<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : warashina_model_2004.xml
CREATED : 3rd February 2004
LAST MODIFIED : 27th April 2005
AUTHOR : Catherine Lloyd
Bioengineering Instute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Warashina and Ogura's 2004 mathematical model of stimulation-secretion coupling in a chromaffin cell.
CHANGES:
27/04/2005 - PJV - Made MathML id's unique. Changed unit dimension
to correct inconsistancy. Removed undefined
initial values.
-->
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="warashina_2004" name="warashina_2004">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modeling of stimulation-secretion coupling in a chromaffin cell</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 CellML model description is currently incomplete. In order to fully describe the original model it would be necessary to create 6 different compartments and then decribe the diffusion of calcium between these. Further there are other parameter values which are missing.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We constructed a chromaffin cell model for analysis of stimulation-secretion coupling in computer simulation studies. The model includes mechanisms involved in the excitatory synapse, voltage-dependent Na(+), K(+) and Ca(2+) channels, Ca(2+)-activated K(+) channels (SK type), buffered Ca(2+) diffusion, Ca(2+) extrusion, fluorescent Ca(2+) indicators and Ca(2+)-triggered exocytosis. Calculations of the modeled mechanisms were carried out using the NEURON simulation environment (Hines and Carnevale, Neural Computation 9:1179-1209, 1997). A set of parameter values was determined so as to fit basic experimental results reported in the literature. The model was also applied to simulate our experimental results obtained from chromaffin cells in the perfused rat adrenal medulla. Observed profiles of Ca(2+)responses induced by electrically stimulating the splanchnic nerve with various frequencies (1-50 Hz) were adequately simulated with minor readjustments of parameter values for Ca(2+)influx and extrusion. Secretory responses measured at the same time as the Ca(2+)responses were also simulated with consideration of a time constant to detect catecholamines in the experiment. Similarly, model simulations reproduced both Ca(2+)responses and secretory responses evoked by elevations of the extracellular K(+) concentration for different periods. The results suggest that the presented model provides a useful tool for analyzing and predicting quantitative relations in various events occurring in stimulation-secretion coupling in chromaffin cells.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Modeling of stimulation-secretion coupling in a chromaffin cell, A. Warashina and T. Ogura, 2004, <emphasis>European Journal of Physiology</emphasis>, 448, 369-391. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=14730449&dopt=Abstract">PubMed ID: 14730449</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="warashina_2004.png"/>
</imageobject>
</mediaobject>
<caption>The model chromaffin cell includes mechanisms involved in the excitatory synapse, Hodgkin-Huxley type Na<superscript>+</superscript> and K<superscript>+</superscript> channels, volatage-dependent Ca<superscript>2+</superscript> channels, Ca<superscript>2+</superscript>-dependent K<superscript>+</superscript> channels, Ca<superscript>2+</superscript> extrusion, buffered diffusion of intracellular Ca<superscript>2+</superscript>, Ca<superscript>2+</superscript> indication with a fluorescent dye, and Ca<superscript>2+</superscript>-triggered secretion.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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</component>
<component name="membrane">
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<variable units="microF_per_cm2" name="Cm" initial_value="1.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_sp"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K"/>
<variable units="microA_per_cm2" public_interface="in" name="i_l"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Ca"/>
<variable units="microA_per_cm2" public_interface="in" name="i_SK"/>
<variable units="microA_per_cm2" public_interface="in" name="i_ex"/>
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<ci> i_SK </ci>
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<ci> tau2 </ci>
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</component>
