- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 03:01:45+12:00
- Desc:
- committing version01 of difrancesco_noble_1985
- Permanent Source URI:
- http://models.cellml.org/workspace/difrancesco_noble_1985/rawfile/018af198d8363cc0b888d03e9c0658a1f9394463/difrancesco_noble_1985.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : DFN_purkinje_fibre_model_1985.xml
CREATED : September 2001
LAST MODIFIED : 5th April 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th January 2002.
DESCRIPTION : This file contains a CellML description of cardiac action
potentials in purkinje fibres, based on the Di Francesco-Noble model, 1985.
CHANGES:
19/10/2001 - CML - Removed document type definition as this is declared as
optional according to the W3C recommendation.
24/10/2001 - CML - Made changes to some of the metadata, bringing them up to
date with the most recent working draft (26th September) of
the Metadata specification.
07/12/2001 - CML - Changed equations after using mathml validator.
03/01/2002 - CML - Created two extra components for extracellular sodium and
extracellular calcium concentrations. Then changed the Nao
and Cao variable public interfaces and the connections
between components appropriately.
21/01/2002 - AAC - Updated metadata to conform with the 16/1/02 CellML
Metadata 1.0 Specification.
25/02/2002 - CML - Corrected several equations.
06/05/2002 - CML - Added some initial values.
19/07/2002 - CML - Added more metadata.
05/04/2003 - AAC - Changed the model name so the model loads in the database
easier.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="DFN_purkinje_fibre_model_1985" name="difrancesco_noble_1985_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<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 is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
During the years that followed the formulation of the <ulink url="${HTML_EXMPL_MNT_MODEL}">McAllister-Noble-Tsien Purkinje fibre model</ulink> in 1975 and the <ulink url="${HTML_EXMPL_BR_MODEL}">Beeler-Reuter mammalian ventricular model</ulink> 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 <xref linkend="fig_cell_diagram"/> 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>
<para>
The raw CellML description of the Di Francesco-Noble model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>.
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the DFN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="cell_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the DFN model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the DFN model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the Di Francesco-Noble model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the <ulink url="${HTML_EXMPL_GRAPHICAL_NOTATION}">notation guide</ulink>. For simplicity, not all the variables are shown.</caption>
</informalfigure>
<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>
</documentation>
<!--
Below, are defined some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_second">
<unit units="millivolt" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="microS">
<unit units="siemens" prefix="micro"/>
</units>
<units name="microF">
<unit units="farad" prefix="micro"/>
</units>
<units name="nanoA">
<unit units="ampere" prefix="nano"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule"/>
<unit units="mole" prefix="kilo" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb" exponent="-1"/>
<unit units="mole"/>
</units>
<units name="microlitre">
<unit units="litre" prefix="micro"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<!--
The "membrane" component is really the `root' node of our model.
It defines the action potential variable "V" among other things.
-->
<component name="membrane">
<!-- These variables are defined here and used in other components. -->
<variable units="millivolt" public_interface="out" name="V" initial_value="-87.0"/>
<variable units="joule_per_kilomole_kelvin" public_interface="out" name="R" initial_value="8.314"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96845.0"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microF" name="C" initial_value="0.0756"/>
<variable units="nanoA" name="i_pulse" initial_value="0.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="nanoA" public_interface="in" name="i_f"/>
<variable units="nanoA" public_interface="in" name="i_K"/>
<variable units="nanoA" public_interface="in" name="i_K1"/>
<variable units="nanoA" public_interface="in" name="i_to"/>
<variable units="nanoA" public_interface="in" name="i_Na_b"/>
<variable units="nanoA" public_interface="in" name="i_Ca_b"/>
<variable units="nanoA" public_interface="in" name="i_p"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="nanoA" public_interface="in" name="i_Na"/>
<variable units="nanoA" public_interface="in" name="i_si"/>
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<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>
<!-- The hyperpolarising-activated current (i_f) is a Na-K current. -->
<component name="hyperpolarising_activated_current">
<!-- These variables are defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_f"/>
<variable units="nanoA" public_interface="out" name="i_fNa"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="nanoA" public_interface="out" name="i_fK"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microS" name="g_f_Na" initial_value="3.0"/>
<variable units="microS" name="g_f_K" initial_value="3.0"/>
<variable units="nanoA" name="I_f"/>
<variable units="concentration_units" name="Km_f" initial_value="45.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_f_calculation">
<eq/>
<ci> i_f </ci>
<apply>
<times/>
<ci> y </ci>
<ci> I_f </ci>
</apply>
</apply>
<apply id="i_fNa_calculation">
<eq/>
<ci> i_fNa </ci>
<apply>
<minus/>
<ci> i_f </ci>
<ci> i_fK </ci>
</apply>
</apply>
<apply id="i_fK_calculation">
<eq/>
<ci> i_fK </ci>
<apply>
<minus/>
<ci> i_f </ci>
<ci> i_fNa </ci>
</apply>
</apply>
<apply id="I_f_calculation">
<eq/>
<ci> I_f </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_f </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> g_f_K </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
<apply>
<times/>
<ci> g_f_Na </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Na_calculation">
<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K_calculation">
<eq/>
<ci> E_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Kc </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The y gate is encapsulated within the hyperpolarising-activated current.
