<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 03/11/2009 at 13:56:59 using:
COR (0.9.31.1333)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
<model 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:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="yanagihara_model_1980" cmeta:id="yanagihara_model_1980" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments
</title>
<author>
<firstname>Penny</firstname>
<surname>Noble</surname>
<affiliation>
<shortaffil>University of Oxford</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML version of the model has been checked in both OpenCell and COR and it runs to recreate the published results. The units have been checked and they balance.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The pacemaker activity of the S-A node cell was explained by reconstructing the pacemaker potential using a Hodgkin-Huxley type mathematical model which was based on the reported voltage clamp data. In this model four dynamic currents, the sodium current iNa, the slow inward current, is, the potassium current, iK, and the hyperpolarization-activated current, ih, in addition to a time-dependent leak current, i1 were included. The model simulated the spontaneous action potential the current voltage relationship, and the voltage clamp experiment in normal Tyrode solution of the rabbit S-A node. Furthermore, the changes of activity induced by the potassium current blocker Ba2+, by applying constant current, acetylcholine, and epinephrine were also reconstructed. It was strongly suggested that the pacemaker depolarization in the S-A node cell is mainly due to a gradual increase of iS during diastole, and that the contribution of iK is much less compared to the potassium current iK2 in the Purkinje fiber pacemaker depolarization. The rising phase of the action potential was due to iS and the plateau phase is determined by both the inactivation of iS and activation of iK.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments, K. Yanagihara, A. Noma and H. Irisawa, 1980, <emphasis>The Japanese Journal of Physiology</emphasis>, 30, 841-857. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7265560&dopt=Abstract">PubMed ID: 7265560</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="yanagihara_1980.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the sinoatrial node model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="millisecond">
<unit prefix="milli" units="second"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="per_millisecond">
<unit exponent="-1" units="millisecond"/>
</units>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<units name="per_millivolt">
<unit exponent="-1" prefix="milli" units="volt"/>
</units>
<units name="per_millivolt_second">
<unit exponent="-1" units="millivolt"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_millivolt_millisecond">
<unit exponent="-1" units="millivolt"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="microS">
<unit prefix="micro" units="siemens"/>
</units>
<units name="microF">
<unit prefix="micro" units="farad"/>
</units>
<units name="nanoA">
<unit prefix="nano" units="ampere"/>
</units>
<units name="milliS_per_cm2">
<unit prefix="milli" units="siemens"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="microF_per_cm2">
<unit prefix="micro" units="farad"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="microA_per_cm2">
<unit prefix="micro" units="ampere"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="millisecond"/>
</component>
<component name="membrane">
<variable cmeta:id="membrane_V" initial_value="-62.83" name="V" public_interface="out" units="millivolt"/>
<variable initial_value="1" name="Cm" units="microF_per_cm2"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="i_Na" public_interface="in" units="microA_per_cm2"/>
<variable name="i_K" public_interface="in" units="microA_per_cm2"/>
<variable name="i_Leak" public_interface="in" units="microA_per_cm2"/>
<variable name="i_s" public_interface="in" units="microA_per_cm2"/>
<variable name="i_h" public_interface="in" units="microA_per_cm2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_K</ci>
<ci>i_Leak</ci>
<ci>i_s</ci>
<ci>i_h</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_channel">
<variable cmeta:id="sodium_channel_i_Na" name="i_Na" public_interface="out" units="microA_per_cm2"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="m" private_interface="in" units="dimensionless"/>
<variable name="h" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Na</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="milliS_per_cm2">0.5</cn>
<apply>
<power/>
<ci>m</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<apply>
<minus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_channel_m_gate">
<variable initial_value="0.047938" name="m" public_interface="out" units="dimensionless"/>
<variable name="alpha_m" units="per_millisecond"/>
<variable name="beta_m" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">1</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">37</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">37</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">40</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">62</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">17.8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_m</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_m</ci>
<ci>m</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_channel_h_gate">
<variable initial_value="0.95994" name="h" public_interface="out" units="dimensionless"/>
<variable name="alpha_h" units="per_millisecond"/>
<variable name="beta_h" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_h</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="per_millisecond">1.209 <sep/>
-3</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">6.534</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">30</cn>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_h</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>h</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_h</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_channel">
<variable cmeta:id="potassium_channel_i_K" name="i_K" public_interface="out" units="microA_per_cm2"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K</ci>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="microA_per_cm2">0.7</cn>
<ci>n</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.0277</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">90</cn>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.0277</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_channel_n_gate">
<variable initial_value="0.509494" name="n" public_interface="out" units="dimensionless"/>
<variable name="alpha_n" units="per_millisecond"/>
