Location: Noble, Difrancesco, Denyer, 1989 @ b020f3174337 / noble_difrancesco_denyer_1989.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2009-11-11 15:31:47+13:00
Desc:
Replaced with Alan Garny's corrected model which is in steady state.
Permanent Source URI:
http://models.cellml.org/workspace/noble_difrancesco_denyer_1989/rawfile/b020f3174337a8bfaef6bb1448cc6efe6f7fe94a/noble_difrancesco_denyer_1989.cellml

<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 10/11/2009 at 10:59:31 using:

COR (0.9.31.1333)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk

CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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				<title>Model Status</title>
				<para>
This model has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.  Some dimensional correction (of radius and length) has been carried out by Ivan Cenci of Bologna University.  However some of the curation changes made to the previous version of this CellML model have had to be disregarded as they were made in comparison to the Noble 1984 paper, while this current version has been based on the original Oxsoft code.  It should also be noted that the slight discrepancies between the CellML model simulation output and the figures in the paper maybe be due to different parameter values being used for the ion concentrations.
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				<para>The <ulink url="model_curation.doc">updated curation comment document</ulink> detailing all these changes is available for download.</para>
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				<title>Model Structure</title>
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									<title>model diagram</title>
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						<caption>Schematic diagram of the Noble et al 1989 model.</caption>
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This model was based on the article: "Ionic Mechanisms in Normal and Abnormal Cardiac Pacemaker Activity" which can be found in the book "Neuronal and Cellular Oscillators", pp. 59-85, edited by Jon W. Jacklet.  This book is part of the "Cellular Clocks" series, published by Marcel Dekker Inc.
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                     <ci>Kc</ci>
                     <ci>Ki</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_fNa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <power/>
                        <ci>y</ci>
                        <cn cellml:units="dimensionless">2</cn>
                     </apply>
                     <ci>Kc</ci>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>Kc</ci>
                     <ci>Km_f</ci>
                  </apply>
               </apply>
               <ci>g_f_Na</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_fK</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <power/>
                        <ci>y</ci>
                        <cn cellml:units="dimensionless">2</cn>
                     </apply>
                     <ci>Kc</ci>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>Kc</ci>
                     <ci>Km_f</ci>
                  </apply>
               </apply>
               <ci>g_f_K</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_f</ci>
            <apply>
               <plus/>
               <ci>i_fNa</ci>
               <ci>i_fK</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="hyperpolarising_activated_current_y_gate">
      <variable name="y" units="dimensionless" initial_value="0.0743464067197738" public_interface="out"/>
      <variable name="alpha_y" units="per_second"/>
      <variable name="beta_y" units="per_second"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="speed_y" units="dimensionless" initial_value="2"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_y</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">0.014</cn>
               <apply>
                  <exp/>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                     </apply>
                     <cn cellml:units="millivolt">16</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_y</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">9.75</cn>
               <apply>
                  <exp/>
                  <apply>
                     <divide/>
                     <ci>V</ci>
                     <cn cellml:units="millivolt">19</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>y</ci>
            </apply>
            <apply>
               <times/>
               <ci>speed_y</ci>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>alpha_y</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>y</ci>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>beta_y</ci>
                     <ci>y</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_dependent_potassium_current">
      <variable name="i_K" units="nanoA" public_interface="out"/>
      <variable name="I_K" units="nanoA"/>
      <variable name="i_K_max" units="nanoA" initial_value="0.8"/>
      <variable name="time" units="second" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="RTONF" units="millivolt" public_interface="in"/>
      <variable name="Ki" units="millimolar" public_interface="in"/>
      <variable name="Kc" units="millimolar" public_interface="in"/>
      <variable name="x" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>I_K</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>i_K_max</ci>
                  <apply>
                     <minus/>
                     <ci>Ki</ci>
                     <apply>
                        <times/>
                        <ci>Kc</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="millimolar">140</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_K</ci>
            <apply>
               <times/>
               <ci>x</ci>
               <ci>I_K</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_dependent_potassium_current_x_gate">
      <variable name="x" units="dimensionless" initial_value="0.129303443591363" public_interface="out"/>
      <variable name="alpha_x" units="per_second"/>
      <variable name="beta_x" units="per_second"/>
