- Author:
- James Lawson <j.lawson@auckland.ac.nz>
- Date:
- 2009-06-30 13:50:54+12:00
- Desc:
- updated docs
- Permanent Source URI:
- https://models.cellml.org/workspace/demir_clark_giles_1999/rawfile/9ef7ba3bb2b3434ea223d3bc05d7aeb5766989f9/demir_clark_giles_1999.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 27/02/2007 at 15:14:55 using:
COR (0.9.31.457)
Copyright 2002-2006 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
-->
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<article>
<articleinfo>
<title>A Model Of Parasympathetic Modulation Of Pacemaker Rate, 1999</title>
<author>
<firstname>Penny</firstname>
<surname>Noble</surname>
<affiliation>
<shortaffil>Oxford University</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 to reproduce the published results. A PCEnv session file is also associated with this version.
</para>
<para> ValidateCellML verifies this model as valid CellMl but detects unit inconsistencies.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 1994 S.S. Demir <emphasis>et al</emphasis> published a mathematical modelwhich describes the electrophysiological responses of a rabbit sinoatrial node cell. The model is based on voltage-clamp data from single, isolated myocytes. Ion channels, pumps and exchangers in the sarcolemma are described using equations for these known currents in mammalian pacemaker cells. The extracellular environment is treated as a diffusion limited space, and the myoplasm contains calcium binding proteins (calmodulin and troponin).
</para>
<para>
In 1999 S.S. Demir <emphasis>et al</emphasis> extended their model of the single rabbit SAN cell to enable it to simulate cellular responses to acetylcholine (ACh) and isoprenaline (Iso) and to mimic the effects of the second-messenger cAMP.
</para>
<para>
Several lines of evidence suggest that at least three distinct types of ACh-sensitive pathways are capable of modulating the electrical activity of the SAN sarcolemma; the indirect inhibitory affect of ACH via the cAMP mediated pathway which affects the I<subscript>f</subscript>, I<subscript>NaK</subscript>, I<subscript>Ca,L</subscript> and I<subscript>K</subscript>, the G-protein-mediated, direct affect of ACh on I<subscript>K,ACh</subscript> via the extrajunctional M<subscript>2</subscript>/K<subscript>ACh</subscript> muscarinic receptor, and the neuromuscular junction (J type) pathway which affects I<subscript>Na</subscript> and I<subscript>B,Na</subscript>. The components of this rabbit SAN cell model are shown in <xref linkend="fig_cell_diagram"/> below.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model, Semahat S. Demir, John W. Clark and Wayne R. Giles, 1999,
<emphasis>American Journal of Physiology</emphasis>
, 276, H2221-H2244. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10362707&dopt=Abstract">PubMed ID: 10362707</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
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<title>cell diagram of the Demir et al SAN model showing ionic currents, pumps and exchangers within the sarcolemma</title>
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</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the Demir <emphasis>et al</emphasis> 1999 model of the electrophysiological activity in a SAN cell.</caption>
</informalfigure>
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<title>the cellml rendering of the Demir et al SAN model</title>
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<caption>The network defined in the CellML description of the Demir <emphasis>et al</emphasis> 1999 model. For simplicity, not all the variables are shown.</caption>
</informalfigure>
</sect1>
</article>
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<ci>alpha_d_L</ci>
<ci>beta_d_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>d_L_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>V</ci>
<cn cellml:units="millivolt">14.1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<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>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f_L" initial_value="0.98651"/>
<variable units="per_second" name="alpha_f_L"/>
<variable units="per_second" name="beta_f_L"/>
<variable units="dimensionless" name="f_L_infinity"/>
<variable units="second" name="tau_f_L"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_f_L</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second">3.75</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f_L</ci>
<apply>
<divide/>
<cn cellml:units="per_second">30</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_L</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_f_L</ci>
<ci>beta_f_L</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_L_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>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<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>
</math>
</component>
<component name="T_type_Ca_channel">
<variable units="picoA" public_interface="out" cmeta:id="T_type_Ca_channel_i_Ca_T" name="i_Ca_T"/>
<variable units="microS" name="g_Ca_T" initial_value="0.02521"/>
<variable units="millivolt" name="E_Ca_T" initial_value="45"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d_T"/>
<variable units="dimensionless" private_interface="in" name="f_T"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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="0.02012114"/>
<variable units="per_second" name="alpha_d_T"/>
<variable units="per_second" name="beta_d_T"/>
<variable units="dimensionless" name="d_T_infinity"/>
<variable units="second" name="tau_d_T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_d_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">1068</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.3</cn>
</apply>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">1068</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d_T</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_d_T</ci>
<ci>beta_d_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>d_T_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>V</ci>
<cn cellml:units="millivolt">26.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<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>
