<?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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<documentation xmlns="http://cellml.org/tmp-documentation">
<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. The units have been checked and are balanced.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We have extended our compartmental model [Am. J. Physiol. 266 (Cell Physiol. 35): C832-C852, 1994] of the single rabbit sinoatrial node (SAN) cell so that it can simulate cellular responses to bath applications of ACh and isoprenaline as well as the effects of neuronally released ACh. The model employs three different types of muscarinic receptors to explain the variety of responses observed in mammalian cardiac pacemaking cells subjected to vagal stimulation. The response of greatest interest is the ACh-sensitive change in cycle length that is not accompanied by a change in action potential duration or repolarization or hyperpolarization of the maximum diastolic potential. In this case, an ACh-sensitive K+ current is not involved. Membrane hyperpolarization occurs in response to much higher levels of vagal stimulation, and this response is also mimicked by the model. Here, an ACh-sensitive K+ current is involved. The well-known phase-resetting response of the SAN cell to single and periodically applied vagal bursts of impulses is also simulated in the presence and absence of the beta-agonist isoprenaline. Finally, the responses of the SAN cell to longer continuous trains of periodic vagal stimulation are simulated, and this can result in the complete cessation of pacemaking. Therefore, this model is 1) applicable over the full range of intensity and pattern of vagal input and 2) can offer biophysically based explanations for many of the phenomena associated with the autonomic control of cardiac pacemaking.
</para>
<para>
The 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">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the Demir et al SAN model showing ionic currents, pumps and exchangers within the sarcolemma</title>
</objectinfo>
<imagedata fileref="demir_1999.png"/>
</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>
</sect1>
</article>
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<cn cellml:units="per_millivolt">0.4</cn>
<apply>
<minus/>
<ci>V</ci>
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</apply>
<cn cellml:units="dimensionless">1</cn>
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</apply>
</apply>
<apply>
<eq/>
<ci>tau_d_L</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<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>
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<variable name="alpha_f_L" units="per_second"/>
<variable name="beta_f_L" units="per_second"/>
<variable name="f_L_infinity" units="dimensionless"/>
<variable name="tau_f_L" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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>
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</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>
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<variable name="i_Ca_T" units="nanoA" public_interface="out"/>
<variable name="g_Ca_T" units="microS" initial_value="0.02521"/>
<variable name="E_Ca_T" units="millivolt" initial_value="45"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="d_T" units="dimensionless" private_interface="in"/>
<variable name="f_T" units="dimensionless" private_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="T_type_Ca_channel_d_gate">
<variable name="d_T" units="dimensionless" initial_value="0.02012114" public_interface="out"/>
<variable name="alpha_d_T" units="per_second"/>
<variable name="beta_d_T" units="per_second"/>
<variable name="d_T_infinity" units="dimensionless"/>
<variable name="tau_d_T" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="T_type_Ca_channel_f_gate">
<variable name="f_T" units="dimensionless" initial_value="0.1945111" public_interface="out"/>
<variable name="alpha_f_T" units="per_second"/>
<variable name="beta_f_T" units="per_second"/>
<variable name="f_T_infinity" units="dimensionless"/>
<variable name="tau_f_T" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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>
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</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 xmlns="http://www.cellml.org/cellml/1.0#" name="delayed_rectifying_potassium_current">
<variable name="i_K" units="nanoA" public_interface="out"/>
<variable name="g_K" units="microS"/>
<variable name="F_cAMP_K" units="dimensionless"/>
<variable name="cAMP" units="millimolar" public_interface="in"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="K_b" units="millimolar" public_interface="in"/>
<variable name="P_a" units="dimensionless" private_interface="in"/>
<variable name="P_i" units="dimensionless" private_interface="in"/>
