassium_concentration" component_2="fast_sodium_current" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components component_1="hyperpolarising_activated_current" component_2="Na_Ca_exchanger" />
<map_variables variable_1="E_Na" variable_2="E_Na" />
</connection>
<connection>
<map_components component_1="intracellular_potassium_concentration" component_2="fast_sodium_current" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components component_1="membrane" component_2="hyperpolarising_activated_current" />
<map_variables variable_1="RTONF" variable_2="RTONF" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="hyperpolarising_activated_current" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_fNa" variable_2="i_fNa" />
</connection>
<connection>
<map_components component_1="environment" component_2="time_independent_potassium_current" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="extracellular_potassium_concentration" component_2="second_inward_current" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components component_1="extracellular_sodium_concentration" component_2="Na_Ca_exchanger" />
<map_variables variable_1="Nao" variable_2="Nao" />
</connection>
<connection>
<map_components component_1="extracellular_sodium_concentration" component_2="hyperpolarising_activated_current" />
<map_variables variable_1="Nao" variable_2="Nao" />
</connection>
<connection>
<map_components component_1="fast_sodium_current_m_gate" component_2="fast_sodium_current" />
<map_variables variable_1="m" variable_2="m" />
</connection>
<connection>
<map_components component_1="second_inward_current" component_2="membrane" />
<map_variables variable_1="i_si" variable_2="i_si" />
</connection>
<connection>
<map_components component_1="membrane" component_2="second_inward_current" />
<map_variables variable_1="RTONF" variable_2="RTONF" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components component_1="transient_outward_current_s_gate" component_2="transient_outward_current" />
<map_variables variable_1="s" variable_2="s" />
</connection>
<connection>
<map_components component_1="extracellular_potassium_concentration" component_2="hyperpolarising_activated_current" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components component_1="membrane" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components component_1="hyperpolarising_activated_current" component_2="sodium_background_current" />
<map_variables variable_1="E_Na" variable_2="E_Na" />
</connection>
<connection>
<map_components component_1="time_dependent_potassium_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="i_K" variable_2="i_K" />
</connection>
<connection>
<map_components component_1="sodium_potassium_pump" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_p" variable_2="i_p" />
</connection>
<connection>
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<dcterms:description>NaK pump Na half activation concentration</dcterms:description>
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<rdf:value>added metadata</rdf:value>
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<vCard:N rdf:resource="rdf:#814fb257-21e6-4042-9d8b-276b277c8af5" vCard:Given="Peter" vCard:Family="Villiger" vCard:Other="J" />
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<dc:publisher>Department of Physiology, Anatomy & Genetics, University of Oxford</dc:publisher>
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<vCard:FN>James Lawson</vCard:FN>
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<rdf:value>This model has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.</rdf:value>
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<rdf:value>added cmeta:id's to some variables to allow referencing by PCEnv session file</rdf:value>
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<rdf:value>Units checked, curated.</rdf:value>
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<dcterms:description>Calcium background current</dcterms:description>
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<dcterms:description>Cardiac myocyte membrane potential</dcterms:description>
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<dcterms:description>Delayed K current</dcterms:description>
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<dcterms:description>Bulk extracellular potassium</dcterms:description>
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<dc:title>A Model of Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes</dc:title>
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<dc:title>Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences</dc:title>
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<rdf:li>Purkinje Fibre</rdf:li>
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