- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 00:11:47+12:00
- Desc:
- committing version01 of mcallister_noble_tsien_1975
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/mcallister_noble_tsien_1975/rawfile/d573f657fa87d081b750bf7a652b98ac3e7e119d/mcallister_noble_tsien_1975.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : MNT_purkinje_fibre_model_1975.xml
CREATED : September 2001
LAST MODIFIED : 5th April 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16
January 2002.
DESCRIPTION : This file contains a CellML description of cardiac action
potentials in purkinje fibres, based on the McAllister-Noble-Tsien model, 1975.
CHANGES:
19/10/2001 - CML - Removed document type definition as this is declared as
optional according to the W3C recommendation.
24/10/2001 - CML - Made changes to some of the metadata, bringing them up to
date with the most recent working draft (26th September) of
the Metadata specification.
10/12/2001 - CML - Changed equations after checking with the mathml validator.
03/01/2002 - CML - Altered parent-child relationships as x1 and x2 were made
to be gates of the plateau potassium currents.
20/01/2002 - AAC - Updated metadata to conform to the 16/01/2002 CellML
Metadata Specification.
28/02/2002 - CML - Corrected units.
19/07/2002 - CML - Added more metadata.
05/04/2003 - AAC - Changed the model name so the model loads in the database
easier.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="MNT_purkinje_fibre_model_1975" name="mcallister_noble_tsien_1975_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>McAllister-Noble-Tsien Purkinje Fibre Model 1975</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>
Following <ulink url="${HTML_EXMPL_N_MODEL}">D. Noble's 1962 model</ulink> of cardiac action potentials in Purkinje fibres, the next significant development in cardiac membrane modelling occurred when R.E. McAllister, D. Noble and R.W. Tsien (1975) published a paper which formulated new ionic current equations based on new experimental data. The description of the kinetics of the currents is still based on the Hodgkin-Huxley formalism, but the currents themselves incorporate some significant new changes, and the total ionic current is broken down into nine discrete, individual ionic fluxes (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.jphysiol.org/cgi/content/abstract/251/1/1b">Reconstruction of the Electrical Activity of Cardiac Purkinje Fibres</ulink>, McAllister, R.E. Noble, D. and Tsien, R.W. 1975, <ulink url="http://www.jphysiol.org/">
<emphasis>Journal of Physiology</emphasis>
</ulink>, 251, 1-59. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=1185607&dopt=Abstract">PubMed ID: 1185607</ulink>
</para>
<para>
The raw CellML description of the McAllister-Noble-Tsien model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${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 MNT model showing ionic currents across the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="mcallister_noble_tsien_1975.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the MNT model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the MNT model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the McAllister-Noble-Tsien model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the <ulink url="${HTML_EXMPL_GRAPHICAL_NOTATION}">notation guide</ulink>. For simplicity, not all the variables are shown.</caption>
</informalfigure>
<para>
The membrane physically contains the currents as indicated by the blue arrows in <xref linkend="fig_cellml_rendering"/>. The currents act independently and are not connected to each other. Several of the channels encapsulate <emphasis>and</emphasis> contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.
</para>
<para>
The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.
</para>
</sect1>
</article>
</documentation>
<!--
Below, are defined some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_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_cm2">
<unit units="siemens" prefix="milli"/>
<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_cm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</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"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microF_per_cm2" name="C" initial_value="10.0"/>
<!-- 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_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_si"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K2"/>
<variable units="microA_per_cm2" public_interface="in" name="i_x1"/>
<variable units="microA_per_cm2" public_interface="in" name="i_x2"/>
<variable units="microA_per_cm2" public_interface="in" name="i_qr"/>
<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_Cl_b"/>
<!--
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>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_si </ci>
<ci> i_K2 </ci>
<ci> i_x1 </ci>
<ci> i_x2 </ci>
<ci> i_qr </ci>
<ci> i_K1 </ci>
<ci> i_Na_b </ci>
<ci> i_Cl_b </ci>
</apply>
<ci> C </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current" component contains the differential equations
governing the influx of sodium ions through the cell surface membrane
into the cell.
-->
<component name="fast_sodium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na" initial_value="40.0"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_cm2" name="g_Na" initial_value="150.0"/>
<!--
Time is imported from the "environment", and membrane potential is
imported from the "membrane" component. These variables are used in the
"sodium_current" parent component, which also acts as an interface,
passing the variables to its encapsulated gate components.
