- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 13:15:20+12:00
- Desc:
- committing version02 of clancy_rudy_2001
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/clancy_rudy_2001/rawfile/e07bd47353ef12ca289a73362a47cea1b1c02dad/clancy_rudy_2001.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : clancy_rudy_markovian_model_of_ion_channels_2001.xml
CREATED : October 2001
LAST MODIFIED : 20th April 2005
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 the Clancy-Rudy 2001
Markovian model of wild-type, ikr channels, incorporated into a comprehensive
model of the cardiac ventricular cell. This description was based on the
modified Luo-Rudy II model of a ventricular cell.
CHANGES:
19/10/2001 - CML - Removed document type definition as this is declared as
optional according to the WC3 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.
10/12/2001 - CML - Changed equations after checking them with the mathml
validator.
06/01/2002 - CML - Altered some of the connections.
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
20/02/2002 - CML - Changed the equations of the fast_sodium_current from the
Hodgkin-Huxley type to the Markovian Type (defined in
Clancy-Rudy 1999).
25/02/2002 - CML - Corrected beta_K1_calculation.
26/02/2002 - CML - Corrected units.
18/07/2002 - CML - Added more metadata.
05/04/2003 - AAC - Changed the model name so the model loads in the database
easier.
20/04/2005 - PJV - Made MathML id's unique
--><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="clancy_rudy_markovian_model_of_ion_channels_2001" name="clancy_rudy_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Clancy-Rudy Markovian Model of Ion Channels 2001</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 is unsuitably constrained and is not able to be solved.
</para>
<para>
ValidateCellML verifies this model as valid CellML, but detects unit inconsistencies.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 2001, Colleen E. Clancy and Yoram Rudy published a paper which investigated the cellular consequences of mutations in the HERG gene in the congenital Long-QT syndrome and how such mutations can lead to sudden cardiac death. Their model was based on the dynamic Luo-Rudy model of the cardiac ventricular action potential (1994) with modifications described in later publications (see <ulink url="${HTML_EXMPL_LR_II_MODEL}">Luo-Rudy II model</ulink>). However, the traditional <ulink url="${HTML_EXMPL_HHSA_INTRO}">Hodgkin-Huxley formulation</ulink> for the fast sodium current (INa) and the rapid, time-dependent potassium current (IKr)were replaced by a Markovian approach. Clancy and Rudy had recently reformulated INa in an earlier paper (Nature, 1999) and the current paper reference (cited below) develops Markovian models of wild-type and mutant Ikr.
</para>
<para>
The use of Markovian models to represent INa and Ikr deviates from the traditional <ulink url="${HTML_EXMPL_HHSA_INTRO}">Hodgkin-Huxley formulation</ulink>, and it allows the modellers to define distinct channel states. The model for cardiac INa includes three closed states (C3, C2 and C1), an open, conducting state (O) and fast and slow inactivation states (IF and Is, respectively). IKr has three closed states (C3, C2 and C1), an open, conducting state (O) and a single inactivation states (I).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Cellular consequences of HERG mutations in the long QT syndrome: precursors to sudden cardiac death, Colleen E. Clancy and Yoram Rudy, 2001,
<emphasis>Cardiovascular Research</emphasis>
, 50, 301-313. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11334834&dopt=Abstract">PubMed ID: 11334834</ulink>
</para>
<para>
The raw CellML description of the Clancy-Rudy model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${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 Clancy-Rudy model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="clancy_2001.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the Clancy-Rudy model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the Clancy-Rudy model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the Clancy-Rudy 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>
</sect1>
</article>
</documentation>
<!--
Below, we define 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_millisecond">
<unit units="second" prefix="milli" 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_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="milliS_per_microF">
<unit units="siemens" prefix="milli"/>
<unit units="farad" prefix="micro" exponent="-1"/>
</units>
<units name="nanoS_per_cm2">
<unit units="siemens" prefix="nano"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_microF">
<unit units="ampere" prefix="micro"/>
<unit units="farad" prefix="micro" exponent="-1"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="millimolar_per_millisecond">
<unit units="millimolar"/>
<unit units="millisecond" 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"/>
<unit units="mole" exponent="-1"/>
</units>
<units name="cm_per_second">
<unit units="metre" prefix="centi"/>
<unit units="second" exponent="-1"/>
</units>
<units name="cm2">
<unit units="metre" prefix="centi" exponent="2"/>
</units>
<units name="mm2">
<unit units="metre" prefix="milli" exponent="2"/>
</units>
<units name="micro_litre">
<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="millisecond" 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="-84.624"/>
<variable units="joule_per_kilomole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
<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"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microF_per_cm2" name="C" initial_value="1.0"/>
<variable units="microA_per_microF" name="I_stim" initial_value="-100.0"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_T"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kr"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ks"/>
<variable units="microA_per_microF" public_interface="in" name="i_K_ATP"/>
<variable units="microA_per_microF" public_interface="in" name="i_KNa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Ca"/>
<!--
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/>
<ci> I_stim </ci>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca_L </ci>
<ci> i_Ca_T </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K_ATP </ci>
<ci> i_KNa </ci>
<ci> i_NaCa </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_p_Ca </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_ns_Ca </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current" cmeta:id="fast_sodium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na" initial_value="70.0"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Na" initial_value="16.0"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" 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="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="P_O_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!-- The following equation calculates the sodium current. -->
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<ci> P_O_Na </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</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>
</math>
</component>
<component name="Na_channel_states" cmeta:id="Na_channel_states">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="P_O_Na"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="P_C1"/>
<variable units="dimensionless" name="P_C2"/>
<variable units="dimensionless" name="P_C3"/>
<variable units="dimensionless" name="P_IF"/>
<variable units="dimensionless" name="P_IS"/>
<variable units="per_millisecond" name="alpha_11"/>
<variable units="per_millisecond" name="beta_11"/>
<variable units="per_millisecond" name="alpha_12"/>
<variable units="per_millisecond" name="beta_12"/>
<variable units="per_millisecond" name="alpha_13"/>
<variable units="per_millisecond" name="beta_13"/>
<variable units="per_millisecond" name="alpha_2"/>
<variable units="per_millisecond" name="beta_2"/>
<variable units="per_millisecond" name="alpha_3"/>
<variable units="per_millisecond" name="beta_3"/>
<variable units="per_millisecond" name="alpha_4"/>
<variable units="per_millisecond" name="beta_4"/>
<!-- These variables are imported from the parent component. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equations calculate the probabilities of the
fast sodium channel (Na) being in a particular state.