<component name="sodium_channel">
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<variable units="millivolt" name="E_Na" initial_value="50.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
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<variable units="dimensionless" private_interface="in" name="h"/>
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<ci> V </ci>
<cn cellml:units="millivolt"> 2.0 </cn>
</apply>
<cn cellml:units="millivolt"> 8.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_channel_m_gate_dm_dt">
<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"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_channel_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="dimensionless" name="Fr" initial_value="0.000"/>
<variable units="dimensionless" name="Ff" initial_value="0.79"/>
<variable units="dimensionless" name="Fm" initial_value="0.0"/>
<variable units="dimensionless" name="Fs" initial_value="0.0"/>
<variable units="millisecond" name="tau_f" initial_value="500.0"/>
<variable units="millisecond" name="tau_m" initial_value="0.000"/>
<variable units="millisecond" name="tau_s" initial_value="0.000"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="h_calculation">
<eq/>
<ci> h </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> Ff </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> time </ci>
</apply>
<ci> tau_f </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Fm </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> time </ci>
</apply>
<ci> tau_m </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Fs </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> time </ci>
</apply>
<ci> tau_s </ci>
</apply>
</apply>
</apply>
<ci> Fr </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_dependent_potassium_channel">
<variable units="microA_per_cm2" public_interface="out" name="i_SK"/>
<variable units="milliS_per_cm2" name="g_SK" initial_value="3.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Ca0"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_SK_calculation">
<eq/>
<ci> i_SK </ci>
<apply>
<times/>
<ci> g_SK </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_dependent_potassium_channel_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.001"/>
<variable units="dimensionless" name="m_infinity"/>
<variable units="metre_per_second" name="beta_k" initial_value="0.1"/>
<variable units="dimensionless" name="n_SK" initial_value="1.7"/>
<variable units="millisecond" name="tau_m"/>
<variable units="millimolar" name="Car"/>
<variable units="nanomolar" name="Cac" initial_value="700.0"/>
<variable units="millimolar" public_interface="in" name="Ca0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<ci> Car </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Car </ci>
</apply>
</apply>
</apply>
<apply id="tau_m_calculation">
<eq/>
<ci> tau_m </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 1.0 </cn>
<apply>
<times/>
<ci> beta_k </ci>
<apply>
<plus/>
<cn cellml:units="millimolar"> 1.0 </cn>
<ci> Car </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Car_calculation">
<eq/>
<ci> Car </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca0 </ci>
<ci> Cac </ci>
</apply>
<ci> n_SK </ci>
</apply>
</apply>
<apply id="calcium_dependent_potassium_channel_m_gate_dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> m </ci>
<ci> m_infinity </ci>
</apply>
</apply>
<ci> tau_m </ci>
</apply>
</apply>
</math>
</component>
<component name="buffered_calcium_diffusion">
<variable units="millimolar" public_interface="out" name="Bu"/>
<variable units="millimolar" public_interface="out" name="CaBu"/>
<variable units="per_millimolar_per_millisecond" public_interface="out" name="k1b" initial_value="100.0"/>
<variable units="per_millisecond" public_interface="out" name="k2b" initial_value="10.0"/>
<variable units="per_millisecond" public_interface="out" name="kfc"/>
<variable units="per_millisecond" public_interface="out" name="kbc"/>
<variable units="millimolar" name="Cai"/>
<variable units="micrometre2_per_millisecond" name="DCa" initial_value="0.22"/>
<variable units="millimolar" name="TBu" initial_value="4.0"/>
<variable units="micrometre" public_interface="in" name="delta_r"/>
<variable units="micrometre2" public_interface="in" name="Ai2"/>
<variable units="micrometre3" public_interface="in" name="vol_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cai_calculation">
