- Author:
- James Lawson <j.lawson@auckland.ac.nz>
- Date:
- 2009-07-09 15:03:26+12:00
- Desc:
- updated documentation
- Permanent Source URI:
- http://models.cellml.org/workspace/dokos_celler_lovell_1996/rawfile/25321b7715b6f9967e8723d92d9572ecef753a8d/dokos_celler_lovell_1996.cellml
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<article>
<articleinfo>
<title>A Single Cell Mathematical Model of the Ion Currents Underlying Sinoatrial Node Pacemaker Activity</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model has been validated by Penny Noble of Oxford University and is known to run in COR and PCEnv. A PCEnv session file is also associated with this version.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Sinoatrial (SA) node cells have an inherent ability to generate a depolarising, unstable resting potential leading to automaticity. The rhythmic, electrical activity of the sinoatrial cells set the rate at which the entire heart beats, hence the sinoatrial node myocytes are referred to as the pacemaker cells. The mechanism underlying this automaticity is a net inward ion flux, which immediately follows the action potential repolarisation phase. The relative contributions of the various ionic currents involved in this net ionic influx are the subject of a study by Socrates Dokos, Branko Celler and Nigel Lovell (1996). Using Hodgkin-Huxley (The Hodgkin-Huxley Squid Axon Model, 1952) type formulations of gated membrane currents, they develop a single cell mathematical model of the ion currents underlying sinoatrial node pacemaker activity (the complete original paper reference is cited below).
</para>
<para>
In their paper they review the existing theories of pacemaker generation. These include:
<itemizedlist>
<listitem>
<para>The idea that pacemaker potential is primarily due to the decline of the outward delayed rectifier current, <emphasis>i<subscript>K</subscript>
</emphasis>, which uncovers a background inward current, leading to membrane depolarisation.</para>
</listitem>
<listitem>
<para>The hypothesis that pacemaker activity arises from a time-dependent inward current, such as the hyperpolarisation-activated current,<emphasis>i<subscript>f</subscript>
</emphasis>.</para>
</listitem>
<listitem>
<para>The idea that the L-type Ca<superscript>2+</superscript> current <emphasis>i<subscript>Ca,L</subscript>
</emphasis>, supplies the inward flux for pacemaker depolarisation.</para>
</listitem>
</itemizedlist>
</para>
<para>
Earlier efforts to simulate the pacemaker activity of the SA node cells include mathematical models developed by Noble and Noble, 1984, and Demir <emphasis>et al.</emphasis>, 1994. (Since this model was published in 1996, other SA node models have been developed, including: Demir <emphasis>et al.</emphasis>, 1999, Zhang <emphasis>et al.</emphasis>, 2000, and Boyett <emphasis>et al.</emphasis>, 2001). However, despite the developments in enzyme isolation techniques which have led to the improved characterisation of SA node currents, the single cell mathematical models which have been developed are significantly different from each other. In addition, despite the relatively large number of models, none specifically focus on the ionic currents underlying the various phases of the mammalian SA node pacemaker action potential.
</para>
<para>
This has become the focus of the Dokos <emphasis>et al.</emphasis> 1996 model, which is based on experimental data recorded in isolated rabbit SA node myocytes, and taken from a number of different published studies. The model is an extension of previously published SA cell models (see above), and the complete cell model (see the figure below) includes nine membrane currents which interact to generate spontaneous pacemaker activity. The model also includes variations in extracellular and cytosolic ion concentrations, and ion fluxes between the cytosol and the sarcoplasmic reticulum.
</para>
<para>
Model simulations suggest that the main ion current underlying pacemaker activity is the inward background sodium current <emphasis>i<subscript>b,Na</subscript>
</emphasis>. The decay of the delayed rectifying K<superscript>+</superscript> current <emphasis>i<subscript>K</subscript>
</emphasis>, and the presence of the hyperpolarisation-activated current <emphasis>i<subscript>f</subscript>
</emphasis>, were insignificant, and were not essential to pacemaker activity.
