- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-11-27 14:57:49+13:00
- Desc:
- Added images in ai and svg format
- Permanent Source URI:
- https://models.cellml.org/workspace/boyett_zhang_garny_holden_2001/rawfile/40d44ae3435f2a253355be7184db0b27a6bfe010/boyett_zhang_garny_holden_2001.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : boyett_SAN_model_2001.xml
CREATED : 28th January 2002
LAST MODIFIED : 20th April 2005
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Boyett et al's 2001
mathematical model of control of the pacemaker activity of the sinoatrial node.
CHANGES:
25/02/2002 - CML - Corrected several equations.
19/07/2002 - CML - Added more metadata.
20/04/2005 - PJV - Updated syntax to conform with cellml 1.1 specs
--><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="boyett_zhang_garny_holden_2001_version01" name="boyett_zhang_garny_holden_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling The Effect Of Intracellular Ca2+ On Sinoatrial Node Action Potentials, 2001</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model can not be solved as it is unsuitably constrained.
</para>
<para>
ValidateCellML verifies this model as valid CellML but detects unit inconsistencies.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 2000 H. Zhang <emphasis>et al</emphasis> published a mathematical model which describes the action potentials in the periphery and center of the rabbit sinoatrial node. The SA node is functionally, anatomically and electrophysiologically heterogeneous. In their model, Zhang <emphasis>et al</emphasis> accounted for this heterogeneity by defining two distinct models for the peripheral and the central cells of the SA node. These models have the same equations to define the ionic currents but they vary in their parameters.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node, H. Zhang, A.V. Holden, I. Honjo, M. Lei, T. Varghese and M.R. Boyett, 2000,
<emphasis>Am. J. Physiol. Heart Circ. Physiol.</emphasis>
, 279, H397-H421. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10899081&dopt=Abstract">PubMed ID: 10899081</ulink>
</para>
<para>
In 2001, Boyett <emphasis>et al</emphasis> reviewed the results of several experiments which suggested that intracellular calcium controls a number of ionic currents in the SA node cells. This had not been considered in previous SA node cell models and Boyett <emphasis>et al</emphasis> incorporated an intracellular calcium handling element into the model of Zhang <emphasis>et al</emphasis> (2000). In addition, they included a sustained inward current based on the experiments and equations of Shinagawa <emphasis>et al</emphasis> (2000) (see the figure below). Like in Zhang et al's orginal model, differences between the central and peripheral SA node cells are taken into consideration by defining different parameters. The CellML description here is of the peripheral SA node cell model. To make it appropriate for the central SA node cells, certain parameters need to be changed (refer to the original paper reference which is cited below).
</para>
<para>
Control of the pacemaker activity of the sinoatrial node by intracellular Ca<superscript>2+</superscript>. Experiments and modelling, M.R. Boyett, H. Zhang, A. Garny and A.V. Holden, 2001, <ulink url="http://www.pubs.royalsoc.ac.uk/">
<emphasis>Phil. Trans. R. Soc. Lond. A.</emphasis>
</ulink>, 359, 1091-1110.
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the Boyett et al SAN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="boyett_2001.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the Boyett <emphasis>et al</emphasis> 2001 model of the action potentials in the peripheral cells of the SA node.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the Boyett et al SAN model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the Boyett <emphasis>et al</emphasis> 2001 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="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_second">
<unit units="millivolt" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="microS">
<unit units="siemens" prefix="micro"/>
</units>
<units name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units name="nanoA">
<unit units="ampere" prefix="nano"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="per_second_millimolar">
<unit units="second" exponent="-1"/>
<unit units="millimolar" exponent="-1"/>
</units>
<units name="millimole_per_second">
<unit units="mole" prefix="milli"/>
<unit units="second" exponent="-1"/>
</units>
<units name="millijoule_per_mole_kelvin">
<unit units="joule" prefix="milli"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb" exponent="-1"/>
<unit units="mole"/>
</units>
<units name="microlitre">
<unit units="litre" prefix="micro"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<!--
The "membrane" component is really the `root' node of our model.
It defines the action potential variable "V" among other things.
-->
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_value="-63.25"/>
<variable units="millijoule_per_mole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96845.0"/>
<variable units="picoF" name="C" initial_value="65.0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="nanoA" public_interface="in" name="i_Na"/>
<variable units="nanoA" public_interface="in" name="i_Ca_L"/>
<variable units="nanoA" public_interface="in" name="i_Ca_T"/>
<variable units="nanoA" public_interface="in" name="i_to"/>
<variable units="nanoA" public_interface="in" name="i_sus"/>
<variable units="nanoA" public_interface="in" name="i_K_r"/>
<variable units="nanoA" public_interface="in" name="i_K_s"/>
<variable units="nanoA" public_interface="in" name="i_f"/>
<variable units="nanoA" public_interface="in" name="i_b_Na"/>
<variable units="nanoA" public_interface="in" name="i_b_Ca"/>
<variable units="nanoA" public_interface="in" name="i_b_K"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="nanoA" public_interface="in" name="i_p"/>
<variable units="nanoA" public_interface="in" name="i_st"/>
<variable units="nanoA" public_interface="in" name="i_Ca_P"/>
<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>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<ci> C </ci>
</apply>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca_L </ci>
<ci> i_Ca_T </ci>
<ci> i_to </ci>
<ci> i_sus </ci>
<ci> i_K_r </ci>
<ci> i_K_s </ci>
<ci> i_f </ci>
<ci> i_b_Na </ci>
<ci> i_b_Ca </ci>
<ci> i_b_K </ci>
<ci> i_NaCa </ci>
<ci> i_p </ci>
<ci> i_st </ci>
<ci> i_Ca_P </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_current" cmeta:id="sodium_current">
<variable units="nanoA" public_interface="out" name="i_Na"/>
<variable units="microS" name="g_Na" initial_value="0.0000012"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<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">
<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>
<ci> Na_o </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
<ci> V </ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.135"/>
<variable units="dimensionless" name="m_infinity"/>
<variable units="second" name="tau_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> m_infinity </ci>
<ci> m </ci>
</apply>
<ci> tau_m </ci>
</apply>
</apply>
<apply id="m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<power/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 5.46 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply id="tau_m_calculation">
<eq/>
<ci> tau_m </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="second" type="e-notation">0.6247<sep/>-3</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.832 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.335 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 56.7 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.627 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.082 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 65.01 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second"> 0.00004 </cn>
