Rendering of the source text

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<!--
This CellML file was generated on 13/05/2010 at 5:34:04 at p.m. using:

COR (0.9.31.1371)
Copyright 2002-2010 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>A Hodgkin-Huxley Model Exhibiting Bursting Oscillations</title>
				<author>
					<firstname>Catherine</firstname>
					<surname>Lloyd</surname>
					<affiliation>
						<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
					</affiliation>
				</author>
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				<title>Model Status</title>
				<para>
            This model runs in OpenCell and COR and the units are consistent throughout. It it an accurate reproduction of the paper equations but does not reproduce the published results for unknown reasons, possibly because initial conditions for state variables were guessed. 
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			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
ABSTRACT: We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca2+ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.
</para>

<para>
The original paper reference is cited below:
</para>
				<para>
A Hodgkin-Huxley Model Exhibiting Bursting Oscillations, Paul R. Shorten and David J.N. Wall, 2000, <emphasis>Bulletin of Mathematical Biology</emphasis>, 62, 695-715.   <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10938629&amp;dopt=Abstract">PubMed ID: 10938629</ulink>
				</para>
				
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								<title>cell schematic for the model</title>
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					<caption>Schematic diagram of a pituitary corticotroph cell showing the transmembrane ionic currents and the intracellular Ca<superscript>2+</superscript> dynamics captured by the mathematical model.  Arrows indicate ionic channels and pumps.  <emphasis>I<subscript>Ca-L</subscript>
						</emphasis> represents an L-type Ca<superscript>2+</superscript> current responsible for most of the Ca<superscript>2+</superscript> influx during an action potential.  <emphasis>I<subscript>Ca-T</subscript>
						</emphasis> is a T-type voltage-sensitive Ca<superscript>2+</superscript> current.  A voltage-sensitive K<superscript>+</superscript> current, <emphasis>I<subscript>K-DR</subscript>
						</emphasis>, is mainly responsible for action potential repolarisation.  A Ca<superscript>2+</superscript>-activated K<superscript>+</superscript> current, <emphasis>I<subscript>K-Ca</subscript>
						</emphasis>, is essential for bursting behaviour.  The remaining leak current, <emphasis>I<subscript>leak</subscript>
						</emphasis>, represents all other ionic fluxes across the plasma membrane which are not specifically described by the model.  <emphasis>J<subscript>eff</subscript>
						</emphasis> and <emphasis>J<subscript>up</subscript>
						</emphasis> are the ER and plasma membrane Ca<superscript>2+</superscript>-ATPase pumps, and <emphasis>J<subscript>rel</subscript>
						</emphasis> represents the ER Ca<superscript>2+</superscript> leakage term.  Within the ER and the cytosol, significant portions of Ca<superscript>2+</superscript> are bound to buffers, denoted by B<subscript>er</subscript> and B<subscript>c</subscript> respectively.</caption>
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         Shorten and Wall's 2000 Hodgkin-Huxley type mathematical model of 
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            A Hodgkin-Huxley Model Exhibiting Bursting Oscillations
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               </apply>
               <ci>tau_m_L</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>m_L_infinity</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V_m_L</ci>
                           <ci>V</ci>
                        </apply>
                        <ci>k_m_L</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_m_L</ci>
            <apply>
               <divide/>
               <ci>tau_m_L_max</ci>
               <apply>
                  <plus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <ci>V_tau</ci>
                        </apply>
                        <ci>k_tau</ci>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">2</cn>
                              <apply>
                                 <minus/>
                                 <ci>V_tau</ci>
                                 <ci>V</ci>
                              </apply>
                           </apply>
                           <ci>k_tau</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="T_type_calcium_current">
      <variable name="i_Ca_T" units="picoA" public_interface="out"/>
      <variable name="g_Ca_T" units="nanoS_per_millimolar" initial_value="10"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="V_tau" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="k_tau" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="phi_Ca" units="millivolt_millimolar" public_interface="in"/>
      <variable name="m_T" units="dimensionless" private_interface="in"/>
      <variable name="h_T" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Ca_T</ci>
            <apply>
               <times/>
               <ci>g_Ca_T</ci>
               <apply>
                  <power/>
                  <ci>m_T</ci>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
               <ci>h_T</ci>
               <ci>phi_Ca</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="T_type_calcium_current_m_gate">
      <variable name="m_T" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="m_T_infinity" units="dimensionless"/>
      <variable name="tau_m_T" units="millisecond"/>