</para>
<para>
Ion Currents Underlying Sinoatrial Node Pacemaker Activity: A New Single Cell Mathematical Model, Socrates Dokos, Branko Celler, and Nigel Lovell, 1996,
<emphasis>Theoretical Journal of Biology</emphasis>
, 181, 245-272. (A PDF version of the article is available to subscribers of the Theoretical Journal of Biology.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8869126&dopt=Abstract">PubMed ID: 8869126</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
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<objectinfo>
<title>cell diagram</title>
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<imagedata fileref="dokos_1996.png"/>
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</mediaobject>
<caption>A schematic diagram of the Dokos <emphasis>et al.</emphasis> 1996 mathematical model of the SA node cell. Sodium, calcium and potassium ions are exchanged between the intracellular and extracellular environments through channels, the sodium-potassium pump and the sodium-calcium exchanger. Calcium is transferred between the cytosol and the sarcoplasmic reticulum (SR), and between the local regions of the SR.</caption>
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</sect1>
</article>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">200</cn>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">34.3</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.09</cn>
</apply>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">34.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<times/>
<cn cellml:units="per_second">8000</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.15</cn>
</apply>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">56.2</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 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="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.0087"/>
<variable units="per_second" name="alpha_h"/>
<variable units="per_second" name="beta_h"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_h</ci>
<apply>
<times/>
<cn cellml:units="per_second">32.4</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.14</cn>
</apply>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">93.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<apply>
<divide/>
<cn cellml:units="per_second">709</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4.2</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.06</cn>
</apply>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">45.4</cn>
</apply>
</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 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="delayed_rectifying_potassium_current">
<variable units="picoA" public_interface="out" name="i_K" cmeta:id="delayed_rectifying_potassium_current_i_K"/>
<variable units="picoA" public_interface="out" name="i_KK"/>
<variable units="picoA" public_interface="out" name="i_KNa"/>
<variable units="picoA_per_millimolar" name="Kk" initial_value="0.00026"/>
<variable units="dimensionless" name="P_KNa" initial_value="0.035"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
<variable units="dimensionless" private_interface="in" name="x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_KK</ci>
<apply>
<times/>
<ci>x</ci>
<ci>Kk</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ko</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<cn cellml:units="dimensionless">0.59</cn>
</apply>
<apply>
<minus/>
<ci>Ki</ci>
<apply>
<times/>
<ci>Ko</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_KNa</ci>
<apply>
<times/>
<ci>x</ci>
<ci>Kk</ci>
<ci>P_KNa</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ko</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<cn cellml:units="dimensionless">0.59</cn>
</apply>
<apply>
<minus/>
<ci>Nai</ci>
<apply>
<times/>
<ci>Nao</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_K</ci>
<apply>
<plus/>
<ci>i_KK</ci>
<ci>i_KNa</ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifying_potassium_current_x_gate">
<variable units="dimensionless" public_interface="out" name="x" initial_value="0.5682"/>
<variable units="dimensionless" name="x_infinity"/>
<variable units="second" name="tau_x"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>x_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">25.1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">7.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_x</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">17</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0398</cn>
<ci>E</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.211</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.051</cn>
</apply>
<ci>E</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>x_infinity</ci>
<ci>x</ci>
</apply>
<ci>tau_x</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarising_activated_current">
<variable units="picoA" public_interface="out" name="i_f" cmeta:id="hyperpolarising_activated_current_i_f"/>
<variable units="picoA" public_interface="out" name="i_fNa"/>
<variable units="picoA" public_interface="out" name="i_fK"/>
<variable units="millimolar" name="Kmf" initial_value="10.3"/>
<variable units="nanoS" name="g_fNa" initial_value="0.0081"/>
<variable units="nanoS" name="g_fK" initial_value="0.0135"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_fNa</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>y</ci>
<apply>
<power/>
<ci>Ko</ci>
<cn cellml:units="dimensionless">1.83</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ko</ci>
<cn cellml:units="dimensionless">1.83</cn>