</apply>
</apply>
</math>
</component>
<component name="sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="dimensionless" name="F_Na"/>
<variable units="dimensionless" name="h1" initial_value="0.03123"/>
<variable units="dimensionless" name="h2" initial_value="4.894"/>
<variable units="dimensionless" name="h1_infinity"/>
<variable units="dimensionless" name="h2_infinity"/>
<variable units="second" name="tau_h1"/>
<variable units="second" name="tau_h2"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="h_calculation">
<eq/>
<ci> h </ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> F_Na </ci>
</apply>
<ci> h1 </ci>
</apply>
<apply>
<times/>
<ci> F_Na </ci>
<ci> h2 </ci>
</apply>
</apply>
</apply>
<apply id="h1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h1 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h1_infinity </ci>
<ci> h1 </ci>
</apply>
<ci> tau_h1 </ci>
</apply>
</apply>
<apply id="h2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h2 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h2_infinity </ci>
<ci> h2 </ci>
</apply>
<ci> tau_h2 </ci>
</apply>
</apply>
<apply id="h1_infinity_calculation">
<eq/>
<ci> h1_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 66.1 </cn>
</apply>
<cn cellml:units="millivolt"> 6.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="h2_infinity_calculation">
<eq/>
<ci> h2_infinity </ci>
<ci> h1_infinity </ci>
</apply>
<apply id="tau_h1_calculation">
<eq/>
<ci> tau_h1 </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="second"> 0.000003171 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.2815 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 17.11 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="second"> 0.003732 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.3426 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 37.76 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second"> 0.0005977 </cn>
</apply>
</apply>
<apply id="tau_h2_calculation">
<eq/>
<ci> tau_h2 </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="second"> 0.00000003186 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.6219 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 18.8 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="second"> 0.00007189 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.6683 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 34.07 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="second"> 0.003556 </cn>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel" cmeta:id="L_type_Ca_channel">
<variable units="nanoA" public_interface="out" name="i_Ca_L"/>
<variable units="microS" name="g_Ca_L" initial_value="0.0659"/>
<variable units="millivolt" name="E_Ca_L" initial_value="46.4"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d_L"/>
<variable units="dimensionless" private_interface="in" name="f_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply>
<times/>
<ci> g_Ca_L </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> f_L </ci>
<ci> d_L </ci>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.006 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.1 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 6.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca_L </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d_L" initial_value="0.02248"/>
<variable units="per_second" name="alpha_d_L"/>
<variable units="per_second" name="beta_d_L"/>
<variable units="dimensionless" name="d_L_infinity"/>
<variable units="second" name="tau_d_L"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d_L_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d_L </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_L_infinity </ci>
<ci> d_L </ci>
</apply>
<ci> tau_d_L </ci>
</apply>
</apply>
<apply id="alpha_d_L_calculation">
<eq/>
<ci> alpha_d_L </ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> -14.19 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 2.5 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 42.45 </cn>
<ci> V </ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.208 </cn>
<ci> V </ci>
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</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_L_calculation">
<eq/>
<ci> beta_d_L </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 5.71 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.4 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="tau_d_L_calculation">
<eq/>
<ci> tau_d_L </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_d_L </ci>
<ci> beta_d_L </ci>
</apply>
</apply>
</apply>
<apply id="d_L_infinity_calculation">
<eq/>
<ci> d_L_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 23.1 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 6.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f_L" initial_value="0.531"/>
<variable units="per_second" name="alpha_f_L"/>
<variable units="per_second" name="beta_f_L"/>
<variable units="dimensionless" name="f_L_infinity"/>
<variable units="second" name="tau_f_L"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_L_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f_L </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> f_L_infinity </ci>
<ci> f_L </ci>
</apply>
<ci> tau_f_L </ci>
</apply>
</apply>
<apply id="alpha_f_L_calculation">
<eq/>
<ci> alpha_f_L </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 3.12 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="beta_f_L_calculation">
<eq/>
<ci> beta_f_L </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 25.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_f_L_calculation">
<eq/>
<ci> tau_f_L </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_f_L </ci>
<ci> beta_f_L </ci>
</apply>
</apply>
</apply>
<apply id="f_L_infinity_calculation">
<eq/>
<ci> f_L_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 45.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel" cmeta:id="T_type_Ca_channel">
<variable units="nanoA" public_interface="out" name="i_Ca_T"/>
<variable units="microS" name="g_Ca_T" initial_value="0.0139"/>
<variable units="millivolt" name="E_Ca_T" initial_value="45.0"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d_T"/>
<variable units="dimensionless" private_interface="in" name="f_T"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_T_calculation">
<eq/>
<ci> i_Ca_T </ci>
<apply>
<times/>
<ci> g_Ca_T </ci>
<ci> d_T </ci>
<ci> f_T </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca_T </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d_T" initial_value="0.02217"/>
<variable units="per_second" name="alpha_d_T"/>
<variable units="per_second" name="beta_d_T"/>
<variable units="dimensionless" name="d_T_infinity"/>
<variable units="second" name="tau_d_T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d_T_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d_T </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_T_infinity </ci>
<ci> d_T </ci>
</apply>
<ci> tau_d_T </ci>
</apply>
</apply>
<apply id="alpha_d_T_calculation">
<eq/>
<ci> alpha_d_T </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 1068.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 26.3 </cn>
</apply>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_T_calculation">
<eq/>
<ci> beta_d_T </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 1068.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 26.3 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_T_calculation">
<eq/>
<ci> tau_d_T </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_d_T </ci>
<ci> beta_d_T </ci>
</apply>
</apply>
</apply>
<apply id="d_T_infinity_calculation">
<eq/>
<ci> d_T_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 37.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 6.8 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f_T" initial_value="0.06274"/>
<variable units="per_second" name="alpha_f_T"/>
<variable units="per_second" name="beta_f_T"/>