-->
<component name="hyperpolarising_activated_current_y_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.2"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_y"/>
<variable units="per_second" name="beta_y"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_y_calculation">
<eq/>
<ci> alpha_y </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 0.025 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.067 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 52.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_y_calculation">
<eq/>
<ci> beta_y </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_second"> 0.5 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 52.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 52.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dy_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_y </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> y </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_y </ci>
<ci> y </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The time-dependent (delayed) potassium current is equivalent to the plateau
potassium current (1) in the MNT model. It is controlled by a single gate,
x.
-->
<component name="time_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="K"/>
<variable units="nanoA" name="I_K"/>
<variable units="nanoA" name="i_K_max" initial_value="180.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> x </ci>
<ci> I_K </ci>
</apply>
</apply>
<apply id="I_K_calculation">
<eq/>
<ci> I_K </ci>
<apply>
<times/>
<ci> i_K_max </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 140.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The x gate encapsulated within the time-dependent potassium current. -->
<component name="time_dependent_potassium_current_x_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="x" initial_value="0.01"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_x"/>
<variable units="per_second" name="beta_x"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_x_calculation">
<eq/>
<ci> alpha_x </ci>
<apply>
<times/>
<cn cellml:units="nanoA"> 5e-4 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.1 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_x_calculation">
<eq/>
<ci> beta_x </ci>
<apply>
<times/>
<cn cellml:units="nanoA"> 0.0013 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dx_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_x </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_x </ci>
<ci> x </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The time-independent (background) potassium current (i_K1). -->
<component name="time_independent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_K1"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microS" name="g_K1" initial_value="920.0"/>
<variable units="concentration_units" name="Km_K1" initial_value="210.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_K1 </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<ci> E_K </ci>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The transient outward current (i_to) replaces the i_qr chloride-based
current of the MNT model. This current is a calcium-activated, outward
rectifier. It has an inactivation gate, r.
-->
<component name="transient_outward_current">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_to"/>
<!-- These variables are defined here and only used internally. -->
<variable units="micromolar" name="Km_to" initial_value="10.0"/>
<variable units="micromolar" name="Km_Ca" initial_value="0.0005"/>
<variable units="microS" name="g_to" initial_value="0.28"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<!-- this variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_to_calculation">
<eq/>
<ci> i_to </ci>
<apply>
<times/>
<ci> s </ci>
<ci> g_to </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="concentration_units"> 0.2 </cn>
<ci> Kc </ci>
</apply>
<apply>
<plus/>
<ci> Km_to </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Km_Ca </ci>
<ci> Cai </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.2 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.5 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.5 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The inactivation process is described by the following r component. -->
<component name="transient_outward_current_s_gate">
<!-- this variable is defined here and used in other components -->
<variable units="dimensionless" public_interface="out" name="s" initial_value="1.0"/>
<!-- these variables are defined here and only used internally -->
<variable units="per_second" name="alpha_s"/>
<variable units="per_second" name="beta_s"/>
<!-- these variables are imported from parent and sibling components -->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_s_calculation">
<eq/>
<ci> alpha_s </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 0.033 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_s_calculation">
<eq/>
<ci> beta_s </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 33.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 8.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="ds_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> s </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_s </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> s </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_s </ci>
<ci> s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The sodium background current is a simple, time-independent current which
is similar to the i_Na_b of the MNT model. i_Ch_b is a background current
due to choline, or some other sodium substitute.