</apply>
<apply>
<power/>
<ci>Kmf</ci>
<cn cellml:units="dimensionless">1.83</cn>
</apply>
</apply>
</apply>
<ci>g_fNa</ci>
<apply>
<minus/>
<ci>E</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_fK</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>y</ci>
<apply>
<power/>
<ci>Ko</ci>
<cn cellml:units="dimensionless">1.83</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ko</ci>
<cn cellml:units="dimensionless">1.83</cn>
</apply>
<apply>
<power/>
<ci>Kmf</ci>
<cn cellml:units="dimensionless">1.83</cn>
</apply>
</apply>
</apply>
<ci>g_fK</ci>
<apply>
<minus/>
<ci>E</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f</ci>
<apply>
<plus/>
<ci>i_fK</ci>
<ci>i_fNa</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarising_activated_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.0287"/>
<variable units="per_second" name="alpha_y"/>
<variable units="per_second" name="beta_y"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_y</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">0.36</cn>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">137.8</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.066</cn>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">137.8</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_y</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">0.1</cn>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">76.3</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.21</cn>
</apply>
<apply>
<plus/>
<ci>E</ci>
<cn cellml:units="millivolt">76.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_y</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_y</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="picoA" public_interface="out" name="i_p"/>
<variable units="millimolar" name="KmNa" initial_value="40"/>
<variable units="millimolar" name="KmK" initial_value="1"/>
<variable units="picoA" name="i_pmax" initial_value="0.226"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_pmax</ci>
<ci>Nai</ci>
</apply>
<apply>
<plus/>
<ci>Nai</ci>
<ci>KmNa</ci>
</apply>
</apply>
<ci>Ko</ci>
</apply>
<apply>
<plus/>
<ci>Ko</ci>
<ci>KmK</ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>E</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="millivolt">211</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchange_current">
<variable units="picoA" public_interface="out" name="i_NaCa" cmeta:id="sodium_calcium_exchange_current_i_NaCa"/>
<variable units="picoA" name="kNaCa" initial_value="4"/>
<variable units="dimensionless" name="x1"/>
<variable units="dimensionless" name="x2"/>
<variable units="dimensionless" name="x3"/>
<variable units="dimensionless" name="x4"/>
<variable units="dimensionless" name="k41"/>
<variable units="dimensionless" name="k34"/>
<variable units="dimensionless" name="k23"/>
<variable units="dimensionless" name="k21"/>
<variable units="dimensionless" name="k32"/>
<variable units="dimensionless" name="k43"/>
<variable units="dimensionless" name="k12"/>
<variable units="dimensionless" name="k14"/>
<variable units="dimensionless" name="Qci" initial_value="0.1369"/>
<variable units="dimensionless" name="Qn" initial_value="0.4315"/>
<variable units="dimensionless" name="Qco" initial_value="0"/>
<variable units="millimolar" name="K3ni" initial_value="26.44"/>
<variable units="millimolar" name="Kci" initial_value="0.0207"/>
<variable units="millimolar" name="K1ni" initial_value="395.3"/>
<variable units="millimolar" name="K2ni" initial_value="2.289"/>
<variable units="millimolar" name="Kcni" initial_value="26.44"/>
<variable units="millimolar" name="K3no" initial_value="4.663"/>
<variable units="millimolar" name="K1no" initial_value="1628"/>
<variable units="millimolar" name="K2no" initial_value="561.4"/>
<variable units="millimolar" name="Kco" initial_value="3.663"/>
<variable units="dimensionless" name="do"/>
<variable units="dimensionless" name="di"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millivolt" public_interface="in" name="E"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>do</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Cao</ci>
<ci>Kco</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>Cao</ci>
<ci>Kco</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qco</ci>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci>Nao</ci>
<ci>K1no</ci>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>Nao</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>K1no</ci>
<ci>K2no</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>Nao</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>K1no</ci>
<ci>K2no</ci>
<ci>K3no</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k32</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qn</ci>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k23</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<power/>
<ci>Nao</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>K1no</ci>
<ci>K2no</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>Nao</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>K1no</ci>
<ci>K2no</ci>
<ci>K3no</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qn</ci>
</apply>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>do</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k21</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Cao</ci>
<ci>Kco</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qco</ci>
</apply>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>do</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k34</ci>
<apply>
<divide/>
<ci>Nao</ci>
<apply>
<plus/>
