- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:35:46+12:00
- Desc:
- committing version01 of noble_noble_1984
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/noble_noble_1984/rawfile/ceff1ef8d55005347f94aa517ebf67ac0d37f1b9/noble_noble_1984.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : NN_SAN_model_1984.xml
CREATED : 24th January 2002
LAST MODIFIED : 12th August 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of the 1984 Noble and Noble mathematical model of sino-atrial node electrical activity.
CHANGES:
25/02/2002 - CML - Corrected Cai differential equation.
06/05/2002 - CML - Added some initial values.
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
05/06/2003 - CML - Fixed the MathML in one component.
12/08/2003 - CML - Corrected equations.
--><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="noble_noble_1984_version01" name="noble_noble_1984_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Noble-Noble Model Of Sino-Atrial Node Electrical Activity, 1984</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 1984 D. Noble and S.J. Noble published a mathematical model which describes electrical activity in the sino-atrial node (see <xref linkend="fig_cell_diagram"/> below). Their model is based on the Purkinje fibre model developed by D. DiFrancesco and D. Noble (see <ulink url="${HTML_EXMPL_DFN_MODEL}">The DiFrancesco-Noble Purkinje Fibre Model, 1985</ulink>). Most of the equations of this cardiac cell model remain unchanged. However, based on the results of experimental work, where necessary, certain parameters have been modified in order to make the model appropriate to a sino-atrial node.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A Model of Sino-Atrial Node Electrical Activity Based on a Modification of the DiFrancesco-Noble (1984) Equations, D. Noble and S.J. Noble, <ulink url="http://www.pubs.royalsoc.ac.uk/proc_bio/proc_bio.html">
<emphasis>Proceedings of the Royal Society of London. Series B, Biological Sciences</emphasis>
</ulink>, 222, 295-304. (The <ulink url="http://links.jstor.org/sici?sici=0080-4649%2819840922%29222%3A1228%3C295%3AAMOSNE%3E2.0.CO%3B2-P">full text</ulink> of the article is available to members on the JSTOR website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=6149553&dopt=Abstract">PubMed ID: 6149553</ulink>
</para>
<para>
The raw CellML description of the Noble-Noble sino-atrial node model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${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 NN SAN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="noble_noble_1984.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the NN SAN model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the NN SAN model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the Noble-Noble SAN model. For simplicity, not all the variables are shown.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, are defined some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_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="microS">
<unit units="siemens" prefix="micro"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_cm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="nanoA">
<unit units="ampere" prefix="nano"/>
</units>
<units name="nanoA_per_cm2">
<unit units="ampere" prefix="nano"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule"/>
<unit units="mole" prefix="kilo" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb" exponent="-1"/>
<unit units="mole"/>
</units>
<units name="microlitre">
<unit units="litre" prefix="micro"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="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="-60.0"/>
<variable units="joule_per_kilomole_kelvin" public_interface="out" name="R" initial_value="8.314"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96845.0"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microF_per_cm2" name="C" initial_value="1.0"/>
<variable units="microA_per_cm2" name="i_pulse" initial_value="0.0"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_cm2" public_interface="in" name="i_f"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K1"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_cm2" public_interface="in" name="i_p"/>
<variable units="microA_per_cm2" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_si"/>
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_f </ci>
<apply>
<plus/>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_p </ci>
<ci> i_NaCa </ci>
<ci> i_Na </ci>
<ci> i_si </ci>
<ci> i_pulse </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<!-- The hyperpolarising-activated current (i_f) is a Na-K current. -->
<component cmeta:id="hyperpolarising_activated_current" name="hyperpolarising_activated_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_f"/>
<variable units="microA_per_cm2" public_interface="out" name="i_fNa"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="microA_per_cm2" public_interface="out" name="i_fK"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microS" name="g_f_Na" initial_value="6.0"/>
<variable units="microS" name="g_f_K" initial_value="6.0"/>
<variable units="microA_per_cm2" name="I_f"/>
<variable units="concentration_units" name="Km_f" initial_value="45.0"/>
<!-- 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="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_f_calculation">
<eq/>
<ci> i_f </ci>
<apply>
<times/>
<ci> y </ci>
<ci> I_f </ci>
</apply>
</apply>
<apply id="i_fNa_calculation">
<eq/>
<ci> i_fNa </ci>
<apply>
<minus/>
<ci> i_f </ci>
<ci> i_fK </ci>
</apply>
</apply>
<apply id="i_fK_calculation">
<eq/>
<ci> i_fK </ci>
<apply>
<minus/>
<ci> i_f </ci>
<ci> i_fNa </ci>
</apply>
</apply>
<apply id="I_f_calculation">
<eq/>
<ci> I_f </ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> g_f_K </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> g_f_Na </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Na_calculation">
<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K_calculation">
<eq/>
<ci> E_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Kc </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The y gate is encapsulated within the hyperpolarising-activated current.