-->
<component name="sodium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_Na_b"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microS" name="g_Nab" initial_value="0.18"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_b_calculation">
<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>
<!--
The calcium background current is in the same form as the sodium background
current.
-->
<component name="calcium_background_current">
<!-- These variables are defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_Ca_b"/>
<variable units="millivolt" public_interface="out" name="E_Ca"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microS" name="g_Cab" initial_value="0.02"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<variable units="concentration_units" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_b_calculation">
<eq/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<ci> g_Cab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca </ci>
</apply>
</apply>
</apply>
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The Na-K exchange pump couples the free energy released by the hydrolysis of
ATP to transfer sodium and potassium ions across the cell membrane against
their electrochemical gradients. 3 Na ions are pumped out for every 2 K
ions pumped into the cell.
-->
<component name="sodium_potassium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_p"/>
<!-- This variable is defined here and only used internally. -->
<variable units="nanoA" name="I_p" initial_value="125.0"/>
<variable units="concentration_units" name="K_mK" initial_value="1.0"/>
<variable units="concentration_units" name="K_mNa" initial_value="40.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="concentration_units" public_interface="in" name="Nai"/> <variable units="concentration_units" public_interface="in" name="Kc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_calculation">
<eq/>
<ci> i_p </ci>
<apply>
<times/>
<ci> I_p </ci>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> K_mK </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Nai </ci>
<apply>
<plus/>
<ci> K_mNa </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The equation for the Na-Ca exchange current assumes that i_NaCa depends
soley on the sodium and calcium ion electrochemical gradients and the
transmembrane potential. The stoichiometry of the exchange is 3Na : 1Ca,
producing a net outward current.
-->
<component cmeta:id="Na_Ca_exchanger" name="Na_Ca_exchanger">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_NaCa"/>
<variable units="dimensionless" public_interface="out" name="n_NaCa" initial_value="3.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="concentration_units" name="K_NaCa" initial_value="0.02"/>
<variable units="millivolt" name="E_NaCa"/>
<variable units="concentration_units" name="d_NaCa" initial_value="0.001"/>
<variable units="dimensionless" name="gamma" initial_value="0.5"/>
<variable units="dimensionless" name="n"/>
<!-- These variables are imported in from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Cao"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<!-- The current is given as: -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!-- <apply id="Na_Ca_exchanger_calculation1"><eq />
<ci> i_NaCa </ci>
<apply><times />
<ci> K_NaCa </ci>
<apply><sinh />
<apply><divide />
<apply><times />
<apply><minus />
<ci> V </ci>
<ci> E_NaCa </ci>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply> -->
<apply id="Na_Ca_exchanger_calculation2">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<ci> n </ci>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> gamma </ci>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<ci> n </ci>
</apply>
<ci> Cai </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> d_NaCa </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> Cai </ci>
<apply>
<power/>
<ci> Nao </ci>
<ci> n </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Cao </ci>
<apply>
<power/>
<ci> Nai </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="E_NaCa_calculation">
<eq/>
<ci> E_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> n_NaCa </ci>
<ci> E_Na </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> E_Ca </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model retains a two-variable mode; of the sodium kinetics, with new
equations for the gates m and h. It is acknowledged however that the model
does not represent the slower components of Na inactivation and recovery.
It is also assumed that the sodium channel shows a 12% permeability to k
ions.
-->
<component name="fast_sodium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_Na"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microS" name="g_Na" initial_value="750.0"/>
<variable units="millivolt" name="E_mh"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the sodium current in terms
of the conductance, the membrane voltage, and the gate variables.