<ci>K3no</ci>
<ci>Nao</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>di</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Cai</ci>
<ci>Kci</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>Cai</ci>
<ci>Kci</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qci</ci>
</apply>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Cai</ci>
<ci>Nai</ci>
</apply>
<apply>
<times/>
<ci>Kci</ci>
<ci>Kcni</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>Nai</ci>
<ci>K1ni</ci>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>Nai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>K1ni</ci>
<ci>K2ni</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>Nai</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>K1ni</ci>
<ci>K2ni</ci>
<ci>K3ni</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k41</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qn</ci>
</apply>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k14</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<power/>
<ci>Nai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>K1ni</ci>
<ci>K2ni</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci>Nai</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<times/>
<ci>K1ni</ci>
<ci>K2ni</ci>
<ci>K3ni</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qn</ci>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>di</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k12</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Cai</ci>
<ci>Kci</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qci</ci>
</apply>
<ci>E</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>di</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k43</ci>
<apply>
<divide/>
<ci>Nai</ci>
<apply>
<plus/>
<ci>K3ni</ci>
<ci>Nai</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k41</ci>
<ci>k34</ci>
<apply>
<plus/>
<ci>k23</ci>
<ci>k21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k21</ci>
<ci>k32</ci>
<apply>
<plus/>
<ci>k43</ci>
<ci>k41</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k32</ci>
<ci>k43</ci>
<apply>
<plus/>
<ci>k14</ci>
<ci>k12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k41</ci>
<ci>k12</ci>
<apply>
<plus/>
<ci>k34</ci>
<ci>k32</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x3</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k14</ci>
<ci>k43</ci>
<apply>
<plus/>
<ci>k23</ci>
<ci>k21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k12</ci>
<ci>k23</ci>
<apply>
<plus/>
<ci>k43</ci>
<ci>k41</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x4</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k23</ci>
<ci>k34</ci>
<apply>
<plus/>
<ci>k14</ci>
<ci>k12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k14</ci>
<ci>k21</ci>
<apply>
<plus/>
<ci>k34</ci>
<ci>k32</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kNaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>x2</ci>
<ci>k21</ci>
</apply>
<apply>
<times/>
<ci>x1</ci>
<ci>k12</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>x1</ci>
<ci>x2</ci>
<ci>x3</ci>
<ci>x4</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_sodium_current">
<variable units="picoA" public_interface="out" name="i_bNa"/>
<variable units="nanoS" name="g_Nab" initial_value="0.00024"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_bNa</ci>
<apply>
<times/>
<ci>g_Nab</ci>
<apply>
<minus/>
<ci>E</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_potassium_current">
<variable units="picoA" public_interface="out" name="i_bK"/>
<variable units="picoA_per_millimolar" name="KbK" initial_value="0.00007"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_bK</ci>
<apply>
<times/>
<ci>KbK</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ko</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<cn cellml:units="dimensionless">0.41</cn>
</apply>
<apply>
<minus/>
<ci>Ki</ci>
<apply>
<times/>
<ci>Ko</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcoplasmic_reticulum_kinetics">
<variable units="picoA" public_interface="out" name="i_up"/>
<variable units="picoA" public_interface="out" name="i_tr"/>
<variable units="picoA" public_interface="out" name="i_rel"/>
<variable units="microlitre" public_interface="in" name="V_i"/>
<variable units="microlitre" public_interface="out" name="V_rel"/>
<variable units="microlitre" public_interface="out" name="V_up"/>
<variable units="picoA" name="i_up_max" initial_value="0.0212"/>
<variable units="millimolar" name="KmCaup" initial_value="0.0005"/>
<variable units="millimolar" name="KmCarel" initial_value="0.001"/>
<variable units="second" name="tau_rel" initial_value="0.005"/>
<variable units="second" name="tau_tr" initial_value="0.4"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Caup"/>
<variable units="millimolar" public_interface="in" name="Carel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_rel</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.006</cn>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_up</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.014</cn>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_up_max</ci>
<apply>
<power/>
<ci>Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>KmCaup</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_tr</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<ci>tau_tr</ci>
</apply>
</apply>
<ci>Caup</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<ci>tau_rel</ci>
</apply>
</apply>
<ci>Carel</ci>
<apply>
<power/>
<ci>Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Cai</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>KmCarel</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ion_concentrations">
