- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 00:29:55+12:00
- Desc:
- committing version01 of zhang_holden_kodama_honjo_lei_varghese_boyett_2000
- Permanent Source URI:
- https://models.cellml.org/workspace/zhang_holden_kodama_honjo_lei_varghese_boyett_2000/rawfile/690a72cc18e3f68617c01f18041e9a7a3757e088/zhang_holden_kodama_honjo_lei_varghese_boyett_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : zhang_SAN_model_2000.xml
CREATED : 25th 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 Zhang et al's 2000
mathematical model of action potentials in the rabbit sinoatrial node.
CHANGES:
19/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
20/04/2005 - PJV - Updated syntax to conform with cellml1.1 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="zhang_holden_kodama_honjo_lei_varghese_boyett_2000_version01" name="zhang_holden_kodama_honjo_lei_varghese_boyett_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical Model Of Action Potentials In The Periphery Of The Sinoatrial Node, 2000</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 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 (see <xref linkend="fig_cell_diagram"/> below). 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. 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>
<ulink url="http://ajpheart.physiology.org/cgi/content/abstract/279/1/H397">Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node</ulink>, H. Zhang, A.V. Holden, I. Honjo, M. Lei, T. Varghese and M.R. Boyett, 2000, <ulink url="http://ajpheart.physiology.org/">
<emphasis>Am. J. Physiol. Heart Circ. Physiol.</emphasis>
</ulink>, 279, H397-H421. (The <ulink url="http://ajpheart.physiology.org/cgi/content/full/279/1/H397">full text</ulink> of the article is available on the American Journal of Physiology website for Journal Members.) <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>
The raw CellML description of the Zhang <emphasis>et al</emphasis> 2000 peripheral SA node cell 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 Zhang et al SAN model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="cell_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the Zhang <emphasis>et al</emphasis> 2000 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 Zhang et al SAN model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the Zhang <emphasis>et al</emphasis> 2000 model. For simplicity, not all the variables are shown.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, are defined some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="microS">
<unit units="siemens" prefix="micro"/>
</units>
<units name="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="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>
<!--
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">
<variable units="millivolt" public_interface="out" name="V" initial_value="-64.35"/>
<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="millisecond" 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"/>
<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>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="sodium_current" name="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="millisecond" 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"/>
<variable units="dimensionless" name="m_infinity"/>
<variable units="millisecond" name="tau_m"/>
<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="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="millisecond"> 0.0006247 </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="millisecond"> 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="0.595"/>
<variable units="dimensionless" name="h2" initial_value="0.05250"/>
<variable units="dimensionless" name="h1_infinity"/>
<variable units="dimensionless" name="h2_infinity"/>
<variable units="millisecond" name="tau_h1"/>
<variable units="millisecond" name="tau_h2"/>
<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="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="millisecond"> 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="millisecond"> 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="millisecond"> 0.0005977 </cn>
</apply>
</apply>
<apply id="tau_h2_calculation">
<eq/>
<ci> tau_h2 </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="millisecond"> 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="millisecond"> 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="millisecond"> 0.003556 </cn>
</apply>
</apply>
</math>
</component>
<component cmeta:id="L_type_Ca_channel" name="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="millisecond" 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="0.0845"/>
<variable units="per_millisecond" name="alpha_d_L"/>
<variable units="per_millisecond" name="beta_d_L"/>
<variable units="dimensionless" name="d_L_infinity"/>
<variable units="millisecond" name="tau_d_L"/>
<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="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_millisecond"> -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>
</apply>
</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_millisecond"> 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="0.987"/>
<variable units="per_millisecond" name="alpha_f_L"/>
<variable units="per_millisecond" name="beta_f_L"/>
<variable units="dimensionless" name="f_L_infinity"/>
<variable units="millisecond" name="tau_f_L"/>
<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="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_millisecond"> 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_millisecond"> 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 cmeta:id="T_type_Ca_channel" name="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="millisecond" 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="0.01725"/>
<variable units="per_millisecond" name="alpha_d_T"/>
<variable units="per_millisecond" name="beta_d_T"/>
<variable units="dimensionless" name="d_T_infinity"/>
<variable units="millisecond" name="tau_d_T"/>
<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="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_millisecond"> 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_millisecond"> 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="0.436"/>
<variable units="per_millisecond" name="alpha_f_T"/>
<variable units="per_millisecond" name="beta_f_T"/>
<variable units="dimensionless" name="f_T_infinity"/>
<variable units="millisecond" name="tau_f_T"/>
<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="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_millisecond"> 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_millisecond"> 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 cmeta:id="four_AP_sensitive_currents" name="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="0.03649"/>
<variable units="microS" name="g_sus" initial_value="0.01"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millisecond" 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="0.663"/>
