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<!--
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Copyright 2002-2008 Dr Alan Garny
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CellML 1.0 was used to generate this cellular model
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<article>
<articleinfo>
<title>Improved Mathematical Model for the Primary Pacemaker Cell</title>
<author>
<firstname>Penny</firstname>
<surname>Noble</surname>
<affiliation>
<shortaffil>Cardiac Electrophysiology Group, Oxford University</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model was created from Version 01 by Penny Noble of Oxford University. Version 02 is known to run in COR and PCEnv. A PCEnv session is also associated with this model.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The pacemaker activity of the sinoatrial (SA) node initiates the spontaneous beating of the heart. Over the past decade a large body of data on the ionic currents underlying this pacemaker activity has been elucidated in patch-clamp experiments. On the basis of this data, several mathematical models describing the pace maker activity of a single rabbit SA node cell have been developed. These include:
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_D_SAN_MODEL}">Demir <emphasis>et al.</emphasis> Sinoatrial Node Model, 1994;</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_DOKOS_MODEL}">Modelling the Ion Currents Underlying Sinoatrial Node Pacemaker Activity, Dokos <emphasis>et al.</emphasis>, 1996;</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_DOKOS_MODEL_II}">A Model of Sinoatrial Node Vagal Control, Dokos <emphasis>et al.</emphasis>, 1996;</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_D99_SAN_MODEL}">Demir <emphasis>et al.</emphasis> Sinoatrial Node Model, 1999;</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_Z_SAN_MODEL}">Zhang <emphasis>et al.</emphasis> Sinoatrial Node Model, 2000; and</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_B_SAN_MODEL}">Boyett <emphasis>et al.</emphasis> Sinoatrial Node Model, 2001.</ulink>
</para>
</listitem>
</itemizedlist>
</para>
<para>
With the elucidation of more experimental data, these models have become increasingly complex, with equations that describe calcium buffering, intracellular compartmentation, and additional ionic currents through channels, pumps and exchangers. In the study by Kurata <emphasis>et al.</emphasis> described here, the aim is to develop an improved mathematical model of a single primary pacemaker cell of the rabbit SA node, in order to investigate the mechanisms underlying pacemaker generation. On the basis of the most recent experimental data, Kurata <emphasis>et al.</emphasis> updated the previously published models (see list above) in several ways:
</para>
<itemizedlist>
<listitem>
<para>A sustained inward current has been added (<emphasis>I<subscript>st</subscript>
</emphasis>).</para>
</listitem>
<listitem>
<para>The voltage- and Ca<superscript>2+</superscript>-dependent activation kinetics of the L-type calcium channel current (<emphasis>I<subscript>Ca,L</subscript>
</emphasis>) have been reformulated.</para>
</listitem>
<listitem>
<para>Expressions for the activation kinetics of the rapidly activating delayed rectifier potassium current (<emphasis>I<subscript>Kr</subscript>
</emphasis>) have been updated.</para>
</listitem>
<listitem>
<para>Revised kinetic equations for two 4-AP sensitive currents (<emphasis>I<subscript>to</subscript>
</emphasis> and <emphasis>I<subscript>sus</subscript>
</emphasis>) have been incorporated.</para>
</listitem>
<listitem>
<para>Voltage- and concentration-dependent kinetics of the Na<superscript>+</superscript>-K<superscript>+</superscript> pump current (<emphasis>I<subscript>NaK</subscript>
</emphasis>) have been reformulated.</para>
</listitem>
<listitem>
<para>The subsarcolemmal space (see <xref linkend="fig_cell_diagram"/> below) as a diffusion barrier for intracellular Ca<superscript>2+</superscript> has been added.</para>
</listitem>
</itemizedlist>
<para>
The model was validated by comparing simulation results with experimental data, and also by comparing them with those of previous mathematical models. The authors concluded that their model represented a significant improvement over previous models because it can:
<itemizedlist>
<listitem>
<para>Simulate whole cell voltage-clamp data for <emphasis>I<subscript>Ca,L</subscript>
</emphasis>, <emphasis>I<subscript>Kr</subscript>
</emphasis>, and <emphasis>I<subscript>st</subscript>
</emphasis>;</para>
</listitem>
<listitem>
<para>Reproduce the wave shapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and</para>
</listitem>
<listitem>
<para>Mimic the effects of channel blockers or Ca <superscript>2+</superscript> buffers on pacemaker activity more accurately than the previous models.</para>
</listitem>
</itemizedlist>
</para>
<para>
The model has been described here in CellML (the raw CellML description of the Kurata <emphasis>et al.</emphasis> 2002 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://ajpheart.physiology.org/cgi/content/abstract/283/5/H2074">Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell</ulink>, Yasutaka Kurata, Ichiro Hisatome, Sunao Imanishi, and Toshishige Shibamoto, 2002, <ulink url="http://ajpheart.physiology.org/">