<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">0.00693</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>K_b</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="delayed_rectifying_potassium_current_P_a_gate">
<variable name="P_a" units="dimensionless" initial_value="0.02302278" public_interface="out"/>
<variable name="tau_P_a" units="second"/>
<variable name="P_a_infinity" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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="per_second">17</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0398</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">2.11</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">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 xmlns="http://www.cellml.org/cellml/1.0#" name="delayed_rectifying_potassium_current_P_i_gate">
<variable name="P_i" units="dimensionless" initial_value="0.3777728" public_interface="out"/>
<variable name="alpha_P_i" units="per_second"/>
<variable name="beta_P_i" units="per_second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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="per_millivolt">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="per_millivolt">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>
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<variable name="i_B_K" units="nanoA" public_interface="out"/>
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<variable name="g_B_Ca" units="microS" initial_value="0.0000364"/>
<variable name="g_B_K" units="microS" initial_value="0.0000694"/>
<variable name="E_Na" units="millivolt" public_interface="in"/>
<variable name="E_Ca" units="millivolt" public_interface="in"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="F_ACh_bNa" units="dimensionless"/>
<variable name="ACh" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<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>
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</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 xmlns="http://www.cellml.org/cellml/1.0#" name="hyperpolarisation_activated_current">
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<variable name="i_f_Na" units="nanoA" public_interface="out"/>
<variable name="i_f_K" units="nanoA" public_interface="out"/>
<variable name="g_f_Na" units="microS" initial_value="0.0067478"/>
<variable name="g_f_K" units="microS" initial_value="0.0128821"/>
<variable name="time" units="second" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="cAMP" units="millimolar" public_interface="in" private_interface="out"/>
<variable name="y" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<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>
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</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>
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</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 xmlns="http://www.cellml.org/cellml/1.0#" name="hyperpolarisation_activated_current_y_gate">
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<variable name="cAMP" units="millimolar" public_interface="in"/>
<variable name="tau_y" units="second"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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>
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<apply>
<minus/>
<cn cellml:units="millimolar" type="e-notation">5<sep/>-4</cn>
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</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millivolt">78.56</cn>
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</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 xmlns="http://www.cellml.org/cellml/1.0#" name="sodium_potassium_pump">
<variable name="i_NaK" units="nanoA" public_interface="out"/>
<variable name="K_m_Na" units="millimolar" initial_value="5.46"/>
<variable name="K_m_K" units="millimolar" initial_value="0.621"/>
<variable name="i_NaK_max" units="nanoA" initial_value="0.2192"/>
<variable name="F_cAMP_NaK" units="dimensionless"/>
<variable name="cAMP" units="millimolar" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="calcium_pump_current">
<variable name="i_Ca_P" units="nanoA" public_interface="out"/>
<variable name="i_Ca_P_max" units="nanoA" initial_value="0.02869"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="sodium_calcium_pump">
<variable name="i_NaCa" units="nanoA" public_interface="out"/>
<variable name="K_NaCa" units="nanoA" initial_value="0.00001248"/>
<variable name="d_NaCa" units="dimensionless" initial_value="0.0001"/>
<variable name="gamma" units="dimensionless" initial_value="0.5"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_c" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="Ca_c" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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="per_millivolt">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="per_millivolt">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="millimolar_4">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 xmlns="http://www.cellml.org/cellml/1.0#" name="muscarinic_potassium_current">