-->
<component name="hyperpolarising_activated_current_y_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.007"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_y"/>
<variable units="per_millisecond" name="beta_y"/>
<!-- These variables are imported from parent and sibling components. -->
<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="alpha_y_calculation">
<eq/>
<ci> alpha_y </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.067 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 52.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_y_calculation">
<eq/>
<ci> beta_y </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 2.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 52.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.2 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 52.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dy_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_y </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> y </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_y </ci>
<ci> y </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The time-dependent (delayed) potassium current is equivalent to the plateau
potassium current (1) in the MNT model. It is controlled by a single gate,
x.
-->
<component cmeta:id="time_dependent_potassium_current" name="time_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="K"/>
<variable units="microA_per_cm2" name="I_K"/>
<variable units="nanoA" name="i_K_max" initial_value="20.0"/>
<!-- 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="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> x </ci>
<ci> I_K </ci>
</apply>
</apply>
<apply id="I_K_calculation">
<eq/>
<ci> I_K </ci>
<apply>
<times/>
<ci> i_K_max </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 140.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The x gate encapsulated within the time-dependent potassium current. -->
<component name="time_dependent_potassium_current_x_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="x" initial_value="0.54"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_x"/>
<variable units="per_millisecond" name="beta_x"/>
<!-- 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="alpha_x_calculation">
<eq/>
<ci> alpha_x </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 0.5 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 22.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 22.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_x_calculation">
<eq/>
<ci> beta_x </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 0.178 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 22.0 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 22.0 </cn>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dx_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_x </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_x </ci>
<ci> x </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The time-independent (background) potassium current (i_K1). -->
<component cmeta:id="time_independent_potassium_current" name="time_independent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_K1"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microS" name="g_K1" initial_value="0.75"/>
<variable units="concentration_units" name="Km_K1" initial_value="10.0"/>
<!-- 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_K"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_K1 </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<ci> E_K </ci>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_Na_b"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microS" name="g_Nab" initial_value="0.07"/>
<!-- 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_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_b_calculation">
<eq/>
<ci> i_Na_b </ci>
<apply>
<times/>
<ci> g_Nab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The calcium background current is in the same form as the sodium background
current.
-->
<component name="calcium_background_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_Ca_b"/>
<variable units="millivolt" public_interface="out" name="E_Ca"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microS" name="g_Cab" initial_value="0.01"/>
<!-- 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="concentration_units" public_interface="in" name="Cai"/>
<variable units="concentration_units" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_b_calculation">
<eq/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<ci> g_Cab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca </ci>
</apply>
</apply>
</apply>
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The Na-K exchange pump couples the free energy released by the hydrolysis of
ATP to transfer sodium and potassium ions across the cell membrane against
their electrochemical gradients. 3 Na ions are pumped out for every 2 K
ions pumped into the cell.
-->
<component name="sodium_potassium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_p"/>
<!-- This variable is defined here and only used internally. -->
<variable units="nanoA" name="I_p" initial_value="50.0"/>
<variable units="concentration_units" name="K_mK" initial_value="1.0"/>
<variable units="concentration_units" name="K_mNa" initial_value="40.0"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="concentration_units" public_interface="in" name="Nai"/> <variable units="concentration_units" public_interface="in" name="Kc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_calculation">
<eq/>
<ci> i_p </ci>
<apply>
<times/>
<ci> I_p </ci>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> K_mK </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Nai </ci>
<apply>
<plus/>
<ci> K_mNa </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The equation for the Na-Ca exchange current assumes that i_NaCa depends
soley on the sodium and calcium ion electrochemical gradients and the
transmembrane potential. The stoichiometry of the exchange is 3Na : 1Ca,
producing a net outward current.