-->
<apply id="Na_channel_states_P_C3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C3 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> beta_11 </ci>
<ci> P_C2 </ci>
</apply>
<apply>
<times/>
<ci> alpha_11 </ci>
<ci> P_C3 </ci>
</apply>
</apply>
</apply>
<apply id="Na_channel_states_P_C2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C2 </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_11 </ci>
<ci> alpha_12 </ci>
</apply>
<ci> P_C2 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> alpha_11 </ci>
<ci> P_C3 </ci>
</apply>
<apply>
<times/>
<ci> beta_12 </ci>
<ci> P_C1 </ci>
</apply>
</apply>
</apply>
<apply id="Na_channel_states_P_C1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C1 </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_12 </ci>
<ci> alpha_13 </ci>
<ci> beta_3 </ci>
</apply>
<ci> P_C1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> alpha_12 </ci>
<ci> P_C2 </ci>
</apply>
<apply>
<times/>
<ci> beta_13 </ci>
<ci> P_O_Na </ci>
</apply>
<apply>
<times/>
<ci> alpha_3 </ci>
<ci> P_IF </ci>
</apply>
</apply>
</apply>
<apply id="P_O_Na_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_O_Na </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> alpha_2 </ci>
<ci> beta_13 </ci>
</apply>
<ci> P_O_Na </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_2 </ci>
<ci> P_IF </ci>
</apply>
<apply>
<times/>
<ci> alpha_13 </ci>
<ci> P_C1 </ci>
</apply>
</apply>
</apply>
<apply id="P_IF_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_IF </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_2 </ci>
<ci> alpha_3 </ci>
<ci> alpha_4 </ci>
</apply>
<ci> P_IF </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_3 </ci>
<ci> P_C1 </ci>
</apply>
<apply>
<times/>
<ci> beta_4 </ci>
<ci> P_IS </ci>
</apply>
<apply>
<times/>
<ci> alpha_2 </ci>
<ci> P_O_Na </ci>
</apply>
</apply>
</apply>
<apply id="P_IS_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_IS </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_4 </ci>
<ci> P_IS </ci>
</apply>
<apply>
<times/>
<ci> beta_4 </ci>
<ci> P_IF </ci>
</apply>
</apply>
</apply>
<!--
The following equations calculate the wild-type rate constants for the
ion channel state changes.
-->
<apply id="alpha_11_calculation">
<eq/>
<ci> alpha_11 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 3.802 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1027 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.20 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 150.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_12_calculation">
<eq/>
<ci> alpha_12 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 3.802 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1027 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.23 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 150.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_13_calculation">
<eq/>
<ci> alpha_13 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 3.802 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1027 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.25 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 150.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_11_calculation">
<eq/>
<ci> beta_11 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1917 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 20.3 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_12_calculation">
<eq/>
<ci> beta_12 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.20 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 20.3 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_13_calculation">
<eq/>
<ci> beta_13 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.22 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 20.3 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_2_calculation">
<eq/>
<ci> alpha_2 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 9.178 </cn>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 29.68 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_2_calculation">
<eq/>
<ci> beta_2 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> alpha_13 </ci>
<ci> alpha_2 </ci>
<ci> alpha_3 </ci>
</apply>
<apply>
<times/>
<ci> beta_13 </ci>
<ci> beta_3 </ci>
</apply>
</apply>
</apply>
<apply id="alpha_3_calculation">
<eq/>
<ci> alpha_3 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0000000037933 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 7.7 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_3_calculation">
<eq/>
<ci> beta_3 </ci>
<apply>
<plus/>
<cn cellml:units="per_millisecond"> 0.0084</cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.00002</cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply id="alpha_4_calculation">
<eq/>
<ci> alpha_4 </ci>
<apply>
<divide/>
<ci> alpha_2 </ci>
<cn cellml:units="dimensionless"> 100.0 </cn>
</apply>
</apply>
<apply id="beta_4_calculation">
<eq/>
<ci> beta_4 </ci>
<ci> alpha_3 </ci>
</apply>
</math>
</component>
<!--
The "L_type_Ca_channel" component describes an inward ionic current which is
the sum of Ca, Na and K ions through the membrane channel. The channel is
permeable to these three ions in the ratio of 2800:3.5:1 respectively, and
therefore the flux of Ca ions is the dominant current through the channel.
The channel has one activation gate (d) and two inactivation gates (f and
f_Ca).
-->
<component name="L_type_Ca_channel">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Ca_L"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaCa"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaK"/>
<variable units="microA_per_microF" public_interface="out" name="i_CaNa"/>
<variable units="dimensionless" public_interface="out" name="gamma_Nai" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Nao" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Ki" initial_value="0.75"/>
<variable units="dimensionless" public_interface="out" name="gamma_Ko" initial_value="0.75"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microA_per_microF" name="I_CaCa"/>
<variable units="microA_per_microF" name="I_CaK"/>
<variable units="microA_per_microF" name="I_CaNa"/>
<variable units="cm_per_second" name="P_Ca" initial_value="0.00054"/>
<variable units="cm_per_second" name="P_Na" initial_value="0.000000675"/>
<variable units="cm_per_second" name="P_K" initial_value="0.000000193"/>
<variable units="dimensionless" name="gamma_Cai" initial_value="1.0"/>
<variable units="dimensionless" name="gamma_Cao" initial_value="0.34"/>
<!--
Time is imported from the "environment", and membrane potential, R, T and
F are imported from the "membrane" component. These variables are used in
the "L_type_Ca_channel" parent component, which also acts as an interface,
passing the variables to its encapsulated gate component. Calcium
concentration is imported from the "ionic_concentrations" component.
-->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="micromolar" public_interface="in" private_interface="out" name="Cai"/>
<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="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<!-- 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="f_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equations calculate the ionic current through the L-type
Ca channel in terms of the conductance, the membrane voltage and the
gate variables.
-->
<apply id="i_CaCa_calculation">
<eq/>
<ci> i_CaCa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaCa </ci>
</apply>
</apply>
<apply id="i_CaNa_calculation">
<eq/>
<ci> i_CaNa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaNa </ci>
</apply>
</apply>
<apply id="i_CaK_calculation">
<eq/>
<ci> i_CaK </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f_Ca </ci>
<ci> I_CaK </ci>
</apply>
</apply>
<apply id="I_CaCa_calculation">
<eq/>
<ci> I_CaCa </ci>
<apply>
<times/>
<ci> P_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Cai </ci>
<ci> Cai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Cao </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_CaNa_calculation">
<eq/>
<ci> I_CaNa </ci>
<apply>
<times/>
<ci> P_Na </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Nai </ci>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Nao </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_CaK_calculation">
<eq/>
<ci> I_CaK </ci>
<apply>
<times/>
<ci> P_K </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Ki </ci>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Ko </ci>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply> <plus/>
<ci> i_CaCa </ci>
<ci> i_CaK </ci>
<ci> i_CaNa </ci>
</apply>
</apply>
</math>
</component>
<!--
The "L_type_Ca_channel_d_gate" is an activation gate encapsulated within the
L-type Ca channel.