<variable name="i_K_ACh" units="nanoA" public_interface="out"/>
<variable name="I_K_ACh" units="nanoA"/>
<variable name="ACh" units="millimolar" public_interface="in"/>
<variable name="g_K_ACh" units="microS"/>
<variable name="g_K_ACh_base" units="microS" initial_value="7.833e-3"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="P_M2_KACh" units="dimensionless"/>
<variable name="a" units="dimensionless" initial_value="0"/>
<variable name="alpha_a" units="per_second"/>
<variable name="beta_a" units="per_second"/>
<variable name="f_Vagal" units="per_second" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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="per_millivolt">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 xmlns="http://www.cellml.org/cellml/1.0#" name="intracellular_concentrations_and_buffer_equations">
<variable name="Na_i" units="millimolar" initial_value="9.701621" public_interface="out"/>
<variable name="Ca_i" units="millimolar" initial_value="3.787018e-4" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="1.407347e2" public_interface="out"/>
<variable name="Ca_Calmod" units="dimensionless" initial_value="0.1411678"/>
<variable name="Ca_Trop" units="dimensionless" initial_value="0.07331396"/>
<variable name="Ca_Mg_Trop" units="dimensionless" initial_value="0.7618549"/>
<variable name="Mg_Mg_Trop" units="dimensionless" initial_value="0.2097049"/>
<variable name="phi_C" units="per_second"/>
<variable name="phi_TC" units="per_second"/>
<variable name="phi_TMgC" units="per_second"/>
<variable name="phi_TMgM" units="per_second"/>
<variable name="phi_B" units="millimolar_per_second"/>
<variable name="Mg_i" units="millimolar" initial_value="2.5"/>
<variable name="F_C" units="millimolar_per_second"/>
<variable name="F_TC" units="millimolar_per_second"/>
<variable name="F_TMgC" units="millimolar_per_second"/>
<variable name="Vol" units="mm_cubed" public_interface="in"/>
<variable name="V_i" units="mm_cubed" public_interface="out"/>
<variable name="i_NaK" units="nanoA" public_interface="in"/>
<variable name="i_NaCa" units="nanoA" public_interface="in"/>
<variable name="i_B_Na" units="nanoA" public_interface="in"/>
<variable name="i_f_Na" units="nanoA" public_interface="in"/>
<variable name="i_Na" units="nanoA" public_interface="in"/>
<variable name="i_K" units="nanoA" public_interface="in"/>
<variable name="i_B_K" units="nanoA" public_interface="in"/>
<variable name="i_f_K" units="nanoA" public_interface="in"/>
<variable name="i_Ca_L" units="nanoA" public_interface="in"/>
<variable name="i_Ca_T" units="nanoA" public_interface="in"/>
<variable name="i_Ca_P" units="nanoA" public_interface="in"/>
<variable name="i_B_Ca" units="nanoA" public_interface="in"/>
<variable name="i_up" units="nanoA" public_interface="in"/>
<variable name="i_rel" units="nanoA" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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="per_millimolar_second">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="per_second">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="per_millimolar_second">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="per_second">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="per_millimolar_second">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="per_second">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="per_millimolar_second">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="per_second">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="millimolar">0.09</cn>
<ci>phi_C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>F_TC</ci>
<apply>
<times/>
<cn cellml:units="millimolar">0.031</cn>
<ci>phi_TC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>F_TMgC</ci>
<apply>
<times/>
<cn cellml:units="millimolar">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 xmlns="http://www.cellml.org/cellml/1.0#" name="cleft_space_equations">
<variable name="Na_c" units="millimolar" initial_value="139.9988" public_interface="out"/>
<variable name="Ca_c" units="millimolar" initial_value="2.00474" public_interface="out"/>
<variable name="K_c" units="millimolar" initial_value="5.389014" public_interface="out"/>
<variable name="K_b" units="millimolar" initial_value="5.4" public_interface="out"/>
<variable name="Na_b" units="millimolar" initial_value="140"/>
<variable name="Ca_b" units="millimolar" initial_value="2"/>
<variable name="Vol" units="mm_cubed" initial_value="3.497e-6" public_interface="out"/>
<variable name="V_c" units="mm_cubed"/>
<variable name="tau_p" units="second" initial_value="0.01"/>
<variable name="i_NaK" units="nanoA" public_interface="in"/>
<variable name="i_NaCa" units="nanoA" public_interface="in"/>
<variable name="i_B_Na" units="nanoA" public_interface="in"/>
<variable name="i_f_Na" units="nanoA" public_interface="in"/>
<variable name="i_Na" units="nanoA" public_interface="in"/>
<variable name="i_K" units="nanoA" public_interface="in"/>