-->
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_mh </ci>
</apply>
</apply>
</apply>
<apply id="E_mh_calculation">
<eq/>
<ci> E_mh </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci> Nao </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Nai </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_m_gate" is the activation m gate encapsulated
inside the "fast sodium current" component.
-->
<component name="fast_sodium_current_m_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.01"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_m"/>
<variable units="per_second" name="beta_m"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 200.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 41.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 41.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 8000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.056 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 66.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_h_gate" component is the inactivation h gate
encapsulated in the "fast sodium current" component.
-->
<component name="fast_sodium_current_h_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.8"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_h"/>
<variable units="per_second" name="beta_h"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 20.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.125 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 2000.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 320.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
Like the MNT model, the kinetics of the secondary inward current are still
described in terms of two gate variables d and f, but the time constants for
activation and inactivation processes are much shorter. The fast component,
i_si of this current has been divided into the individual ion movements of
Ca, K and Na.
-->
<component name="secondary_inward_current">
<!-- These variables are defined here and used in other components. -->
<variable units="nanoA" public_interface="out" name="i_si"/>
<variable units="nanoA" public_interface="out" name="i_siCa"/>
<variable units="nanoA" public_interface="out" name="i_siK"/>
<variable units="nanoA" public_interface="out" name="i_siNa"/>
<!-- This variable is defined here and only used internally. -->
<variable units="dimensionless" name="P_si" initial_value="15.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Cao"/>
<variable units="concentration_units" public_interface="in" private_interface="out" name="Cai"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_si_calculation">
<eq/>
<ci> i_si </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply>
<plus/>
<ci> i_siCa </ci>
<ci> i_siK </ci>
<ci> i_siNa </ci>
</apply>
</apply>
</apply>
<apply id="i_siCa_calculation">
<eq/>
<ci> i_siCa </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> P_si </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Cai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 100.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Cao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_siK_calculation">
<eq/>
<ci> i_siK </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.001 </cn>
<ci> P_si </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_siNa_calculation">
<eq/>
<ci> i_siNa </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.001 </cn>
<ci> P_si </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Nao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_d_gate" component is the d gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_d_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.005"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_d"/>
<variable units="per_second" name="beta_d"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "secondary_inward_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The rate constants on the d gate are functions of membrane voltage.
-->
<apply id="alpha_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 30.0 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 12.0 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_f_gate" component is the f gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_f_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f" initial_value="1.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_f"/>
<variable units="per_second" name="beta_f"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The rate constants on the f gate are functions of membrane voltage.
-->
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 6.25 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 50.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model also includes a description of Ca-dependent inactivation.
When calcium ions bind to a regulatory site on the channel protein, they
induce a conformational change such that the channel no longer conducts,
and the secondary current slows or ceases.
-->
<component name="secondary_inward_current_f2_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f2" initial_value="1.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_second" name="alpha_f2"/>
<variable units="per_second" name="beta_f2"/>
<variable units="micromolar" name="K_mf2" initial_value="1.0"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="df2_dt">
<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 id="alpha_f2_calculation">
<eq/>
<ci> alpha_f2 </ci>
<cn cellml:units="dimensionless"> 5.0 </cn>
</apply>
<apply id="beta_f2_calculation">
<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>
<!--
Additionally, the DFN model attempted to quantify the changes in several ion
concentrations, as well as the [Ca]i of earlier models.
-->
<component name="extracellular_sodium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Nao" initial_value="14.0"/>
</component>
<component name="intracellular_sodium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Nai" initial_value="8.0"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microlitre" name="Vi"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="nanoA" public_interface="in" name="i_Na"/>
<variable units="nanoA" public_interface="in" name="i_Na_b"/>
<variable units="nanoA" public_interface="in" name="i_siNa"/>
<variable units="nanoA" public_interface="in" name="i_p"/>
<variable units="nanoA" public_interface="in" name="i_fNa"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<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 cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaCa </ci>
<apply>
<divide/>
<ci> n_NaCa </ci>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_calcium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Cao" initial_value="2.0"/>
</component>
<!--
Changes in [Ca]i were first modelled in the BR model and has only been
slightly developed in the DFN model. Calcium is sequestered in the
sarcoplasmic reticulum ([Ca]up). A fraction is transferred to a release
store in the junctional SR ([Ca]rel) before being released into the
intracellular space. The Ca concentrations in each of these various
stores is modelled together with the transfer between the calcium sites
and the ca transfer across the cell membrane via the other ionic
currents.