</math>
</component>
<component name="T_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f_T" initial_value="0.1945111"/>
<variable units="per_second" name="alpha_f_T"/>
<variable units="per_second" name="beta_f_T"/>
<variable units="dimensionless" name="f_T_infinity"/>
<variable units="second" name="tau_f_T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_f_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">15.3</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">61.7</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">83.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_f_T</ci>
<apply>
<times/>
<cn cellml:units="per_second">15</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">61.7</cn>
</apply>
<cn cellml:units="millivolt">15.38</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f_T</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_f_T</ci>
<ci>beta_f_T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_T_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>V</ci>
<cn cellml:units="millivolt">61.7</cn>
</apply>
<cn cellml:units="millivolt">5.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<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>
</math>
</component>
<component name="delayed_rectifying_potassium_current">
<variable units="picoA" public_interface="out" cmeta:id="delayed_rectifying_potassium_current_i_K" name="i_K"/>
<variable units="microS" name="g_K"/>
<variable units="dimensionless" name="F_cAMP_K"/>
<variable units="millimolar" public_interface="in" name="cAMP"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="K_b"/>
<variable units="dimensionless" private_interface="in" name="P_a"/>
<variable units="dimensionless" private_interface="in" name="P_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>F_cAMP_K</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.62</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2.6129</cn>
<ci>cAMP</ci>
</apply>
<apply>
<plus/>
<ci>cAMP</ci>
<cn cellml:units="millimolar" type="e-notation">9<sep/>-3</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.025</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>g_K</ci>
<apply>
<times/>
<ci>F_cAMP_K</ci>
<cn cellml:units="microS_per_millimolar">0.00693</cn>
<apply>
<power/>
<ci>K_b</ci>
<cn cellml:units="dimensionless">0.59</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_K</ci>
<apply>
<times/>
<ci>g_K</ci>
<ci>P_a</ci>
<ci>P_i</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifying_potassium_current_P_a_gate">
<variable units="dimensionless" public_interface="out" name="P_a" initial_value="0.02302278"/>
<variable units="second" name="tau_P_a"/>
<variable units="dimensionless" name="P_a_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_a_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>V</ci>
<cn cellml:units="millivolt">5.1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">7.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_P_a</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">17</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0398</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2.11</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.051</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_a</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>P_a_infinity</ci>
<ci>P_a</ci>
</apply>
<ci>tau_P_a</ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifying_potassium_current_P_i_gate">
<variable units="dimensionless" public_interface="out" name="P_i" initial_value="0.3777728"/>
<variable units="per_second" name="alpha_P_i"/>
<variable units="per_second" name="beta_P_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_P_i</ci>
<apply>
<times/>
<cn cellml:units="per_second">100</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.0183</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_P_i</ci>
<apply>
<times/>
<cn cellml:units="per_second">656</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.00942</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_i</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_P_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>P_i</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_P_i</ci>
<ci>P_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="linear_background_current">
<variable units="picoA" public_interface="out" name="i_B"/>
<variable units="picoA" public_interface="out" name="i_B_Na"/>
<variable units="picoA" public_interface="out" name="i_B_Ca"/>
<variable units="picoA" public_interface="out" name="i_B_K"/>
<variable units="microS" name="g_B_Na" initial_value="0.00016"/>
<variable units="microS" name="g_B_Ca" initial_value="0.0000364"/>
<variable units="microS" name="g_B_K" initial_value="0.0000694"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" name="F_ACh_bNa"/>
<variable units="millimolar" public_interface="in" name="ACh"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>F_ACh_bNa</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>ACh</ci>
<apply>
<plus/>
<ci>ACh</ci>
<cn cellml:units="millimolar" type="e-notation">5<sep/>-1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_B_Na</ci>
<apply>
<times/>
<ci>F_ACh_bNa</ci>
<ci>g_B_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
<apply>
<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>
<apply>
<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>
<apply>
<eq/>
<ci>i_B</ci>
<apply>
<plus/>
<ci>i_B_Na</ci>
<ci>i_B_Ca</ci>
<ci>i_B_K</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current">
<variable units="picoA" public_interface="out" name="i_f"/>
<variable units="picoA" public_interface="out" name="i_f_Na"/>
<variable units="picoA" public_interface="out" name="i_f_K"/>
<variable units="microS" name="g_f_Na" initial_value="0.0067478"/>
<variable units="microS" name="g_f_K" initial_value="0.0128821"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="cAMP"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_f_Na</ci>
<apply>
<times/>
<ci>g_f_Na</ci>
<apply>
<power/>
<ci>y</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f_K</ci>
<apply>
<times/>
<ci>g_f_K</ci>
<apply>
<power/>