-->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<!-- 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_Na </ci>
</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"/>
<!-- 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">
<!--
The rate constants on the m, h and j gates are functions
of membrane voltage.
-->
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 40.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 72.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.86 </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"/>
<!-- 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"> 0.0085 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 71.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.435 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 2.5 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.2 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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>
<!--
The secondary (or sometimes slow) inward current activates much more slowly
than the sodium current and it is responsible for holding up the plateau
after the initial activation and for controlling the duration of the action
potential. At the time of this model, it was assumed that the flux of both
Na and Ca ions through the cell membrane was responsible for this current.
This channel has an activation gate d and an inactivation gate f. It was
observed in earlier experiments that a portion of this current would not
completely inactivate. This is represented by the second term in the
secondary current equation which has an activation variable d1, but no
deactivation variable.
-->
<component name="secondary_inward_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_si"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_cm2" name="g_si" initial_value="0.8"/>
<variable units="milliS_per_cm2" name="g_si_" initial_value="0.04"/>
<variable units="millivolt" name="E_si" initial_value="70.0"/>
<!--
Time is imported from the "environment", and membrane potential is
imported from the "membrane" component. These variables are used in the
"secondary_inward_current" parent component, which also acts as an
interface, passing the variables to its encapsulated gate component.
-->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<!-- 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="d1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the secondary inward current in terms
of the conductance, the membrane voltage and the gate variables.
-->
<apply id="i_si_calculation">
<eq/>
<ci> i_si </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> g_si </ci>
<ci> d </ci>
<ci> f </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_si </ci>
</apply>
</apply>
<apply>
<times/>
<ci> g_si_ </ci>
<ci> d1 </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_si </ci>
</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"/>
<!-- 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 "slow_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>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="millivolt"> 500.0 </cn>
<apply>
<minus/>
<cn cellml:units="millisecond"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.02 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 11.26 </cn>
</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="0.994"/>
<!-- 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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The rate constants on the f gate are functions of membrane voltage.
-->
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.000987 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 0.02 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 26.0 </cn>
</apply>
<cn cellml:units="millivolt"> 11.5 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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 "secondary_inward_current_d1_gate" component is the d1 gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_d1_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="d1"/>
<!-- These variables are imported from other 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">
<!-- d1 can be calculated by the following time-independent equation. -->
<apply id="d1_calculation">
<eq/>
<ci> d1 </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"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.667 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The pacemaker potassium current describes an outward flux of potassium ions
in terms of a single gate variable, s.
-->
<component name="pacemaker_potassium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_K2"/>
<variable units="microA_per_cm2" public_interface="out" name="I_K2"/>
<!-- This variable is defined here and only used internally. -->
<variable units="millivolt" name="E_K" initial_value="-110.0"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K2_calculation">
<eq/>
<ci> i_K2 </ci>
<apply>
<times/>
<ci> I_K2 </ci>
<ci> s </ci>
</apply>
</apply>
<apply id="I_K2_calculation">
<eq/>
<ci> I_K2 </ci>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 2.8 </cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.5 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The s gate component is encapsulated within the pacemaker potassium current.
-->
<component name="pacemaker_potassium_current_s_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="s"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_s"/>
<variable units="per_millisecond" name="beta_s"/>
<variable units="millivolt" name="E_s" initial_value="-52.0"/>
<!-- 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">
<!--
The rate constants on the s gate are functions of membrane voltage.
-->
<apply id="alpha_s_calculation">
<eq/>
<ci> alpha_s </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.001 </cn>
<apply>
<minus/>
<ci> V </ci>
<ci> E_s </ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_s </ci>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_s_calculation">
<eq/>
<ci> beta_s </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.00005 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_s </ci>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="ds_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> s </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_s </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> s </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_s </ci>
<ci> s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The equations for the plateau potassium currents (x1 and x2) are based on
experiments performed by Noble and Tsien (1969) which showed that additional
potassium currents were activated in the plateau range of potentials. They
appear to play an essential role in membrane repolarisation.
-->
<component name="plateau_potassium_current1">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_x1"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microA_per_cm2" name="I_x1"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="x1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_x1_calculation">
<eq/>
<ci> i_x1 </ci>
<apply>
<times/>
<ci> x1 </ci>
<ci> I_x1 </ci>
</apply>
</apply>
<apply id="I_x1_calculation">
<eq/>
<ci> I_x1 </ci>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 1.2 </cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 95.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 45.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The x1 gate component is encapsulated within the plateau potassium current
1.