<emphasis>American Journal of Physiology</emphasis>
</ulink>, 283, H2074-H2101. (<ulink url="http://ajpheart.physiology.org/cgi/content/full/283/5/H2074">Full text (HTML)</ulink> and <ulink url="http://ajpheart.physiology.org/cgi/reprint/283/5/H2074.pdf">PDF</ulink> versions of the article are available on the <emphasis>American Journal of Physiology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12384487&dopt=Abstract">PubMed ID: 12384487</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
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<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="kurata_2002.png"/>
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<caption>Schematic diagram depicting the intracellular compartments for Ca<superscript>2+</superscript>.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<cn cellml:units="millivolt">26.3</cn>
</apply>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.068</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>
<times/>
<cn cellml:units="dimensionless">1.068</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">26.3</cn>
</apply>
</apply>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_infinity</ci>
<ci>d</ci>
</apply>
<ci>tau_d</ci>
</apply>
</apply>
</math>
</component>
<component name="T_type_calcium_channel_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.249637570396"/>
<variable units="dimensionless" name="f_infinity"/>
<variable units="millisecond" name="tau_f"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_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/>
<ci>tau_f</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0153</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">61.7</cn>
</apply>
</apply>
<cn cellml:units="millivolt">83.3</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.015</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>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_infinity</ci>
<ci>f</ci>
</apply>
<ci>tau_f</ci>
</apply>
</apply>
</math>
</component>
<component name="rapidly_activating_delayed_rectifier_potassium_current">
<variable units="picoA" public_interface="out" name="i_Kr"/>
<variable units="nanoS" name="g_Kr"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="dimensionless" private_interface="in" name="paS"/>
<variable units="dimensionless" private_interface="in" name="paF"/>
<variable units="dimensionless" private_interface="in" name="piy"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_Kr</ci>
<apply>
<times/>
<cn cellml:units="nanoS">0.025</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ko</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<cn cellml:units="dimensionless">0.59</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Kr</ci>
<apply>
<times/>
<ci>g_Kr</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.6</cn>
<ci>paF</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.4</cn>
<ci>paS</ci>
</apply>
</apply>
<ci>piy</ci>
</apply>
</apply>
</math>
</component>
<component name="rapidly_activating_delayed_rectifier_potassium_current_pa_gate">
<variable units="dimensionless" public_interface="out" name="paS" initial_value="0.629323128348"/>
<variable units="dimensionless" public_interface="out" name="paF" initial_value="0.3493633709533"/>
<variable units="dimensionless" name="pa_infinity"/>
<variable units="millisecond" name="tau_paS"/>
<variable units="millisecond" name="tau_paF"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pa_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">23.2</cn>
</apply>
</apply>
<cn cellml:units="millivolt">10.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_paS</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">0.84655354</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0042</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.00015</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">21.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_paF</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">0.84655354</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0372</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">15.9</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.00096</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">22.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>paS</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>pa_infinity</ci>
<ci>paS</ci>
</apply>
<ci>tau_paS</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>paF</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>pa_infinity</ci>
<ci>paF</ci>
</apply>
<ci>tau_paF</ci>
</apply>
</apply>
</math>
</component>
<component name="rapidly_activating_delayed_rectifier_potassium_current_pi_gate">
<variable units="dimensionless" public_interface="out" name="piy" initial_value="0.852396631172"/>
<variable units="dimensionless" name="pi_infinity"/>
<variable units="millisecond" name="tau_pi"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pi_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">28.6</cn>
</apply>