      <variable name="tau_m_T_max" units="millisecond" initial_value="10"/>
      <variable name="V_m_T" units="millivolt" initial_value="-30"/>
      <variable name="k_m_T" units="millivolt" initial_value="10.5"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="V_tau" units="millivolt" public_interface="in"/>
      <variable name="k_tau" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>m_T</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>m_T_infinity</ci>
                  <ci>m_T</ci>
               </apply>
               <ci>tau_m_T</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>m_T_infinity</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V_m_T</ci>
                           <ci>V</ci>
                        </apply>
                        <ci>k_m_T</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_m_T</ci>
            <apply>
               <divide/>
               <ci>tau_m_T_max</ci>
               <apply>
                  <plus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <ci>V_tau</ci>
                        </apply>
                        <ci>k_tau</ci>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">2</cn>
                              <apply>
                                 <minus/>
                                 <ci>V_tau</ci>
                                 <ci>V</ci>
                              </apply>
                           </apply>
                           <ci>k_tau</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="T_type_calcium_current_h_gate">
      <variable name="h_T" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="h_T_infinity" units="dimensionless"/>
      <variable name="tau_h_T" units="millisecond" initial_value="15"/>
      <variable name="V_h_T" units="millivolt" initial_value="-57"/>
      <variable name="k_h_T" units="millivolt" initial_value="5"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>h_T</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>h_T_infinity</ci>
                  <ci>h_T</ci>
               </apply>
               <ci>tau_h_T</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>h_T_infinity</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <ci>V_h_T</ci>
                        </apply>
                        <ci>k_h_T</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="voltage_sensitive_K_current">
      <variable name="i_K_DR" units="picoA" public_interface="out"/>
      <variable name="phi_K" units="millivolt_millimolar" public_interface="out"/>
      <variable name="g_K_DR" units="nanoS_per_millimolar" initial_value="0.1"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="R" units="joule_per_kilomole_kelvin" public_interface="in"/>
      <variable name="T" units="kelvin" public_interface="in"/>
      <variable name="F" units="coulomb_per_mole" public_interface="in"/>
      <variable name="K_e" units="millimolar" public_interface="in"/>
      <variable name="K_i" units="millimolar" public_interface="in"/>
      <variable name="n" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K_DR</ci>
            <apply>
               <times/>
               <ci>g_K_DR</ci>
               <ci>n</ci>
               <ci>phi_K</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>phi_K</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>V</ci>
                  <apply>
                     <minus/>
                     <ci>K_i</ci>
                     <ci>K_e</ci>
                  </apply>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">1</cn>
                           </apply>
                           <ci>F</ci>
                           <ci>V</ci>
                        </apply>
                        <apply>
                           <times/>
                           <ci>R</ci>
                           <ci>T</ci>
                        </apply>
                     </apply>
                  </apply>
               </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>F</ci>
                           <ci>V</ci>
                        </apply>
                        <apply>
                           <times/>
                           <ci>R</ci>
                           <ci>T</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="voltage_sensitive_K_current_n_gate">
      <variable name="n" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="n_infinity" units="dimensionless"/>
      <variable name="tau_n" units="millisecond" initial_value="20"/>
      <variable name="V_n" units="millivolt" initial_value="-20"/>
      <variable name="k_n" units="millivolt" initial_value="4.5"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <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>
         <apply>
            <eq/>
            <ci>n_infinity</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V_n</ci>
                           <ci>V</ci>
                        </apply>
                        <ci>k_n</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="Ca_activated_K_current">
      <variable name="i_K_Ca" units="picoA" public_interface="out"/>
      <variable name="g_K_Ca" units="nanoS_per_millimolar" initial_value="0.09"/>
      <variable name="Kc" units="millimolar" initial_value="0.0004"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="phi_K" units="millivolt_millimolar" public_interface="in"/>
      <variable name="Ca_i" units="millimolar" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K_Ca</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>g_K_Ca</ci>
                     <apply>
                        <power/>
                        <ci>Ca_i</ci>
                        <cn cellml:units="dimensionless">4</cn>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <power/>
                        <ci>Ca_i</ci>