<variable units="dimensionless" name="f_T_infinity"/>
<variable units="second" name="tau_f_T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_T_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f_T </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> f_T_infinity </ci>
<ci> f_T </ci>
</apply>
<ci> tau_f_T </ci>
</apply>
</apply>
<apply id="alpha_f_T_calculation">
<eq/>
<ci> alpha_f_T </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 15.3 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 71.7 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 83.3 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_T_calculation">
<eq/>
<ci> beta_f_T </ci>
<apply>
<times/>
<cn cellml:units="per_second"> 15.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 71.7 </cn>
</apply>
<cn cellml:units="millivolt"> 15.38 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_f_T_calculation">
<eq/>
<ci> tau_f_T </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_f_T </ci>
<ci> beta_f_T </ci>
</apply>
</apply>
</apply>
<apply id="f_T_infinity_calculation">
<eq/>
<ci> f_T_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 71.0 </cn>
</apply>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="four_AP_sensitive_currents" cmeta:id="four_AP_sensitive_currents">
<variable units="nanoA" public_interface="out" name="i_to"/>
<variable units="nanoA" public_interface="out" name="i_sus"/>
<variable units="microS" name="g_to" initial_value="0.003649"/>
<variable units="microS" name="g_sus" initial_value="0.0114"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<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_to_calculation">
<eq/>
<ci> i_to </ci>
<apply>
<times/>
<ci> g_to </ci>
<ci> q </ci>
<ci> r </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="i_sus_calculation">
<eq/>
<ci> i_sus </ci>
<apply>
<times/>
<ci> g_sus </ci>
<ci> r </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="four_AP_sensitive_currents_q_gate">
<variable units="dimensionless" public_interface="out" name="q" initial_value="0.06609"/>
<variable units="dimensionless" name="q_infinity"/>
<variable units="second" name="tau_q"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="q_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> q </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> q_infinity </ci>
<ci> q </ci>
</apply>
<ci> tau_q </ci>
</apply>
</apply>
<apply id="q_infinity_calculation">
<eq/>
<ci> q_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 59.37 </cn>
</apply>
<cn cellml:units="millivolt"> 13.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_q_calculation">
<eq/>
<ci> tau_q </ci>
<apply>
<plus/>
<cn cellml:units="second" type="e-notation">10.1<sep/>-3</cn>
<apply>
<divide/>
<cn cellml:units="second"> 0.006517 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.57 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> -0.08 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 49.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="second"> 0.000024 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.93 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="four_AP_sensitive_currents_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="0.05733"/>
<variable units="dimensionless" name="r_infinity"/>
<variable units="second" name="tau_r"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="r_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> r </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> r_infinity </ci>
<ci> r </ci>
</apply>
<ci> tau_r </ci>
</apply>
</apply>
<apply id="r_infinity_calculation">
<eq/>
<ci> r_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.93 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 19.7 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_r_calculation">
<eq/>
<ci> tau_r </ci>
<apply>
<plus/>
<cn cellml:units="second"> 0.00298 </cn>
<apply>
<divide/>
<cn cellml:units="second"> 0.001559 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.037 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.09 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.61 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.369 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> -0.12 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 23.84 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current" cmeta:id="rapid_delayed_rectifying_potassium_current">
<variable units="nanoA" public_interface="out" name="i_K_r"/>
<variable units="microS" name="g_K_r" initial_value="0.0160"/>
<variable units="dimensionless" name="P_a"/>
<variable units="dimensionless" name="F_K_r"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="P_af"/>
<variable units="dimensionless" private_interface="in" name="P_as"/>
<variable units="dimensionless" private_interface="in" name="P_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_r_calculation">
<eq/>
<ci> i_K_r </ci>
<apply>
<times/>
<ci> g_K_r </ci>
<ci> P_a </ci>
<ci> P_i </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="P_a_calculation">
<eq/>
<ci> P_a </ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> F_K_r </ci>
</apply>
<ci> P_af </ci>
</apply>
<apply>
<times/>
<ci> F_K_r </ci>
<ci> P_as </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current_P_af_gate">
<variable units="dimensionless" public_interface="out" name="P_af" initial_value="0.660"/>
<variable units="dimensionless" public_interface="out" name="P_af_infinity"/>
<variable units="second" name="tau_P_af"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="P_af_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_af </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> P_af_infinity </ci>
<ci> P_af </ci>
</apply>
<ci> tau_P_af </ci>
</apply>
</apply>
<apply id="P_af_infinity_calculation">
<eq/>
<ci> P_af_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 14.2 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 10.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_P_af_calculation">
<eq/>
<ci> tau_P_af </ci>
<apply>
<divide/>
<cn cellml:units="second"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 37.2 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
<cn cellml:units="millivolt"> 15.9 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.96 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 22.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current_P_as_gate">
<variable units="dimensionless" public_interface="out" name="P_as" initial_value="0.359"/>
<variable units="dimensionless" name="P_as_infinity"/>
<variable units="second" name="tau_P_as"/>
<variable units="dimensionless" public_interface="in" name="P_af_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="P_as_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_as </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> P_as_infinity </ci>
<ci> P_as </ci>
</apply>
<ci> tau_P_as </ci>
</apply>
</apply>
<apply id="P_as_infinity_calculation">
<eq/>
<ci> P_as_infinity </ci>
<ci> P_af_infinity </ci>
</apply>
<apply id="tau_P_as_calculation">
<eq/>
<ci> tau_P_as </ci>
<apply>
<divide/>
<cn cellml:units="second"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.2 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
<cn cellml:units="millivolt"> 17.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.15 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 21.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="rapid_delayed_rectifying_potassium_current_P_i_gate">
<variable units="dimensionless" public_interface="out" name="P_i" initial_value="0.976"/>
<variable units="dimensionless" name="P_i_infinity"/>
<variable units="second" name="tau_P_i" initial_value="0.002"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="P_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_i </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> P_i_infinity </ci>
<ci> P_i </ci>
</apply>
<ci> tau_P_i </ci>
</apply>
</apply>
<apply id="P_i_infinity_calculation">
<eq/>