-->
<component name="L_type_Ca_channel_d_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="d"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<variable units="dimensionless" name="d_infinity"/>
<variable units="millisecond" name="tau_d"/>
<!--
These variables are imported from the environment and the membrane via
the "L_type_Ca_channel" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" 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>
<divide/>
<ci> d_infinity </ci>
<ci> tau_d </ci>
</apply>
</apply>
<apply id="d_infinity_calculation">
<eq/>
<ci> d_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </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"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_calculation">
<eq/>
<ci> tau_d </ci>
<apply>
<times/>
<ci> d_infinity </ci>
<apply>
<divide/>
<apply>
<minus/>
<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"> 6.24 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.035 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d_infinity </ci>
</apply>
<ci> tau_d </ci>
</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 "L_type_Ca_channel_f_gate" is an inactivation gate encapsulated within
the L-type Ca channel.
-->
<component name="L_type_Ca_channel_f_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_f"/>
<variable units="per_millisecond" name="beta_f"/>
<variable units="dimensionless" name="f_infinity"/>
<variable units="millisecond" name="tau_f"/>
<!--
These variables are imported from the environment and the membrane via
the "L_type_Ca_channel" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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>
<divide/>
<ci> f_infinity </ci>
<ci> tau_f </ci>
</apply>
</apply>
<apply id="f_infinity_calculation">
<eq/>
<ci> f_infinity </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.06 </cn>
</apply>
<cn cellml:units="millivolt"> 8.6 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.6 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 50.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_f_calculation">
<eq/>
<ci> tau_f </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0197 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.0337 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f_infinity </ci>
</apply>
<ci> tau_f </ci>
</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 "L_type_Ca_channel_f_Ca_gate" is a second inactivation gate encapsulated
within the L-type Ca channel.
-->
<component name="L_type_Ca_channel_f_Ca_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f_Ca"/>
<!-- This variable is defined here and only used internally. -->
<variable units="micromolar" name="Km_Ca" initial_value="0.6"/>
<!--
These variables are imported from the environment and the membrane via
the "L_type_Ca_channel" component. Calcium concentration is imported
from the "ionic_concentrations" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_Ca_calculation">
<eq/>
<ci> f_Ca </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Cai </ci>
<ci> Km_Ca </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The T-type Ca channel can also be called a low-threshold Ca channel and it
displays fast inactivation. This channel allows the influx of calcium ions
into the cytoplasm, through the cell surface membrane, down their
electrochemical gradient. The channel has two gates, an activation gate b
and an inactivation gate g.
-->
<component name="T_type_Ca_channel" cmeta:id="T_type_Ca_channel">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Ca_T"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Ca_T" initial_value="0.05"/>
<variable units="millivolt" name="E_Ca"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<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"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="b"/>
<variable units="dimensionless" private_interface="in" name="g"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_T_calculation">
<eq/>
<ci> i_Ca_T </ci>
<apply>
<times/>
<ci> g_Ca_T </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> g </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>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "T_type_Ca_channel" component has an encapsulated activation gate b.
-->
<component name="T_type_Ca_channel_b_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="b_infinity"/>
<variable units="millisecond" name="tau_b"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="b_infinity_calculation">
<eq/>
<ci> b_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </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"> 14.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.8 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_b_calculation">
<eq/>
<ci> tau_b </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="per_millivolt_millisecond"> 3.7 </cn>
<cn cellml:units="per_millivolt_millisecond"> 6.1 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 25.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 4.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="b_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> b </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> b_infinity </ci>
<ci> b </ci>
</apply>
<ci> tau_b </ci>
</apply>
</apply>
</math>
</component>
<!--
The "T_type_Ca_channel" component has an encapsulated inactivation gate g.
-->
<component name="T_type_Ca_channel_g_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="g"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="g_infinity"/>
<variable units="millisecond" name="tau_g"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="g_infinity_calculation">
<eq/>
<ci> g_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_g_calculation">
<eq/>
<ci> tau_g </ci>
<piecewise>
<piece>
<cn cellml:units="millisecond"> 12.0 </cn>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="millivolt"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -0.875 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millisecond"> 12.0 </cn>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="g_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> g </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> g_infinity </ci>
<ci> g </ci>
</apply>
<ci> tau_g </ci>
</apply>
</apply>
</math>
</component>
<!--
The use of a Markovian model to represent i_Kr deviates from the traditional
Hodgkin-Huxley approach used in many ionic models (including Luo-Rudy II).
The Markovian scheme represents distinct channel states and coupling between
these states, which allowed Clancy and Rudy to relate state-specific kinetic
properties of ion channels to the electophysiological behaviour of the whole
cell.
-->
<component name="rapid_time_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Kr"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Kr"/>
<variable units="millivolt" name="E_Kr"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<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"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="P_O"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the rapid time-dependent potassium
current.
-->
<apply id="i_Kr_calculation">
<eq/>
<ci> i_Kr </ci>
<apply>
<times/>
<ci> g_Kr </ci>
<ci> P_O </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Kr </ci>
</apply>
</apply>
</apply>
<!--
The following equation calculates the maximum conductance of the
rapid potassium channel (gKr).
-->
<apply id="g_Kr_calculation">
<eq/>
<ci> g_Kr </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.0135 </cn>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 0.59 </cn>
</apply>
</apply>
</apply>
<apply id="E_Kr_calculation">
<eq/>
<ci> E_Kr </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The model for cardiac i_Kr includes three closed states (C3, C2, C1) an
open state (O) and an inactivation state (I). P_i is the probability of a
channel occupying a particular state (i), which is determined by a system of
linear first oder differential equations.
-->
<component name="Kr_channel_states">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="P_O"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="P_C1"/>
<variable units="dimensionless" name="P_C2"/>
<variable units="dimensionless" name="P_C3"/>
<variable units="dimensionless" name="P_I"/>
<variable units="per_millisecond" name="alpha"/>
<variable units="per_millisecond" name="beta"/>
<variable units="per_millisecond" name="alpha_in" initial_value="2.172"/>
<variable units="per_millisecond" name="beta_in" initial_value="1.077"/>
<variable units="per_millisecond" name="alpha_alpha"/>
<variable units="per_millisecond" name="beta_beta"/>
<variable units="per_millisecond" name="alpha_i"/>
<variable units="per_millisecond" name="beta_i"/>
<variable units="per_millisecond" name="mu"/>
<!-- These variables are imported from the parent component. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equations calculate the probabilities of the
rapid potassium channel (Kr) being in a particular state.