<ci>y</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">85</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_f</ci>
<apply>
<plus/>
<ci>i_f_Na</ci>
<ci>i_f_K</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.09227776"/>
<variable units="dimensionless" name="y_infinity"/>
<variable units="millivolt" name="V_half"/>
<variable units="millimolar" public_interface="in" name="cAMP"/>
<variable units="second" name="tau_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_half</ci>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="millivolt">20.5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>cAMP</ci>
<cn cellml:units="millimolar" type="e-notation">3.4<sep/>-3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millimolar" type="e-notation">5<sep/>-4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millivolt">78.56</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>y_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_half</ci>
</apply>
<cn cellml:units="millivolt">9</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_y</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.6483</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">54.06</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">24.33</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless">14.01055</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">0.7</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">5.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<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>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="picoA" public_interface="out" cmeta:id="sodium_potassium_pump_i_NaK" name="i_NaK"/>
<variable units="millimolar" name="K_m_Na" initial_value="5.46"/>
<variable units="millimolar" name="K_m_K" initial_value="0.621"/>
<variable units="nanoA" name="i_NaK_max" initial_value="0.2192"/>
<variable units="dimensionless" name="F_cAMP_NaK"/>
<variable units="millimolar" public_interface="in" name="cAMP"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="K_c"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>F_cAMP_NaK</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.6</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>cAMP</ci>
<cn cellml:units="millimolar" type="e-notation">3.75<sep/>-3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millimolar" type="e-notation">1.5<sep/>-4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.99</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>i_NaK</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
<ci>F_cAMP_NaK</ci>
</apply>
<ci>i_NaK_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</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_c</ci>
<apply>
<plus/>
<ci>K_m_K</ci>
<ci>K_c</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dimensionless">1.6</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00015</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>F_cAMP_NaK</ci>
<ci>i_NaK_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</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>K_c</ci>
<apply>
<plus/>
<ci>K_m_K</ci>
<ci>K_c</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="dimensionless">1.6</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="calcium_pump_current">
<variable units="picoA" public_interface="out" cmeta:id="calcium_pump_current_i_Ca_P" name="i_Ca_P"/>
<variable units="nanoA" name="i_Ca_P_max" initial_value="0.02869"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca_P</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_Ca_P_max</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.0004</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_pump">
<variable units="picoA" public_interface="out" cmeta:id="sodium_calcium_pump_i_NaCa" name="i_NaCa"/>
<variable units="nanoA_per_nanomolar_4" name="K_NaCa" initial_value="0.00001248"/>
<variable units="millimolar_4" name="d_NaCa" initial_value="0.0001"/>
<variable units="dimensionless" name="gamma" initial_value="0.5"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_c"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_c"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_c</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.03743</cn>
<ci>V</ci>
<ci>gamma</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>Na_c</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.03743</cn>
<ci>V</ci>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>d_NaCa</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<power/>
<ci>Na_c</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<ci>Ca_c</ci>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="muscarinic_potassium_current">
<variable units="picoA" public_interface="out" name="i_K_ACh"/>
<variable units="picoA" name="I_K_ACh"/>
<variable units="millimolar" public_interface="in" name="ACh"/>
<variable units="microS" name="g_K_ACh"/>
<variable units="microS" name="g_K_ACh_base" initial_value="7.833e-3"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" name="P_M2_KACh"/>
<variable units="dimensionless" name="a" initial_value="0"/>
<variable units="per_second" name="alpha_a"/>
<variable units="per_second" name="beta_a"/>
<variable units="per_second" public_interface="in" name="f_Vagal"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K_ACh</ci>
<apply>
<times/>
<ci>a</ci>
<ci>I_K_ACh</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>a</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_a</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>a</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha_a</ci>
<ci>a</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_a</ci>
<apply>
<divide/>
<cn cellml:units="per_second">12.32</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<cn cellml:units="millimolar">0.0042</cn>
<ci>ACh</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_a</ci>
<apply>
<times/>
<cn cellml:units="per_second">17</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0133</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_K_ACh</ci>
<apply>
<times/>
<ci>g_K_ACh</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_K_ACh</ci>
<apply>
<times/>
<ci>P_M2_KACh</ci>