      <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>alpha_x</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">2.1</cn>
               <apply>
                  <exp/>
                  <apply>
                     <divide/>
                     <ci>V</ci>
                     <cn cellml:units="millivolt">28</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_x</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">0.96</cn>
               <apply>
                  <exp/>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                     </apply>
                     <cn cellml:units="millivolt">24</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>x</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_x</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>x</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_x</ci>
                  <ci>x</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_independent_potassium_current">
      <variable name="i_K1" units="nanoA" public_interface="out"/>
      <variable name="g_K1" units="microS" initial_value="0.0075"/>
      <variable name="Km_K1" units="millimolar" initial_value="10"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="E_K" units="millivolt" public_interface="in"/>
      <variable name="Kc" units="millimolar" public_interface="in"/>
      <variable name="RTONF" units="millivolt" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>g_K1</ci>
                        <ci>Kc</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>Kc</ci>
                        <ci>Km_K1</ci>
                     </apply>
                  </apply>
                  <apply>
                     <minus/>
                     <ci>V</ci>
                     <ci>E_K</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">10</cn>
                              </apply>
                              <ci>E_K</ci>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <ci>RTONF</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_background_current">
      <variable name="i_Na_b" units="nanoA" public_interface="out"/>
      <variable name="g_Nab" units="microS" initial_value="0.0007"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="E_Na" units="millivolt" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Na_b</ci>
            <apply>
               <times/>
               <ci>g_Nab</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="calcium_background_current">
      <variable name="i_Ca_b" units="nanoA" public_interface="out"/>
      <variable name="E_Ca" units="millivolt" public_interface="out"/>
      <variable name="g_Cab" units="microS" initial_value="0.0001"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="RTONF" units="millivolt" public_interface="in"/>
      <variable name="Cai" units="millimolar" public_interface="in"/>
      <variable name="Cao" units="millimolar" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_Ca</ci>
            <apply>
               <times/>
               <cn cellml:units="dimensionless">0.5</cn>
               <ci>RTONF</ci>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <ci>Cao</ci>
                     <ci>Cai</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Ca_b</ci>
            <apply>
               <times/>
               <ci>g_Cab</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Ca</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_potassium_pump">
      <variable name="i_p" units="nanoA" public_interface="out"/>
      <variable name="I_p" units="nanoA" initial_value="0.45"/>
      <variable name="K_mK" units="millimolar" initial_value="1"/>
      <variable name="K_mNa" units="millimolar" initial_value="40"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="Nai" units="millimolar" public_interface="in"/>
      <variable name="Kc" units="millimolar" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_p</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>I_p</ci>
                        <ci>Kc</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>K_mK</ci>
                        <ci>Kc</ci>
                     </apply>
                  </apply>
                  <ci>Nai</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>K_mNa</ci>
                  <ci>Nai</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Na_Ca_exchanger">
      <variable name="i_NaCa" units="nanoA" public_interface="out"/>
      <variable name="n_NaCa" units="dimensionless" initial_value="3" public_interface="out"/>
      <variable name="K_NaCa" units="nanoA" initial_value="2e-5"/>
      <variable name="d_NaCa" units="dimensionless" initial_value="0.0001"/>
      <variable name="gamma" units="dimensionless" initial_value="0.5"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="RTONF" units="millivolt" public_interface="in"/>
      <variable name="Cao" units="millimolar" public_interface="in"/>
      <variable name="Cai" units="millimolar" public_interface="in"/>
      <variable name="Nai" units="millimolar" public_interface="in"/>
      <variable name="Nao" units="millimolar" 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>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>gamma</ci>
                                 <apply>
                                    <minus/>
                                    <ci>n_NaCa</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                                 <ci>V</ci>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Nai</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <ci>Cao</ci>
                     </apply>
                     <apply>
                        <times/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <ci>gamma</ci>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>n_NaCa</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                                 <ci>V</ci>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Nao</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <ci>Cai</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <apply>
                     <plus/>
                     <cn cellml:units="millimolar4">1</cn>
                     <apply>
                        <times/>