<ci> P_i_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 18.6 </cn>
</apply>
<cn cellml:units="millivolt"> 10.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_delayed_rectifying_potassium_current" cmeta:id="slow_delayed_rectifying_potassium_current">
<variable units="nanoA" public_interface="out" name="i_K_s"/>
<variable units="microS" name="g_K_s" initial_value="0.0104"/>
<variable units="millivolt" public_interface="in" name="E_K_s"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="xs"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_s_calculation">
<eq/>
<ci> i_K_s </ci>
<apply>
<times/>
<ci> g_K_s </ci>
<apply>
<power/>
<ci> xs </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K_s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_delayed_rectifying_potassium_current_xs_gate">
<variable units="dimensionless" public_interface="out" name="xs"/>
<variable units="per_second" name="alpha_xs"/>
<variable units="per_second" name="beta_xs"/>
<variable units="dimensionless" name="xs_infinity"/>
<variable units="second" name="tau_xs"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="xs_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> xs </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> xs_infinity </ci>
<ci> xs </ci>
</apply>
<ci> tau_xs </ci>
</apply>
</apply>
<apply id="alpha_xs_calculation">
<eq/>
<ci> alpha_xs </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 14.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_xs_calculation">
<eq/>
<ci> beta_xs </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 45.0 </cn>
</apply>
</apply>
</apply>
<apply id="xs_infinity_calculation">
<eq/>
<ci> xs_infinity </ci>
<apply>
<divide/>
<ci> alpha_xs </ci>
<apply>
<plus/>
<ci> alpha_xs </ci>
<ci> beta_xs </ci>
</apply>
</apply>
</apply>
<apply id="tau_xs_calculation">
<eq/>
<ci> tau_xs </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_xs </ci>
<ci> beta_xs </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current" cmeta:id="hyperpolarisation_activated_current">
<variable units="nanoA" public_interface="out" name="i_f"/>
<variable units="nanoA" name="i_f_Na"/>
<variable units="nanoA" name="i_f_K"/>
<variable units="microS" name="g_f_Na" initial_value="0.0069"/>
<variable units="microS" name="g_f_K" initial_value="0.0069"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<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>
<plus/>
<ci> i_f_Na </ci>
<ci> i_f_K </ci>
</apply>
</apply>
<apply id="i_f_Na_calculation">
<eq/>
<ci> i_f_Na </ci>
<apply>
<times/>
<ci> g_f_Na </ci>
<ci> y </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
<apply id="i_f_K_calculation">
<eq/>
<ci> i_f_K </ci>
<apply>
<times/>
<ci> g_f_K </ci>
<ci> y </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.007645"/>
<variable units="per_second" name="alpha_y"/>
<variable units="per_second" name="beta_y"/>
<variable units="dimensionless" name="y_infinity"/>
<variable units="second" name="tau_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="y_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> y_infinity </ci>
<ci> y </ci>
</apply>
<ci> tau_y </ci>
</apply>
</apply>
<apply id="alpha_y_calculation">
<eq/>
<ci> alpha_y </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 78.91 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 26.62 </cn>
</apply>
</apply>
</apply>
<apply id="beta_y_calculation">
<eq/>
<ci> beta_y </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.13 </cn>
</apply>
<cn cellml:units="millivolt"> 21.25 </cn>
</apply>
</apply>
</apply>
<apply id="y_infinity_calculation">
<eq/>
<ci> y_infinity </ci>
<apply>
<divide/>
<ci> alpha_y </ci>
<apply>
<plus/>
<ci> alpha_y </ci>
<ci> beta_y </ci>
</apply>
</apply>
</apply>
<apply id="tau_y_calculation">
<eq/>
<ci> tau_y </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_y </ci>
<ci> beta_y </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="nanoA" public_interface="out" name="i_b_Na"/>
<variable units="microS" name="g_b_Na" initial_value="0.000189"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_b_Na_calculation">
<eq/>
<ci> i_b_Na </ci>
<apply>
<times/>
<ci> g_b_Na </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_background_current">
<variable units="nanoA" public_interface="out" name="i_b_K"/>
<variable units="microS" name="g_b_K" initial_value="0.0000819"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_b_K_calculation">
<eq/>
<ci> i_b_K </ci>
<apply>
<times/>
<ci> g_b_K </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="nanoA" public_interface="out" name="i_b_Ca"/>
<variable units="microS" name="g_b_Ca" initial_value="0.000043"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_b_Ca_calculation">
<eq/>
<ci> i_b_Ca </ci>
<apply>
<times/>
<ci> g_b_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_pump">
<variable units="nanoA" public_interface="out" name="i_NaCa"/>
<variable units="nanoA" name="K_NaCa" initial_value="0.0000440"/>
<variable units="dimensionless" name="d_NaCa" initial_value="0.0001"/>
<variable units="dimensionless" name="gamma_NaCa" initial_value="0.5"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaCa_calculation">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_o </ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.03743 </cn>
<ci> V </ci>
<ci> gamma_NaCa </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci> Na_o </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_i </ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0374 </cn>
<ci> V </ci>
<apply>
<minus/>
<ci> gamma_NaCa </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> d_NaCa </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> Ca_i </ci>
<apply>
<power/>
<ci> Na_o </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> Ca_o </ci>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="nanoA" public_interface="out" name="i_p"/>
<variable units="dimensionless" name="K_m_Na" initial_value="5.64"/>
<variable units="dimensionless" name="K_m_K" initial_value="0.621"/>
<variable units="nanoA" name="i_p_max" initial_value="0.16"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_calculation">
<eq/>
<ci> i_p </ci>
<apply>
<times/>
<ci> i_p_max </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> Na_i </ci>
<apply>
<plus/>
<ci> K_m_Na </ci>
<ci> Na_i </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> K_o </ci>
<apply>
<plus/>
<ci> K_m_K </ci>
<ci> K_o </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.6 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.5 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 60.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sustained_inward_current" cmeta:id="sustained_inward_current">
<variable units="nanoA" public_interface="out" name="i_st"/>
<variable units="microS" name="g_st" initial_value="0.00214"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d_s"/>
<variable units="dimensionless" private_interface="in" name="f_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_st_calculation">
<eq/>
<ci> i_st </ci>
<apply>
<times/>
<ci> g_st </ci>
<ci> d_s </ci>
<ci> f_s </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 18.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sustained_inward_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d_s" initial_value="0.230"/>
<variable units="per_second" name="alpha_d_s"/>
<variable units="per_second" name="beta_d_s"/>
<variable units="dimensionless" name="d_s_infinity"/>
<variable units="second" name="tau_d_s"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d_s_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d_s </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_s_infinity </ci>
<ci> d_s </ci>
</apply>
<ci> tau_d_s </ci>
</apply>
</apply>
<apply id="alpha_d_s_calculation">
<eq/>
<ci> alpha_d_s </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 1000.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.15 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 700.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_s_calculation">