<ci>g_K_ACh_base</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_M2_KACh</ci>
<piecewise>
<piece>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.026</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>f_Vagal</ci>
<cn cellml:units="per_second">11.05</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="per_second">7.5095</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.99</cn>
</apply>
<apply>
<and/>
<apply>
<lt/>
<ci>f_Vagal</ci>
<cn cellml:units="per_second">100</cn>
</apply>
<apply>
<gt/>
<ci>f_Vagal</ci>
<cn cellml:units="per_second">25</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0.0006</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="intracellular_concentrations_and_buffer_equations">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="9.701621"/>
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="3.787018e-4"/>
<variable units="millimolar" public_interface="out" name="K_i" initial_value="1.407347e2"/>
<variable units="millimolar" name="Ca_Calmod" initial_value="0.1411678"/>
<variable units="millimolar" name="Ca_Trop" initial_value="0.07331396"/>
<variable units="millimolar" name="Ca_Mg_Trop" initial_value="0.7618549"/>
<variable units="millimolar" name="Mg_Mg_Trop" initial_value="0.2097049"/>
<variable units="dimensionless" name="phi_C"/>
<variable units="dimensionless" name="phi_TC"/>
<variable units="dimensionless" name="phi_TMgC"/>
<variable units="dimensionless" name="phi_TMgM"/>
<variable units="dimensionless" name="phi_B"/>
<variable units="millimolar" name="Mg_i" initial_value="2.5"/>
<variable units="dimensionless" name="F_C"/>
<variable units="dimensionless" name="F_TC"/>
<variable units="dimensionless" name="F_TMgC"/>
<variable units="mm_cubed" public_interface="in" name="Vol"/>
<variable units="mm_cubed" public_interface="out" name="V_i"/>
<variable units="picoA" public_interface="in" name="i_NaK"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_B_Na"/>
<variable units="picoA" public_interface="in" name="i_f_Na"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_B_K"/>
<variable units="picoA" public_interface="in" name="i_f_K"/>
<variable units="picoA" public_interface="in" name="i_Ca_L"/>
<variable units="picoA" public_interface="in" name="i_Ca_T"/>
<variable units="picoA" public_interface="in" name="i_Ca_P"/>
<variable units="picoA" public_interface="in" name="i_B_Ca"/>
<variable units="picoA" public_interface="in" name="i_up"/>
<variable units="picoA" public_interface="in" name="i_rel"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_i</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.465</cn>
<ci>Vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>phi_C</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">129000</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Ca_Calmod</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">307</cn>
<ci>Ca_Calmod</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_Calmod</ci>
</apply>
<ci>phi_C</ci>
</apply>
<apply>
<eq/>
<ci>phi_TC</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">50500</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Ca_Trop</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">252</cn>
<ci>Ca_Trop</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_Trop</ci>
</apply>
<ci>phi_TC</ci>
</apply>
<apply>
<eq/>
<ci>phi_TMgC</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">129000</cn>
<ci>Ca_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>Ca_Mg_Trop</ci>
<ci>Mg_Mg_Trop</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4.25</cn>
<ci>Ca_Mg_Trop</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_Mg_Trop</ci>
</apply>
<ci>phi_TMgC</ci>
</apply>
<apply>
<eq/>
<ci>phi_TMgM</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">1290</cn>
<ci>Mg_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>Ca_Mg_Trop</ci>
<ci>Mg_Mg_Trop</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">429</cn>
<ci>Mg_Mg_Trop</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Mg_Mg_Trop</ci>
</apply>
<ci>phi_TMgM</ci>
</apply>
<apply>
<eq/>
<ci>F_C</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.09</cn>
<ci>phi_C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>F_TC</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.031</cn>
<ci>phi_TC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>F_TMgC</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.062</cn>
<ci>phi_TMgC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>phi_B</ci>
<apply>
<plus/>
<ci>F_C</ci>
<ci>F_TC</ci>
<ci>F_TMgC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<ci>i_B_Na</ci>
<ci>i_f_Na</ci>
<ci>i_Na</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>V_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<plus/>
<ci>i_K</ci>
<ci>i_f_K</ci>
<ci>i_B_K</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>V_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
<ci>i_rel</ci>
</apply>
<apply>
<plus/>
<ci>i_Ca_L</ci>
<ci>i_Ca_T</ci>
<ci>i_Ca_P</ci>
<ci>i_B_Ca</ci>
<ci>i_up</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_i</ci>
<ci>F</ci>
</apply>
</apply>
<ci>phi_B</ci>
</apply>
</apply>
</math>
</component>
<component name="cleft_space_equations">
<variable units="millimolar" public_interface="out" name="Na_c" initial_value="139.9988"/>
<variable units="millimolar" public_interface="out" name="Ca_c" initial_value="2.00474"/>
<variable units="millimolar" public_interface="out" name="K_c" initial_value="5.389014"/>
<variable units="millimolar" public_interface="out" name="K_b" initial_value="5.4"/>
<variable units="millimolar" name="Na_b" initial_value="140"/>
<variable units="millimolar" name="Ca_b" initial_value="2"/>
<variable units="mm_cubed" public_interface="out" name="Vol" initial_value="3.497e-6"/>
<variable units="mm_cubed" name="V_c"/>
<variable units="second" name="tau_p" initial_value="0.01"/>
<variable units="picoA" public_interface="in" name="i_NaK"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_B_Na"/>
<variable units="picoA" public_interface="in" name="i_f_Na"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_B_K"/>
<variable units="picoA" public_interface="in" name="i_f_K"/>
<variable units="picoA" public_interface="in" name="i_Ca_L"/>