<cn cellml:units="millivolt">17.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_pi</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">54.645</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.656</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">106.157</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>piy</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>pi_infinity</ci>
<ci>piy</ci>
</apply>
<ci>tau_pi</ci>
</apply>
</apply>
</math>
</component>
<component name="slowly_activating_delayed_rectifier_potassium_current">
<variable units="picoA" public_interface="out" name="i_Ks"/>
<variable units="nanoS" name="g_Ks" initial_value="0.0259"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millivolt" name="E_Ks"/>
<variable units="millisecond" 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="Ki"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="attojoule_per_millimole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="femtocoulomb_per_millimole" public_interface="in" name="F"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Ks</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci>Ko</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.12</cn>
<ci>Nao</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Ki</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.12</cn>
<ci>Nai</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ks</ci>
</apply>
<apply>
<power/>
<ci>n</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slowly_activating_delayed_rectifier_potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.054409723782"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n"/>
<variable units="per_millisecond" name="alpha_n"/>
<variable units="per_millisecond" name="beta_n"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>n_infinity</ci>
<apply>
<divide/>
<ci>alpha_n</ci>
<apply>
<plus/>
<ci>alpha_n</ci>
<ci>beta_n</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_n</ci>
<ci>beta_n</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_n</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.014</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
<cn cellml:units="millivolt">9</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_n</ci>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.001</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">45</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>n_infinity</ci>
<ci>n</ci>
</apply>
<ci>tau_n</ci>
</apply>
</apply>
</math>
</component>
<component name="AP_sensitive_currents">
<variable units="picoA" public_interface="out" name="i_to"/>
<variable units="picoA" public_interface="out" name="i_sus"/>
<variable units="nanoS" name="g_to" initial_value="0.18"/>
<variable units="nanoS" name="g_sus" initial_value="0.02"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="q"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<ci>q</ci>
<ci>r</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_sus</ci>
<apply>
<times/>
<ci>g_sus</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<ci>r</ci>
</apply>
</apply>
</math>
</component>
<component name="AP_sensitive_currents_q_gate">
<variable units="dimensionless" public_interface="out" name="q" initial_value="0.531446952485"/>
<variable units="dimensionless" name="q_infinity"/>
<variable units="millisecond" name="tau_q"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_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">49</cn>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_q</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.6</cn>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">65.17</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.57</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.08</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">44</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.065</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.1</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45.93</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">10.1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>q_infinity</ci>
<ci>q</ci>
</apply>
<ci>tau_q</ci>
</apply>
</apply>
</math>
</component>
<component name="AP_sensitive_currents_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="0.005550489445"/>
<variable units="dimensionless" name="r_infinity"/>
<variable units="millisecond" name="tau_r"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">19.3</cn>
</apply>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.66</cn>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond">15.59</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">1.037</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.09</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30.61</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.369</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.12</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">23.84</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">2.98</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_infinity</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarisation_activated_current">
<variable units="picoA" public_interface="out" name="i_h"/>