                        <cn cellml:units="dimensionless">4</cn>
                     </apply>
                     <apply>
                        <power/>
                        <ci>Kc</ci>
                        <cn cellml:units="dimensionless">4</cn>
                     </apply>
                  </apply>
               </apply>
               <ci>phi_K</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="leak_current">
      <variable name="i_leak" units="picoA" public_interface="out"/>
      <variable name="g_L" units="nanoS" initial_value="0.3"/>
      <variable name="V_L" units="millivolt" initial_value="-67"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_leak</ci>
            <apply>
               <times/>
               <ci>g_L</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>V_L</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="ER_calcium">
      <variable name="Ca_er" units="millimolar" initial_value="0.0172" public_interface="out"/>
      <variable name="J_rel" units="millimolar_picoL_per_millisecond" public_interface="out"/>
      <variable name="J_up" units="millimolar_picoL_per_millisecond" public_interface="out"/>
      <variable name="V_er" units="picoL"/>
      <variable name="K_er" units="millimolar" initial_value="0.0002"/>
      <variable name="f_er" units="dimensionless" initial_value="0.0025"/>
      <variable name="P" units="picoL_per_millisecond" initial_value="0.0012"/>
      <variable name="v_er" units="millimolar_picoL_per_millisecond" initial_value="0.00005"/>
      <variable name="Ca_i" units="millimolar" public_interface="in"/>
      <variable name="V_cell" units="picoL" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_er</ci>
            </apply>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <ci>f_er</ci>
                  </apply>
                  <ci>V_er</ci>
               </apply>
               <apply>
                  <minus/>
                  <ci>J_rel</ci>
                  <ci>J_up</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_rel</ci>
            <apply>
               <times/>
               <ci>P</ci>
               <apply>
                  <minus/>
                  <ci>Ca_er</ci>
                  <ci>Ca_i</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_up</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>v_er</ci>
                  <apply>
                     <power/>
                     <ci>Ca_i</ci>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <ci>Ca_i</ci>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
                  <apply>
                     <power/>
                     <ci>K_er</ci>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_er</ci>
            <apply>
               <times/>
               <ci>V_cell</ci>
               <cn cellml:units="dimensionless">0.15</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="cytosolic_calcium">
      <variable name="Ca_i" units="millimolar" initial_value="0.00026" public_interface="out"/>
      <variable name="V_c" units="picoL"/>
      <variable name="K_p" units="millimolar" initial_value="0.00008"/>
      <variable name="f_cyt" units="dimensionless" initial_value="0.01"/>
      <variable name="v_p" units="millimolar_micrometre_per_millisecond" initial_value="0.000045"/>
      <variable name="J_in" units="millimolar_micrometre_per_millisecond"/>
      <variable name="J_eff" units="millimolar_micrometre_per_millisecond"/>
      <variable name="alpha" units="millimolar_micrometre_per_millisecond_per_picoA" initial_value="0.0000074"/>
      <variable name="beta" units="per_micrometre" initial_value="0.47"/>
      <variable name="i_Ca_L" units="picoA" public_interface="in"/>
      <variable name="i_Ca_T" units="picoA" public_interface="in"/>
      <variable name="J_rel" units="millimolar_picoL_per_millisecond" public_interface="in"/>
      <variable name="J_up" units="millimolar_picoL_per_millisecond" public_interface="in"/>
      <variable name="V_cell" units="picoL" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_i</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <ci>f_cyt</ci>
                     <ci>V_c</ci>
                  </apply>
                  <apply>
                     <minus/>
                     <ci>J_rel</ci>
                     <ci>J_up</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>f_cyt</ci>
                  <ci>beta</ci>
                  <apply>
                     <minus/>
                     <ci>J_in</ci>
                     <ci>J_eff</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_in</ci>
            <apply>
               <times/>
               <apply>
                  <minus/>
                  <ci>alpha</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>i_Ca_L</ci>
                  <ci>i_Ca_T</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_eff</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>v_p</ci>
                  <apply>
                     <power/>
                     <ci>Ca_i</ci>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <ci>Ca_i</ci>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
                  <apply>
                     <power/>
                     <ci>K_p</ci>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_c</ci>
            <apply>
               <times/>
               <ci>V_cell</ci>
               <cn cellml:units="dimensionless">0.85</cn>
            </apply>
         </apply>
      </math>
   </component>
   <group xmlns="http://www.cellml.org/cellml/1.0#">
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="L_type_calcium_current">
            <component_ref component="L_type_calcium_current_m_gate"/>
         </component_ref>