<variable name="beta_n" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_n</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.009</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">3.8</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">9.71</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.0006</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_n</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="per_millivolt_millisecond">2.25 <sep/>
-4</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">13.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_n</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>n</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_n</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="leakage_current">
<variable cmeta:id="leakage_current_i_Leak" name="i_Leak" public_interface="out" units="microA_per_cm2"/>
<variable name="V" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Leak</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="microA_per_cm2">0.8</cn>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">60</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_channel">
<variable cmeta:id="calcium_channel_i_s" name="i_s" public_interface="out" units="microA_per_cm2"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="d" private_interface="in" units="dimensionless"/>
<variable name="f" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_s</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="microA_per_cm2">12.5</cn>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.95</cn>
<ci>d</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.95</cn>
<ci>f</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">15</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_channel_d_gate">
<variable initial_value="0.000032" name="d" public_interface="out" units="dimensionless"/>
<variable name="alpha_d" units="per_millisecond"/>
<variable name="beta_d" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_d</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.0145</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">35</cn>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">2.5</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.03125</cn>
<ci>V</ci>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4.8</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="per_millivolt_millisecond">4.21 <sep/>
-3</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">2.5</cn>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_d</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>d</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_d</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_channel_f_gate">
<variable initial_value="1" name="f" public_interface="out" units="dimensionless"/>
<variable name="alpha_f" units="per_millisecond"/>
<variable name="beta_f" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_f</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="per_millivolt_millisecond">3.55 <sep/>
-4</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5.633</cn>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f</ci>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.000944</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">60</cn>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">29.5</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4.16</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_f</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>f</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_f</ci>
<ci>f</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarization_activated_channel">
<variable cmeta:id="hyperpolarization_activated_channel_i_h" name="i_h" public_interface="out" units="microA_per_cm2"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="q" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_h</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="milliS_per_cm2">0.4</cn>
<ci>q</ci>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">45</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarization_activated_channel_q_gate">
<variable initial_value="0.010759" name="q" public_interface="out" units="dimensionless"/>
<variable name="alpha_q" units="per_millisecond"/>
<variable name="beta_q" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_q</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.00034</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">100</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">100</cn>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4.4</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.0000495</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_q</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.0005</cn>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">40</cn>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.0000845</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_q</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>q</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_q</ci>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_channel">
<component_ref component="sodium_channel_m_gate"/>
<component_ref component="sodium_channel_h_gate"/>
</component_ref>
<component_ref component="potassium_channel">
<component_ref component="potassium_channel_n_gate"/>
</component_ref>
<component_ref component="leakage_current"/>
<component_ref component="calcium_channel">
<component_ref component="calcium_channel_d_gate"/>
<component_ref component="calcium_channel_f_gate"/>
</component_ref>
<component_ref component="hyperpolarization_activated_channel">
<component_ref component="hyperpolarization_activated_channel_q_gate"/>
</component_ref>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="sodium_channel">
<component_ref component="sodium_channel_m_gate"/>
<component_ref component="sodium_channel_h_gate"/>
</component_ref>
<component_ref component="potassium_channel">
<component_ref component="potassium_channel_n_gate"/>
</component_ref>
<component_ref component="calcium_channel">
<component_ref component="calcium_channel_d_gate"/>
<component_ref component="calcium_channel_f_gate"/>
</component_ref>
<component_ref component="hyperpolarization_activated_channel">
<component_ref component="hyperpolarization_activated_channel_q_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="calcium_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="potassium_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="hyperpolarization_activated_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_channel"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="potassium_channel"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K" variable_2="i_K"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="calcium_channel"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_s" variable_2="i_s"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="leakage_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Leak" variable_2="i_Leak"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="hyperpolarization_activated_channel"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_h" variable_2="i_h"/>