<variable units="picoA" public_interface="out" name="i_h_Na"/>
<variable units="picoA" public_interface="out" name="i_h_K"/>
<variable units="nanoS" name="g_h_Na" initial_value="0.1437375"/>
<variable units="nanoS" name="g_h_K" initial_value="0.2312625"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_h_Na</ci>
<apply>
<times/>
<ci>g_h_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
<apply>
<power/>
<ci>y</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_h_K</ci>
<apply>
<times/>
<ci>g_h_K</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
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<power/>
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<apply>
<eq/>
<ci>i_h</ci>
<apply>
<plus/>
<ci>i_h_Na</ci>
<ci>i_h_K</ci>
</apply>
</apply>
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<variable units="dimensionless" name="y_infinity"/>
<variable units="millisecond" name="tau_y"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>y_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
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<apply>
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<apply>
<plus/>
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<cn cellml:units="millivolt">13.5</cn>
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</apply>
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<apply>
<eq/>
<ci>tau_y</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">0.7166529</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
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</apply>
</apply>
<cn cellml:units="millivolt">45.302</cn>
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<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">73.08</cn>
</apply>
<cn cellml:units="millivolt">19.231</cn>
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</apply>
</apply>
</apply>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
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<apply>
<divide/>
<apply>
<minus/>
<ci>y_infinity</ci>
<ci>y</ci>
</apply>
<ci>tau_y</ci>
</apply>
</apply>
</math>
</component>
<component name="sustained_inward_current">
<variable units="picoA" public_interface="out" name="i_st"/>
<variable units="nanoS" name="g_st" initial_value="0.015"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millivolt" name="E_st" initial_value="37.4"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="qa"/>
<variable units="dimensionless" private_interface="in" name="qi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_st</ci>
<apply>
<times/>
<ci>g_st</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_st</ci>
</apply>
<ci>qa</ci>
<ci>qi</ci>
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</apply>
</math>
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<component name="sustained_inward_current_qa_gate">
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<variable units="dimensionless" name="qa_infinity"/>
<variable units="millisecond" name="tau_qa"/>
<variable units="per_millisecond" name="alpha_qa"/>
<variable units="per_millisecond" name="beta_qa"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>qa_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
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</apply>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
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<eq/>
<ci>tau_qa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_qa</ci>
<ci>beta_qa</ci>
</apply>
</apply>
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<apply>
<eq/>
<ci>alpha_qa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">0.15</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">11</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millisecond">0.2</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">700</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_qa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">16</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">8</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millisecond">15</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>qa</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>qa_infinity</ci>
<ci>qa</ci>
</apply>
<ci>tau_qa</ci>
</apply>
</apply>
</math>
</component>
<component name="sustained_inward_current_qi_gate">
<variable units="dimensionless" public_interface="out" name="qi" initial_value="0.333330378068"/>
<variable units="dimensionless" name="qi_infinity"/>
<variable units="millisecond" name="tau_qi"/>
<variable units="per_millisecond" name="alpha_qi"/>
<variable units="per_millisecond" name="beta_qi"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>qi_infinity</ci>
<apply>
<divide/>
<ci>alpha_qi</ci>
<apply>
<plus/>
<ci>alpha_qi</ci>
<ci>beta_qi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_qi</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">6.65</cn>
<apply>
<plus/>
<ci>alpha_qi</ci>
<ci>beta_qi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_qi</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">3100</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millisecond">700</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>V</ci>