<variable name="i_B_K" units="nanoA" public_interface="in"/>
<variable name="i_f_K" units="nanoA" public_interface="in"/>
<variable name="i_Ca_L" units="nanoA" public_interface="in"/>
<variable name="i_Ca_T" units="nanoA" public_interface="in"/>
<variable name="i_Ca_P" units="nanoA" public_interface="in"/>
<variable name="i_B_Ca" units="nanoA" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="SR_Ca_uptake_and_release">
<variable name="i_rel" units="nanoA" public_interface="out"/>
<variable name="i_up" units="nanoA" public_interface="out"/>
<variable name="Ca_up" units="millimolar" initial_value="16.95311"/>
<variable name="alpha_up" units="nanoA" initial_value="0.08"/>
<variable name="beta_up" units="nanoA" initial_value="0.072"/>
<variable name="Ca_rel" units="millimolar" initial_value="16.85024"/>
<variable name="alpha_rel" units="nanoA_per_millimolar" initial_value="0.5"/>
<variable name="i_tr" units="nanoA"/>
<variable name="K1" units="dimensionless"/>
<variable name="K2" units="millimolar"/>
<variable name="k_cyca" units="millimolar" initial_value="0.00005"/>
<variable name="k_xcs" units="dimensionless" initial_value="0.9"/>
<variable name="k_SRCa" units="millimolar" initial_value="22"/>
<variable name="k_rel" units="millimolar" initial_value="0.004"/>
<variable name="r_act" units="per_second"/>
<variable name="r_inact" units="per_second"/>
<variable name="Ca_Calse" units="dimensionless" initial_value="0.9528726"/>
<variable name="phi_Calse" units="per_second"/>
<variable name="F1" units="dimensionless" initial_value="0.1133251"/>
<variable name="F2" units="dimensionless" initial_value="0.0007594214"/>
<variable name="F3" units="dimensionless" initial_value="0.8859153"/>
<variable name="V_i" units="mm_cubed" public_interface="in"/>
<variable name="V_up" units="mm_cubed"/>
<variable name="V_rel" units="mm_cubed"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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="per_second">240</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="per_millivolt">0.08</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">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="per_second">40</cn>
<apply>
<times/>
<cn cellml:units="per_second">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="per_millimolar_second">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="per_second">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="per_second">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="per_second">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="second">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="millimolar">11.48</cn>
<ci>phi_Calse</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="reversal_potentials">
<variable name="E_Na" units="millivolt" public_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="out"/>
<variable name="E_Ca" units="millivolt" public_interface="out"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="Na_c" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Ca_c" units="millimolar" public_interface="in"/>
<variable name="Ca_i" units="millimolar" public_interface="in"/>
<variable name="R" units="joule_per_kilomole_kelvin" public_interface="in"/>
<variable name="T" units="kelvin" public_interface="in"/>
<variable name="F" units="coulomb_per_mole" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="cAMP_balance">
<variable name="cAMP" units="millimolar" initial_value="3e-3" public_interface="out"/>
<variable name="cGMP" units="millimolar" initial_value="2e-3"/>
<variable name="Iso" units="millimolar" initial_value="0"/>
<variable name="ACh" units="millimolar" initial_value="0" public_interface="out"/>
<variable name="Km_Iso" units="millimolar" initial_value="0.14e-3"/>
<variable name="Km_ACh" units="millimolar" initial_value="0.14e-3"/>
<variable name="K_PDE" units="dimensionless" initial_value="6"/>
<variable name="K_ADC" units="millimolar_per_second" initial_value="8e-3"/>
<variable name="V_PDE" units="per_second" initial_value="20"/>
<variable name="P_M2_ADC" units="dimensionless" initial_value="0.02"/>
<variable name="time" units="second" public_interface="in"/>
<variable name="f_Vagal" units="per_second" initial_value="200" public_interface="out"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#">
<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 xmlns="http://www.cellml.org/cellml/1.0#">