<variable units="picoA" public_interface="in" name="i_Ca_T"/>
<variable units="picoA" public_interface="in" name="i_Ca_P"/>
<variable units="picoA" public_interface="in" name="i_B_Ca"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_c</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.136</cn>
<ci>Vol</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Na_b</ci>
<ci>Na_c</ci>
</apply>
<ci>tau_p</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>i_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<ci>i_B_Na</ci>
<ci>i_f_Na</ci>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>V_c</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>K_b</ci>
<ci>K_c</ci>
</apply>
<ci>tau_p</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>i_NaK</ci>
</apply>
<ci>i_K</ci>
<ci>i_B_K</ci>
<ci>i_f_K</ci>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>V_c</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_c</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_b</ci>
<ci>Ca_c</ci>
</apply>
<ci>tau_p</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>i_NaCa</ci>
</apply>
<ci>i_Ca_L</ci>
<ci>i_Ca_T</ci>
<ci>i_Ca_P</ci>
<ci>i_B_Ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>V_c</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SR_Ca_uptake_and_release">
<variable units="picoA" public_interface="out" name="i_rel"/>
<variable units="picoA" public_interface="out" name="i_up"/>
<variable units="millimolar" name="Ca_up" initial_value="16.95311"/>
<variable units="nanoA" name="alpha_up" initial_value="0.08"/>
<variable units="nanoA" name="beta_up" initial_value="0.072"/>
<variable units="millimolar" name="Ca_rel" initial_value="16.85024"/>
<variable units="nanoA_per_millimolar" name="alpha_rel" initial_value="0.5"/>
<variable units="picoA" name="i_tr"/>
<variable units="millimolar" name="K1"/>
<variable units="millimolar" name="K2"/>
<variable units="millimolar" name="k_cyca" initial_value="0.00005"/>
<variable units="dimensionless" name="k_xcs" initial_value="0.9"/>
<variable units="millimolar" name="k_SRCa" initial_value="22"/>
<variable units="millimolar" name="k_rel" initial_value="0.004"/>
<variable units="per_second" name="r_act"/>
<variable units="per_second" name="r_inact"/>
<variable units="millimolar" name="Ca_Calse" initial_value="0.9528726"/>
<variable units="dimensionless" name="phi_Calse"/>
<variable units="dimensionless" name="F1" initial_value="0.1133251"/>
<variable units="dimensionless" name="F2" initial_value="0.0007594214"/>
<variable units="dimensionless" name="F3" initial_value="0.8859153"/>
<variable units="mm_cubed" public_interface="in" name="V_i"/>
<variable units="mm_cubed" name="V_up"/>
<variable units="mm_cubed" name="V_rel"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_up</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01166</cn>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_rel</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.001296</cn>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_cyca</ci>
<ci>k_xcs</ci>
</apply>
<ci>k_SRCa</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K2</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<apply>
<times/>
<ci>Ca_up</ci>
<ci>K1</ci>
</apply>
<apply>
<times/>
<ci>k_cyca</ci>
<ci>k_xcs</ci>
</apply>
<ci>k_cyca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>r_act</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">240</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="millivolt">0.08</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">240</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>r_inact</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">40</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">240</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>k_rel</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>phi_Calse</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">770</cn>
<ci>Ca_rel</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Ca_Calse</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">641</cn>
<ci>Ca_Calse</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_Calse</ci>
</apply>
<ci>phi_Calse</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.96</cn>
<ci>F3</ci>
</apply>
<apply>
<times/>
<ci>r_act</ci>
<ci>F1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>r_act</ci>
<ci>F1</ci>
</apply>
<apply>
<times/>
<ci>r_inact</ci>
<ci>F2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>r_inact</ci>
<ci>F2</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.96</cn>
<ci>F3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<ci>alpha_rel</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>F2</ci>
<apply>
<plus/>
<ci>F2</ci>
<cn cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>Ca_rel</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_tr</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>V_up</ci>
</apply>
<cn cellml:units="dimensionless">0.06418</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_up</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>beta_up</ci>
<ci>Ca_up</ci>
<ci>K1</ci>
</apply>
</apply>
<ci>K2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_up</ci>
<ci>i_tr</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_up</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_rel</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">11.48</cn>
<ci>phi_Calse</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="reversal_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_Ca"/>
<variable units="millimolar" public_interface="in" name="K_c"/>
<variable units="millimolar" public_interface="in" name="Na_c"/>
<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_c"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<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="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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_c</ci>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<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_c</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_c</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cAMP_balance">