<cn cellml:units="millivolt">70</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_qi</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">95</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millisecond">50</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">700</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.000229</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>qi</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>qi_infinity</ci>
<ci>qi</ci>
</apply>
<ci>tau_qi</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_dependent_background_current">
<variable units="picoA" public_interface="out" name="i_b_Na"/>
<variable units="nanoS" name="g_b_Na" initial_value="0.0054"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_b_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_muscarinic_potassium_channel_current">
<variable units="picoA" public_interface="out" name="i_K_ACh"/>
<variable units="picoA" name="g_K_ACh"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="attojoule_per_millimole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="femtocoulomb_per_millimole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>g_K_ACh</ci>
<apply>
<times/>
<cn cellml:units="picoA">0.0011</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ko</ci>
<cn cellml:units="millimolar">1</cn>
</apply>
<cn cellml:units="dimensionless">0.41</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_K_ACh</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K_ACh</ci>
<apply>
<minus/>
<ci>Ki</ci>
<apply>
<times/>
<ci>Ko</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millimolar">1</cn>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump_current">
<variable units="picoA" public_interface="out" name="i_NaK"/>
<variable units="millimolar" name="Km_Kp" initial_value="1.4"/>
<variable units="millimolar" name="Km_Nap" initial_value="14"/>
<variable units="picoA" name="i_NaK_max" initial_value="3.6"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<times/>
<ci>i_NaK_max</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Km_Kp</ci>
<ci>Ko</ci>
</apply>
<cn cellml:units="dimensionless">1.2</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Km_Nap</ci>
<ci>Nai</ci>
</apply>
<cn cellml:units="dimensionless">1.3</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
<cn cellml:units="millivolt">120</cn>
</apply>
</apply>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchange_current">
<variable units="picoA" public_interface="out" name="i_NaCa"/>
<variable units="picoA" name="kNaCa" initial_value="125"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="dimensionless" name="x1"/>
<variable units="dimensionless" name="x2"/>
<variable units="dimensionless" name="x3"/>
<variable units="dimensionless" name="x4"/>
<variable units="dimensionless" name="k41"/>
<variable units="dimensionless" name="k34"/>
<variable units="dimensionless" name="k23"/>
<variable units="dimensionless" name="k21"/>
<variable units="dimensionless" name="k32"/>
<variable units="dimensionless" name="k43"/>
<variable units="dimensionless" name="k12"/>
<variable units="dimensionless" name="k14"/>
<variable units="dimensionless" name="Qci" initial_value="0.1369"/>
<variable units="dimensionless" name="Qn" initial_value="0.4315"/>
<variable units="dimensionless" name="Qco" initial_value="0"/>
<variable units="millimolar" name="K3ni" initial_value="26.44"/>
<variable units="millimolar" name="Kci" initial_value="0.0207"/>
<variable units="millimolar" name="K1ni" initial_value="395.3"/>
<variable units="millimolar" name="K2ni" initial_value="2.289"/>
<variable units="millimolar" name="Kcni" initial_value="26.44"/>
<variable units="millimolar" name="K3no" initial_value="4.663"/>
<variable units="millimolar" name="K1no" initial_value="1628"/>
<variable units="millimolar" name="K2no" initial_value="561.4"/>
<variable units="millimolar" name="Kco" initial_value="3.663"/>
<variable units="dimensionless" name="do"/>
<variable units="dimensionless" name="di"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ca_sub"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="attojoule_per_millimole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="femtocoulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kNaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>x2</ci>
<ci>k21</ci>
</apply>
<apply>
<times/>
<ci>x1</ci>
<ci>k12</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>x1</ci>
<ci>x2</ci>
<ci>x3</ci>
<ci>x4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k41</ci>
<ci>k34</ci>
<apply>
<plus/>
<ci>k23</ci>
<ci>k21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k21</ci>
<ci>k32</ci>
<apply>
<plus/>
<ci>k43</ci>
<ci>k41</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k32</ci>
<ci>k43</ci>
<apply>
<plus/>
<ci>k14</ci>
<ci>k12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k41</ci>
<ci>k12</ci>
<apply>
<plus/>
<ci>k34</ci>
<ci>k32</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x3</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k14</ci>
<ci>k43</ci>
<apply>
<plus/>
<ci>k23</ci>
<ci>k21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k12</ci>
<ci>k23</ci>
<apply>
<plus/>
<ci>k43</ci>