<eq/>
<ci> beta_d_s </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 1000.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 16.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 8.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_s_calculation">
<eq/>
<ci> tau_d_s </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_d_s </ci>
<ci> beta_d_s </ci>
</apply>
</apply>
</apply>
<apply id="d_s_infinity_calculation">
<eq/>
<ci> d_s_infinity </ci>
<apply>
<divide/>
<ci> alpha_d_s </ci>
<apply>
<plus/>
<ci> alpha_d_s </ci>
<ci> beta_d_s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sustained_inward_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f_s" initial_value="0.283"/>
<variable units="per_second" name="alpha_f_s"/>
<variable units="per_second" name="beta_f_s"/>
<variable units="dimensionless" name="f_s_infinity"/>
<variable units="second" name="tau_f_s"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_s_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f_s </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> f_s_infinity </ci>
<ci> f_s </ci>
</apply>
<ci> tau_f_s </ci>
</apply>
</apply>
<apply id="alpha_f_s_calculation">
<eq/>
<ci> alpha_f_s </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 1000.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3100.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 13.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 700.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 70.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_s_calculation">
<eq/>
<ci> beta_f_s </ci>
<apply>
<divide/>
<cn cellml:units="per_second"> 1000.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 16.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 8.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_f_s_calculation">
<eq/>
<ci> tau_f_s </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> alpha_f_s </ci>
<ci> beta_f_s </ci>
</apply>
</apply>
</apply>
<apply id="f_s_infinity_calculation">
<eq/>
<ci> f_s_infinity </ci>
<apply>
<divide/>
<ci> alpha_f_s </ci>
<apply>
<plus/>
<ci> alpha_f_s </ci>
<ci> beta_f_s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_calcium_handling" cmeta:id="intracellular_calcium_handling">
<variable units="nanoA" public_interface="out" name="i_Ca_P"/>
<variable units="dimensionless" name="U_d"/>
<variable units="dimensionless" name="U_s"/>
<variable units="nanoA" name="i_Ca_P_max" initial_value="0.24"/>
<variable units="millimole_per_second" name="J_Ca_ds"/>
<variable units="millimole_per_second" name="J_Ca_r"/>
<variable units="millimole_per_second" name="J_Ca_P"/>
<variable units="millimole_per_second" name="J_Ca_P_max"/>
<variable units="millimole_per_second" name="J_Ca_u"/>
<variable units="millimole_per_second" name="J_Ca_u_max" initial_value="0.00000000096"/>
<variable units="millimole_per_second" name="J_Ca_ur"/>
<variable units="millimole_per_second" name="J_Ca_1"/>
<variable units="millimolar" name="Ca_d" initial_value="0.001544"/>
<variable units="millimolar" name="Ca_s" initial_value="0.05487"/>
<variable units="millimolar" name="Ca_u" initial_value="6.983"/>
<variable units="millimolar" name="Ca_r" initial_value="4.909"/>
<variable units="millimolar" name="B_d" initial_value="0.4"/>
<variable units="millimolar" name="B_s" initial_value="0.2"/>
<variable units="litre" name="Vol_u"/>
<variable units="litre" name="Vol_r"/>
<variable units="litre" name="Vol_d"/>
<variable units="litre" name="Vol_s"/>
<variable units="litre" name="Vol_c" initial_value="8.0e-12"/>
<variable units="millimolar" name="K_m_b" initial_value="0.002"/>
<variable units="millimolar" name="K_m_r" initial_value="0.001"/>
<variable units="millimolar" name="K_m_u" initial_value="0.005"/>
<variable units="dimensionless" name="f_d" initial_value="0.1"/>
<variable units="dimensionless" name="f_r" initial_value="0.3"/>
<variable units="dimensionless" name="f_u" initial_value="0.06"/>
<variable units="per_second" name="alpha_ds" initial_value="3300.0"/>
<variable units="per_second_millimolar" name="alpha_fR" initial_value="6670.0"/>
<variable units="per_second" name="alpha_1" initial_value="0.172"/>
<variable units="per_second" name="alpha_r" initial_value="333.5"/>
<variable units="per_second" name="alpha_ur" initial_value="533.6"/>
<variable units="per_second" name="beta_fR" initial_value="2.0"/>
<variable units="dimensionless" name="f_R" initial_value="0.188"/>
<variable units="millimolar" name="i_Ca"/>
<variable units="nanoA" public_interface="in" name="i_Ca_L"/>
<variable units="nanoA" public_interface="in" name="i_Ca_T"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="nanoA" public_interface="in" name="i_b_Ca"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="U_d_calculation">
<eq/>
<ci> U_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> B_d </ci>
<apply>
<plus/>
<ci> K_m_b </ci>
<ci> Ca_d </ci>
<ci> B_d </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="J_Ca_ds_calculation">
<eq/>
<ci> J_Ca_ds </ci>
<apply>
<times/>
<ci> alpha_ds </ci>
<ci> Vol_d </ci>
<apply>
<minus/>
<ci> Ca_d </ci>
<ci> Ca_s </ci>
</apply>
</apply>
</apply>
<apply id="i_Ca_P_calculation">
<eq/>
<ci> i_Ca_P </ci>
<apply>
<times/>
<ci> i_Ca_P_max </ci>
<apply>
<divide/>
<ci> Ca_s </ci>
<apply>
<plus/>
<ci> Ca_s </ci>
<cn cellml:units="millimolar"> 0.0004 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="J_Ca_r_calculation">
<eq/>
<ci> J_Ca_r </ci>
<apply>
<times/>
<ci> alpha_r </ci>
<ci> f_R </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_d </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_m_r </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_d </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> Vol_r </ci>
<ci> Ca_r </ci>
</apply>
</apply>
<apply id="f_R_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f_R </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> alpha_fR </ci>
</apply>
<ci> Ca_d </ci>
<ci> f_R </ci>
</apply>
<apply>
<times/>
<ci> beta_fR </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f_R </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="U_s_calculation">
<eq/>
<ci> U_s </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> B_s </ci>
<apply>
<plus/>
<ci> K_m_b </ci>
<ci> Ca_s </ci>
<ci> B_s </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="J_Ca_P_calculation">
<eq/>
<ci> J_Ca_P </ci>
<apply>
<times/>
<ci> J_Ca_P_max </ci>
<apply>
<divide/>
<ci> Ca_s </ci>
<apply>
<plus/>
<ci> Ca_s </ci>
<cn cellml:units="millimolar"> 0.0004 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="J_Ca_u_calculation">
<eq/>
<ci> J_Ca_u </ci>
<apply>
<times/>
<ci> J_Ca_u_max </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_s </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_m_u </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_s </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="J_Ca_ur_calculation">
<eq/>
<ci> J_Ca_ur </ci>
<apply>
<times/>
<ci> alpha_ur </ci>
<ci> Vol_u </ci>
<apply>
<minus/>
<ci> Ca_u </ci>
<ci> Ca_r </ci>
</apply>
</apply>
</apply>
<apply id="J_Ca_1_calculation">
<eq/>
<ci> J_Ca_1 </ci>
<apply>
<times/>
<ci> alpha_1 </ci>
<ci> Vol_u </ci>
<ci> Ca_u </ci>
</apply>
</apply>
<apply id="i_Ca_calculation">
<eq/>
<ci> i_Ca </ci>
<apply>
<plus/>
<ci> i_Ca_L </ci>
<ci> i_Ca_T </ci>
</apply>
</apply>
<apply id="Ca_d_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_d </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> U_d </ci>
<ci> Vol_d </ci>
</apply>
<apply>
<minus/>
<ci> J_Ca_ds </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.95 </cn>
<ci> i_Ca </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_s_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_s </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> U_s </ci>
<ci> Vol_s </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci> J_Ca_ds </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<ci> i_Ca </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