-->
<apply id="Kr_channel_states_P_C3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C3 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> beta </ci>
<ci> P_C2 </ci>
</apply>
<apply>
<times/>
<ci> alpha </ci>
<ci> P_C3 </ci>
</apply>
</apply>
</apply>
<apply id="Kr_channel_states_P_C2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C2 </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> beta </ci>
<ci> alpha_in </ci>
</apply>
<ci> P_C2 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> alpha </ci>
<ci> P_C3 </ci>
</apply>
<apply>
<times/>
<ci> beta_in </ci>
<ci> P_C1 </ci>
</apply>
</apply>
</apply>
<apply id="Kr_channel_states_P_C1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C1 </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_in </ci>
<ci> alpha_alpha </ci>
<ci> alpha_alpha </ci>
</apply>
<ci> P_C1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> alpha_in </ci>
<ci> P_C2 </ci>
</apply>
<apply>
<times/>
<ci> beta_beta </ci>
<ci> P_O </ci>
</apply>
</apply>
</apply>
<apply id="P_O_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_O </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_beta </ci>
<ci> beta_i </ci>
</apply>
<ci> P_O </ci>
</apply>
</apply>
<apply>
<times/>
<ci> alpha_alpha </ci>
<ci> P_C1 </ci>
</apply>
<apply>
<times/>
<ci> alpha_i </ci>
<ci> P_I </ci>
</apply>
</apply>
</apply>
<apply id="P_I_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_I </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> mu </ci>
<ci> alpha_i </ci>
</apply>
<ci> P_I </ci>
</apply>
</apply>
<apply>
<times/>
<ci> alpha_alpha </ci>
<ci> P_C1 </ci>
</apply>
<apply>
<times/>
<ci> beta_i </ci>
<ci> P_O </ci>
</apply>
</apply>
</apply>
<!--
The following equations calculate the wild-type rate constants for the
ion channel state changes.
-->
<apply id="alpha_calculation">
<eq/>
<ci> alpha </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.00555 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05547153 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_calculation">
<eq/>
<ci> beta </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.002357 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.036588 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_alpha_calculation">
<eq/>
<ci> alpha_alpha </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.00655 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05547153 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 36.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_beta_calculation">
<eq/>
<ci> beta_beta </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0029357 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.02158 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_i_calculation">
<eq/>
<ci> alpha_i </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.439 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.02352 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="micromolar"> 4.5 </cn>
<ci> Ko </ci>
</apply>
</apply>
</apply>
<apply id="beta_i_calculation">
<eq/>
<ci> beta_i </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.656 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.000942 </cn>
<ci> V </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<cn cellml:units="micromolar"> 4.5 </cn>
<cn cellml:units="dimensionless"> 0.3 </cn>
</apply>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 0.3 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="mu_calculation">
<eq/>
<ci> mu </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> alpha_i </ci>
<ci> beta_beta </ci>
<ci> alpha_alpha </ci>
</apply>
<apply>
<times/>
<ci> alpha_alpha </ci>
<ci> beta_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The slow time-dependent potassium current has two encapsulated
activation gates, one fast and one slow; Xs1 and Xs2.
-->
<component name="slow_time_dependent_potassium_current" cmeta:id="slow_time_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Ks"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Ks"/>
<variable units="millivolt" name="E_Ks"/>
<variable units="dimensionless" name="P_NaK" initial_value="0.01833"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<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"/>
<!-- This variable is imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="Xs1"/>
<variable units="dimensionless" private_interface="in" name="Xs2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the maximum conductance of the
slow potassium channel (gKs).
-->
<apply id="g_Ks_calculation">
<eq/>
<ci> g_Ks </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.433 </cn>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 0.6 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<cn cellml:units="micromolar"> 0.000038 </cn>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 1.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Ks_calculation">
<eq/>
<ci> E_Ks </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> Ko </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the slow time-dependent potassium
current in terms of the conductance, the membrane voltage and the
gate variables.
-->
<apply id="i_Ks_calculation">
<eq/>
<ci> i_Ks </ci>
<apply>
<times/>
<ci> g_Ks </ci>
<ci> Xs1 </ci>
<ci> Xs2 </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ks </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "slow_time_dependent_potassium_current_Xs1_gate" component is the
fast activation gate encapsulated in the slow_time-dependent potassium
current.
-->
<component name="slow_time_dependent_potassium_current_Xs1_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="Xs1"/>
<variable units="millisecond" public_interface="out" name="tau_Xs1"/>
<variable units="dimensionless" public_interface="out" name="Xs_infinity"/>
<!--
These variables are imported from the environment and the membrane via
the "rapid_time_dependent_potassium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Xs_infinity_calculation">
<eq/>
<ci> Xs_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </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"> -1.5 </cn>
</apply>
<cn cellml:units="millivolt"> 16.7 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_Xs1_calculation">
<eq/>
<ci> tau_Xs1 </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0000719 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.148 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.000131 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0687 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Xs1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Xs1 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Xs_infinity </ci>
<ci> Xs1 </ci>
</apply>
<ci> tau_Xs1 </ci>
</apply>
</apply>
</math>
</component>
<!--
The "slow_time_dependent_potassium_current_Xs2_gate" component is the
slow activation gate encapsulated in the slow_time-dependent potassium
current.
-->
<component name="slow_time_dependent_potassium_current_Xs2_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="Xs2"/>
<!-- These variables are defined here and only used internally. -->
<variable units="millisecond" name="tau_Xs2"/>
<!--
These variables are imported from the environment and the membrane via
the "rapid_time_dependent_potassium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millisecond" public_interface="in" name="tau_Xs1"/>
<variable units="dimensionless" public_interface="in" name="Xs_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="tau_Xs2_calculation">
<eq/>
<ci> tau_Xs2 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> tau_Xs1 </ci>
</apply>
</apply>
<apply id="Xs2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Xs2 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Xs_infinity </ci>
<ci> Xs2 </ci>
</apply>
<ci> tau_Xs2 </ci>
</apply>
</apply>
</math>
</component>
<!--
The sodium-activated potassium current describes an outwardly rectifying,
time-independent current with [Na]i and voltage dependence.
-->
<component name="sodium_activated_potassium_current" cmeta:id="sodium_activated_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_KNa"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_KNa" initial_value="0.12848"/>
<variable units="dimensionless" name="P_oV"/>
<variable units="dimensionless" name="P_oNai"/>
<variable units="millivolt" name="E_K"/>
<variable units="millimolar" name="K_D" initial_value="66.0"/>
<variable units="dimensionless" name="n" initial_value="2.8"/>
<!-- These variables are imported in from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<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"/>
<!-- The current is given as. -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_KNa_calculation">
<eq/>
<ci> i_KNa </ci>
<apply>
<times/>
<ci> g_KNa </ci>
<ci> P_oNai </ci>
<ci> P_oV </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="sodium_activated_potassium_current_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> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="P_oV_calculation">
<eq/>
<ci> P_oV </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.8 </cn>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.65 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 125.0 </cn>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="P_oNai_calculation">
<eq/>
<ci> P_oNai </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.85 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_D </ci>
<ci> Nai </ci>
</apply>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "ATP_dependent_potassium_current" component describes the efflux of K
ions through an ATP-sensitive potassium channel in the cell surface
membrane. This current is independent of both time and voltage.