<ci>k41</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>x4</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k23</ci>
<ci>k34</ci>
<apply>
<plus/>
<ci>k14</ci>
<ci>k12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k14</ci>
<ci>k21</ci>
<apply>
<plus/>
<ci>k34</ci>
<ci>k32</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k43</ci>
<apply>
<divide/>
<ci>Nai</ci>
<apply>
<plus/>
<ci>K3ni</ci>
<ci>Nai</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k12</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Ca_sub</ci>
<ci>Kci</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qci</ci>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>di</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k14</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Nai</ci>
<ci>K1ni</ci>
</apply>
<ci>Nai</ci>
</apply>
<ci>K2ni</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Nai</ci>
<ci>K3ni</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qn</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>di</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k41</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qn</ci>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>di</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<apply>
<divide/>
<ci>Ca_sub</ci>
<ci>Kci</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qci</ci>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci>Nai</ci>
<ci>Kcni</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>Nai</ci>
<ci>K1ni</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<apply>
<divide/>
<ci>Nai</ci>
<ci>K2ni</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Nai</ci>
<ci>K3ni</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k34</ci>
<apply>
<divide/>
<ci>Nao</ci>
<apply>
<plus/>
<ci>K3no</ci>
<ci>Nao</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k21</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Cao</ci>
<ci>Kco</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qco</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>do</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k23</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Nao</ci>
<ci>K1no</ci>
</apply>
<ci>Nao</ci>
</apply>
<ci>K2no</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Nao</ci>
<ci>K3no</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>Qn</ci>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>do</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k32</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qn</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>do</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<apply>
<divide/>
<ci>Cao</ci>
<ci>Kco</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Qco</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>Nao</ci>
<ci>K1no</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Nao</ci>
<ci>K2no</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Nao</ci>
<ci>K3no</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_calcium_dynamics">
<variable units="millimolar_per_millisecond" public_interface="out" name="j_Ca_dif"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="j_rel"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="j_up"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="j_tr"/>
<variable units="millisecond" name="tau_dif_Ca" initial_value="0.04"/>
<variable units="millisecond" name="tau_tr" initial_value="60"/>
<variable units="millimolar" name="K_rel" initial_value="0.0012"/>
<variable units="millimolar_per_millisecond" name="P_up" initial_value="0.005"/>
<variable units="per_millisecond" name="P_rel" initial_value="0.5"/>
<variable units="millimolar" name="K_up" initial_value="0.0006"/>
<variable units="millimolar" public_interface="in" name="Ca_up"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Ca_sub"/>
<variable units="millimolar" public_interface="in" name="Ca_rel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>j_Ca_dif</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_sub</ci>
<ci>Cai</ci>
</apply>
<ci>tau_dif_Ca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>j_rel</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_rel</ci>
<apply>
<minus/>
<ci>Ca_rel</ci>
<ci>Ca_sub</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>K_rel</ci>
<ci>Ca_sub</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>j_up</ci>
<apply>
<divide/>
<ci>P_up</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K_up</ci>
<ci>Cai</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>j_tr</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_up</ci>
<ci>Ca_rel</ci>
</apply>
<ci>tau_tr</ci>
</apply>
</apply>
</math>
</component>
<component name="intracellular_ion_concentrations">
<variable units="millimolar" public_interface="out" name="Cai" initial_value="0.000312494921"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="2"/>
<variable units="millimolar" public_interface="out" name="Ca_up" initial_value="1.462338380106"/>
<variable units="millimolar" public_interface="out" name="Ca_rel" initial_value="0.296742023718"/>
<variable units="millimolar" public_interface="out" name="Ca_sub" initial_value="0.00019074741"/>