</apply>
<ci> i_b_Ca </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<ci> J_Ca_u </ci>
</apply>
</apply>
<ci> J_Ca_r </ci>
<ci> J_Ca_1 </ci>
</apply>
</apply>
</apply>
<apply id="Ca_u_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_u </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> J_Ca_u </ci>
<apply>
<plus/>
<ci> J_Ca_1 </ci>
<ci> J_Ca_ur </ci>
</apply>
</apply>
<ci> Vol_u </ci>
</apply>
</apply>
<apply id="Ca_r_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_r </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> J_Ca_ur </ci>
<ci> J_Ca_r </ci>
</apply>
<ci> Vol_r </ci>
</apply>
</apply>
<apply id="Vol_u_calculation">
<eq/>
<ci> Vol_u </ci>
<apply>
<times/>
<ci> f_u </ci>
<ci> Vol_c </ci>
</apply>
</apply>
<apply id="Vol_r_calculation">
<eq/>
<ci> Vol_r </ci>
<apply>
<times/>
<ci> f_r </ci>
<ci> Vol_c </ci>
</apply>
</apply>
<apply id="Vol_d_calculation">
<eq/>
<ci> Vol_d </ci>
<apply>
<times/>
<ci> f_d </ci>
<ci> Vol_c </ci>
</apply>
</apply>
<apply id="Vol_s_calculation">
<eq/>
<ci> Vol_s </ci>
<apply>
<minus/>
<ci> Vol_c </ci>
<apply>
<plus/>
<ci> Vol_u </ci>
<ci> Vol_d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ionic_concentrations" cmeta:id="ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="8.0"/>
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="0.0001"/>
<variable units="millimolar" public_interface="out" name="Ca_o" initial_value="2.0"/>
<variable units="millimolar" public_interface="out" name="K_i" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="K_o" initial_value="5.4"/>
</component>
<component name="reversal_and_equilibrium_potentials">
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="millivolt" public_interface="out" name="E_K_s"/>
<variable units="millivolt" public_interface="out" name="E_Ca"/>
<variable units="dimensionless" name="z"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_Na_calculation">
<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<ci> z </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Na_o </ci>
<ci> Na_i </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>
<apply>
<times/>
<ci> z </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> K_o </ci>
<ci> K_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<ci> z </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ca_o </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K_s_calculation">
<eq/>
<ci> E_K_s </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> K_o </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Na_o </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> K_i </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Na_i </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
</component_ref>
<component_ref component="T_type_Ca_channel">
<component_ref component="T_type_Ca_channel_d_gate"/>
<component_ref component="T_type_Ca_channel_f_gate"/>
</component_ref>
<component_ref component="four_AP_sensitive_currents">
<component_ref component="four_AP_sensitive_currents_q_gate"/>
<component_ref component="four_AP_sensitive_currents_r_gate"/>
</component_ref>
<component_ref component="rapid_delayed_rectifying_potassium_current">
<component_ref component="rapid_delayed_rectifying_potassium_current_P_af_gate"/>
<component_ref component="rapid_delayed_rectifying_potassium_current_P_as_gate"/>
<component_ref component="rapid_delayed_rectifying_potassium_current_P_i_gate"/>
</component_ref>
<component_ref component="slow_delayed_rectifying_potassium_current">
<component_ref component="slow_delayed_rectifying_potassium_current_xs_gate"/>
</component_ref>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="potassium_background_current"/>
<component_ref component="sodium_calcium_pump"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="ionic_concentrations"/>
<component_ref component="reversal_and_equilibrium_potentials"/>
<component_ref component="sustained_inward_current">
<component_ref component="sustained_inward_current_d_gate"/>
<component_ref component="sustained_inward_current_f_gate"/>
</component_ref>
<component_ref component="intracellular_calcium_handling"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
</component_ref>
<component_ref component="T_type_Ca_channel">
<component_ref component="T_type_Ca_channel_d_gate"/>
<component_ref component="T_type_Ca_channel_f_gate"/>
</component_ref>
<component_ref component="four_AP_sensitive_currents">
<component_ref component="four_AP_sensitive_currents_q_gate"/>
<component_ref component="four_AP_sensitive_currents_r_gate"/>
</component_ref>
<component_ref component="rapid_delayed_rectifying_potassium_current">
<component_ref component="rapid_delayed_rectifying_potassium_current_P_af_gate"/>
<component_ref component="rapid_delayed_rectifying_potassium_current_P_as_gate"/>
<component_ref component="rapid_delayed_rectifying_potassium_current_P_i_gate"/>
</component_ref>
<component_ref component="slow_delayed_rectifying_potassium_current">
<component_ref component="slow_delayed_rectifying_potassium_current_xs_gate"/>
</component_ref>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
<component_ref component="sustained_inward_current">
<component_ref component="sustained_inward_current_d_gate"/>
<component_ref component="sustained_inward_current_f_gate"/>
</component_ref>
</group>
<!--
"Time" is passed from the "environment" component into the
"membrane" and other 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="sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="T_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="four_AP_sensitive_currents"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rapid_delayed_rectifying_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_delayed_rectifying_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="hyperpolarisation_activated_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="potassium_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_calcium_pump"/>
<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="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sustained_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_calcium_handling"/>
<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="sodium_current" component_1="membrane"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<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"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="T_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="i_Ca_T" variable_1="i_Ca_T"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="four_AP_sensitive_currents" component_1="membrane"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
<map_variables variable_2="i_sus" variable_1="i_sus"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="rapid_delayed_rectifying_potassium_current" component_1="membrane"/>
<map_variables variable_2="i_K_r" variable_1="i_K_r"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_delayed_rectifying_potassium_current" component_1="membrane"/>
<map_variables variable_2="i_K_s" variable_1="i_K_s"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="hyperpolarisation_activated_current" component_1="membrane"/>
<map_variables variable_2="i_f" variable_1="i_f"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_Na" variable_1="i_b_Na"/>
</connection>
<connection>
<map_components component_2="potassium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_K" variable_1="i_b_K"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
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<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
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<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
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<connection>
<map_components component_2="sustained_inward_current" component_1="membrane"/>
<map_variables variable_2="i_st" variable_1="i_st"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