-->
<component name="plateau_potassium_current1_x1_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="x1"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_x1"/>
<variable units="per_millisecond" name="beta_x1"/>
<!-- 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_x1_calculation">
<eq/>
<ci> alpha_x1 </ci>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 5e-4 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.1 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_x1_calculation">
<eq/>
<ci> beta_x1 </ci>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 0.0013 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dx1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_x1 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_x1 </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current2">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_x2"/>
<!-- This variable is defined here and only used internally. -->
<variable units="microA_per_cm2" name="I_x2"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="x2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_x2_calculation">
<eq/>
<ci> i_x2 </ci>
<apply>
<times/>
<ci> x2 </ci>
<ci> I_x2 </ci>
</apply>
</apply>
<apply id="I_x2_calculation">
<eq/>
<ci> I_x2 </ci>
<apply>
<plus/>
<cn cellml:units="microA_per_cm2"> 25.0 </cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.385 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The x2 gate component is encapsulated within the plateau potassium current
2.
-->
<component name="plateau_potassium_current2_x2_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="x2"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_x2"/>
<variable units="per_millisecond" name="beta_x2"/>
<!-- 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_x2_calculation">
<eq/>
<ci> alpha_x2 </ci>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 0.000127 </cn>
<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"> 19.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_x2_calculation">
<eq/>
<ci> beta_x2 </ci>
<apply>
<times/>
<cn cellml:units="microA_per_cm2"> 0.0003 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dx2_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_x2 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x2 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_x2 </ci>
<ci> x2 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The transient chloride current (i_qr) is responsible for the rapid
repolarisation from the peak of the depolarisation spike of the action
potential, to the start of the plateau. The current has 2 gating variables,
q and r.
-->
<component name="transient_chloride_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_qr"/>
<variable units="millivolt" public_interface="out" name="E_Cl" initial_value="-70.0"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_cm2" name="g_qr" initial_value="2.5"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="q"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_qr_calculation">
<eq/>
<ci> i_qr </ci>
<apply>
<times/>
<ci> g_qr </ci>
<ci> q </ci>
<ci> r </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Cl </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The encapsulated q gate. -->
<component name="transient_chloride_current_q_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="q"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_q"/>
<variable units="per_millisecond" name="beta_q"/>
<!-- 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_q_calculation">
<eq/>
<ci> alpha_q </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.008 </cn>
<apply>
<divide/>
<ci> V </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_q_calculation">
<eq/>
<ci> beta_q </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.08 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 11.26 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dq_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> q </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_q </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> q </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_q </ci>
<ci> q </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The encapsualted r gate. -->
<component name="transient_chloride_current_r_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="r"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_r"/>
<variable units="per_millisecond" name="beta_r"/>
<!-- 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_r_calculation">
<eq/>
<ci> alpha_r </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.00018 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_r_calculation">
<eq/>
<ci> beta_r </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 0.02 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 26.0 </cn>
</apply>
<cn cellml:units="millivolt"> 11.5 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="dr_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> r </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_r </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> r </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_r </ci>
<ci> r </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The outward time-independent (or background) ionic current is carried
predominately by potassium ions and is represented by i_K1.
-->
<component name="time_independent_outward_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_K1"/>
<!-- This variable is defined here and only used internally. -->
<variable units="millivolt" name="E_K1" initial_value="-30.0"/>
<!-- 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="microA_per_cm2" public_interface="in" name="I_K2"/>
<!--
The following equation calculates the time-independent outward
potassium current in terms of membrane voltage.
-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<plus/>
<apply>
<divide/>
<ci> I_K2 </ci>
<cn cellml:units="dimensionless"> 2.8 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</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_cm2" public_interface="out" name="i_Na_b"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_cm2" name="g_Nab" initial_value="0.105"/>
<!--
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="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 "chloride_background_current" contributes to maintaining the plateau and
helps to determine the action potential duration.