-->
<component name="ATP_dependent_potassium_current" cmeta:id="ATP_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_K_ATP"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_K_ATP"/>
<variable units="nanoS_per_cm2" name="G_K_ATP"/>
<variable units="dimensionless" name="P_ATP"/>
<variable units="millivolt" name="E_K"/>
<variable units="millimolar" name="Ko_normal" initial_value="4.0"/>
<variable units="dimensionless" name="n" initial_value="0.24"/>
<variable units="dimensionless" name="H" initial_value="2.0"/>
<variable units="cm2" name="Nichols_area" initial_value="0.005"/>
<!-- These variables are imported in from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<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"/>
<!-- The current is given as. -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_ATP_calculation">
<eq/>
<ci> i_K_ATP </ci>
<apply>
<times/>
<ci> g_K_ATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="g_K_ATP_calculation">
<eq/>
<ci> g_K_ATP </ci>
<apply>
<times/>
<ci> G_K_ATP </ci>
<ci> P_ATP </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ko_normal </ci>
</apply>
<ci> n </ci>
</apply>
</apply>
</apply>
<apply id="ATP_dependent_potassium_current_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> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="G_K_ATP_calculation">
<eq/>
<ci> G_K_ATP </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.00000195 </cn>
<ci> Nichols_area </ci>
</apply>
</apply>
</math>
</component>
<!--
The "Na_Ca_exchanger" component describes how a protein molecule in the cell
surface membrane transports Na ions into the cytosol and exports Ca ions
into the extracellular matrix, in a ratio of 3:1 respectively.
-->
<component name="Na_Ca_exchanger">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microA_per_microF" name="K_NaCa" initial_value="2000.0"/>
<variable units="millimolar" name="K_mNa" initial_value="87.5"/>
<variable units="millimolar" name="K_mCa" initial_value="1.38"/>
<variable units="dimensionless" name="K_sat" initial_value="0.1"/>
<variable units="dimensionless" name="eta" initial_value="0.35"/>
<!-- These variables are imported in from other components. -->
<variable units="millisecond" 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="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<!-- The current is given as: -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger_calculation">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> K_mCa </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> K_sat </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<ci> eta </ci>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_potassium_current" component is identical to that in
the original LR-I model except that the maximum conductance (g_K1) can be
increased slightly to a more realistic level.
-->
<component name="time_independent_potassium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_K1"/>
<variable units="millivolt" public_interface="out" private_interface="out" name="E_K1"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_K1" initial_value="0.282"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" 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="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="K1_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation determines the maximum conductance of the
potassium channel.
-->
<apply id="g_K1_calculation">
<eq/>
<ci> g_K1 </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.75 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="micromolar"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the reversal potential of the
time-independent potassium current.
-->
<apply id="E_K1_calculation">
<eq/>
<ci> E_K1 </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the time-independent potassium
current in terms of the conductance, the membrane voltage and the
gate variables.
-->
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<ci> K1_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_potassium_current_K1_gate" component is the K1 gate
encapsulated in the time-independent potassium current.
-->
<component name="time_independent_potassium_current_K1_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="K1_infinity"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_K1"/>
<variable units="per_millisecond" name="beta_K1"/>
<!--
These variables are imported from the "environment", "membrane" and
"time_independent_potassium_current" components.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The rate constants on the K1 gate are functions of membrane voltage.
-->
<apply id="alpha_K1_calculation">
<eq/>
<ci> alpha_K1 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 1.02 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2385 </cn>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="millivolt"> 59.215 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_K1_calculation">
<eq/>
<ci> beta_K1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.49124 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08032 </cn>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.476 </cn>
</apply>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.06175 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 594.31 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.5143 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 4.753 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The steady-state value K1_infinity is given by the following
equation:
-->
<apply id="K1_infinity_calculation">
<eq/>
<ci> K1_infinity </ci>
<apply>
<divide/>
<ci> alpha_K1 </ci>
<apply>
<plus/>
<ci> alpha_K1 </ci>
<ci> beta_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "plateau_potassium_current" is identical to that described in the LR-I
model.
-->
<component name="plateau_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
<!-- These variables are defined here and only used internally. -->
<variable units="millivolt" name="E_Kp"/>
<variable units="milliS_per_microF" name="g_Kp" initial_value="0.00552"/>
<variable units="dimensionless" name="Kp"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the plateau potassium current
reversal potential:
-->
<apply id="E_Kp_calculation">
<eq/>
<ci> E_Kp </ci>
<ci> E_K1 </ci>
</apply>
<!-- The following equation calculates the constant Kp. -->
<apply id="Kp_calculation">
<eq/>
<ci> Kp </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 7.488 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 5.98 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation determines the plateau potassium current in
terms of the membrane voltage.
-->
<apply id="i_Kp_calculation">
<eq/>
<ci> i_Kp </ci>
<apply>
<times/>
<ci> g_Kp </ci>
<ci> Kp </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Kp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sarcolemmal_calcium_pump" is an additional mechanism for removing Ca
ions from the myoplasm to help maintain a low intracellular calcium
concentration when at rest.
-->
<component name="sarcolemmal_calcium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
<!-- These variables are defined here and only used internally. -->
<variable units="micromolar" name="K_mpCa" initial_value="0.5"/>
<variable units="microA_per_microF" name="I_pCa" initial_value="1.15"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_Ca_calculation">
<eq/>
<ci> i_p_Ca </ci>
<apply>
<times/>
<ci> I_pCa </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> K_mpCa </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_background_current" is a time-independent diffusion of Na ions
down their electrochemical gradient, through the cell surface membrane into
the cytosol.
-->
<component name="sodium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Na_b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Nab" initial_value="0.00141"/>
<variable units="millivolt" name="E_NaN"/>
<!--
Time and membrane potential are imported from the "environment" and the
"membrane" components. The reversal potential is imported from the
"fast_sodium_current" component.
-->
<variable units="millisecond" 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="E_NaN_calculation">
<eq/>
<ci> E_NaN </ci>
<ci> E_Na </ci>
</apply>
<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_NaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "calcium_background_current" describes a time-independent diffusion of
Ca ions down their electrochemical gradient through the cell surface
membrane into the cytosol. However, calcium is not allowed to accumulate to
high intracellular concentrations. This influx is balanced by the Ca ion
extrusion through the Na-Ca exchanger and the sarcolemmal Ca pump.
-->
<component name="calcium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Cab" initial_value="0.003016"/>
<variable units="millivolt" name="E_CaN"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" 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="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_CaN_calculation">
<eq/>
<ci> E_CaN </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
<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_CaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_potassium_pump" is an active protein in the cell membrane which
couples the free energy released by the hydrolysis of ATP to the movement of
Na and K ions against their electrochemical gradients through the cell
surface membrane.
-->
<component name="sodium_potassium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microA_per_microF" name="I_NaK"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="millimolar" name="K_mNai" initial_value="10.0"/>
<variable units="millimolar" name="K_mKo" initial_value="1.5"/>
<variable units="dimensionless" name="sigma"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" 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="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_NaK_calculation">
<eq/>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1245 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0365 </cn>
<ci> sigma </ci>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="sigma_calculation">
<eq/>
<ci> sigma </ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 7.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 67.3 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> I_NaK </ci>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<root/>
<apply>
<power/>
<apply>
<divide/>
<ci> K_mNai </ci>
<ci> Nai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Ko </ci>
<apply>
<plus/>
<ci> Ko </ci>
<ci> K_mKo </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "non_specific_calcium_activated_current" describes a channel which is activated by calcium ions, but is permeable to only sodium and potassium
ions.