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<map_variables variable_2="i_Ca_P" variable_1="i_Ca_P"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- Several variables are passed between the sibling components. -->
<connection>
<map_components component_2="sodium_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
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<connection>
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<connection>
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<connection>
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<connection>
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<map_variables variable_2="E_Na" variable_1="E_Na"/>
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<connection>
<map_components component_2="sodium_background_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="potassium_background_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_Ca" variable_1="E_Ca"/>
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<connection>
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<connection>
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<connection>
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<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
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<connection>
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<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_potassium_pump"/>
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<map_variables variable_2="K_o" variable_1="K_o"/>
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<connection>
<map_components component_2="ionic_concentrations" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
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<map_variables variable_2="Na_i" variable_1="Na_i"/>
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<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<!--
Various variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components component_2="sodium_current_m_gate" component_1="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="sodium_current_h_gate" component_1="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"/>
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<connection>
<map_components component_2="L_type_Ca_channel_d_gate" component_1="L_type_Ca_channel"/>
<map_variables variable_2="d_L" variable_1="d_L"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel_f_gate" component_1="L_type_Ca_channel"/>
<map_variables variable_2="f_L" variable_1="f_L"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="T_type_Ca_channel_d_gate" component_1="T_type_Ca_channel"/>
<map_variables variable_2="d_T" variable_1="d_T"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="T_type_Ca_channel_f_gate" component_1="T_type_Ca_channel"/>
<map_variables variable_2="f_T" variable_1="f_T"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="four_AP_sensitive_currents_q_gate" component_1="four_AP_sensitive_currents"/>
<map_variables variable_2="q" variable_1="q"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="four_AP_sensitive_currents_r_gate" component_1="four_AP_sensitive_currents"/>
<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="rapid_delayed_rectifying_potassium_current_P_af_gate" component_1="rapid_delayed_rectifying_potassium_current"/>
<map_variables variable_2="P_af" variable_1="P_af"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="rapid_delayed_rectifying_potassium_current_P_as_gate" component_1="rapid_delayed_rectifying_potassium_current"/>
<map_variables variable_2="P_as" variable_1="P_as"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="rapid_delayed_rectifying_potassium_current_P_as_gate" component_1="rapid_delayed_rectifying_potassium_current_P_af_gate"/>
<map_variables variable_2="P_af_infinity" variable_1="P_af_infinity"/>
</connection>
<connection>
<map_components component_2="rapid_delayed_rectifying_potassium_current_P_i_gate" component_1="rapid_delayed_rectifying_potassium_current"/>
<map_variables variable_2="P_i" variable_1="P_i"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="slow_delayed_rectifying_potassium_current_xs_gate" component_1="slow_delayed_rectifying_potassium_current"/>
<map_variables variable_2="xs" variable_1="xs"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="hyperpolarisation_activated_current_y_gate" component_1="hyperpolarisation_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"/>
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<connection>
<map_components component_2="sustained_inward_current_d_gate" component_1="sustained_inward_current"/>
<map_variables variable_2="d_s" variable_1="d_s"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="sustained_inward_current_f_gate" component_1="sustained_inward_current"/>
<map_variables variable_2="f_s" variable_1="f_s"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<rdf:value>This is the CellML description of Boyett et al's mathematical model of pacemaker activity in the sinoatrial node. Their model is a development of Zhang et al's earlier 2000 model of action potentials in SA node cells by considering intracellular Ca2+ handling. The SA node is functionally, anatomically and electrophysiologically heterogeneous. Boyett et al have considered this heterogeneity and they define two distinct models for the peripheral SA node and the central SA node. These models have the same equations but they vary in their parameters. Below is a CellML description of the model of action potentials in the periphery of the sinoatrial(SA) node. For a model of the central SA node action potential, use the equations below but substitute some parameters with the appropriate ones listed in the original paper.</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
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<vCard:Other>May</vCard:Other>
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
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<rdf:value>
The sodium current was originally thought to be absent in SA node
cells and consequently, most of the earlier models of the SA node
action potential do not include i_Na. However, more recent
experimental results show that i_Na is present and that it is
physiologically important. The sodium channel has one activation
gate m and one inactivation gate which has two components, a fast and
a slow inactivation variable; h1 and h2.
</rdf:value>
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<vCard:Given>James</vCard:Given>
<vCard:Family>Lawson</vCard:Family>
<vCard:Other>Richard</vCard:Other>
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<rdf:value>
Experimental evidence suggests that intracellular calcium controls a
number of ionic currents. Boyett et al incorporated intracellular
calcium handling into the model of Zhang et al (2000).
</rdf:value>
</rdf:Description>
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<dc:title>Boyett et al's 2001 mathematical model of control of pacemaker
activity of the sinoatrial node</dc:title>
<cmeta:bio_entity>Sinoatrial Node Cell</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#2c7108cb-490a-44f7-aac7-6ba63b4c6149"/>
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<rdf:Bag>
<rdf:li>pace-maker</rdf:li>
<rdf:li>atrial myocyte</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>electrophysiological</rdf:li>
<rdf:li>sinoatrial node</rdf:li>
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<vCard:Given>A.</vCard:Given>
<vCard:Family>Garny</vCard:Family>
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<rdf:Description rdf:about="rdf:#4796d6ca-441e-437f-a008-c591de5f933c">
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In their model, Boyett et al added the sustained inward current
described by Guo et al (1995) and Shinagawa et al (2000) in rabbit
and rat SA node cells. The equations defined below are taken from
Shinagawa et al (2000).