                        <ci>d_NaCa</ci>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <ci>Cai</ci>
                              <apply>
                                 <power/>
                                 <ci>Nao</ci>
                                 <ci>n_NaCa</ci>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <ci>Cao</ci>
                              <apply>
                                 <power/>
                                 <ci>Nai</ci>
                                 <ci>n_NaCa</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <divide/>
                        <ci>Cai</ci>
                        <cn cellml:units="millimolar">0.0069</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current">
      <variable name="i_Na" units="nanoA" public_interface="out"/>
      <variable name="g_Na" units="microS" initial_value="0.0125"/>
      <variable name="E_mh" units="millivolt"/>
      <variable name="time" units="second" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="RTONF" units="millivolt" public_interface="in"/>
      <variable name="Nao" units="millimolar" public_interface="in"/>
      <variable name="Nai" units="millimolar" public_interface="in"/>
      <variable name="Kc" units="millimolar" public_interface="in"/>
      <variable name="Ki" units="millimolar" public_interface="in"/>
      <variable name="m" units="dimensionless" private_interface="in"/>
      <variable name="h" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_mh</ci>
            <apply>
               <times/>
               <ci>RTONF</ci>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <ci>Nao</ci>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">0.12</cn>
                           <ci>Kc</ci>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>Nai</ci>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">0.12</cn>
                           <ci>Ki</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Na</ci>
            <apply>
               <times/>
               <ci>g_Na</ci>
               <apply>
                  <power/>
                  <ci>m</ci>
                  <cn cellml:units="dimensionless">3</cn>
               </apply>
               <ci>h</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_mh</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_m_gate">
      <variable name="m" units="dimensionless" initial_value="0.042697621819783" public_interface="out"/>
      <variable name="alpha_m" units="per_second"/>
      <variable name="beta_m" units="per_second"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="delta_m" units="millivolt" initial_value="1e-5"/>
      <variable name="E0_m" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_m</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn cellml:units="millivolt">41</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_m</ci>
            <piecewise>
               <piece>
                  <cn cellml:units="per_second">2000</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_m</ci>
                     </apply>
                     <ci>delta_m</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt_second">200</cn>
                        <ci>E0_m</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="per_millivolt">0.1</cn>
                              </apply>
                              <ci>E0_m</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_m</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">8000</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="per_millivolt">0.056</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">66</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>m</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_m</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>m</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_m</ci>
                  <ci>m</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_h_gate">
      <variable name="h" units="dimensionless" initial_value="0.138105285882671" public_interface="out"/>
      <variable name="alpha_h" units="per_second"/>
      <variable name="beta_h" 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_h</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">20</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="per_millivolt">0.125</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">75</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_h</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_second">2000</cn>
               <apply>
                  <plus/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">320</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="per_millivolt">0.1</cn>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">75</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>h</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_h</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>h</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_h</ci>
                  <ci>h</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current">
      <variable name="i_si" units="nanoA" public_interface="out"/>
      <variable name="i_siCa" units="nanoA" public_interface="out"/>
      <variable name="i_siK" units="nanoA" public_interface="out"/>
      <variable name="i_siNa" units="nanoA" public_interface="out"/>
      <variable name="P_si" units="nanoA_per_millimolar" initial_value="0.12"/>
      <variable name="time" units="second" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="RTONF" units="millivolt" public_interface="in"/>
      <variable name="Nao" units="millimolar" public_interface="in"/>
      <variable name="Nai" units="millimolar" public_interface="in"/>
      <variable name="Kc" units="millimolar" public_interface="in"/>
      <variable name="Ki" units="millimolar" public_interface="in"/>
      <variable name="Cao" units="millimolar" public_interface="in"/>
      <variable name="Cai" units="millimolar" public_interface="in" private_interface="out"/>
      <variable name="d" units="dimensionless" private_interface="in"/>
      <variable name="f" units="dimensionless" private_interface="in"/>