-->
<component cmeta:id="Na_Ca_exchanger" name="Na_Ca_exchanger">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_NaCa"/>
<variable units="dimensionless" public_interface="out" name="n_NaCa" initial_value="3.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="K_NaCa" initial_value="0.002"/>
<variable units="millivolt" name="E_NaCa"/>
<variable units="dimensionless" name="d_NaCa" initial_value="0.0001"/>
<variable units="dimensionless" name="gamma" initial_value="0.5"/>
<variable units="dimensionless" name="n"/>
<!-- 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="concentration_units" public_interface="in" name="Cao"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<!-- The current is given as: -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!-- <apply id="Na_Ca_exchanger_calculation1"><eq />
<ci> i_NaCa </ci>
<apply><times />
<ci> K_NaCa </ci>
<apply><sinh />
<apply><divide />
<apply><times />
<apply><minus />
<ci> V </ci>
<ci> E_NaCa </ci>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply> -->
<apply id="Na_Ca_exchanger_calculation2">
<eq/>
<ci> i_NaCa </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> gamma </ci>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<ci> n </ci>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> gamma </ci>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<ci> n </ci>
</apply>
<ci> Cai </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> d_NaCa </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> Cai </ci>
<apply>
<power/>
<ci> Nao </ci>
<ci> n </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Cao </ci>
<apply>
<power/>
<ci> Nai </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Cai </ci>
<cn cellml:units="concentration_units"> 0.0069 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="E_NaCa_calculation">
<eq/>
<ci> E_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> n_NaCa </ci>
<ci> E_Na </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> E_Ca </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model retains a two-variable mode; of the sodium kinetics, with new
equations for the gates m and h. It is acknowledged however that the model
does not represent the slower components of Na inactivation and recovery.
It is also assumed that the sodium channel shows a 12% permeability to k
ions.
-->
<component cmeta:id="fast_sodium_current" name="fast_sodium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_Na"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microS" name="g_Na" initial_value="1.25"/>
<variable units="millivolt" name="E_mh" initial_value="40.0"/>
<!-- 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="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the sodium current in terms
of the conductance, the membrane voltage, and the gate variables.
-->
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_mh </ci>
</apply>
</apply>
</apply>
<apply id="E_mh_calculation">
<eq/>
<ci> E_mh </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci> Nao </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Nai </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_m_gate" is the activation m gate encapsulated
inside the "fast sodium current" component.
-->
<component name="fast_sodium_current_m_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.076"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 200.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 41.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 41.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 8000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.056 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 66.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_h_gate" component is the inactivation h gate
encapsulated in the "fast sodium current" component.
-->
<component name="fast_sodium_current_h_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.015"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 20.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.125 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 2000.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 320.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
Like the MNT model, the kinetics of the secondary inward current are still
described in terms of two gate variables d and f, but the time constants for
activation and inactivation processes are much shorter. The fast component,
i_si of this current has been divided into the individual ion movements of
Ca, K and Na.
-->
<component name="secondary_inward_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_si"/>
<variable units="microA_per_cm2" public_interface="out" name="i_siCa"/>
<variable units="microA_per_cm2" public_interface="out" name="i_siK"/>
<variable units="microA_per_cm2" public_interface="out" name="i_siNa"/>
<!-- This variable is defined here and only used internally. -->
<variable units="dimensionless" name="P_si" initial_value="7.5"/>
<!-- 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="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<variable units="concentration_units" public_interface="in" name="Kc"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Cao"/>
<variable units="concentration_units" public_interface="in" private_interface="out" name="Cai"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_si_calculation">
<eq/>
<ci> i_si </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply>
<plus/>
<ci> i_siCa </ci>
<ci> i_siK </ci>
<ci> i_siNa </ci>
</apply>
</apply>
</apply>
<apply id="i_siCa_calculation">
<eq/>
<ci> i_siCa </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> P_si </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Cai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 100.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Cao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_siK_calculation">
<eq/>
<ci> i_siK </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.01 </cn>
<ci> P_si </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_siNa_calculation">
<eq/>
<ci> i_siNa </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.01 </cn>
<ci> P_si </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Nao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_d_gate" component is the d gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_d_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.0011"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "secondary_inward_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="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>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 30.0 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -12.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 24.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_f_gate" component is the f gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_f_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.785"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_f"/>
<variable units="per_millisecond" name="beta_f"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The rate constants on the f gate are functions of membrane voltage.