<variable units="dimensionless" name="q_infinity"/>
<variable units="millisecond" name="tau_q"/>
<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="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="millisecond"> 0.0101 </cn>
<apply>
<divide/>
<cn cellml:units="millisecond"> 0.06517 </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="millisecond"> 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="0.01970"/>
<variable units="dimensionless" name="r_infinity"/>
<variable units="millisecond" name="tau_r"/>
<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="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="millisecond"> 0.00298 </cn>
<apply>
<divide/>
<cn cellml:units="millisecond"> 0.01559 </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 cmeta:id="rapid_delayed_rectifying_potassium_current" name="rapid_delayed_rectifying_potassium_current">
<variable units="nanoA" public_interface="out" name="i_K_r"/>
<variable units="microS" name="g_K_r" initial_value="0.016"/>
<variable units="dimensionless" name="P_a"/>
<variable units="dimensionless" name="F_K_r"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millisecond" 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="0.4"/>
<variable units="dimensionless" public_interface="out" name="P_af_infinity"/>
<variable units="millisecond" name="tau_P_af"/>
<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="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="millisecond"> 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="0.327"/>
<variable units="dimensionless" name="P_as_infinity"/>
<variable units="millisecond" name="tau_P_as"/>
<variable units="dimensionless" public_interface="in" name="P_af_infinity"/>
<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="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="millisecond"> 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="0.991"/>
<variable units="dimensionless" name="P_i_infinity"/>
<variable units="millisecond" name="tau_P_i" initial_value="0.002"/>
<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="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 cmeta:id="slow_delayed_rectifying_potassium_current" name="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="millisecond" 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_millisecond" name="alpha_xs"/>
<variable units="per_millisecond" name="beta_xs"/>
<variable units="dimensionless" name="xs_infinity"/>
<variable units="millisecond" name="tau_xs"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="xs_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_millisecond"> 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 cmeta:id="hyperpolarisation_activated_current" name="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="millisecond" 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="0.05280"/>
<variable units="per_millisecond" name="alpha_y"/>
<variable units="per_millisecond" name="beta_y"/>
<variable units="dimensionless" name="y_infinity"/>
<variable units="millisecond" name="tau_y"/>
<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="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="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="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="millisecond" 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="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="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_exchanger">
<variable units="nanoA" public_interface="out" name="i_NaCa"/>
<variable units="nanoA" name="K_NaCa" initial_value="0.0000088"/>
<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="millisecond" 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="millimolar" name="K_m_Na" initial_value="5.64"/>
<variable units="millimolar" 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="millisecond" 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 cmeta:id="ionic_concentrations" name="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="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="millisecond" 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>
<ci> F </ci>
</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>
<ci> F </ci>
</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/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<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_exchanger"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="ionic_concentrations"/>
<component_ref component="reversal_and_equilibrium_potentials"/>
</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>
</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_exchanger"/>
<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>
<!--
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"/>
<map_variables variable_2="i_b_Ca" variable_1="i_b_Ca"/>
</connection>
<connection>
<map_components component_2="sodium_calcium_exchanger" component_1="membrane"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<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>
<map_components component_2="reversal_and_equilibrium_potentials" component_1="membrane"/>
<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>
<!-- 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"/>
</connection>
<connection>
<map_components component_2="sodium_current" component_1="ionic_concentrations"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
</connection>
<connection>
<map_components component_2="four_AP_sensitive_currents" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="rapid_delayed_rectifying_potassium_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="slow_delayed_rectifying_potassium_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_K_s" variable_1="E_K_s"/>
</connection>
<connection>
<map_components component_2="hyperpolarisation_activated_current" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<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"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_calcium_exchanger"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_potassium_pump"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="reversal_and_equilibrium_potentials"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
<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"/>
</connection>
<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"/>
</connection>
<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"/>
</connection>
<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"/>
</connection>
<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"/>
</connection>
<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"/>
</connection>
<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"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#72390433-0efe-4769-a32c-9e1e557200bd">
<rdf:li>Sinoatrial Node</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:li rdf:resource="rdf:#author4Vcard"/>