      <variable name="f2" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_siCa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">4</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">50</cn>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>RTONF</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">50</cn>
                                 </apply>
                                 <cn cellml:units="dimensionless">2</cn>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Cai</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <cn cellml:units="millivolt">100</cn>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Cao</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">2</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">50</cn>
                              </apply>
                           </apply>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <ci>d</ci>
               <ci>f</ci>
               <ci>f2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_siK</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.01</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">50</cn>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>RTONF</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">50</cn>
                                 </apply>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Ki</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <cn cellml:units="millivolt">50</cn>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Kc</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">1</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">50</cn>
                              </apply>
                           </apply>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <ci>d</ci>
               <ci>f</ci>
               <ci>f2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_siNa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.01</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">50</cn>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>RTONF</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">50</cn>
                                 </apply>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Nai</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <cn cellml:units="millivolt">50</cn>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Nao</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">1</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">50</cn>
                              </apply>
                           </apply>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <ci>d</ci>
               <ci>f</ci>
               <ci>f2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_si</ci>
            <apply>
               <plus/>
               <ci>i_siCa</ci>
               <ci>i_siK</ci>
               <ci>i_siNa</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current_d_gate">
      <variable name="d" units="dimensionless" initial_value="1.26333192869164e-5" public_interface="out"/>
      <variable name="alpha_d" units="per_second"/>
      <variable name="beta_d" units="per_second"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="delta_d" units="millivolt" initial_value="0.0001"/>
      <variable name="E0_d" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_d</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn cellml:units="millivolt">24</cn>
               </apply>
               <cn cellml:units="millivolt">5</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_d</ci>
            <piecewise>
               <piece>
                  <cn cellml:units="per_second">120</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_d</ci>
                     </apply>
                     <ci>delta_d</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt_second">30</cn>
                        <ci>E0_d</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <ci>E0_d</ci>
                              </apply>
                              <cn cellml:units="millivolt">4</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_d</ci>
            <piecewise>
               <piece>
                  <cn cellml:units="per_second">120</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_d</ci>
                     </apply>
                     <ci>delta_d</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt_second">12</cn>
                        <ci>E0_d</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <ci>E0_d</ci>
                              <cn cellml:units="millivolt">10</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>d</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_d</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>d</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_d</ci>
                  <ci>d</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current_f_gate">
      <variable name="f" units="dimensionless" initial_value="0.999507224159629" public_interface="out"/>
      <variable name="alpha_f" units="per_second"/>
      <variable name="beta_f" units="per_second"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="delta_f" units="millivolt" initial_value="0.0001"/>
      <variable name="E0_f" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_f</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn cellml:units="millivolt">34</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_f</ci>
            <piecewise>
               <piece>
                  <cn cellml:units="per_second">25</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_f</ci>
                     </apply>
                     <ci>delta_f</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt_second">6.25</cn>
                        <ci>E0_f</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <ci>E0_f</ci>
                              <cn cellml:units="millivolt">4</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_f</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_second">50</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">1</cn>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">34</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_f</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>f</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_f</ci>