-->
<component name="intracellular_calcium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Cai" initial_value="0.00005"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microlitre" name="V_up"/>
<variable units="microlitre" name="V_rel"/>
<variable units="microlitre" name="Vi"/>
<variable units="nanoA" name="i_up"/>
<variable units="nanoA" name="i_tr"/>
<variable units="nanoA" name="i_rel"/>
<variable units="per_second" name="alpha_up"/>
<variable units="per_second" name="beta_up"/>
<variable units="per_second" name="alpha_tr"/>
<variable units="per_second" name="beta_tr"/>
<variable units="per_second" name="alpha_rel"/>
<variable units="per_second" name="beta_rel"/>
<variable units="concentration_units" name="Ca_up" initial_value="2.0"/>
<variable units="concentration_units" name="Ca_rel" initial_value="1.0"/>
<variable units="concentration_units" name="Ca_up_max" initial_value="5.0"/>
<variable units="concentration_units" name="K_mCa" initial_value="0.001"/>
<variable units="dimensionless" name="p" initial_value="1.0"/>
<variable units="per_second" name="alpha_p"/>
<variable units="per_second" name="beta_p"/>
<variable units="millisecond" name="tau_up" initial_value="0.025"/>
<variable units="second" name="tau_rep" initial_value="2.0"/>
<variable units="millisecond" name="tau_rel" initial_value="0.05"/>
<variable units="dimensionless" name="rCa" initial_value="2.0"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="nanoA" public_interface="in" name="i_Ca_b"/>
<variable units="nanoA" public_interface="in" name="i_siCa"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_up </ci>
<ci> Cai </ci>
<apply>
<minus/>
<ci> Ca_up_max </ci>
<ci> Ca_up </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_up </ci>
<ci> Ca_up </ci>
</apply>
</apply>
</apply>
<apply id="alpha_up_calculation">
<eq/>
<ci> alpha_up </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Vi </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> tau_up </ci>
<ci> Ca_up_max </ci>
</apply>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<times/>
<ci> alpha_tr </ci>
<ci> p </ci>
<apply>
<minus/>
<ci> Ca_up </ci>
<ci> Ca_rel </ci>
</apply>
</apply>
</apply>
<apply id="alpha_tr_calculation">
<eq/>
<ci> alpha_tr </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
<ci> tau_rep </ci>
</apply>
</apply>
<apply id="alpha_p_calculation">
<eq/>
<ci> alpha_p </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 60.25 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_p_calculation">
<eq/>
<ci> beta_p </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 500.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> alpha_rel </ci>
<ci> Ca_rel </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<ci> rCa </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<ci> rCa </ci>
</apply>
<ci> K_mCa </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_rel_calculation">
<eq/>
<ci> alpha_rel </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
<ci> tau_rel </ci>
</apply>
</apply>
<apply id="dp_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> p </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_p </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> p </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_p </ci>
<ci> p </ci>
</apply>
</apply>
</apply>
<apply id="Ca_up_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_up </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_up </ci>
<ci> i_tr </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_up </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="V_up_calculation">
<eq/>
<ci> V_up </ci>
<apply>
<times/>
<ci> Vi </ci>
<cn cellml:units="dimensionless"> 0.05 </cn>
</apply>
</apply>
<apply id="Ca_rel_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_rel </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_tr </ci>
<ci> i_rel </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="V_rel_calculation">
<eq/>
<ci> V_rel </ci>
<apply>
<times/>
<ci> Vi </ci>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
</apply>
<apply id="Cai_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_siCa </ci>
<ci> i_Ca_b </ci>
<ci> i_up </ci>
</apply>
<apply>
<plus/>
<ci> i_rel </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model assumes that the potassium ion concentration is homogeneous
throughout the three-compartment model.