         <component_ref component="T_type_calcium_current">
            <component_ref component="T_type_calcium_current_m_gate"/>
            <component_ref component="T_type_calcium_current_h_gate"/>
         </component_ref>
         <component_ref component="voltage_sensitive_K_current">
            <component_ref component="voltage_sensitive_K_current_n_gate"/>
         </component_ref>
         <component_ref component="Ca_activated_K_current"/>
         <component_ref component="leak_current"/>
         <component_ref component="ER_calcium"/>
         <component_ref component="cytosolic_calcium"/>
      </component_ref>
   </group>
   <group xmlns="http://www.cellml.org/cellml/1.0#">
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="L_type_calcium_current">
         <component_ref component="L_type_calcium_current_m_gate"/>
      </component_ref>
      <component_ref component="T_type_calcium_current">
         <component_ref component="T_type_calcium_current_m_gate"/>
         <component_ref component="T_type_calcium_current_h_gate"/>
      </component_ref>
      <component_ref component="voltage_sensitive_K_current">
         <component_ref component="voltage_sensitive_K_current_n_gate"/>
      </component_ref>
   </group>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="membrane" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="L_type_calcium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="Ca_e" variable_2="Ca_e"/>
      <map_variables variable_1="V_tau" variable_2="V_tau"/>
      <map_variables variable_1="k_tau" variable_2="k_tau"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="T_type_calcium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V_tau" variable_2="V_tau"/>
      <map_variables variable_1="k_tau" variable_2="k_tau"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="voltage_sensitive_K_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="K_e" variable_2="K_e"/>
      <map_variables variable_1="K_i" variable_2="K_i"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="Ca_activated_K_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="leak_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="ER_calcium" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V_cell" variable_2="V_cell"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="cytosolic_calcium" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V_cell" variable_2="V_cell"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="membrane" component_2="L_type_calcium_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Ca_L" variable_2="i_Ca_L"/>
      <map_variables variable_1="R" variable_2="R"/>
      <map_variables variable_1="F" variable_2="F"/>
      <map_variables variable_1="T" variable_2="T"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="membrane" component_2="T_type_calcium_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Ca_T" variable_2="i_Ca_T"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="membrane" component_2="voltage_sensitive_K_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_K_DR" variable_2="i_K_DR"/>
      <map_variables variable_1="R" variable_2="R"/>
      <map_variables variable_1="F" variable_2="F"/>
      <map_variables variable_1="T" variable_2="T"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="membrane" component_2="Ca_activated_K_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_K_Ca" variable_2="i_K_Ca"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="membrane" component_2="leak_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_leak" variable_2="i_leak"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="L_type_calcium_current" component_2="T_type_calcium_current"/>
      <map_variables variable_1="phi_Ca" variable_2="phi_Ca"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="L_type_calcium_current" component_2="cytosolic_calcium"/>
      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="i_Ca_L" variable_2="i_Ca_L"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="T_type_calcium_current" component_2="cytosolic_calcium"/>
      <map_variables variable_1="i_Ca_T" variable_2="i_Ca_T"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="voltage_sensitive_K_current" component_2="Ca_activated_K_current"/>
      <map_variables variable_1="phi_K" variable_2="phi_K"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="Ca_activated_K_current" component_2="cytosolic_calcium"/>
      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="ER_calcium" component_2="cytosolic_calcium"/>
      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
      <map_variables variable_1="J_rel" variable_2="J_rel"/>
      <map_variables variable_1="J_up" variable_2="J_up"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="L_type_calcium_current" component_2="L_type_calcium_current_m_gate"/>
      <map_variables variable_1="m_L" variable_2="m_L"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="V_tau" variable_2="V_tau"/>
      <map_variables variable_1="k_tau" variable_2="k_tau"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="T_type_calcium_current" component_2="T_type_calcium_current_m_gate"/>
      <map_variables variable_1="m_T" variable_2="m_T"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="V_tau" variable_2="V_tau"/>
      <map_variables variable_1="k_tau" variable_2="k_tau"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="T_type_calcium_current" component_2="T_type_calcium_current_h_gate"/>
      <map_variables variable_1="h_T" variable_2="h_T"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="voltage_sensitive_K_current" component_2="voltage_sensitive_K_current_n_gate"/>
      <map_variables variable_1="n" variable_2="n"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
</model>