-->
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -6.25 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.25 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 50.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model also includes a description of Ca-dependent inactivation.
When calcium ions bind to a regulatory site on the channel protein, they
induce a conformational change such that the channel no longer conducts,
and the secondary current slows or ceases.
-->
<component name="secondary_inward_current_f2_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f2" initial_value="0.785"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_f2"/>
<variable units="per_millisecond" name="beta_f2"/>
<variable units="concentration_units" name="K_mf2" initial_value="0.0005"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="df2_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f2 </ci>
</apply>
<apply>
<minus/>
<ci> alpha_f2 </ci>
<apply>
<times/>
<ci> f2 </ci>
<apply>
<plus/>
<ci> alpha_f2 </ci>
<ci> beta_f2 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_f2_calculation">
<eq/>
<ci> alpha_f2 </ci>
<cn cellml:units="dimensionless"> 5.0 </cn>
</apply>
<apply id="beta_f2_calculation">
<eq/>
<ci> beta_f2 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Cai </ci>
<ci> alpha_f2 </ci>
</apply>
<ci> K_mf2 </ci>
</apply>
</apply>
</math>
</component>
<!--
Additionally, the DFN model attempted to quantify the changes in several ion
concentrations, as well as the [Ca]i of earlier models.
-->
<component name="extracellular_sodium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Nao" initial_value="140.0"/>
</component>
<component name="intracellular_sodium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Nai" initial_value="7.5"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microlitre" name="Vi"/>
<!-- 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_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_cm2" public_interface="in" name="i_siNa"/>
<variable units="microA_per_cm2" public_interface="in" name="i_p"/>
<variable units="microA_per_cm2" public_interface="in" name="i_fNa"/>
<variable units="microA_per_cm2" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Na_b </ci>
<ci> i_fNa </ci>
<ci> i_siNa </ci>
<apply>
<times/>
<ci> i_p </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaCa </ci>
<apply>
<divide/>
<ci> n_NaCa </ci>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_calcium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Cao" initial_value="2.0"/>
</component>
<!--
Changes in [Ca]i were first modelled in the BR model and has only been
slightly developed in the DFN model. Calcium is sequestered in the
sarcoplasmic reticulum ([Ca]up). A fraction is transferred to a release
store in the junctional SR ([Ca]rel) before being released into the
intracellular space. The Ca concentrations in each of these various
stores is modelled together with the transfer between the calcium sites
and the ca transfer across the cell membrane via the other ionic
currents.
-->
<component cmeta:id="intracellular_calcium_concentration" name="intracellular_calcium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Cai" initial_value="0.000058"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microlitre" name="V_up"/>
<variable units="microlitre" name="V_rel"/>
<variable units="microlitre" name="Vi"/>
<variable units="microA_per_cm2" name="i_up"/>
<variable units="microA_per_cm2" name="i_tr"/>
<variable units="microA_per_cm2" name="i_rel"/>
<variable units="per_millisecond" name="alpha_up"/>
<variable units="per_millisecond" name="beta_up"/>
<variable units="per_millisecond" name="alpha_tr"/>
<variable units="per_millisecond" name="beta_tr"/>
<variable units="per_millisecond" name="alpha_rel"/>
<variable units="per_millisecond" name="beta_rel"/>
<variable units="concentration_units" name="Ca_up" initial_value="1.98"/>
<variable units="concentration_units" name="Ca_rel" initial_value="0.55"/>
<variable units="concentration_units" name="Ca_up_max" initial_value="5.0"/>
<variable units="concentration_units" name="K_mCa" initial_value="2.0"/>
<variable units="dimensionless" name="p" initial_value="0.785"/>
<variable units="per_millisecond" name="alpha_p"/>
<variable units="per_millisecond" name="beta_p"/>
<variable units="millisecond" name="tau_up" initial_value="0.005"/>
<variable units="millisecond" name="tau_rep" initial_value="0.2"/>
<variable units="millisecond" name="tau_rel" initial_value="0.01"/>
<variable units="dimensionless" name="rCa" initial_value="2.0"/>
<!-- 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="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_cm2" public_interface="in" name="i_siCa"/>
<variable units="microA_per_cm2" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> alpha_up </ci>
<ci> Cai </ci>
<apply>
<minus/>
<ci> Ca_up_max </ci>
<ci> Ca_up </ci>
</apply>
</apply>
</apply>
<apply id="alpha_up_calculation">
<eq/>
<ci> alpha_up </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Vi </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> tau_up </ci>
<ci> Ca_up_max </ci>
</apply>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<times/>
<ci> alpha_tr </ci>
<ci> p </ci>
<apply>
<minus/>
<ci> Ca_up </ci>
<ci> Ca_rel </ci>
</apply>
</apply>
</apply>
<apply id="alpha_tr_calculation">
<eq/>
<ci> alpha_tr </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
<ci> tau_rep </ci>
