<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 11/05/2010 at 2:36:52 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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<article>
<articleinfo>
<title>Amplitude-Dependent Spike-Broadening In GnRH-Secreting Neurons</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This model runs in OpenCell and COR and the units are consistent throughout. Although it is a accurate reproduction of the published model it does not recreate the published results. Although the steady state values for some parameters are similar to published results, the model does not recreate the bursting seen in the paper and a stimulus protocl might need to be added. </para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: In GnRH-secreting (GT1) neurons, activation of Ca(2+)-mobilizing receptors induces a sustained membrane depolarization that shifts the profile of the action potential (AP) waveform from sharp, high-amplitude to broad, low-amplitude spikes. Here we characterize this shift in the firing pattern and its impact on Ca(2+) influx experimentally by using prerecorded sharp and broad APs as the voltage-clamp command pulse. As a quantitative test of the experimental data, a mathematical model based on the membrane and ionic current properties of GT1 neurons was also used. Both experimental and modeling results indicated that inactivation of the tetrodotoxin-sensitive Na(+) channels by sustained depolarization accounted for a reduction in the amplitude of the spike upstroke. The ensuing decrease in tetraethylammonium-sensitive K(+) current activation slowed membrane repolarization, leading to AP broadening. This change in firing pattern increased the total L-type Ca(2+) current and facilitated AP-driven Ca(2+) entry. The leftward shift in the current-voltage relation of the L-type Ca(2+) channels expressed in GT1 cells allowed the depolarization-induced AP broadening to facilitate Ca(2+) entry despite a decrease in spike amplitude. Thus the gating properties of the L-type Ca(2+) channels expressed in GT1 neurons are suitable for promoting AP-driven Ca(2+) influx in receptor- and non-receptor-depolarized cells.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Amplitude-Dependent Spike-Broadening and Enhanced Ca<superscript>2+</superscript> Signaling in GnRH-Secreting Neurons, Fredrick Van Goor, Andrew P. LeBeau, Lazar Z. Krsmanovic, Arthur Sherman, Kevin J. Catt and Stanko S. Stojikovic, 2000, <emphasis>Biophysical Journal</emphasis>, 79, 1310-1323. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10968994&dopt=Abstract">PubMed ID: 10968994</ulink>
</para>
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<title>diagram of the cell model</title>
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<informalfigure float="0" id="fig_reaction_diagram">
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<title>diagram of the cell model</title>
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</article>
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In their original model, Van Goor et al. used a Hodgkin-Huxley type
equation to represent the sodium current (see CellML description
below). However, in this description, INa exhibited a large surge of
activation during the spike repolarisation, and also did not spike
during broadening, suggesting that the model gating kinetics don't
accurately represent those in GTI neurons.
Consequently, they replaced the Hodgkin-Huxley-like description with
Kuo and Bean's 1994 model of INa. In this description the Na+ channel
is composed of subunits with four possible states: deactivated (D),
activated (A), deactivated-inhibited (D*), and activated-inhibited
(A*). The open, conducting state (O) is given by A3 in the reaction
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Following is the original reaction scheme.
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<rdf:li>neuron</rdf:li>
<rdf:li>gnrh</rdf:li>
<rdf:li>Neuron</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
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<rdf:value>This is the CellML description of Van Goor et al's 2000 mathematical
model of amplitude-dependent spike broadening and enhanced Ca2+
signaling in GnRH-secreting neurons.</rdf:value>
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<dc:title>
Van Goor et al's 2000 mathematical model of amplitude-dependent spike
broadening and enhanced Ca2+ signaling in GnRH-secreting neurons.
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<rdf:value>The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology.