<rdf:li rdf:resource="rdf:#author5Vcard"/>
<rdf:li rdf:resource="rdf:#author6Vcard"/>
<rdf:li rdf:resource="rdf:#author7Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#db945292-1096-40b9-b755-ac120d1200c6">
<dc:creator rdf:resource="rdf:#da25f799-1808-4157-af1f-b0a229d44401"/>
<rdf:value>Peripheral and central action potentials differ in their kinetics and other characteristics. The peripheral action potential has a more negative takeoff potential, faster upstroke, a greater positive peak value, prominent phase 1 repolarisation, greater amplitude, shorter duration and more negative maximum diastolic potential than the central action potential. The SA node is functionally, anatomically and electrophysiologically heterogeneous. Zhang 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 Zhang et al's 2000 mathematical model of action potentials in the periphery of the rabbit 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>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
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<dcterms:created rdf:resource="rdf:#01114ef9-c622-43ec-927d-22996e9e02e3"/>
<dc:creator rdf:resource="rdf:#25527b18-2b3d-4fd8-958d-d9c68ebd9585"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author7VcardN">
<vCard:Given>M</vCard:Given>
<vCard:Family>Boyett</vCard:Family>
<vCard:Other>R</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#682e1320-532b-4040-9d57-ed11a75bd51c">
<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:#1531d5d9-020d-47f1-85ee-3da70d169002">
<dcterms:W3CDTF>2005-04-20</dcterms:W3CDTF>
</rdf:Description>
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<vCard:Given>T</vCard:Given>
<vCard:Family>Varghese</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author7Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author7VcardN"/>
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<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:#dffb7831-94b8-438d-b955-658d59eb9dca">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ec2a88a6-9bea-4765-bf98-345ac1ddd3de">
<bqs:Pubmed_id>10899081</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#a536d30b-d602-40c2-9556-012a74adc9a5"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author3VcardN">
<vCard:Given>I</vCard:Given>
<vCard:Family>Kodama</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1ebfd481-1be0-4bb6-85d0-1f108fe67811">
<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="rdf:#b76d5dae-d9bd-436a-9af0-4bffd4466184">
<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:#fee47eec-5eee-4ab6-aef4-a9db15768964">
<dc:title>American Journal of Physiology: Heart and Circulatory Physiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>A</vCard:Given>
<vCard:Family>Holden</vCard:Family>
<vCard:Other>V</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#691b1d30-5425-4edd-a634-33843c42c11d">
<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:#643568a0-6e80-4440-abe9-d17074e0c8a9">
<dcterms:modified rdf:resource="rdf:#f530e23b-d187-4a5c-87bb-7b9531201a81"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#3327804c-8afb-422c-9dca-f376bdfd9be4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#25527b18-2b3d-4fd8-958d-d9c68ebd9585">
<vCard:ORG rdf:resource="rdf:#515543be-c02b-43b8-bd3f-a4f12cc6071a"/>
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<rdf:Description rdf:about="rdf:#2595b373-66b5-4b6b-ab41-6229066fdd60">
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b4413092-85fb-48f8-9383-64e15dbf0073">
<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
</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="#ionic_concentrations">
<cmeta:comment rdf:resource="rdf:#96faf0d6-d52d-492d-a08e-349bcbe1c527"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author5VcardN">
<vCard:Given>M</vCard:Given>
<vCard:Family>Lei</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#499ab080-5540-4a3a-a060-1f836a7b2090">
<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.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#four_AP_sensitive_currents">
<cmeta:comment rdf:resource="rdf:#691b1d30-5425-4edd-a634-33843c42c11d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#96faf0d6-d52d-492d-a08e-349bcbe1c527">
<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.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#97eb8dc8-4fc5-4e99-86e0-5374b603f7da">
<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="#sodium_current">
<cmeta:comment rdf:resource="rdf:#2595b373-66b5-4b6b-ab41-6229066fdd60"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6bfd56dd-cb2b-4f06-9b80-402224bc89f3">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3fbc61f2-c8e8-40a4-b5c7-219d5cd115b9">
<dcterms:W3CDTF>2000-07-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fc814919-3aa8-4c10-ba99-a95033684661">
<vCard:N rdf:resource="rdf:#b4413092-85fb-48f8-9383-64e15dbf0073"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#01114ef9-c622-43ec-927d-22996e9e02e3">
<dcterms:W3CDTF>2002-01-25</dcterms:W3CDTF>
</rdf:Description>
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
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<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:#9acab3c0-b190-42cb-8fdc-cb8f48c34b81">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#slow_delayed_rectifying_potassium_current">
<cmeta:comment rdf:resource="rdf:#499ab080-5540-4a3a-a060-1f836a7b2090"/>
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<dcterms:modified rdf:resource="rdf:#1531d5d9-020d-47f1-85ee-3da70d169002"/>
<rdf:value>
Updated syntax to conform with cellml1.1 specs
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<vCard:Given>Catherine</vCard:Given>
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<vCard:Family>Zhang</vCard:Family>
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Added publication date information.
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<dc:title>Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node</dc:title>
<bqs:volume>279</bqs:volume>
<bqs:first_page>H397</bqs:first_page>
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<dcterms:issued rdf:resource="rdf:#3fbc61f2-c8e8-40a4-b5c7-219d5cd115b9"/>
<bqs:last_page>H421</bqs:last_page>
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<rdf:Description rdf:about="rdf:#f530e23b-d187-4a5c-87bb-7b9531201a81">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#author4VcardN">
<vCard:Given>H</vCard:Given>
<vCard:Family>Honjo</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="#hyperpolarisation_activated_current">
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<rdf:Description rdf:about="rdf:#82c0603d-3f18-4fd0-8a78-ef2ae8bec3ef">
<vCard:N rdf:resource="rdf:#dffb7831-94b8-438d-b955-658d59eb9dca"/>
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<dc:subject rdf:resource="rdf:#d0757963-7be8-4c0e-a183-ce0c5307c3e1"/>
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