-->
<component name="extracellular_potassium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Kc" initial_value="4.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microlitre" name="V_e"/>
<variable units="concentration_units" name="Kb" initial_value="4.0"/>
<variable units="nanoA" name="i_mK"/>
<variable units="per_second" name="P" initial_value="0.2"/>
<variable units="nanoA" name="i_K_b"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="nanoA" public_interface="in" name="i_K1"/>
<variable units="nanoA" public_interface="in" name="i_K"/>
<variable units="nanoA" public_interface="in" name="i_fK"/>
<variable units="nanoA" public_interface="in" name="i_siK"/>
<variable units="nanoA" public_interface="in" name="i_p"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Kc_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Kc </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> P </ci>
<apply>
<minus/>
<ci> Kc </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> i_mK </ci>
<apply>
<times/>
<ci> V_e </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_mK_calculation">
<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_K_b </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_p </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The intracellular potassium concentration is related to the total potassium
ion membrane flux.
-->
<component name="intracellular_potassium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Ki" initial_value="140.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microlitre" name="Vi"/>
<variable units="nanoA" name="i_mK"/>
<!-- These variables are imported from other components. -->
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ki_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_mK </ci>
</apply>
<apply>
<times/>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The following <group> element specifies a single containment hierarchy
that encompasses all of the components in the model, with the exception of
the "environment" component.
-->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current"/>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
</component_ref>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="Na_Ca_exchanger"/>
<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="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate"/>
<component_ref component="secondary_inward_current_f_gate"/>
<component_ref component="secondary_inward_current_f2_gate"/>
</component_ref>
<component_ref component="intracellular_sodium_concentration"/>
<component_ref component="extracellular_sodium_concentration"/>
<component_ref component="intracellular_calcium_concentration"/>
<component_ref component="extracellular_calcium_concentration"/>
<component_ref component="extracellular_potassium_concentration"/>
<component_ref component="intracellular_potassium_concentration"/>
</component_ref>
</group>
<!--
The following <group> element specifies how the components representing
activation and inactivation gates are encapsulated inside their parent
currents.
-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_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="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate"/>
<component_ref component="secondary_inward_current_f_gate"/>
<component_ref component="secondary_inward_current_f2_gate"/>
</component_ref>
</group>
<!--
"time" is passed from the "environment" component into the
"membrane" and current components.
-->
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="secondary_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<!--
Several variables are passed between the "membrane" and its sub-components.
-->
<connection>
<map_components component_2="membrane" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_f" variable_1="i_f"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_independent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="transient_outward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="calcium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_potassium_pump"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="fast_sodium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="secondary_inward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_si" variable_1="i_si"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_fK" variable_1="i_fK"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="i_fNa" variable_1="i_fNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="calcium_background_current"/>
<map_variables variable_2="E_Ca" variable_1="E_Ca"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siCa" variable_1="i_siCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siK" variable_1="i_siK"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siNa" variable_1="i_siNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<!--
Several variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components component_2="hyperpolarising_activated_current_y_gate" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="y" variable_1="y"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_dependent_potassium_current_x_gate" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="x" variable_1="x"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="m" variable_1="m"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_d_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_f_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="f" variable_1="f"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_f2_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="f2" variable_1="f2"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="transient_outward_current_s_gate" component_1="transient_outward_current"/>
<map_variables variable_2="s" variable_1="s"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<rdf:RDF>
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The Di Francesco-Noble Model of Cardiac Action Potentials in Purkinje
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Added some initial values from Penny Noble's documentation.
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Created two extra components for extracellular sodium and
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variable public interfaces and the connections between components
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<dc:title>A model of cardiac electrical activity incorporating ionic pumps and concentration changes</dc:title>
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The University of Auckland, Bioengineering Research Group
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The DiFrancesco-Noble gives two alternative equations for the
i_NaCa current. The simplest makes the current a sine function of
the total energy gradient. The more realistic model uses an
equation which is likely to reproduce better dependence of i_NaCa
on intracellular calcium ions.
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Corrected several equations.
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Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
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Added more metadata.
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Made changes to some of the metadata, bringing them up to date with
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