-->
<component name="chloride_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_cm2" public_interface="out" name="i_Cl_b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_cm2" name="g_Clb" initial_value="0.01"/>
<!--
Time and memebrane potential are imported from the "environment" and the
"membrane" components. The reversal potential is imported from the
"transient_chloride_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_Cl"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Cl_b_calculation">
<eq/>
<ci> i_Cl_b </ci>
<apply>
<times/>
<ci> g_Clb </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Cl </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="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_d1_gate"/>
</component_ref>
<component_ref component="pacemaker_potassium_current">
<component_ref component="pacemaker_potassium_current_s_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current1">
<component_ref component="plateau_potassium_current1_x1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current2">
<component_ref component="plateau_potassium_current2_x2_gate"/>
</component_ref>
<component_ref component="transient_chloride_current">
<component_ref component="transient_chloride_current_q_gate"/>
<component_ref component="transient_chloride_current_r_gate"/>
</component_ref>
<component_ref component="time_independent_outward_current"/>
<component_ref component="sodium_background_current"/>
<component_ref component="chloride_background_current"/>
</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="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_d1_gate"/>
</component_ref>
<component_ref component="pacemaker_potassium_current">
<component_ref component="pacemaker_potassium_current_s_gate"/>
</component_ref>
<component_ref component="transient_chloride_current">
<component_ref component="transient_chloride_current_q_gate"/>
<component_ref component="transient_chloride_current_r_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current1">
<component_ref component="plateau_potassium_current1_x1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current2">
<component_ref component="plateau_potassium_current2_x2_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="secondary_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="pacemaker_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="transient_chloride_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="chloride_background_current"/>
<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"/>
</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"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="pacemaker_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K2" variable_1="i_K2"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="plateau_potassium_current1"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_x1" variable_1="i_x1"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="plateau_potassium_current2"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_x2" variable_1="i_x2"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="transient_chloride_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_qr" variable_1="i_qr"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_independent_outward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<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="chloride_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Cl_b" variable_1="i_Cl_b"/>
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components component_2="fast_sodium_current" component_1="sodium_background_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="pacemaker_potassium_current" component_1="time_independent_outward_current"/>
<map_variables variable_2="I_K2" variable_1="I_K2"/>
</connection>
<connection>
<map_components component_2="chloride_background_current" component_1="transient_chloride_current"/>
<map_variables variable_2="E_Cl" variable_1="E_Cl"/>
</connection>
<!--
Several variables are passed between parent components and their
encapsulated gates.
-->
<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"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_d1_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="d1" variable_1="d1"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="pacemaker_potassium_current_s_gate" component_1="pacemaker_potassium_current"/>
<map_variables variable_2="s" variable_1="s"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="transient_chloride_current_q_gate" component_1="transient_chloride_current"/>
<map_variables variable_2="q" variable_1="q"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="transient_chloride_current_r_gate" component_1="transient_chloride_current"/>
<map_variables variable_2="r" variable_1="r"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current1_x1_gate" component_1="plateau_potassium_current1"/>
<map_variables variable_2="x1" variable_1="x1"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current2_x2_gate" component_1="plateau_potassium_current2"/>