The model does not run in the PCEnv simulator because the model is underconstrained. Apparently i_ir could not be defined - but there is an equation included to define i_ir, and all the elements in this equation either have an initial value or a defining equation themselves. So I'm not sure what exactly is missing.</rdf:value>
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<vCard:Given>Arthur</vCard:Given>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<vCard:Given>Stanko</vCard:Given>
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<dcterms:W3CDTF>2000-09</dcterms:W3CDTF>
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<vCard:Given>Catherine</vCard:Given>
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</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond">15</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">1</cn>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="delayed_rectifier_K_channel_current_h_gate">
<variable name="h" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="h_infinity" units="dimensionless"/>
<variable name="tau_h" units="millisecond" initial_value="1000"/>
<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</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>h_infinity</ci>
<ci>h</ci>
</apply>
<ci>tau_h</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>h_infinity</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.7</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.3</cn>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="M_like_K_current">
<variable name="i_M" units="picoA" public_interface="out"/>
<variable name="g_M" units="nanoS" initial_value="4"/>
<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_K" units="millivolt" public_interface="in"/>
<variable name="n" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_M</ci>
<apply>
<times/>
<ci>g_M</ci>
<ci>n</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>V_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="M_like_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"/>
<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/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37</cn>
</apply>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">80</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="inward_rectifier_K_current">
<variable name="i_ir" units="picoA" public_interface="out"/>
<variable name="g_ir" units="nanoS" initial_value="1.71"/>
<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_K" units="millivolt" public_interface="in"/>
<variable name="n_infinity" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_ir</ci>
<apply>
<times/>
<ci>g_ir</ci>
<ci>n_infinity</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>V_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="inward_rectifier_K_current_n_gate">
<variable name="n_infinity" units="dimensionless" public_interface="out"/>
<variable name="V" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>n_infinity</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.8</cn>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">80</cn>
</apply>
<cn cellml:units="millivolt">12</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.2</cn>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="inward_leak_current">
<variable name="i_d" units="picoA" public_interface="out"/>
<variable name="g_d" units="nanoS" initial_value="0.044"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="V_Ca" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_d</ci>
<apply>
<times/>
<ci>g_d</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>V_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current"/>
<component_ref component="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="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
<component_ref component="delayed_rectifier_K_channel_current_h_gate"/>
</component_ref>
<component_ref component="M_like_K_current">
<component_ref component="M_like_K_current_n_gate"/>
</component_ref>
<component_ref component="inward_rectifier_K_current">
<component_ref component="inward_rectifier_K_current_n_gate"/>
</component_ref>
<component_ref component="inward_leak_current"/>
</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="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
<component_ref component="delayed_rectifier_K_channel_current_h_gate"/>
</component_ref>
<component_ref component="M_like_K_current">
<component_ref component="M_like_K_current_n_gate"/>
</component_ref>
<component_ref component="inward_rectifier_K_current">
<component_ref component="inward_rectifier_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="sodium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L_type_calcium_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="T_type_calcium_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="delayed_rectifier_K_channel_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="M_like_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="inward_rectifier_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="inward_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="A" 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="A_" 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="D" 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="D_" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L_type_calcium_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<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="membrane"/>
<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="delayed_rectifier_K_channel_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K_dr" variable_2="i_K_dr"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_like_K_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_M" variable_2="i_M"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="inward_rectifier_K_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_ir" variable_2="i_ir"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="inward_leak_current" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_d" variable_2="i_d"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="reaction_constants" component_2="membrane"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_current" component_2="A"/>
<map_variables variable_1="A" variable_2="A"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="A" component_2="D"/>
<map_variables variable_1="A" variable_2="A"/>
<map_variables variable_1="D" variable_2="D"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="A" component_2="A_"/>
<map_variables variable_1="A" variable_2="A"/>
<map_variables variable_1="A_" variable_2="A_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="A_" component_2="D_"/>
<map_variables variable_1="A_" variable_2="A_"/>
<map_variables variable_1="D_" variable_2="D_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="D" component_2="D_"/>
<map_variables variable_1="D" variable_2="D"/>
<map_variables variable_1="D_" variable_2="D_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="A" component_2="reaction_constants"/>
<map_variables variable_1="alpha" variable_2="alpha"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="k1" variable_2="k1"/>
<map_variables variable_1="k1_" variable_2="k1_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="A_" component_2="reaction_constants"/>
<map_variables variable_1="alpha" variable_2="alpha"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="a" variable_2="a"/>
<map_variables variable_1="k1" variable_2="k1"/>
<map_variables variable_1="k1_" variable_2="k1_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="D" component_2="reaction_constants"/>
<map_variables variable_1="alpha" variable_2="alpha"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="k2" variable_2="k2"/>
<map_variables variable_1="k2_" variable_2="k2_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="D_" component_2="reaction_constants"/>
<map_variables variable_1="alpha" variable_2="alpha"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="a" variable_2="a"/>
<map_variables variable_1="k2" variable_2="k2"/>
<map_variables variable_1="k2_" variable_2="k2_"/>
</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="V_Ca" variable_2="V_Ca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="L_type_calcium_current" component_2="inward_leak_current"/>
<map_variables variable_1="V_Ca" variable_2="V_Ca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="delayed_rectifier_K_channel_current" component_2="M_like_K_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="delayed_rectifier_K_channel_current" component_2="inward_rectifier_K_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</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" variable_2="m"/>
<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="T_type_calcium_current" component_2="T_type_calcium_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 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" variable_2="h"/>
<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="delayed_rectifier_K_channel_current" component_2="delayed_rectifier_K_channel_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>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="delayed_rectifier_K_channel_current" component_2="delayed_rectifier_K_channel_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 xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_like_K_current" component_2="M_like_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>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="inward_rectifier_K_current" component_2="inward_rectifier_K_current_n_gate"/>
<map_variables variable_1="n_infinity" variable_2="n_infinity"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
</model>