</apply>
</apply>
<apply id="alpha_p_calculation">
<eq/>
<ci> alpha_p </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -0.625 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.25 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_p_calculation">
<eq/>
<ci> beta_p </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 5.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> alpha_rel </ci>
<ci> Ca_rel </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<ci> rCa </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<ci> rCa </ci>
</apply>
<ci> K_mCa </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_rel_calculation">
<eq/>
<ci> alpha_rel </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
<ci> tau_rel </ci>
</apply>
</apply>
<apply id="dp_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> p </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_p </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> p </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_p </ci>
<ci> p </ci>
</apply>
</apply>
</apply>
<apply id="Ca_up_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_up </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_up </ci>
<ci> i_tr </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_up </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="V_up_calculation">
<eq/>
<ci> V_up </ci>
<apply>
<times/>
<ci> Vi </ci>
<cn cellml:units="dimensionless"> 0.05 </cn>
</apply>
</apply>
<apply id="Ca_rel_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_rel </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_tr </ci>
<ci> i_rel </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="V_rel_calculation">
<eq/>
<ci> V_rel </ci>
<apply>
<times/>
<ci> Vi </ci>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
</apply>
<apply id="Cai_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_siCa </ci>
<ci> i_Ca_b </ci>
<ci> i_up </ci>
</apply>
<apply>
<plus/>
<ci> i_rel </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model assumes that the potassium ion concentration is homogeneous
throughout the three-compartment model.
-->
<component name="extracellular_potassium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Kc" initial_value="3.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microlitre" name="V_e"/>
<variable units="concentration_units" name="Kb" initial_value="3.0"/>
<variable units="microA_per_cm2" name="i_mK"/>
<variable units="per_millisecond" name="P" initial_value="200.0"/>
<variable units="microA_per_cm2" name="i_K_b"/>
<!-- 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_cm2" public_interface="in" name="i_K1"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K"/>
<variable units="microA_per_cm2" public_interface="in" name="i_fK"/>
<variable units="microA_per_cm2" public_interface="in" name="i_siK"/>
<variable units="microA_per_cm2" public_interface="in" name="i_p"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Kc_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Kc </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> P </ci>
<apply>
<minus/>
<ci> Kc </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> i_mK </ci>
<apply>
<times/>
<ci> V_e </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_mK_calculation">
<eq/>
<ci> i_mK </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_K1 </ci>
<ci> i_K </ci>
<ci> i_fK </ci>
<ci> i_siK </ci>
<ci> i_K_b </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_p </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The intracellular potassium concentration is related to the total potassium
ion membrane flux.
-->
<component name="intracellular_potassium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Ki" initial_value="140.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microlitre" name="Vi"/>
<variable units="microA_per_cm2" name="i_mK"/>
<!-- 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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ki_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_mK </ci>
</apply>
<apply>
<times/>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The following <group> element specifies a single containment hierarchy
that encompasses all of the components in the model, with the exception of
the "environment" component.
-->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current"/>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate"/>
<component_ref component="secondary_inward_current_f_gate"/>
<component_ref component="secondary_inward_current_f2_gate"/>
</component_ref>
<component_ref component="intracellular_sodium_concentration"/>
<component_ref component="extracellular_sodium_concentration"/>
<component_ref component="intracellular_calcium_concentration"/>
<component_ref component="extracellular_calcium_concentration"/>
<component_ref component="extracellular_potassium_concentration"/>
<component_ref component="intracellular_potassium_concentration"/>
</component_ref>
</group>
<!--
The following <group> element specifies how the components representing
activation and inactivation gates are encapsulated inside their parent
currents.
-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate"/>
<component_ref component="secondary_inward_current_f_gate"/>
<component_ref component="secondary_inward_current_f2_gate"/>
</component_ref>
</group>
<!--
"time" is passed from the "environment" component into the
"membrane" and current components.