<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 xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L_type_Ca_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T_type_Ca_channel" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="delayed_rectifying_potassium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="linear_background_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="hyperpolarisation_activated_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_potassium_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="calcium_pump_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_calcium_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="muscarinic_potassium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="intracellular_concentrations_and_buffer_equations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="cleft_space_equations" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="SR_Ca_uptake_and_release" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="reversal_potentials" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="cAMP_balance" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="sodium_current"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
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<rdf:RDF>
<rdf:Bag rdf:about="rdf:#d19e13e7-c8dd-4c28-bcc3-06380bf8f491">
<rdf:li>cardiac</rdf:li>
<rdf:li>signal transduction</rdf:li>
<rdf:li>sinoatrial node</rdf:li>
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
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<dcterms:modified rdf:resource="rdf:#6da77758-e06f-47be-9a78-ed6199f8dcd1"/>
<rdf:value>added cmeta:id's for some variables to allow referencing by PCEnv session</rdf:value>
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<rdf:Description rdf:about="rdf:#13ed244b-610e-4717-b7d8-d5092bdb3c99">
<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
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<rdf:Description rdf:about="rdf:#$5yM4i3">
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<rdf:first rdf:resource="rdf:#$6yM4i3"/>
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<rdf:Description rdf:about="rdf:#e8543daf-bc07-480a-ad68-2c1ae176c5e3">
<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<rdf:value>This model has been validated by Penny Noble of Oxford University.</rdf:value>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dcterms:modified rdf:resource="rdf:#bbb0a67d-98c6-48dc-a28b-c7bd992b62f4"/>
<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>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<dcterms:modified rdf:resource="rdf:#6713501e-5de1-47b7-b5d0-91f87b5a430f"/>
<rdf:value>Corrected some units.</rdf:value>
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<rdf:Description rdf:about="#sodium_potassium_pump">
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<rdf:Description rdf:about="rdf:#4b555643-8880-4858-ba44-d5306efb1f56">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#sodium_current">
<cmeta:comment rdf:resource="rdf:#a148579a-13ad-4ce5-ab34-c5796d608ad7"/>
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<dcterms:modified rdf:resource="rdf:#b2ead0e0-589d-492a-8a9b-bf395dcf69c4"/>
<rdf:value>Added more metadata.</rdf:value>
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<rdf:Description rdf:about="rdf:#6713501e-5de1-47b7-b5d0-91f87b5a430f">
<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#6da77758-e06f-47be-9a78-ed6199f8dcd1">
<dcterms:W3CDTF>2007-12-19T13:48:43+13:00</dcterms:W3CDTF>
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<dc:creator rdf:resource="rdf:#a1facdbc-b851-4a8e-aa0d-d8e2ae379e17"/>
<rdf:value>Below is a CellML description of Demir et al's 1999 mathematical model of parasympathetic modulation of sinoatrial node (SAN) pacemaker activity in a rabbit heart. Based on experimental data, this model is a development of their earlier model of the single rabbit SAN cell (1994). Modifications have been made enabling it to mimic the important effects of the second-messenger cAMP and to simulate the response of SAN cells to the neurotransmitter acetylcholine (ACh) and isoprenaline (Iso).</rdf:value>
</rdf:Description>
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:Description rdf:about="rdf:#4b82cb56-55dc-4d6a-a414-4934078d22b1">
<vCard:Given>John</vCard:Given>
<vCard:Family>Clark</vCard:Family>
<vCard:Other>W</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9d35de97-b0e8-4b67-bd1c-cbce96ab70c3">
<vCard:Given>Semahat</vCard:Given>
<vCard:Family>Demir</vCard:Family>
<vCard:Other>S</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cbb64d35-321e-4a06-9083-a2ce5bee5a76">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a7d225a0-b87b-4275-a28f-e2e2393acfa3">
<dcterms:W3CDTF>2005-04-25</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d2719631-8fd3-4cc7-8124-48eb39dc8215">
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$6yM4i3">
<ns7:endingValue>2</ns7:endingValue>
<ns7:nonstandard-pointDensity>100000</ns7:nonstandard-pointDensity>
<ns7:maximumStepSize>0.1</ns7:maximumStepSize>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5dd9a12d-084e-4b4d-946e-0d1603bf6586">
<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"/>
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<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"/>
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<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"/>
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<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>