<map_variables variable_2="x2" variable_1="x2"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#f8b3315f-0b36-49eb-872b-c47465517334">
<rdf:li>Purkinje Fibre</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>electrophysiology</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
<rdf:li rdf:resource="rdf:#author3Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#387740ca-55f8-454f-b553-aed664912e06">
<dcterms:modified rdf:resource="rdf:#f8fb75ed-c8e8-457a-9414-87d249331163"/>
<rdf:value>
Updated metadata to conform to the 16/01/2002 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#ead04d40-a224-493b-93e9-05a5ac5c0788"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9b57a336-8719-4b50-8946-fee42a5f3a0f">
<dcterms:modified rdf:resource="rdf:#e96e6ce8-9eaa-4c20-8f83-999efdecd8cc"/>
<rdf:value>
Altered parent-child relationships as x1 and x2 were made to be gates
of the plateau potassium currents.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#124232fa-337a-4d19-b9c1-10f75f9ae511"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2ed0ead8-ab67-4970-8aa3-5274d4c290af">
<dc:creator rdf:resource="rdf:#cb868a35-4b4d-4f13-8d7c-a4290bbf5665"/>
<rdf:value>This is the CellML description of McAllister, Noble and Tsien's mathematical model of cardiac action potentials of Purkinje fibres. It describes transmembrane ionic currents in terms of Hodgkin-Huxley type equations. It is a significant development of the Noble (1962) model as more currents are added based on new experimental data.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#MNT_purkinje_fibre_model_1975">
<dc:title>
The McAllister-Noble-Tsien Model of Cardiac Action Potentials in
Purkinje fibres, 1975
</dc:title>
<cmeta:bio_entity>Purkinje Fibre</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#2ed0ead8-ab67-4970-8aa3-5274d4c290af"/>
<bqs:reference rdf:resource="rdf:#19578cef-16b4-4133-87ec-e50064de1dda"/>
<bqs:reference rdf:resource="rdf:#e0f974fb-ba6d-4db4-97b4-869268552341"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#1608793b-3942-48dc-bca1-c21956a3ad12"/>
<cmeta:modification rdf:resource="rdf:#33b3b4ef-c060-4f02-8370-c68104f1250e"/>
<cmeta:modification rdf:resource="rdf:#387740ca-55f8-454f-b553-aed664912e06"/>
<cmeta:modification rdf:resource="rdf:#5f3c5a37-b0c9-41bb-b429-abd5791b3c9d"/>
<cmeta:modification rdf:resource="rdf:#9b57a336-8719-4b50-8946-fee42a5f3a0f"/>
<cmeta:modification rdf:resource="rdf:#cf610c86-f3d6-47bb-9c43-175be95e4dab"/>
<cmeta:modification rdf:resource="rdf:#d011243e-2dc1-4471-8390-6026990c3801"/>
<cmeta:modification rdf:resource="rdf:#ece8263c-c027-46f0-9d01-b131187b002b"/>
<dcterms:created rdf:resource="rdf:#3a4048cb-04dc-47dc-b2c4-95c71e9970dc"/>
<dc:creator rdf:resource="rdf:#f94b6122-33ae-4aef-b05f-f1703c5a9217"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e96e6ce8-9eaa-4c20-8f83-999efdecd8cc">
<dcterms:W3CDTF>2002-01-03</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f94b6122-33ae-4aef-b05f-f1703c5a9217">
<vCard:ORG rdf:resource="rdf:#03a22516-a00c-43b5-b132-3abfa925e466"/>
<vCard:EMAIL rdf:resource="rdf:#c1e990e3-92b1-434c-bb5e-eca080339701"/>
<vCard:N rdf:resource="rdf:#1c543e78-9727-42e7-82ac-5d4bf694e8b6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b20ba3be-8601-48d0-ad37-a5deed88f79e">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9d4cf1d2-5b18-41f7-abc1-1396fe8f0432">
<vCard:N rdf:resource="rdf:#b20ba3be-8601-48d0-ad37-a5deed88f79e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1ed202cf-ebf6-435d-bf77-0b8a2510efd6">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author3VcardN">
<vCard:Given>R</vCard:Given>
<vCard:Family>Tsien</vCard:Family>
<vCard:Other>W</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2bbb0756-5238-494c-8430-ad75ce8f8f05">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#f8b3315f-0b36-49eb-872b-c47465517334"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9d4de729-e67f-4e23-b2f0-13841150862c">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f7f1e56b-7695-451e-a16e-e5484393418f">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#33b3b4ef-c060-4f02-8370-c68104f1250e">
<dcterms:modified rdf:resource="rdf:#5bade7db-0543-4f45-9325-87602a97f81b"/>
<rdf:value>
Removed document type definition as this is declared as optional
according to the W3C recommendation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#9ef9ba0a-35b1-42d3-99d8-57bbf83d23e2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f0effb3a-56d3-473d-8e49-b3330c8401c0">
<vCard:N rdf:resource="rdf:#0995a204-5329-4aff-be75-3dded4346e4a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4cd6b8d0-6312-4809-bb58-fd24eb04aa68">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f8fb75ed-c8e8-457a-9414-87d249331163">
<dcterms:W3CDTF>2002-01-20</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1608793b-3942-48dc-bca1-c21956a3ad12">
<dcterms:modified rdf:resource="rdf:#e7c5efae-c9db-40d8-b7a8-402b4d0ff42d"/>
<rdf:value>
Corrected units