-->
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="secondary_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<!--
Several variables are passed between the "membrane" and its sub-components.
-->
<connection>
<map_components component_2="membrane" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_f" variable_1="i_f"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_independent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="calcium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_potassium_pump"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="fast_sodium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="secondary_inward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_si" variable_1="i_si"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_fK" variable_1="i_fK"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="i_fNa" variable_1="i_fNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="calcium_background_current"/>
<map_variables variable_2="E_Ca" variable_1="E_Ca"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siCa" variable_1="i_siCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siK" variable_1="i_siK"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siNa" variable_1="i_siNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<!--
Several variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components component_2="hyperpolarising_activated_current_y_gate" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="y" variable_1="y"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_dependent_potassium_current_x_gate" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="x" variable_1="x"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="m" variable_1="m"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_d_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_f_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="f" variable_1="f"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_f2_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="f2" variable_1="f2"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#cdff751e-73d8-442c-8d01-bfbc2f213fa0">
<rdf:li>Sinoatrial Node</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>electrophysiology</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#891b02d8-144e-46e5-b9f0-1d5c5ad0bbe3">
<rdf:li rdf:resource="rdf:#e146bd37-d45c-4b7d-a83e-aa0cafb9004f"/>
<rdf:li rdf:resource="rdf:#f209769a-d840-469c-8dab-7a01ac522291"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#2fc7354d-23c7-489b-b45c-0f81847efb57">
<dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#410b7ab4-fe6b-4aba-8f59-3962245a5bbc">
<vCard:Given>S</vCard:Given>
<vCard:Family>Noble</vCard:Family>
<vCard:Other>J</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ee6fb2e9-9151-4aa7-b145-b9f6d3fc1c4e">
<rdf:value>
The delayed K+ current is activated in a similar voltage range in
Purkinje fibres and in sino-atrial nodes but the kinetics are
significantly faster in the sino-atrial node. The DiFrancesco-Noble equation for the time-dependent potassium current is replaced in
this model with equations based on the sino-atrial node results.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4682deea-22fd-4124-a455-5d78cb04de2f">
<rdf:value>
The equations for calcium uptake and release are the same as the
DiFrancesco-Noble model. However, it was found that in sino-atrial
nodes, relaxation starts before the end of repolarisation. The
intracellular Cai transient much reach its peak early in the action
potential and decline to small values during repolarisation. To
achieve this result, some parameters of the DiFrancesco-Noble model
were significantly reduced, including the uptake time constant
(tau_up) and the repriming time constant (tau_rep).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_calcium_concentration">
<cmeta:comment rdf:resource="rdf:#4682deea-22fd-4124-a455-5d78cb04de2f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a07ad919-d1c1-4242-afd0-6f4e755b04af">
<vCard:Given>Denis</vCard:Given>
<vCard:Family>Noble</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0669186f-b504-492d-acae-52d42bdfa252">
<rdf:value>
The fast sodium current is present in the sino-atrial node, but it
is much smaller than the current found in Purkinje fibres. To
adjust for this difference in magnitude, g_Na has been reduced from
750 to 1.25 microS.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d8ccf1ba-cfc3-45d4-85a2-06f7cefc7bc2">
<dcterms:W3CDTF>2003-06-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ea59716e-f738-49d2-a82d-64dabc899595">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_potassium_current">
<cmeta:comment rdf:resource="rdf:#ee6fb2e9-9151-4aa7-b145-b9f6d3fc1c4e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51726a69-7dc4-4e03-92d4-80e65cbd2835">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#86c9bf29-14c1-4225-8fe3-00ca6625b145">
<dcterms:W3CDTF>2003-06-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f209769a-d840-469c-8dab-7a01ac522291">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#410b7ab4-fe6b-4aba-8f59-3962245a5bbc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#60af5fc1-ec9b-48f1-921e-bca12fe34026">