                  <ci>f</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current_f2_gate">
      <variable name="f2" units="dimensionless" initial_value="0.485471180273736" public_interface="out"/>
      <variable name="alpha_f2" units="per_second" initial_value="10"/>
      <variable name="beta_f2" units="per_second"/>
      <variable name="K_mf2" units="millimolar" initial_value="0.0005"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="Cai" units="millimolar" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>beta_f2</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>Cai</ci>
                  <ci>alpha_f2</ci>
               </apply>
               <ci>K_mf2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f2</ci>
            </apply>
            <apply>
               <minus/>
               <ci>alpha_f2</ci>
               <apply>
                  <times/>
                  <ci>f2</ci>
                  <apply>
                     <plus/>
                     <ci>alpha_f2</ci>
                     <ci>beta_f2</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_sodium_concentration">
      <variable name="Nao" units="millimolar" initial_value="140" public_interface="out"/>
   </component>
   <component name="intracellular_sodium_concentration">
      <variable name="Nai" units="millimolar" initial_value="7.51007221193712" public_interface="out"/>
      <variable name="radius" units="millimetre" initial_value="0.008"/>
      <variable name="length" units="millimetre" initial_value="0.11"/>
      <variable name="V_e_ratio" units="dimensionless" initial_value="0.1"/>
      <variable name="V_Cell" units="millimetre3"/>
      <variable name="Vi" units="millimetre3" public_interface="out"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="F" units="coulomb_per_mole" public_interface="in"/>
      <variable name="i_Na" units="nanoA" public_interface="in"/>
      <variable name="i_Na_b" units="nanoA" public_interface="in"/>
      <variable name="i_siNa" units="nanoA" public_interface="in"/>
      <variable name="i_p" units="nanoA" public_interface="in"/>
      <variable name="i_fNa" units="nanoA" public_interface="in"/>
      <variable name="i_NaCa" units="nanoA" public_interface="in"/>
      <variable name="n_NaCa" units="dimensionless" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>V_Cell</ci>
            <apply>
               <times/>
               <cn cellml:units="dimensionless">3.141592654</cn>
               <apply>
                  <power/>
                  <ci>radius</ci>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
               <ci>length</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>Vi</ci>
            <apply>
               <times/>
               <ci>V_Cell</ci>
               <apply>
                  <minus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <ci>V_e_ratio</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Nai</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn cellml:units="mA_nA">1</cn>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>i_Na</ci>
                     <ci>i_Na_b</ci>
                     <ci>i_fNa</ci>
                     <ci>i_siNa</ci>
                     <apply>
                        <times/>
                        <ci>i_p</ci>
                        <cn cellml:units="dimensionless">3</cn>
                     </apply>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <ci>i_NaCa</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <ci>n_NaCa</ci>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="litre_millimetre3">1</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_calcium_concentration">
      <variable name="Cao" units="millimolar" initial_value="2" public_interface="out"/>
   </component>
   <component name="intracellular_calcium_concentration">
      <variable name="Cai" units="millimolar" initial_value="5.84191784887783e-5" public_interface="out"/>
      <variable name="V_up" units="millimetre3"/>
      <variable name="V_rel" units="millimetre3"/>
      <variable name="Vi" units="millimetre3" public_interface="in"/>
      <variable name="i_up" units="nanoA"/>
      <variable name="i_tr" units="nanoA"/>
      <variable name="i_rel" units="nanoA"/>
      <variable name="Ca_up" units="millimolar" initial_value="3.70806465918854"/>
      <variable name="Ca_rel" units="millimolar" initial_value="0.177741556496929"/>
      <variable name="Ca_up_max" units="millimolar" initial_value="5"/>
      <variable name="K_mCa" units="millimolar" initial_value="0.002"/>
      <variable name="p" units="dimensionless" initial_value="0.176207580044253"/>
      <variable name="alpha_p" units="per_second"/>
      <variable name="beta_p" units="per_second"/>
      <variable name="E0_p" units="millivolt"/>
      <variable name="tau_up" units="second" initial_value="0.005"/>
      <variable name="tau_rep" units="second" initial_value="0.2"/>
      <variable name="tau_rel" units="second" initial_value="0.01"/>
      <variable name="rCa" units="dimensionless" initial_value="2"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="F" units="coulomb_per_mole" public_interface="in"/>
      <variable name="i_Ca_b" units="nanoA" public_interface="in"/>
      <variable name="i_siCa" units="nanoA" public_interface="in"/>
      <variable name="i_NaCa" units="nanoA" public_interface="in"/>
      <variable name="n_NaCa" units="dimensionless" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_up</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <cn cellml:units="litre_millimetre3">1</cn>
                     <ci>Vi</ci>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="mA_nA">1</cn>
                     <ci>tau_up</ci>
                     <ci>Ca_up_max</ci>
                  </apply>
               </apply>
               <ci>Cai</ci>
               <apply>
                  <minus/>
                  <ci>Ca_up_max</ci>
                  <ci>Ca_up</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_tr</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <cn cellml:units="litre_millimetre3">1</cn>