<variable units="millimolar" public_interface="out" name="cAMP" initial_value="3e-3"/>
<variable units="millimolar" name="cGMP" initial_value="2e-3"/>
<variable units="millimolar" name="Iso" initial_value="0"/>
<variable units="millimolar" public_interface="out" name="ACh" initial_value="0"/>
<variable units="millimolar" name="Km_Iso" initial_value="0.14e-3"/>
<variable units="millimolar" name="Km_ACh" initial_value="0.14e-3"/>
<variable units="millimolar" name="K_PDE" initial_value="6"/>
<variable units="millimolar_per_second" name="K_ADC" initial_value="8e-3"/>
<variable units="millimolar_per_second" name="V_PDE" initial_value="20"/>
<variable units="dimensionless" name="P_M2_ADC" initial_value="0.02"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="per_second" public_interface="out" name="f_Vagal" initial_value="200"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>cAMP</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<minus/>
<apply>
<times/>
<ci>K_ADC</ci>
<apply>
<minus/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Iso</ci>
<apply>
<plus/>
<ci>Iso</ci>
<ci>Km_Iso</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>P_M2_ADC</ci>
<ci>ACh</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>P_M2_ADC</ci>
<ci>ACh</ci>
</apply>
<ci>Km_ACh</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>V_PDE</ci>
<ci>cGMP</ci>
<ci>cAMP</ci>
</apply>
<apply>
<plus/>
<ci>cAMP</ci>
<apply>
<times/>
<ci>K_PDE</ci>
<ci>cGMP</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="delayed_rectifying_potassium_current">
<component_ref component="delayed_rectifying_potassium_current_P_a_gate"/>
<component_ref component="delayed_rectifying_potassium_current_P_i_gate"/>
</component_ref>
<component_ref component="linear_background_current"/>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="calcium_pump_current"/>
<component_ref component="sodium_calcium_pump"/>
<component_ref component="muscarinic_potassium_current"/>
<component_ref component="intracellular_concentrations_and_buffer_equations"/>
<component_ref component="cleft_space_equations"/>
<component_ref component="SR_Ca_uptake_and_release"/>
<component_ref component="reversal_potentials"/>
<component_ref component="cAMP_balance"/>
</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="delayed_rectifying_potassium_current">
<component_ref component="delayed_rectifying_potassium_current_P_a_gate"/>
<component_ref component="delayed_rectifying_potassium_current_P_i_gate"/>
</component_ref>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
</group>
<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="delayed_rectifying_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="linear_background_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_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_pump_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_calcium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="muscarinic_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_concentrations_and_buffer_equations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cleft_space_equations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="SR_Ca_uptake_and_release"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="reversal_potentials"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cAMP_balance"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<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="delayed_rectifying_potassium_current" component_1="membrane"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="linear_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_B" variable_1="i_B"/>
</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="membrane" component_1="calcium_pump_current"/>
<map_variables variable_2="i_Ca_P" variable_1="i_Ca_P"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="sodium_calcium_pump" 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="membrane" component_1="muscarinic_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K_ACh" variable_1="i_K_ACh"/>
</connection>
<connection>
<map_components component_2="intracellular_concentrations_and_buffer_equations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="cleft_space_equations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="SR_Ca_uptake_and_release" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="reversal_potentials" component_1="membrane"/>
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<connection>
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<connection>
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<connection>
<map_components component_2="sodium_current" component_1="cleft_space_equations"/>
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<map_variables variable_2="Na_c" variable_1="Na_c"/>
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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="K_b" variable_1="K_b"/>
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<connection>
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<connection>
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<connection>
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<connection>
<map_components component_2="reversal_potentials" component_1="muscarinic_potassium_current"/>
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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="i_f_Na" variable_1="i_f_Na"/>
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<connection>
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<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
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<connection>
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<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
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<connection>
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<map_variables variable_2="i_Ca_P" variable_1="i_Ca_P"/>
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<connection>
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<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
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<connection>