<variable units="millimolar" public_interface="out" name="Nai" initial_value="9.438646305915"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="140"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="139.984146485614"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4"/>
<variable units="millimolar" public_interface="out" name="Mgi" initial_value="2.5"/>
<variable units="litre" name="V_i" initial_value="0.0000000000015835"/>
<variable units="litre" name="V_rel" initial_value="0.0000000000000042223"/>
<variable units="litre" name="V_up" initial_value="0.000000000000040816"/>
<variable units="litre" name="V_sub" initial_value="0.000000000000035098"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="femtocoulomb_per_millimole" public_interface="in" name="F"/>
<variable units="picoF" public_interface="in" name="Cm"/>
<variable units="picoA" public_interface="in" name="i_b_Na"/>
<variable units="picoA" public_interface="in" name="i_CaL"/>
<variable units="picoA" public_interface="in" name="i_CaT"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="j_rel"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="j_Ca_dif"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="j_tr"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="j_up"/>
<variable units="picoA" public_interface="in" name="i_h_Na"/>
<variable units="picoA" public_interface="in" name="i_st"/>
<variable units="picoA" public_interface="in" name="i_NaK"/>
<variable units="picoA" public_interface="in" name="i_Kr"/>
<variable units="picoA" public_interface="in" name="i_Ks"/>
<variable units="picoA" public_interface="in" name="i_to"/>
<variable units="picoA" public_interface="in" name="i_sus"/>
<variable units="picoA" public_interface="in" name="i_h_K"/>
<variable units="picoA" public_interface="in" name="i_K_ACh"/>
<variable units="dimensionless" public_interface="in" name="TMC_tot"/>
<variable units="dimensionless" public_interface="in" name="CM_tot"/>
<variable units="dimensionless" public_interface="in" name="TC_tot"/>
<variable units="dimensionless" public_interface="in" name="CQ_tot"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="delta_fTMC"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="delta_fCMi"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="delta_fCMs"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="delta_fTC"/>
<variable units="millimolar_per_millisecond" public_interface="in" name="delta_fCQ"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Nai</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_h_Na</ci>
<ci>i_st</ci>
<ci>i_b_Na</ci>
<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>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="picoF">1</cn>
<ci>F</ci>
<apply>
<plus/>
<ci>V_i</ci>
<ci>V_sub</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ki</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
<ci>i_to</ci>
<ci>i_sus</ci>
<ci>i_h_K</ci>
<ci>i_K_ACh</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>i_NaK</ci>
</apply>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="picoF">1</cn>
<ci>F</ci>
<apply>
<plus/>
<ci>V_i</ci>
<ci>V_sub</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cai</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>j_Ca_dif</ci>
<ci>V_sub</ci>
</apply>
<apply>
<times/>
<ci>j_up</ci>
<ci>V_up</ci>
</apply>
</apply>
<ci>V_i</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>CM_tot</ci>
<ci>delta_fCMi</ci>
</apply>
<apply>
<times/>
<ci>TC_tot</ci>
<ci>delta_fTC</ci>
</apply>
<apply>
<times/>
<ci>TMC_tot</ci>
<ci>delta_fTMC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_sub</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_CaL</ci>
<ci>i_CaT</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="picoF">1</cn>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<times/>
<ci>j_rel</ci>
<ci>V_rel</ci>
</apply>
</apply>
<ci>V_sub</ci>
</apply>
<apply>
<plus/>
<ci>j_Ca_dif</ci>
<apply>
<times/>
<ci>CM_tot</ci>
<ci>delta_fCMs</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_up</ci>
</apply>
<apply>
<minus/>
<ci>j_up</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>j_tr</ci>
<ci>V_rel</ci>
</apply>
<ci>V_up</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_rel</ci>
</apply>
<apply>
<minus/>
<ci>j_tr</ci>
<apply>
<plus/>
<ci>j_rel</ci>
<apply>
<times/>
<ci>CQ_tot</ci>
<ci>delta_fCQ</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_buffering">
<variable units="dimensionless" public_interface="out" name="TC_tot" initial_value="0.031"/>
<variable units="dimensionless" public_interface="out" name="TMC_tot" initial_value="0.062"/>
<variable units="dimensionless" public_interface="out" name="CM_tot" initial_value="0.045"/>
<variable units="dimensionless" public_interface="out" name="CQ_tot" initial_value="10"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="delta_fTC"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="delta_fTMC"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="delta_fCMs"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="delta_fCMi"/>
<variable units="millimolar_per_millisecond" public_interface="out" name="delta_fCQ"/>
<variable units="millimolar_per_millisecond" name="delta_fTMM"/>
<variable units="millimolar" name="fTMM" initial_value="0.350600895635"/>