                     <ci>V_rel</ci>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="mA_nA">1</cn>
                     <ci>tau_rep</ci>
                  </apply>
               </apply>
               <ci>p</ci>
               <apply>
                  <minus/>
                  <ci>Ca_up</ci>
                  <ci>Ca_rel</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>E0_p</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn cellml:units="millivolt">34</cn>
               </apply>
               <apply>
                  <minus/>
                  <cn cellml:units="millivolt">30</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_p</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millivolt_second">0.625</cn>
                  <ci>E0_p</ci>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <ci>E0_p</ci>
                        <cn cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_p</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_second">5</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">1</cn>
                           </apply>
                           <ci>E0_p</ci>
                        </apply>
                        <cn cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_rel</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <cn cellml:units="litre_millimetre3">1</cn>
                        <ci>V_rel</ci>
                        <ci>F</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="mA_nA">1</cn>
                        <ci>tau_rel</ci>
                     </apply>
                  </apply>
                  <ci>Ca_rel</ci>
                  <apply>
                     <power/>
                     <ci>Cai</ci>
                     <ci>rCa</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <ci>Cai</ci>
                     <ci>rCa</ci>
                  </apply>
                  <apply>
                     <power/>
                     <ci>K_mCa</ci>
                     <ci>rCa</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>p</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_p</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>p</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_p</ci>
                  <ci>p</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_up</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="mA_nA">1</cn>
                  <apply>
                     <minus/>
                     <ci>i_up</ci>
                     <ci>i_tr</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <cn cellml:units="litre_millimetre3">1</cn>
                  <ci>V_up</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_up</ci>
            <apply>
               <times/>
               <ci>Vi</ci>
               <cn cellml:units="dimensionless">0.05</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_rel</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="mA_nA">1</cn>
                  <apply>
                     <minus/>
                     <ci>i_tr</ci>
                     <ci>i_rel</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <cn cellml:units="litre_millimetre3">1</cn>
                  <ci>V_rel</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_rel</ci>
            <apply>
               <times/>
               <ci>Vi</ci>
               <cn cellml:units="dimensionless">0.02</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Cai</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn cellml:units="mA_nA">1</cn>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>i_siCa</ci>
                              <ci>i_Ca_b</ci>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="dimensionless">2</cn>
                                 <ci>i_NaCa</ci>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>n_NaCa</ci>
                                 <cn cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                        </apply>
                        <ci>i_rel</ci>
                     </apply>
                     <ci>i_up</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <cn cellml:units="litre_millimetre3">1</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_potassium_concentration">
      <variable name="Kc" units="millimolar" initial_value="3" public_interface="out"/>
   </component>
   <component name="intracellular_potassium_concentration">
      <variable name="Ki" units="millimolar" initial_value="139.859968229045" public_interface="out"/>
      <variable name="Vi" units="millimetre3" public_interface="in"/>
      <variable name="i_K1" units="nanoA" public_interface="in"/>
      <variable name="i_K" units="nanoA" public_interface="in"/>
      <variable name="i_fK" units="nanoA" public_interface="in"/>
      <variable name="i_siK" units="nanoA" public_interface="in"/>
      <variable name="i_p" units="nanoA" public_interface="in"/>
      <variable name="i_mK" units="nanoA"/>
      <variable name="time" units="second" public_interface="in"/>
      <variable name="F" units="coulomb_per_mole" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_mK</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>i_K1</ci>
                  <ci>i_K</ci>
                  <ci>i_fK</ci>
                  <ci>i_siK</ci>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>i_p</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ki</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn cellml:units="mA_nA">1</cn>
                  </apply>
                  <ci>i_mK</ci>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="litre_millimetre3">1</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="hyperpolarising_activated_current">
            <component_ref component="hyperpolarising_activated_current_y_gate"/>
         </component_ref>
         <component_ref component="time_dependent_potassium_current">
            <component_ref component="time_dependent_potassium_current_x_gate"/>
         </component_ref>
         <component_ref component="time_independent_potassium_current"/>
         <component_ref component="sodium_background_current"/>
         <component_ref component="calcium_background_current"/>
         <component_ref component="sodium_potassium_pump"/>