<variable units="millimolar" public_interface="out" name="Cai" initial_value="0.000034"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="2.0004"/>
<variable units="millimolar" public_interface="out" name="Caup" initial_value="0.5832"/>
<variable units="millimolar" public_interface="out" name="Carel" initial_value="0.1101"/>
<variable units="millimolar" public_interface="out" name="Nai" initial_value="7.4994"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="139.9929"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="140.0073"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4243"/>
<variable units="microlitre" public_interface="out" name="V_i" initial_value="2.5e-6"/>
<variable units="microlitre" name="V_e"/>
<variable units="second" name="tau_b" initial_value="0.1"/>
<variable units="millimolar" name="Nab" initial_value="140"/>
<variable units="millimolar" name="Cab" initial_value="2"/>
<variable units="millimolar" name="Kb" initial_value="5.4"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="picoA" public_interface="in" name="i_bNa"/>
<variable units="picoA" public_interface="in" name="i_fNa"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_p"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_KNa"/>
<variable units="picoA" public_interface="in" name="i_KK"/>
<variable units="picoA" public_interface="in" name="i_fK"/>
<variable units="picoA" public_interface="in" name="i_bK"/>
<variable units="picoA" public_interface="in" name="i_CaL"/>
<variable units="picoA" public_interface="in" name="i_CaT"/>
<variable units="picoA" public_interface="in" name="i_up"/>
<variable units="picoA" public_interface="in" name="i_rel"/>
<variable units="picoA" public_interface="in" name="i_tr"/>
<variable units="microlitre" public_interface="in" name="V_rel"/>
<variable units="microlitre" public_interface="in" name="V_up"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_e</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Nai</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<plus/>
<ci>i_bNa</ci>
<ci>i_fNa</ci>
<ci>i_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_p</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<ci>i_KNa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Nao</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<plus/>
<ci>i_bNa</ci>
<ci>i_fNa</ci>
<ci>i_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_p</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<ci>i_KNa</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_e</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Nab</ci>
<ci>Nao</ci>
</apply>
<ci>tau_b</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ki</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_KK</ci>
<ci>i_fK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_p</ci>
</apply>
</apply>
<ci>i_bK</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ko</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_KK</ci>
<ci>i_fK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_p</ci>
</apply>
</apply>
<ci>i_bK</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_e</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Kb</ci>
<ci>Ko</ci>
</apply>
<ci>tau_b</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cai</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mA_pA">1</cn>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_CaL</ci>
<ci>i_CaT</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
<ci>i_up</ci>
<apply>
<minus/>
<ci>i_rel</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cao</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_CaL</ci>
<ci>i_CaT</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_e</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Cab</ci>
<ci>Cao</ci>
</apply>
<ci>tau_b</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Caup</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<minus/>
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Carel</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mA_pA">1</cn>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="litre_micrometre3">1</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_d_gate"/>
<component_ref component="L_type_calcium_current_f_gate"/>
<component_ref component="L_type_calcium_current_f2_gate"/>
</component_ref>
<component_ref component="T_type_calcium_current">
<component_ref component="T_type_calcium_current_d_gate"/>
<component_ref component="T_type_calcium_current_f_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="delayed_rectifying_potassium_current">
<component_ref component="delayed_rectifying_potassium_current_x_gate"/>
</component_ref>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sodium_calcium_exchange_current"/>
<component_ref component="background_sodium_current"/>
<component_ref component="background_potassium_current"/>
<component_ref component="sarcoplasmic_reticulum_kinetics"/>
<component_ref component="ion_concentrations"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_d_gate"/>
<component_ref component="L_type_calcium_current_f_gate"/>
<component_ref component="L_type_calcium_current_f2_gate"/>
</component_ref>
<component_ref component="T_type_calcium_current">
<component_ref component="T_type_calcium_current_d_gate"/>
<component_ref component="T_type_calcium_current_f_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="delayed_rectifying_potassium_current">
<component_ref component="delayed_rectifying_potassium_current_x_gate"/>