-->
<component name="non_specific_calcium_activated_current">
<variable units="microA_per_microF" public_interface="out" name="i_ns_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_Na"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_K"/>
<variable units="cm_per_second" name="P_ns_Ca" initial_value="1.75E-7"/>
<variable units="dimensionless" public_interface="in" name="gamma_Nai"/>
<variable units="dimensionless" public_interface="in" name="gamma_Nao"/>
<variable units="dimensionless" public_interface="in" name="gamma_Ki"/>
<variable units="dimensionless" public_interface="in" name="gamma_Ko"/>
<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="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="microA_per_microF" name="I_ns_Na"/>
<variable units="microA_per_microF" name="I_ns_K"/>
<variable units="micromolar" name="K_m_ns_Ca" initial_value="1.2"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_ns_Na_calculation">
<eq/>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> I_ns_Na </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_K_calculation">
<eq/>
<ci> i_ns_K </ci>
<apply>
<times/>
<ci> I_ns_K </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_Ca_calculation">
<eq/>
<ci> i_ns_Ca </ci>
<apply>
<plus/>
<ci> i_ns_Na </ci>
<ci> i_ns_K </ci>
</apply>
</apply>
<apply id="I_ns_Na_calculation">
<eq/>
<ci> I_ns_Na </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Nai </ci>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Nao </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_ns_K_calculation">
<eq/>
<ci> I_ns_K </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> gamma_Ki </ci>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> gamma_Ko </ci>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The LR-II model keeps track of the three main ions; Ca, Na and K as well as
Ca concentrations in the network sarcoplasmic reticulum (NSR) and the
junctional sarcoplasmic reticulum (JSR). The total ca ion entry up to 2 ms
after the onset of a stimulus ([Ca]foot) is also tracked to be used for the
triggering of calcium induced calcium release (CICR). The
"ionic_concentrations" component contains the equations needed to calculate
these ionic concentrations.
-->
<component name="ionic_concentrations">
<!-- these variables are defined here and used in other components -->
<variable units="millimolar" public_interface="out" name="Nai" initial_value="10.0"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="140.0"/>
<variable units="micromolar" public_interface="out" name="Cai" initial_value="0.12"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="1.8"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="145.0"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4"/>
<variable units="millimolar" public_interface="out" name="Ca_JSR"/>
<variable units="millimolar" public_interface="out" name="Ca_NSR" initial_value="15.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mm2" name="A_cap" initial_value="0.000153"/>
<variable units="dimensionless" name="R_A_V"/>
<variable units="micro_litre" name="V_myo"/>
<variable units="dimensionless" name="delta_Ca"/>
<variable units="dimensionless" name="delta_Ca_JSR"/>
<variable units="micro_litre" name="V_cleft"/>
<variable units="micro_litre" name="V_JSR"/>
<variable units="micro_litre" name="V_NSR"/>
<variable units="micromolar" name="Ca_foot"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_CaNa"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_CaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_T"/>
<variable units="microA_per_microF" public_interface="in" name="i_CaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kr"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ks"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_KNa"/>
<variable units="microA_per_microF" public_interface="in" name="i_K_ATP"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/> <variable units="microA_per_microF" public_interface="in" name="i_ns_K"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_tr"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_rel"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_leak"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="i_up"/>
<variable units="micromolar" public_interface="in" name="K_mTn"/>
<variable units="micromolar" public_interface="in" name="K_mCMDN"/>
<variable units="micromolar" public_interface="in" name="Tn_max"/>
<variable units="micromolar" public_interface="in" name="CMDN_max"/>
<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>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_CaNa </ci>
<ci> i_Na_b </ci>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaCa </ci>
<ci> i_p_Ca </ci>
<ci> i_Ca_b </ci>
<ci> i_Ca_T </ci>
</apply>
<ci> i_NaCa </ci>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> i_rel </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_myo </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_leak </ci>
<ci> i_up </ci>
</apply>
<apply>
<divide/>
<ci> V_NSR </ci>
<ci> V_myo </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaK </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K_ATP </ci>
<ci> i_KNa </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_external_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ko </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> i_CaK </ci>
<ci> i_Kr </ci>
<ci> i_Ks </ci>
<ci> i_K_ATP </ci>
<ci> i_KNa </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_cleft </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_JSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_JSR </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci> i_rel </ci>
<ci> i_tr </ci>
</apply>
<apply>
<divide/>
<ci> V_NSR </ci>
<ci> V_JSR </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_NSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_NSR </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_leak </ci>
<ci> i_tr </ci>
</apply>
<ci> i_up </ci>
</apply>
</apply>
</apply>
<apply id="calcium_foot_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_foot </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> i_CaCa </ci>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
<ci> R_A_V </ci>
</apply>
</apply>
</math>
</component>
<!--
The LR-II model begins to define the calcium ion buffers in the myoplasm:
troponin (Tn) and calmodulin (CMDN). The equations needed to calculate
these molecular concentrations are contained within the
"calcium_buffers_in_the_myoplasm" component.
-->
<component name="calcium_buffers_in_the_myoplasm">
<!-- These variables are defined here and used in other components. -->
<variable units="micromolar" public_interface="out" name="K_mTn" initial_value="0.5"/>
<variable units="micromolar" public_interface="out" name="K_mCMDN" initial_value="2.38"/>
<variable units="micromolar" public_interface="out" name="Tn_max" initial_value="70.0"/>
<variable units="micromolar" public_interface="out" name="CMDN_max" initial_value="50.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="micromolar" name="Tn_buff"/>
<variable units="micromolar" name="CMDN_buff"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Tn_buff_calculation">
<eq/>
<ci> Tn_buff </ci>
<apply>
<times/>
<ci> Tn_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mTn </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="CMDN_buff_calculation">
<eq/>
<ci> CMDN_buff </ci>
<apply>
<times/>
<ci> CMDN_max </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mCMDN </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The LR-II model includes a sophisticated model of calcium movement to and
from (and within) the sarcoplasmic reticulum. It includes an additional
current i_leak which describes the leakage of Calcium ions from the NSR to
the myoplasm, as well as a detailed model of the process of calcium-induced
calcium release. These currents are described within the
"calcium_fluxes_in_the_SR" component.