<dcterms:modified rdf:resource="rdf:#86c9bf29-14c1-4225-8fe3-00ca6625b145"/>
<rdf:value>
Corrected equations: alpha_y and beta_y in hyperpolarising_activated_current_y_gate, and beta_d in the secondary_inward_current_d_gate component. Removed i_NaCa calculation1 by commenting it out, and corrected i_NaCa calculation2 in Na_Ca_exchanger component.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a4df7320-1962-47fb-bfb2-ad4720c48d69"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c2551b5e-a8cb-4dfe-9579-7765a08692f4">
<dc:title>
Proceedings of the Royal Society of London. Series B, Biological
Sciences
</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#33b759b6-1277-4c19-8549-8f7fe49a9ec3">
<vCard:N rdf:resource="rdf:#7f64765d-55c2-409b-a838-bc4b1ebc7b37"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bdaf52e2-5e09-4491-9e8d-7db2843aa432">
<vCard:N rdf:resource="rdf:#3265b5af-e2e9-4644-bdf8-92c03b4751a5"/>
</rdf:Description>
<rdf:Description rdf:about="#noble_noble_1984_version01">
<dc:title>
The Noble-Noble Model of Sino-atrial Node Electrical Activity, 1984
</dc:title>
<cmeta:bio_entity>Sinoatrial Node Cell</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#a683bab1-2589-4138-a136-1c06df37f85a"/>
<bqs:reference rdf:resource="rdf:#4b4b5684-a3e3-4454-b435-e7942bd130f5"/>
<bqs:reference rdf:resource="rdf:#a64f21c2-57bc-4fae-9b71-a8006beb7b47"/>
<cmeta:species>Mammalia</cmeta:species>
</rdf:Description>
<rdf:Description rdf:about="#hyperpolarising_activated_current">
<cmeta:comment rdf:resource="rdf:#c3cf7ea4-35dc-4d1a-9569-412f8cb8f8b1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#223ea2ac-6385-476a-a996-342913c57b46">
<vCard:N rdf:resource="rdf:#e6f83f67-d092-403b-b808-fec010fb04bf"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#67f85afd-5158-4de2-a2fe-d53adb3f3ed7">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9598d752-181b-4c6b-9d6a-312a3e6bfe89">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a64f21c2-57bc-4fae-9b71-a8006beb7b47">
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Added some initial values from Penny Noble's documentation.
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dc:title>
A Model of Sino-Atrial Node Electrical Activity Based on a Modification of the DiFrancesco-Noble (1984) Equations
</dc:title>
<bqs:volume>222</bqs:volume>
<bqs:first_page>295</bqs:first_page>
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<bqs:last_page>304</bqs:last_page>
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<rdf:Description rdf:about="#Na_Ca_exchanger">
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This is the CellML description of Noble and Noble's mathematical model
of sino-atrial node electrical activity based on a modification of the
Difrancesco-Noble cardiac cell model. The modifications are based on
experimental work and they reproduce action potential and pacemaker
activity in the node. Most of the equations remain unchanged but
parameters have been altered to make them appropriate to the
sino-atrial node.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
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<dcterms:W3CDTF>2002-05-06</dcterms:W3CDTF>
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<rdf:value>
For the background K+ current, the Noble-Noble model used the same
equation as the DiFrancesco-Noble model but with the maximum value
for g_K1 greatly reduced from 920 to 10 microS.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3265b5af-e2e9-4644-bdf8-92c03b4751a5">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c3cf7ea4-35dc-4d1a-9569-412f8cb8f8b1">
<rdf:value>
In this case, the equations of the DiFrancesco-Noble model with the
kinetics speeded up by a factor of two produced a realistic
simulation of the hyperpolarising-activated current in the
sino-atrial node.
</rdf:value>
</rdf:Description>
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<dcterms:modified rdf:resource="rdf:#2fc7354d-23c7-489b-b45c-0f81847efb57"/>
<rdf:value>
Corrected the Cai differential equations.
</rdf:value>
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<dcterms:W3CDTF>1984-09-22</dcterms:W3CDTF>
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:Description rdf:about="rdf:#ed98bb3d-057e-4ff9-976d-8b184a59586a">
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Like the DiFrancesco-Noble model, two alternative equations for the
i_NaCa current are given by the Noble-Noble model. The simplest
makes the current a sine function of the total energy gradient. The more realistic model uses an equation which is likely to reproduce
better dependence of i_NaCa on intracellular calcium ions.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current">
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<rdf:value>
Fixed maths: beta_h_calculation in fast_sodium_current_h_gate.
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<cmeta:modifier rdf:resource="rdf:#bdaf52e2-5e09-4491-9e8d-7db2843aa432"/>
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<dcterms:W3CDTF>2002-01-24</dcterms:W3CDTF>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<rdf:Description rdf:about="#time_independent_potassium_current">
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</model>