</component_ref>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
</group>
<connection>
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<connection>
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<connection>
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<map_variables variable_2="Cao" variable_1="Cao"/>
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<connection>
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<connection>
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<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_p" variable_1="i_p"/>
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<connection>
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<connection>
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<connection>
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<map_variables variable_2="Carel" variable_1="Carel"/>
<map_variables variable_2="i_tr" variable_1="i_tr"/>
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<map_variables variable_2="i_rel" variable_1="i_rel"/>
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<map_variables variable_2="V_i" variable_1="V_i"/>
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<connection>
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<map_variables variable_2="i_fK" variable_1="i_fK"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
</connection>
<connection>
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<map_variables variable_2="i_bNa" variable_1="i_bNa"/>
</connection>
<connection>
<map_components component_2="L_type_calcium_current_d_gate" component_1="L_type_calcium_current"/>
<map_variables variable_2="dL" variable_1="dL"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="E" variable_1="E"/>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<map_variables variable_2="x" variable_1="x"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="E" variable_1="E"/>
</connection>
<connection>
<map_components component_2="hyperpolarising_activated_current_y_gate" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="y" variable_1="y"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="E" variable_1="E"/>
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<rdf:RDF>
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<rdf:li rdf:resource="rdf:#eca5cc77-0860-4b43-b2f1-32bcfa90e38b"/>
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<rdf:Description rdf:about="rdf:#86c035d1-4adc-4e18-bc4c-eb46192720f1">
<vCard:Given>N</vCard:Given>
<vCard:Family>Lovell</vCard:Family>
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<rdf:Description rdf:about="rdf:#ace57437-aeea-46fd-910e-93aaa6711e62">
<dcterms:modified rdf:resource="rdf:#edd1c5c4-0ad8-4b0f-a37c-92d081a800b5"/>
<rdf:value>cmeta:id's have been added to several variables to allow creation of a PCEnv session file.</rdf:value>
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<rdf:Description rdf:about="rdf:#29b2e279-f828-4d28-869a-4bb483ec2507">
<bqs:Pubmed_id>8869126</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#8df3cc09-f780-42e6-be09-2781df6cdff1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34d6402c-debe-4537-9e31-731d53191d6d">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5ccea1c1-0664-4858-b820-2785fcd42d9a">
<vCard:ORG rdf:resource="rdf:#98e79f29-dc05-486b-8f82-a4523678164a"/>
<vCard:EMAIL rdf:resource="rdf:#acfbbe34-f9dd-4218-90f6-01bdd8000e08"/>
<vCard:N rdf:resource="rdf:#8745b654-170e-45dc-8715-8bf5e193b97e"/>
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<rdf:Description rdf:about="rdf:#75aa486a-f48b-4405-b5e2-dc3a2e627175">
<dc:creator rdf:resource="rdf:#e80f779c-f090-43b2-b7da-a34a6f2fe1a3"/>
<rdf:value>This model has been validated by Penny Noble of Oxford University and is known to run in COR and PCEnv. A PCEnv session file is also associated with this version.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7d1b853b-fee1-434d-b811-84fcdfd20b1a">
<dcterms:W3CDTF>1996-08-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f02d9c27-566e-48ad-a14b-4d7146644dc5">
<dcterms:modified rdf:resource="rdf:#90a8dba4-4417-4f57-a81f-f68fe07f3bb9"/>
<rdf:value>added cmeta:id's for some variables to allow referencing by PCEnv</rdf:value>
<cmeta:modifier rdf:resource="rdf:#20a6f99f-d94a-4f9e-89e5-5fc770b3d9b6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8df3cc09-f780-42e6-be09-2781df6cdff1">
<dc:creator rdf:resource="rdf:#02c5e67d-7325-49df-8c31-eefc2f5d7393"/>
<dc:title>Ion currents underlying sinoatrial node pacemaker activity: a new single cell mathematical model</dc:title>
<bqs:volume>181(3)</bqs:volume>
<bqs:first_page>245</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#1724b578-45c5-4380-8246-fc2dd34bc2b2"/>
<dcterms:issued rdf:resource="rdf:#7d1b853b-fee1-434d-b811-84fcdfd20b1a"/>
<bqs:last_page>272</bqs:last_page>
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<vCard:N rdf:resource="rdf:#f2c2757e-e7ed-4cbb-90a6-8ffaf67f96d9"/>
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<rdf:Description rdf:about="rdf:#1724b578-45c5-4380-8246-fc2dd34bc2b2">
<dc:title>Journal of Theroretical Biology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a574a2ba-22e8-4c75-a2ec-c37859024a4b">
<dc:creator rdf:resource="rdf:#261db724-b5a5-42bc-abed-2388a95a6e0a"/>
<rdf:value>This is the CellML description of Dokos et al's 1996 mathematical
model of the ion currents underlying sinoatrial node pacemaker
activity. Please note that equations for reversal potentials were not included in the original published model and have had to be added.