<variable units="millimolar" name="fCMi" initial_value="0.116947220413"/>
<variable units="millimolar" name="fCMs" initial_value="0.074631965653"/>
<variable units="millimolar" name="fTC" initial_value="0.059206293446"/>
<variable units="millimolar" name="fTMC" initial_value="0.602955114871"/>
<variable units="millimolar" name="fCQ" initial_value="0.260317260703"/>
<variable units="per_millimolar_millisecond" name="kf_TC" initial_value="88.8"/>
<variable units="per_millimolar_millisecond" name="kf_TMM" initial_value="2.277"/>
<variable units="per_millimolar_millisecond" name="kf_TMC" initial_value="227.7"/>
<variable units="per_millimolar_millisecond" name="kf_CM" initial_value="227.7"/>
<variable units="per_millimolar_millisecond" name="kf_CQ" initial_value="0.534"/>
<variable units="per_millisecond" name="kb_TC" initial_value="0.446"/>
<variable units="per_millisecond" name="kb_TMC" initial_value="0.00751"/>
<variable units="per_millisecond" name="kb_TMM" initial_value="0.751"/>
<variable units="per_millisecond" name="kb_CM" initial_value="0.542"/>
<variable units="per_millisecond" name="kb_CQ" initial_value="0.445"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Mgi"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Ca_sub"/>
<variable units="millimolar" public_interface="in" name="Ca_rel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fTC</ci>
</apply>
<ci>delta_fTC</ci>
</apply>
<apply>
<eq/>
<ci>delta_fTC</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kf_TC</ci>
<ci>Cai</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<ci>fTC</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kb_TC</ci>
<ci>fTC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fTMC</ci>
</apply>
<ci>delta_fTMC</ci>
</apply>
<apply>
<eq/>
<ci>delta_fTMC</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kf_TMC</ci>
<ci>Cai</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<apply>
<plus/>
<ci>fTMC</ci>
<ci>fTMM</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kb_TMC</ci>
<ci>fTMC</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fTMM</ci>
</apply>
<ci>delta_fTMM</ci>
</apply>
<apply>
<eq/>
<ci>delta_fTMM</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kf_TMM</ci>
<ci>Mgi</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<apply>
<plus/>
<ci>fTMC</ci>
<ci>fTMM</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kb_TMM</ci>
<ci>fTMM</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCMi</ci>
</apply>
<ci>delta_fCMi</ci>
</apply>
<apply>
<eq/>
<ci>delta_fCMi</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kf_CM</ci>
<ci>Cai</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<ci>fCMi</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kb_CM</ci>
<ci>fCMi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCMs</ci>
</apply>
<ci>delta_fCMs</ci>
</apply>
<apply>
<eq/>
<ci>delta_fCMs</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kf_CM</ci>
<ci>Ca_sub</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<ci>fCMs</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kb_CM</ci>
<ci>fCMs</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCQ</ci>
</apply>
<ci>delta_fCQ</ci>
</apply>
<apply>
<eq/>
<ci>delta_fCQ</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kf_CQ</ci>
<ci>Ca_rel</ci>
<apply>
<minus/>
<cn cellml:units="millimolar">1</cn>
<ci>fCQ</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kb_CQ</ci>
<ci>fCQ</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="L_type_calcium_channel_current">
<component_ref component="L_type_calcium_channel_current_d_gate"/>
<component_ref component="L_type_calcium_channel_current_f_gate"/>
<component_ref component="L_type_calcium_channel_current_fCa_gate"/>
</component_ref>
<component_ref component="T_type_calcium_channel_current">
<component_ref component="T_type_calcium_channel_current_d_gate"/>
<component_ref component="T_type_calcium_channel_current_f_gate"/>
</component_ref>
<component_ref component="rapidly_activating_delayed_rectifier_potassium_current">
<component_ref component="rapidly_activating_delayed_rectifier_potassium_current_pa_gate"/>
<component_ref component="rapidly_activating_delayed_rectifier_potassium_current_pi_gate"/>
</component_ref>
<component_ref component="slowly_activating_delayed_rectifier_potassium_current">
<component_ref component="slowly_activating_delayed_rectifier_potassium_current_n_gate"/>
</component_ref>
<component_ref component="AP_sensitive_currents">
<component_ref component="AP_sensitive_currents_q_gate"/>
<component_ref component="AP_sensitive_currents_r_gate"/>
</component_ref>
<component_ref component="hyperpolarisation_activated_current">
<component_ref component="hyperpolarisation_activated_current_y_gate"/>
</component_ref>
<component_ref component="sustained_inward_current">
<component_ref component="sustained_inward_current_qa_gate"/>
<component_ref component="sustained_inward_current_qi_gate"/>
</component_ref>
<component_ref component="sodium_dependent_background_current"/>
<component_ref component="background_muscarinic_potassium_channel_current"/>
<component_ref component="sodium_potassium_pump_current"/>
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