-->
<component name="calcium_fluxes_in_the_SR">
<!-- These variables are defined here and used in other components. -->
<variable units="millimolar_per_millisecond" public_interface="out" name="i_rel"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_up"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_leak"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="i_tr"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="G_rel"/>
<variable units="per_millisecond" name="G_rel_max"/>
<variable units="millisecond" name="tau_on" initial_value="2.0"/>
<variable units="millisecond" name="tau_off" initial_value="2.0"/>
<variable units="millisecond" name="tau_tr" initial_value="180.0"/>
<variable units="millisecond" name="t" initial_value="0.0"/>
<variable units="micromolar" name="K_mrel" initial_value="0.8"/>
<variable units="micromolar" name="delta_Ca_i2"/>
<variable units="micromolar" name="delta_Ca_ith" initial_value="0.18"/>
<variable units="millimolar" name="CSQN_buff"/>
<variable units="millimolar" name="CSQN_max"/>
<variable units="millimolar" name="CSQN_th"/>
<variable units="millimolar" name="K_mCSQN"/>
<variable units="micromolar" name="K_mup"/>
<variable units="per_millisecond" name="K_leak"/>
<variable units="millimolar_per_millisecond" name="I_up" initial_value="0.005"/>
<variable units="millimolar" name="Ca_NSR_max" initial_value="0.15"/>
<variable units="dimensionless" name="calcium_overload"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Ca_JSR"/>
<variable units="millimolar" public_interface="in" name="Ca_NSR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> G_rel </ci>
<apply>
<minus/>
<ci> Ca_JSR </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
<apply id="G_rel_calculation">
<eq/>
<ci> G_rel </ci>
<piecewise>
<piece>
<apply>
<times/>
<ci> G_rel_max </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_Ca_i2 </ci>
<ci> delta_Ca_ith </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> K_mrel </ci>
<ci> delta_Ca_i2 </ci>
</apply>
<ci> delta_Ca_ith </ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_on </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_off </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> calcium_overload </ci>
<cn cellml:units="dimensionless"> 0.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci> G_rel_max </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_on </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> t </ci>
<ci> tau_off </ci>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="G_rel_max_calculation">
<eq/>
<ci> G_rel_max </ci>
<piecewise>
<piece>
<cn cellml:units="per_millisecond"> 0.0 </cn>
<apply>
<lt/>
<ci> CSQN_buff </ci>
<ci> CSQN_th </ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 4.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="CSQN_buff_calculation">
<eq/>
<ci> CSQN_buff </ci>
<apply>
<times/>
<ci> CSQN_max </ci>
<apply>
<divide/>
<ci> Ca_JSR </ci>
<apply>
<plus/>
<ci> Ca_JSR </ci>
<ci> K_mCSQN </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> I_up </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_mup </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_leak_calcualtion">
<eq/>
<ci> i_leak </ci>
<apply>
<times/>
<ci> K_leak </ci>
<ci> Ca_NSR </ci>
</apply>
</apply>
<apply id="K_leak_calculation">
<eq/>
<ci> K_leak </ci>
<apply>
<divide/>
<ci> I_up </ci>
<ci> Ca_NSR_max </ci>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Ca_JSR </ci>
</apply>
<ci> tau_tr </ci>
</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. The "containment" relationship is used to
describe geometric hierarchies - or how components are physically arranged
in relation to eachother.
-->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="Na_channel_states"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
<component_ref component="L_type_Ca_channel_f_Ca_gate"/>
</component_ref>
<component_ref component="T_type_Ca_channel">
<component_ref component="T_type_Ca_channel_b_gate"/>
<component_ref component="T_type_Ca_channel_g_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="Kr_channel_states"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs1_gate"/>
<component_ref component="slow_time_dependent_potassium_current_Xs2_gate"/>
</component_ref>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current"/>
<component_ref component="sodium_activated_potassium_current"/>
<component_ref component="ATP_dependent_potassium_current"/>
<component_ref component="sarcolemmal_calcium_pump"/>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="non_specific_calcium_activated_current"/>
<component_ref component="ionic_concentrations"/>
<component_ref component="calcium_buffers_in_the_myoplasm"/>
<component_ref component="calcium_fluxes_in_the_SR"/>
</component_ref>
</group>
<!--
The following <group> element specifies how the components
representing activation and inactivation coefficients are
encapsulated inside the sodium and potassium channel components.
Encapsulation describes the logical hierarchy of components in a network,
and may or may not reflect their physical arrangement.
-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="Na_channel_states"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
<component_ref component="L_type_Ca_channel_f_Ca_gate"/>
</component_ref>
<component_ref component="T_type_Ca_channel">
<component_ref component="T_type_Ca_channel_b_gate"/>
<component_ref component="T_type_Ca_channel_g_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="Kr_channel_states"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs1_gate"/>
<component_ref component="slow_time_dependent_potassium_current_Xs2_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_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="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="T_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_time_dependent_potassium_current"/>
<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="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_activated_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ATP_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sarcolemmal_calcium_pump"/>
<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="non_specific_calcium_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ionic_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_buffers_in_the_myoplasm"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_fluxes_in_the_SR"/>
<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="fast_sodium_current" component_1="membrane"/>
<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="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="T_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_T" variable_1="i_Ca_T"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="rapid_time_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="slow_time_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_activated_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_KNa" variable_1="i_KNa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="ATP_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K_ATP" variable_1="i_K_ATP"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="membrane"/>
<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="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="sarcolemmal_calcium_pump" component_1="membrane"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane"/>
<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="calcium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="non_specific_calcium_activated_current" component_1="membrane"/>
<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_ns_Ca" variable_1="i_ns_Ca"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- Several variables are passed between the sibling components. -->
<connection>
<map_components component_2="ionic_concentrations" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="fast_sodium_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="L_type_Ca_channel"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="i_CaCa" variable_1="i_CaCa"/>
<map_variables variable_2="i_CaNa" variable_1="i_CaNa"/>
<map_variables variable_2="i_CaK" variable_1="i_CaK"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="T_type_Ca_channel"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="i_Ca_T" variable_1="i_Ca_T"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="rapid_time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_Kr" variable_1="i_Kr"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="slow_time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="i_Ks" variable_1="i_Ks"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_activated_potassium_current"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_KNa" variable_1="i_KNa"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="ATP_dependent_potassium_current"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="i_K_ATP" variable_1="i_K_ATP"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="plateau_potassium_current"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="plateau_potassium_current"/>
<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sarcolemmal_calcium_pump"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="calcium_background_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_potassium_pump"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="non_specific_calcium_activated_current"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="i_ns_Na" variable_1="i_ns_Na"/>
<map_variables variable_2="i_ns_K" variable_1="i_ns_K"/>
</connection>
<connection>
<map_components component_2="non_specific_calcium_activated_current" component_1="L_type_Ca_channel"/>
<map_variables variable_2="gamma_Nao" variable_1="gamma_Nao"/>
<map_variables variable_2="gamma_Nai" variable_1="gamma_Nai"/>
<map_variables variable_2="gamma_Ko" variable_1="gamma_Ko"/>