         <component_ref component="Na_Ca_exchanger"/>
         <component_ref component="fast_sodium_current">
            <component_ref component="fast_sodium_current_m_gate"/>
            <component_ref component="fast_sodium_current_h_gate"/>
         </component_ref>
         <component_ref component="second_inward_current">
            <component_ref component="second_inward_current_d_gate"/>
            <component_ref component="second_inward_current_f_gate"/>
            <component_ref component="second_inward_current_f2_gate"/>
         </component_ref>
         <component_ref component="intracellular_sodium_concentration"/>
         <component_ref component="extracellular_sodium_concentration"/>
         <component_ref component="intracellular_calcium_concentration"/>
         <component_ref component="extracellular_calcium_concentration"/>
         <component_ref component="extracellular_potassium_concentration"/>
         <component_ref component="intracellular_potassium_concentration"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="hyperpolarising_activated_current">
         <component_ref component="hyperpolarising_activated_current_y_gate"/>
      </component_ref>
      <component_ref component="time_dependent_potassium_current">
         <component_ref component="time_dependent_potassium_current_x_gate"/>
      </component_ref>
      <component_ref component="fast_sodium_current">
         <component_ref component="fast_sodium_current_m_gate"/>
         <component_ref component="fast_sodium_current_h_gate"/>
      </component_ref>
      <component_ref component="second_inward_current">
         <component_ref component="second_inward_current_d_gate"/>
         <component_ref component="second_inward_current_f_gate"/>
         <component_ref component="second_inward_current_f2_gate"/>
      </component_ref>
   </group>
   <connection>
      <map_components component_1="membrane" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="sodium_background_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_calcium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_potassium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
      <map_variables variable_1="i_f" variable_2="i_f"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_K" variable_2="i_K"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
      <map_variables variable_1="i_K1" variable_2="i_K1"/>
   </connection>
   <connection>
      <map_components component_1="sodium_background_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Na_b" variable_2="i_Na_b"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
      <map_variables variable_1="i_Ca_b" variable_2="i_Ca_b"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_p" variable_2="i_p"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Na" variable_2="i_Na"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_si" variable_2="i_si"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="membrane"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_calcium_concentration" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_potassium_concentration" component_2="membrane"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
      <map_variables variable_1="i_fK" variable_2="i_fK"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="time_independent_potassium_current"/>
      <map_variables variable_1="E_K" variable_2="E_K"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="sodium_background_current"/>
      <map_variables variable_1="E_Na" variable_2="E_Na"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_fNa" variable_2="i_fNa"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="extracellular_calcium_concentration"/>
      <map_variables variable_1="Cao" variable_2="Cao"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
      <map_variables variable_1="i_K" variable_2="i_K"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="i_K1" variable_2="i_K1"/>
   </connection>
   <connection>
      <map_components component_1="sodium_background_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_Na_b" variable_2="i_Na_b"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="i_Ca_b" variable_2="i_Ca_b"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="i_p" variable_2="i_p"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_p" variable_2="i_p"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="extracellular_calcium_concentration"/>
      <map_variables variable_1="Cao" variable_2="Cao"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="n_NaCa" variable_2="n_NaCa"/>
      <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="n_NaCa" variable_2="n_NaCa"/>
      <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_Na" variable_2="i_Na"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="i_siCa" variable_2="i_siCa"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="extracellular_calcium_concentration"/>
      <map_variables variable_1="Cao" variable_2="Cao"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="i_siK" variable_2="i_siK"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_siNa" variable_2="i_siNa"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="hyperpolarising_activated_current_y_gate"/>
      <map_variables variable_1="y" variable_2="y"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_x_gate"/>
      <map_variables variable_1="x" variable_2="x"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate"/>
      <map_variables variable_1="m" variable_2="m"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate"/>
      <map_variables variable_1="h" variable_2="h"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="second_inward_current_d_gate"/>
      <map_variables variable_1="d" variable_2="d"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="second_inward_current_f_gate"/>
      <map_variables variable_1="f" variable_2="f"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="second_inward_current_f2_gate"/>
      <map_variables variable_1="f2" variable_2="f2"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="Vi" variable_2="Vi"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Vi" variable_2="Vi"/>
   </connection>
</model>