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<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
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<connection>
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<map_variables variable_2="Ca_c" variable_1="Ca_c"/>
<map_variables variable_2="Na_c" variable_1="Na_c"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
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<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
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<connection>
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<map_variables variable_2="Na_c" variable_1="Na_c"/>
<map_variables variable_2="Ca_c" variable_1="Ca_c"/>
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<connection>
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<map_variables variable_2="Vol" variable_1="Vol"/>
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<connection>
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<map_variables variable_2="i_rel" variable_1="i_rel"/>
<map_variables variable_2="i_up" variable_1="i_up"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="V_i" variable_1="V_i"/>
</connection>
<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="h1" variable_1="h1"/>
<map_variables variable_2="h2" variable_1="h2"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
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<map_variables variable_2="d_L_infinity" variable_1="d_L_infinity"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="L_type_Ca_channel_f_gate" component_1="L_type_Ca_channel"/>
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<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="T_type_Ca_channel_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"/>
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<connection>
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<map_variables variable_2="P_a" variable_1="P_a"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="delayed_rectifying_potassium_current_P_i_gate" component_1="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="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"/>
<map_variables variable_2="cAMP" variable_1="cAMP"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="L_type_Ca_channel"/>
<map_variables variable_2="cAMP" variable_1="cAMP"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="delayed_rectifying_potassium_current"/>
<map_variables variable_2="cAMP" variable_1="cAMP"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="hyperpolarisation_activated_current"/>
<map_variables variable_2="cAMP" variable_1="cAMP"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="sodium_potassium_pump"/>
<map_variables variable_2="cAMP" variable_1="cAMP"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="muscarinic_potassium_current"/>
<map_variables variable_2="ACh" variable_1="ACh"/>
<map_variables variable_2="f_Vagal" variable_1="f_Vagal"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="sodium_current"/>
<map_variables variable_2="ACh" variable_1="ACh"/>
</connection>
<connection>
<map_components component_2="cAMP_balance" component_1="linear_background_current"/>
<map_variables variable_2="ACh" variable_1="ACh"/>
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<rdf:li>cardiac</rdf:li>
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<vCard:Given>Autumn</vCard:Given>
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<vCard:Other>A</vCard:Other>
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<rdf:value>added cmeta:id's for some variables to allow referencing by PCEnv session</rdf:value>
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<vCard:Given>Peter</vCard:Given>
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<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
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<rdf:value>This model has been validated by Penny Noble of Oxford University.</rdf:value>
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<rdf:value>Corrected several equations.</rdf:value>
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<rdf:value>The effects of ACh and Iso on i_Ca_L and i_K are produced indirectly via the cAMP-dependent modulation of L-type Ca2+ and K+ channel
conductance (g_Ca_L and g_K) respectively.</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
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<vCard:Other>May</vCard:Other>
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<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
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<dcterms:W3CDTF>2007-12-19T13:48:43+13:00</dcterms:W3CDTF>
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<bqs:subject_type>keyword</bqs:subject_type>
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<vCard:Given>John</vCard:Given>
<vCard:Family>Clark</vCard:Family>
<vCard:Other>W</vCard:Other>
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<vCard:Given>Semahat</vCard:Given>
<vCard:Family>Demir</vCard:Family>
<vCard:Other>S</vCard:Other>
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<dcterms:W3CDTF>2005-04-25</dcterms:W3CDTF>
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<rdf:value>i_f is modulated via a direct effect of cAMP on the
voltage-dependence of its steady-state activation variable y.</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4ac262c5-fb67-4f03-8863-8430c0142c0c">
<dcterms:modified rdf:resource="rdf:#a7d225a0-b87b-4275-a28f-e2e2393acfa3"/>
<rdf:value>Changed equivalent to eq in apply id line.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#9dd209e8-3623-4e12-af33-e9c9e72ef204"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f52f0c0a-5613-4337-a4c5-1c9592ec92d7">
<rdf:value>ACh has a direct stimulatory affect on the ACh-sensitive potassium
channel. The G-protein-mediated, direct affect of ACh on i_K_ACh
occurs via the extrajunctional M2/K_ACh muscarinic receptor. This
channel has a single gating variable a.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#74e107aa-e69e-4b03-8323-63a8dd374f64">
<dc:subject rdf:resource="rdf:#fdddd685-7dad-464c-960d-b9869185c19c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9d92c8c9-2ae8-4669-9bf0-889b0bfec98a">