</connection>
<connection>
<map_components component_1="sodium_channel" component_2="sodium_channel_m_gate"/>
<map_variables variable_1="m" variable_2="m"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="sodium_channel" component_2="sodium_channel_h_gate"/>
<map_variables variable_1="h" variable_2="h"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="potassium_channel" component_2="potassium_channel_n_gate"/>
<map_variables variable_1="n" variable_2="n"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="calcium_channel" component_2="calcium_channel_d_gate"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="calcium_channel" component_2="calcium_channel_f_gate"/>
<map_variables variable_1="f" variable_2="f"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="hyperpolarization_activated_channel" component_2="hyperpolarization_activated_channel_q_gate"/>
<map_variables variable_1="q" variable_2="q"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:nodeID="n1"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:nodeID="n2"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n3"/></N></rdf:Description><rdf:Description rdf:nodeID="n4"><maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">100</maximumStepSize><pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">100000</pointDensity><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">2000</endingValue></rdf:Description><rdf:Description rdf:nodeID="n5"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">K</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Yanagihara</Family></rdf:Description><rdf:Description rdf:nodeID="n6"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n5"/></N></rdf:Description><rdf:Description rdf:nodeID="n7"><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n8"/></JournalArticle><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">7265560</Pubmed_id></rdf:Description><rdf:Description rdf:nodeID="n9"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n10"/></boundIntervals></rdf:Description><rdf:Description rdf:nodeID="n8"><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">841</first_page><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n11"/></creator><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments
</title><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n12"/></issued><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n13"/></Journal><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">857</last_page><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">30</volume></rdf:Description><rdf:Description rdf:nodeID="n14"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n6"/></Person></rdf:Description><rdf:Description rdf:nodeID="n15"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2009-11-04</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n16"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n17"/></N></rdf:Description><rdf:Description rdf:nodeID="n10"><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest><rdf:first><rdf:Description rdf:nodeID="n4"/></rdf:first></rdf:Description><rdf:Description rdf:nodeID="n18"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n16"/></Person></rdf:Description><rdf:Description rdf:nodeID="n19"><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Oxford</Orgname><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Department of Physiology, Anatomy and Genetics</Orgunit></rdf:Description><rdf:Description rdf:nodeID="n20"><rdf:type><rdf:Description rdf:about="http://www.example.org/foo/bar/bazfoo"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n21"><rdf:value xml:lang="en">penny.noble@dpag.ox.ac.uk</rdf:value><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n22"/></creator><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n15"/></created></rdf:Description><rdf:Description rdf:nodeID="n23"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Penny</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Noble</Family></rdf:Description><rdf:Description rdf:about="#yanagihara_model_1980"><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n9"/></simulation><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n24"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n7"/></reference><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
The Yanagihara et al. 1980 model of the rabbit sinoatrial node pacemaker cell.
</title><cmeta:comment><rdf:Description rdf:nodeID="n25"/></cmeta:comment><cmeta:bio_entity xml:lang="en">sinoatrial node pacemaker cell</cmeta:bio_entity><cmeta:species xml:lang="en">Rabbit</cmeta:species></rdf:Description><rdf:Description rdf:nodeID="n26"><rdf:_4 xml:lang="en">electrophysiology</rdf:_4><rdf:_2 xml:lang="en">pacemaker cell</rdf:_2><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_1 xml:lang="en">sinoatrial nodel</rdf:_1><rdf:_3 xml:lang="en">cardiac</rdf:_3></rdf:Description><rdf:Description rdf:nodeID="n17"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">H</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Irisawa</Family></rdf:Description><rdf:Description rdf:nodeID="n27"><rdf:value><rdf:Description rdf:nodeID="n26"/></rdf:value><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type></rdf:Description><rdf:Description rdf:nodeID="n28"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n2"/></Person></rdf:Description><rdf:Description rdf:nodeID="n25"><rdf:value xml:lang="en">
This is the CellML description of Yanagihara et al.'s mathematical model of membrane action potentials in rabbit sinoatrial nodea pacemaker cells
</rdf:value><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n1"/></creator></rdf:Description><rdf:Description rdf:nodeID="n24"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n27"/></subject></rdf:Description><rdf:Description rdf:nodeID="n12"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">1980</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n11"><rdf:_2><rdf:Description rdf:nodeID="n28"/></rdf:_2><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type><rdf:_1><rdf:Description rdf:nodeID="n14"/></rdf:_1><rdf:_3><rdf:Description rdf:nodeID="n18"/></rdf:_3></rdf:Description><rdf:Description rdf:nodeID="n22"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n23"/></N><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n21"/></EMAIL><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n19"/></ORG></rdf:Description><rdf:Description rdf:nodeID="n13"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">The Japanese Journal of Physiology</title></rdf:Description><rdf:Description rdf:nodeID="n3"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">A</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Noma</Family></rdf:Description></rdf:RDF></model>