<map_variables variable_2="gamma_Ki" variable_1="gamma_Ki"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="calcium_buffers_in_the_myoplasm"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Tn_max" variable_1="Tn_max"/>
<map_variables variable_2="CMDN_max" variable_1="CMDN_max"/>
<map_variables variable_2="K_mTn" variable_1="K_mTn"/>
<map_variables variable_2="K_mCMDN" variable_1="K_mCMDN"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="calcium_fluxes_in_the_SR"/>
<map_variables variable_2="i_rel" variable_1="i_rel"/>
<map_variables variable_2="i_tr" variable_1="i_tr"/>
<map_variables variable_2="i_leak" variable_1="i_leak"/>
<map_variables variable_2="i_up" variable_1="i_up"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="Ca_JSR" variable_1="Ca_JSR"/>
<map_variables variable_2="Ca_NSR" variable_1="Ca_NSR"/>
</connection>
<!--
Various variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components component_2="Na_channel_states" component_1="fast_sodium_current"/>
<map_variables variable_2="P_O_Na" variable_1="P_O_Na"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel_d_gate" component_1="L_type_Ca_channel"/>
<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="L_type_Ca_channel_f_gate" component_1="L_type_Ca_channel"/>
<map_variables variable_2="f" variable_1="f"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel_f_Ca_gate" component_1="L_type_Ca_channel"/>
<map_variables variable_2="f_Ca" variable_1="f_Ca"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="T_type_Ca_channel_b_gate" component_1="T_type_Ca_channel"/>
<map_variables variable_2="b" variable_1="b"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="T_type_Ca_channel_g_gate" component_1="T_type_Ca_channel"/>
<map_variables variable_2="g" variable_1="g"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="Kr_channel_states" component_1="rapid_time_dependent_potassium_current"/>
<map_variables variable_2="P_O" variable_1="P_O"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
</connection>
<connection>
<map_components component_2="slow_time_dependent_potassium_current_Xs1_gate" component_1="slow_time_dependent_potassium_current"/>
<map_variables variable_2="Xs1" variable_1="Xs1"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_time_dependent_potassium_current_Xs2_gate" component_1="slow_time_dependent_potassium_current"/>
<map_variables variable_2="Xs2" variable_1="Xs2"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_time_dependent_potassium_current_Xs2_gate" component_1="slow_time_dependent_potassium_current_Xs1_gate"/>
<map_variables variable_2="tau_Xs1" variable_1="tau_Xs1"/>
<map_variables variable_2="Xs_infinity" variable_1="Xs_infinity"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current_K1_gate" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="K1_infinity" variable_1="K1_infinity"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#b1277f56-1afe-4cf4-8acc-ca1ae18e27e2">
<rdf:li>cardiac</rdf:li>
<rdf:li>Markovian Model</rdf:li>
<rdf:li>electrophysiology</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#ab00ca29-f22a-426d-9ece-aaecb00b6d80">
<rdf:li rdf:resource="rdf:#276b7117-9db8-47c7-93c0-0a4616636154"/>
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<dc:publisher>The University of Auckland, Bioengineering Research Group</dc:publisher>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
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The model for cardiac i_Na includes three closed states (C3, C2 and
C1) an open, conducting state (O) and fast and slow inactivation
states (IF and Is, respectively). P_i is the probability of a
channel occupying a particular state (i), which is determined by a
system of linear first order differential equations.
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<dc:title>
The Clancy-Rudy Markovian Model of Wild-Type Ikr Channels in a Cardiac
Ventricular Cell, 2001
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<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
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<cmeta:species>Mammalia</cmeta:species>
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In 1999, Viswanathan, Shaw and Rudy published a paper which updated
the original Luo-Rudy II Model. It describes how the slow component
of the time-dependent potassium current has two activation gates,
one fast (Xs1) and one slow (Xs2). This paper is referenced below.
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<dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
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Changed the model name so the model loads in the database easier.
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In 1995, Zeng, Laurita, Rosenbaum and Rudy published a paper which
updated the original Luo-Rudy II Model. It describes two distinct
delayed rectifier potassium currents, i_Kr and i_Ks. They also
identified a second "T-type" calcium channel. This paper is
referenced below.
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<dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
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<vCard:Other>May</vCard:Other>
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In 2000, Faber and Rudy published a paper which updated the original
Luo-Rudy II Model. It describes an additional, sodium-activated
potassium current. This paper is referenced below.
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<vCard:Other>May</vCard:Other>
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<dc:title>Cardiovascular Research</dc:title>
</rdf:Description>
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<dcterms:W3CDTF>2009-06-05T15:17:33+12:00</dcterms:W3CDTF>
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<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<dcterms:W3CDTF>2002-01-06</dcterms:W3CDTF>
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In 1997, Shaw and Rudy published a paper which modified the
original Luo-Rudy II Model by adding an ATP-dependent potassium
current. This paper is referenced below.
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<dcterms:W3CDTF>2002-02-20</dcterms:W3CDTF>
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Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
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Changed equations after checking them with the mathml validator.
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Added more metadata.
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<vCard:Given>Catherine</vCard:Given>
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<vCard:Other>May</vCard:Other>
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Changed equations of the fast_sodium_current from Hodgkin-Huxley type
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<vCard:Given>Autumn</vCard:Given>
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<vCard:Other>A.</vCard:Other>
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Made MathML id's unique
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<dcterms:W3CDTF>2001-10-19</dcterms:W3CDTF>
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<dcterms:modified rdf:resource="rdf:#07523e1d-8d0f-4fc4-8450-eac9bb9d9451"/>
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Corrected beta_K1 differential equation.
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<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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Removed document type definition as this is declared as optional
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<dcterms:W3CDTF>2001-10-24</dcterms:W3CDTF>
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<dc:title>Cellular consequences of HERG mutations in the long QT syndrome: precursors to sudden cardiac death</dc:title>
<bqs:volume>50</bqs:volume>
<bqs:first_page>301</bqs:first_page>
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<vCard:Given>James</vCard:Given>
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The use of a Markovian model to represent i_Na deviates from the
traditional Hodgkin-Huxley approach used in many ionic models
(including Luo-Rudy II). The Markovian scheme represents distinct
channel states and coupling between these states, which allowed
Clancy and Rudy to relate state-specific kinetic properties of ion
channels to the electophysiological behaviour of the whole cell.
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<dcterms:modified rdf:resource="rdf:#c33b1106-0629-42f6-a75e-b3121375dfac"/>
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Made changes to some of the metadata, bringing them up to date with
the most recent working draft (26th September) of the Metadata
Specification.
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:modified rdf:resource="rdf:#effea2b4-390f-454f-b848-aa0d73f7baed"/>
<rdf:value>
Corrected units.
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<rdf:value>This is the CellML description of Clancy and Rudy's mathematical Markovian model of the wild-type cardiac delayed rectifier current (Ikr). They incorporate this into a comprehensive model of the cardiac ventricular cell, which is based on the modified Luo-Rudy II Model. The use of a Markovian model to represent IKr deviates from the traditional Hodgkin-Huxley approach.</rdf:value>
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<dcterms:W3CDTF>2001-12-10</dcterms:W3CDTF>
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<dcterms:modified rdf:resource="rdf:#3e2dffc0-2367-4def-af47-54ce2db1699d"/>
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Altered some of the connections.
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<dcterms:W3CDTF>2005-04-20</dcterms:W3CDTF>
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<vCard:Given>Colleen</vCard:Given>
<vCard:Family>Clancy</vCard:Family>
<vCard:Other>E</vCard:Other>
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