Also, a current called i_KACh was included in the equations for
external and internal potassium ion concentration calculation. This
current had not been previously mentioned in the paper, and as i_KACh
is usually referred to in ischemic tissue, and also the background
potassium current i_bK had not been included in the equation, I am
assuming that this was a typo. The model authors have been contacted
and we are awaiting their reply.</rdf:value>
</rdf:Description>
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<dcterms:W3CDTF>2007-06-19T16:01:50+12:00</dcterms:W3CDTF>
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<vCard:Given>unknown</vCard:Given>
<vCard:Family>unknown</vCard:Family>
<vCard:Other>unknown</vCard:Other>
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<cmeta:modification rdf:resource="rdf:#ace57437-aeea-46fd-910e-93aaa6711e62"/>
</rdf:Description>
<rdf:Description rdf:about="#dokos_celler_lovell_1996">
<ns7:simulation rdf:resource="rdf:#$pk2nE"/>
<dc:title>unknown</dc:title>
<cmeta:comment rdf:resource="rdf:#a574a2ba-22e8-4c75-a2ec-c37859024a4b"/>
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<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>cardiac</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>Sinoatrial Node</rdf:li>
<rdf:li>pacemaker</rdf:li>
<rdf:li>sinoatrial node</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
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</rdf:Description>
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<vCard:Given>Penny</vCard:Given>
<vCard:Family>Noble</vCard:Family>
<vCard:Other>J</vCard:Other>
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<rdf:Description rdf:about="rdf:#24727d09-7250-4a4d-bbf0-addb6c67ec23">
<vCard:Given>Penny</vCard:Given>
<vCard:Family>Noble</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e80f779c-f090-43b2-b7da-a34a6f2fe1a3">
<vCard:FN>James Lawson</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#994bbbe8-76fe-4d5c-9bf0-e3afec3f89b4">
<vCard:Given>B</vCard:Given>
<vCard:Family>Celler</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8c05249a-2613-443c-8234-fa601710f804">
<vCard:Given>James</vCard:Given>
<vCard:Family>Lawson</vCard:Family>
<vCard:Other>Richard</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5c2070b9-7348-4845-990d-be21a6a4dd27">
<dcterms:modified rdf:resource="rdf:#16a51c5e-1c96-4dfc-8c81-48e872f171c6"/>
<rdf:value>This model has been validated by Penny Noble</rdf:value>
<cmeta:modifier rdf:resource="rdf:#c0f222ac-f1c1-4aaa-821b-43f5dd20ae0d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fd71e851-3895-44f3-8e03-176c535ca656">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:modified rdf:resource="rdf:#50bd5b2a-64b6-4aaf-beeb-4ec42c7b5865"/>
<rdf:value>Units checked, curated.</rdf:value>
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<ns7:boundIntervals rdf:resource="rdf:#$qk2nE"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d54dfe01-5253-4e09-ba29-2c899b8f43c3">
<dcterms:W3CDTF>2003-04-10T00:00:00+00:00</dcterms:W3CDTF>
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<ns7:endingValue>2</ns7:endingValue>
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<vCard:Given>S</vCard:Given>
<vCard:Family>Dokos</vCard:Family>
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<vCard:Given>James</vCard:Given>
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<vCard:Other>Richard</vCard:Other>
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<dcterms:W3CDTF>2007-06-19T15:55:00+12:00</dcterms:W3CDTF>
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<vCard:Orgname>unknown</vCard:Orgname>
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<vCard:N rdf:resource="rdf:#8c05249a-2613-443c-8234-fa601710f804"/>
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<dc:creator rdf:resource="rdf:#5ccea1c1-0664-4858-b820-2785fcd42d9a"/>
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<dcterms:W3CDTF>2007-12-19T14:19:12+13:00</dcterms:W3CDTF>
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<vCard:N rdf:resource="rdf:#fc49bcaf-1457-4f79-a984-5a0b7afc1205"/>
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<dcterms:W3CDTF>2006-01-01</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#261db724-b5a5-42bc-abed-2388a95a6e0a">
<vCard:FN>Catherine Lloyd</vCard:FN>
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<vCard:N rdf:resource="rdf:#24727d09-7250-4a4d-bbf0-addb6c67ec23"/>
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