<vCard:N rdf:resource="rdf:#4b555643-8880-4858-ba44-d5306efb1f56"/>
</rdf:Description>
<rdf:Description rdf:about="#T_type_Ca_channel">
<cmeta:comment rdf:resource="rdf:#f530ff7d-c7ba-4b1b-83c3-c51de5c7a062"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ca3985aa-b574-4adf-8b57-052b2b5d1681">
<vCard:ORG rdf:resource="rdf:#24d9a681-3baf-4508-9533-c2239be1c593"/>
<vCard:EMAIL rdf:resource="rdf:#cbb64d35-321e-4a06-9083-a2ce5bee5a76"/>
<vCard:N rdf:resource="rdf:#667e6f48-f54f-4120-aee1-945d7eab48d9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#417ffd9b-808c-4862-a98c-d373d6b1cda6">
<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#aa958ea1-adc6-474a-a037-df3c2ddbc52d">
<vCard:FN>James Lawson</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c54bd8a5-a410-4c49-82c9-76908b85ff94">
<dc:creator rdf:resource="rdf:#aa958ea1-adc6-474a-a037-df3c2ddbc52d"/>
<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. Model curated by Penny Noble using Demir 1994 Oxsoft Heart model code and Demir 1999 paper.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#L_type_Ca_channel">
<cmeta:comment rdf:resource="rdf:#4c84c820-8495-42b7-97e6-e3570cc58a74"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#70cc5358-26a2-4176-a99b-07c1a84dc764">
<dcterms:W3CDTF>1999-06-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8595a970-b19b-492e-8acb-840dedb4f9c5">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f530ff7d-c7ba-4b1b-83c3-c51de5c7a062">
<rdf:value>The T-type calcium channel has two gates, an activation gate d_T
and an inactivation gate f_T.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b77ca23e-cadf-4f3c-892b-a1740c6a20b3">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#4b82cb56-55dc-4d6a-a414-4934078d22b1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#61e6be0d-4bfd-490b-af36-69a701824ac0">
<rdf:value>The effects of Iso on i_NaK may be species dependent as it has been observed that Iso directly stimulates Na+-K+-ATPase activity in
rabbit ventricular myocytes (Desilets and Baumgarten, 1986), but
indirectly stimulates i_NaK in guinea pig ventricular myocytes via
a PKA phosphorylation step (Gao et al. 1992, 1994). In the absence of any quantitative evidence, in this model Demir et al. have
assumed that cAMP directly stimulates i_NaK in the rabbit SAN cell
and that this cAMP dependency may be modelled by the equations
below.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fd9c4d2c-b624-4de1-9203-73e936aea096">
<dc:title>American Journal of Physiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9dd209e8-3623-4e12-af33-e9c9e72ef204">
<vCard:N rdf:resource="rdf:#13ed244b-610e-4717-b7d8-d5092bdb3c99"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9427044e-01b8-4ddf-8a6f-2a37d2ae2bc3">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#336d44ff-22e5-433f-a34f-4450ec682f5c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#336d44ff-22e5-433f-a34f-4450ec682f5c">
<vCard:Given>Wayne</vCard:Given>
<vCard:Family>Giles</vCard:Family>
<vCard:Other>R</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b8d25898-a93d-4213-9cd6-43f8b45d9588">
<dcterms:modified rdf:resource="rdf:#e8543daf-bc07-480a-ad68-2c1ae176c5e3"/>
<rdf:value>Changed sign of i_rel in dCai-dt equation. Changed the name of sodium-calcium pump to an exchanger. Changed U_calculation from an equals sign to an equivalent sign.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#bc64dff4-7530-4d25-8a74-731bfa077326"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3097fab8-5ca4-4890-a794-57665ef91cee">
<dcterms:modified rdf:resource="rdf:#417ffd9b-808c-4862-a98c-d373d6b1cda6"/>
<rdf:value>Changed the model name so the model loads in the database easier.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#bf02be6e-6f3c-44c2-85cf-5ebbed9f38b6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ea462339-329a-4a75-b85e-fe8f216b5ac9">
<dc:creator rdf:resource="rdf:#445bd029-2aaa-4801-a87d-5870b1bdfc79"/>
<dc:title>Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model</dc:title>
<bqs:volume>276</bqs:volume>
<bqs:first_page>H2221</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#fd9c4d2c-b624-4de1-9203-73e936aea096"/>
<dcterms:issued rdf:resource="rdf:#70cc5358-26a2-4176-a99b-07c1a84dc764"/>
<bqs:last_page>H2244</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bbb0a67d-98c6-48dc-a28b-c7bd992b62f4">
<dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#demir_SAN_1999">
<cmeta:bio_entity>Sinoatrial Node Cell</cmeta:bio_entity>
<ns7:simulation rdf:resource="rdf:#$4yM4i3"/>
<dc:title>Demir et al's 1999 mathematical model of a rabbit sinoatrial node cell</dc:title>
<cmeta:species>Rabbit</cmeta:species>
<bqs:reference rdf:resource="rdf:#1b92a7f0-389f-4f9e-8b62-36b5e7f37bf0"/>
<bqs:reference rdf:resource="rdf:#74e107aa-e69e-4b03-8323-63a8dd374f64"/>
<cmeta:comment rdf:resource="rdf:#ccea4e26-cdc2-49e2-b9ea-15245fefb912"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fdf68c0f-d228-40d3-8762-71e56453220c">
<dcterms:W3CDTF>2002-02-06T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1b92a7f0-389f-4f9e-8b62-36b5e7f37bf0">
<bqs:Pubmed_id>10362707</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#ea462339-329a-4a75-b85e-fe8f216b5ac9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2668baf5-777a-4154-aed4-98ec9f3f8cf1">
<vCard:Given>James</vCard:Given>
<vCard:Family>Lawson</vCard:Family>
<vCard:Other>Richard</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#hyperpolarisation_activated_current">
<cmeta:comment rdf:resource="rdf:#d2719631-8fd3-4cc7-8124-48eb39dc8215"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e0ecc64f-e5e0-4928-b6e6-ba161efed972">
<dcterms:W3CDTF>2007-06-19T15:32:11+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3a3a01c8-5628-43ec-a2dc-1fd18701bb30">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bc64dff4-7530-4d25-8a74-731bfa077326">
<vCard:N rdf:resource="rdf:#5dd9a12d-084e-4b4d-946e-0d1603bf6586"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c424feac-20a9-42a4-b803-b3650242e85b">
<vCard:Given>Penny</vCard:Given>
<vCard:Family>Noble</vCard:Family>
<vCard:Other>J</vCard:Other>
</rdf:Description>
</rdf:RDF>
</model>