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#f4949ea2-07ea-4b87-89d4-23524ea45e96"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author2VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e899da90-e672-4a99-bd56-1329e6812d8b">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e8ceee1c-5d4b-4e72-80ab-701ac3f2fbd3">
<dc:title>Journal of Physiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>Denis</vCard:Given>
<vCard:Family>Noble</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c1e990e3-92b1-434c-bb5e-eca080339701">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9ef9ba0a-35b1-42d3-99d8-57bbf83d23e2">
<vCard:N rdf:resource="rdf:#72562932-af53-4dab-b753-5d806be736fa"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03a22516-a00c-43b5-b132-3abfa925e466">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cc971ffb-7b2d-4ae6-8691-961ffb33f354">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>Reconstruction of the electrical activity of cardiac purkinje fibres</dc:title>
<bqs:volume>251</bqs:volume>
<bqs:first_page>1</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#e8ceee1c-5d4b-4e72-80ab-701ac3f2fbd3"/>
<dcterms:issued rdf:resource="rdf:#9d0f0e85-c44e-4b1e-a695-fe8f2d40871f"/>
<bqs:last_page>59</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d011243e-2dc1-4471-8390-6026990c3801">
<dcterms:modified rdf:resource="rdf:#51f4fc04-760c-4194-b2ee-494b0b371706"/>
<rdf:value>
Changed the model name so the model loads in the database easier.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#33323790-2b0b-4b16-b3da-276e5f84144b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e0f974fb-ba6d-4db4-97b4-869268552341">
<bqs:Pubmed_id>1185607</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#cc971ffb-7b2d-4ae6-8691-961ffb33f354"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1c543e78-9727-42e7-82ac-5d4bf694e8b6">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cf610c86-f3d6-47bb-9c43-175be95e4dab">
<dcterms:modified rdf:resource="rdf:#e6411db9-769c-4b2c-a6c1-202200fc5b8e"/>
<rdf:value>
Made changes to some of the metadata, bringing them up to date with
the most recent working draft (26th September) of the Metadata
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#9d4cf1d2-5b18-41f7-abc1-1396fe8f0432"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ece8263c-c027-46f0-9d01-b131187b002b">
<dcterms:modified rdf:resource="rdf:#4e865315-ef02-4ab2-bc39-95a75cc34965"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#f0effb3a-56d3-473d-8e49-b3330c8401c0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#33323790-2b0b-4b16-b3da-276e5f84144b">
<vCard:N rdf:resource="rdf:#4cd6b8d0-6312-4809-bb58-fd24eb04aa68"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9ee18b51-20c3-41ef-83ff-b1636cba1d87">
<dcterms:W3CDTF>2001-12-10</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e6411db9-769c-4b2c-a6c1-202200fc5b8e">
<dcterms:W3CDTF>2001-10-24</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3a4048cb-04dc-47dc-b2c4-95c71e9970dc">
<dcterms:W3CDTF>2001-09-27</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#19578cef-16b4-4133-87ec-e50064de1dda">
<dc:subject rdf:resource="rdf:#2bbb0756-5238-494c-8430-ad75ce8f8f05"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51f4fc04-760c-4194-b2ee-494b0b371706">
<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ead04d40-a224-493b-93e9-05a5ac5c0788">
<vCard:N rdf:resource="rdf:#9d4de729-e67f-4e23-b2f0-13841150862c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9d0f0e85-c44e-4b1e-a695-fe8f2d40871f">
<dcterms:W3CDTF>1975-09-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cb868a35-4b4d-4f13-8d7c-a4290bbf5665">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#72562932-af53-4dab-b753-5d806be736fa">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>R</vCard:Given>
<vCard:Family>McAllister</vCard:Family>
<vCard:Other>E</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0995a204-5329-4aff-be75-3dded4346e4a">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#124232fa-337a-4d19-b9c1-10f75f9ae511">
<vCard:N rdf:resource="rdf:#e899da90-e672-4a99-bd56-1329e6812d8b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author3Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author3VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e7c5efae-c9db-40d8-b7a8-402b4d0ff42d">
<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4e865315-ef02-4ab2-bc39-95a75cc34965">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5bade7db-0543-4f45-9325-87602a97f81b">
<dcterms:W3CDTF>2001-10-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#162f93e4-d85d-4c90-8f72-8cdb66b6ef0e">
<vCard:N rdf:resource="rdf:#f7f1e56b-7695-451e-a16e-e5484393418f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f4949ea2-07ea-4b87-89d4-23524ea45e96">
<vCard:N rdf:resource="rdf:#1ed202cf-ebf6-435d-bf77-0b8a2510efd6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5f3c5a37-b0c9-41bb-b429-abd5791b3c9d">
<dcterms:modified rdf:resource="rdf:#9ee18b51-20c3-41ef-83ff-b1636cba1d87"/>
<rdf:value>
Changed equations after checking with the mathml validator.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#162f93e4-d85d-4c90-8f72-8cdb66b6ef0e"/>
</rdf:Description>
</rdf:RDF>
</model>