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<vCard:Given>H.</vCard:Given>
<vCard:Family>Zhang</vCard:Family>
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<cmeta:comment rdf:resource="rdf:#ea0d6d02-19ae-45c4-ae35-0074de6868ac"/>
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<rdf:Description rdf:about="rdf:#447c1196-702b-41f6-bbf1-208d1434d7c0">
<dc:title>Philosophical Transactions of The Royal Society, Mathematical, Physical and Engineering Sciences</dc:title>
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<dcterms:W3CDTF>2002-01-28T00:00:00+00:00</dcterms:W3CDTF>
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<vCard:Given>A.V.</vCard:Given>
<vCard:Family>Holden</vCard:Family>
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<vCard:Given>M.R.</vCard:Given>
<vCard:Family>Boyett</vCard:Family>
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Added more metadata.
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<rdf:value>
Other SA node models have included computation of concentrations of
intracellular Na+ and Ca2+. In this model, Zhang et al have assumed
that all ion concentrations remain constant.
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<dcterms:W3CDTF>2009-05-28T15:58:34+12:00</dcterms:W3CDTF>
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<dc:title>Control of the pacemaker activity of the sinoatrial node by intracellular Ca2+. Experiments and modelling</dc:title>
<bqs:volume>359</bqs:volume>
<bqs:first_page>1045</bqs:first_page>
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<bqs:last_page>1337</bqs:last_page>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<rdf:value>
The slow sigmoidal activation of i_K_s is modelled by squaring the
gating variable xs. The i_K_s channel is also slightly permeable to
Na+ ions.
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<dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
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<rdf:value>
i_f is a mixed current composed of both Na+ and K+ ions. In the
equation to describe i_f, Zhang et al included i_f_Na and i_f_K as
separate components and they also included a single activation
variable y.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#17a8fab7-9ff9-4ef6-ae9f-c5c416f5e2f0">
<vCard:N rdf:resource="rdf:#1e9e6c84-61c7-4aa2-9423-3fe741ab381e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b378fb9b-2ff3-4980-ab79-9f127d16e92f">
<dcterms:modified rdf:resource="rdf:#69132b4c-a4db-4332-b73b-7d4e15955012"/>
<rdf:value>fixed e-notation errors
updated curation status
removed reference link in documentation</rdf:value>
<cmeta:modifier rdf:resource="rdf:#17a8fab7-9ff9-4ef6-ae9f-c5c416f5e2f0"/>
</rdf:Description>
<rdf:Description rdf:about="#sodium_current">
<cmeta:comment rdf:resource="rdf:#b29b9a3e-6e5c-42a3-adb2-d15a76420329"/>
</rdf:Description>
<rdf:Description rdf:about="#four_AP_sensitive_currents">
<cmeta:comment rdf:resource="rdf:#49f80294-f412-4475-a5b3-b74fdfe6b32a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#258313e7-cf34-4d02-963d-d385963e2616">
<vCard:N rdf:resource="rdf:#6ac3bd84-ea1e-468b-9bb2-2a57c833ae03"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e022a12b-fcc4-435a-90f4-0e3a090eb803">
<rdf:value>
The potassium cuurent in rabbit SA node cells can be divided into two
kinetically different components, a fast cuurent i_K_r and a slow
current i_K_s. Activation and inactivation of i_K_r has
double-exponential time courses. To model this, Zhang et al have
used two activation variables; a fast one (P_a_f) and a slow one
(P_a_s). There is a single inactivation variable P_i.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#49f80294-f412-4475-a5b3-b74fdfe6b32a">
<rdf:value>
i_to and i_sus are respectively the transient and sustained
components of the 4-Aminopyridine-sensitive current. The current has
an activation variable r and and inactivation variable q.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5369f8d3-b90c-4f0f-a58d-6b72980c83a5">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="#sustained_inward_current">
<cmeta:comment rdf:resource="rdf:#4796d6ca-441e-437f-a008-c591de5f933c"/>
</rdf:Description>
<rdf:Description rdf:about="#T_type_Ca_channel">
<cmeta:comment rdf:resource="rdf:#a2bd07db-7119-4bc1-ac1c-32835c71483c"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_delayed_rectifying_potassium_current">
<cmeta:comment rdf:resource="rdf:#e7982718-8191-4340-9f32-3395a0f1d925"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6fa7edc3-c3ce-4ef8-adef-991f67861768">
<dcterms:modified rdf:resource="rdf:#b0be39a0-d30f-4258-9092-cd9a8831a039"/>
<rdf:value>
Corrected several equations.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#258313e7-cf34-4d02-963d-d385963e2616"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#02e18c1c-6f5c-41e7-8cd4-2f6009b2c81d">
<rdf:value>
The L-type calcium channel has two gates, an activation gate d_L and
an inactivation gate f_L.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#rapid_delayed_rectifying_potassium_current">
<cmeta:comment rdf:resource="rdf:#e022a12b-fcc4-435a-90f4-0e3a090eb803"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ce73b61e-27f3-4d47-b242-0b41bc42b526">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#116d1b4e-7e0f-4f7a-9a13-2f22b9c6b301">
<dcterms:W3CDTF>2001-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f57efa98-9e21-42a2-a43c-7b5c45ff7c90">
<vCard:N rdf:resource="rdf:#fb401e80-5d6e-42b5-9fda-059a363e37de"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fb401e80-5d6e-42b5-9fda-059a363e37de">
<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9996ac9e-ce05-40e4-be30-84fc38badf7d">
<dcterms:modified rdf:resource="rdf:#c40dbc94-6e60-4bdd-b589-4bbd3e79804e"/>
<rdf:value>
Updated syntax to conform with cellml1.1 specs
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#f57efa98-9e21-42a2-a43c-7b5c45ff7c90"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c40dbc94-6e60-4bdd-b589-4bbd3e79804e">
<dcterms:W3CDTF>2005-04-20</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a2bd07db-7119-4bc1-ac1c-32835c71483c">
<rdf:value>
The T-type calcium channel has two gates, an activation gate d_T and
an inactivation gate f_T.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#721d7928-1492-45ed-8bf2-930e997c2b89">
<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:#6ac3bd84-ea1e-468b-9bb2-2a57c833ae03">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
</rdf:RDF>
</model>