<eq/>
<ci> Cai </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> CaBu </ci>
<ci> k2b </ci>
</apply>
<apply>
<times/>
<ci> Cai </ci>
<ci> Bu </ci>
<ci> k1b </ci>
</apply>
</apply>
</apply>
<apply id="Bu_calculation">
<eq/>
<ci> Bu </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> CaBu </ci>
<ci> k2b </ci>
</apply>
<apply>
<times/>
<ci> Cai </ci>
<ci> Bu </ci>
<ci> k1b </ci>
</apply>
</apply>
</apply>
<apply id="CaBu_calculation">
<eq/>
<ci> CaBu </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Cai </ci>
<ci> Bu </ci>
<ci> k1b </ci>
</apply>
<apply>
<times/>
<ci> CaBu </ci>
<ci> k2b </ci>
</apply>
</apply>
</apply>
<apply id="kfc_calculation">
<eq/>
<ci> kfc </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> DCa </ci>
<ci> Ai2 </ci>
</apply>
<apply>
<times/>
<ci> delta_r </ci>
<ci> vol_i </ci>
</apply>
</apply>
</apply>
<apply id="kbc_calculation">
<eq/>
<ci> kbc </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> DCa </ci>
<ci> Ai2 </ci>
</apply>
<apply>
<times/>
<ci> delta_r </ci>
<ci> vol_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_extrusion">
<variable units="microA_per_cm2" public_interface="out" name="i_ex"/>
<variable units="microA_per_cm2" name="Vmax" initial_value="3.0"/>
<variable units="nanomolar" name="Kex" initial_value="830.0"/>
<variable units="nanomolar" name="Ca_rest" initial_value="100.0"/>
<variable units="millimolar" public_interface="in" name="Ca0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_ex_calculation">
<eq/>
<ci> i_ex </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Vmax </ci>
<apply>
<divide/>
<ci> Ca0 </ci>
<apply>
<plus/>
<ci> Kex </ci>
<ci> Ca0 </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Vmax </ci>
<apply>
<divide/>
<ci> Ca_rest </ci>
<apply>
<plus/>
<ci> Kex </ci>
<ci> Ca_rest </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_triggered_exocytosis">
<variable units="millimolar_per_millisecond" name="SR"/>
<variable units="per_millisecond" name="k1f"/>
<variable units="per_millisecond" name="k1b"/>
<variable units="per_millisecond" name="k2"/>
<variable units="per_millisecond" name="a1" initial_value="9.0E-6"/>
<variable units="per_millisecond" name="a2" initial_value="5.5E-6"/>
<variable units="per_micromolar3_per_millisecond" name="a3" initial_value="2.3E-5"/>
<variable units="micromolar" name="b1" initial_value="1.2"/>
<variable units="dimensionless" name="B"/>
<variable units="dimensionless" name="A" initial_value="2000.0"/>
<variable units="dimensionless" name="C"/>
<variable units="millimolar" public_interface="in" name="Ca0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k1f_calculation">
<eq/>
<ci> k1f </ci>
<apply>
<times/>
<ci> a1 </ci>
<apply>
<divide/>
<ci> Ca0 </ci>
<apply>
<plus/>
<ci> b1 </ci>
<ci> Ca0 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="k1b_calculation">
<eq/>
<ci> k1b </ci>
<ci> a2 </ci>
</apply>
<apply id="k2_calculation">
<eq/>
<ci> k2 </ci>
<apply>
<times/>
<ci> a3 </ci>
<apply>
<power/>
<ci> Ca0 </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply id="B_calculation">
<eq/>
<ci> B </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> A </ci>
<ci> k1f </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> B </ci>
<ci> k1b </ci>
</apply>
<apply>
<times/>
<ci> B </ci>
<ci> k2 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="C_calculation">
<eq/>
<ci> C </ci>
<apply>
<times/>
<ci> B </ci>
<ci> k2 </ci>
</apply>
</apply>
<apply id="SR_calculation">
<eq/>
<ci> SR </ci>
<apply>
<times/>
<ci> k2 </ci>
<ci> B </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_indicator">
<variable units="millimolar" public_interface="out" name="CaDy"/>
<variable units="millimolar" public_interface="out" name="Dy"/>
<variable units="per_millimolar_per_millisecond" public_interface="out" name="k1d" initial_value="500.0"/>
<variable units="per_millisecond" public_interface="out" name="k2d" initial_value="0.12"/>
<variable units="millimolar" name="FDy"/>
<variable units="millimolar" name="Dyi2"/>
<variable units="millimolar" name="Cai"/>
<variable units="millimolar" name="FCaDy"/>
<variable units="micromolar" name="TDy" initial_value="5.0"/>
<variable units="micrometre2_per_millisecond" name="Ddy" initial_value="0.05"/>
<variable units="nanomolar" name="Dkd" initial_value="240.0"/>
<variable units="dimensionless" name="F0" initial_value="0.36"/>
<variable units="per_millisecond" name="kfd"/>
<variable units="per_millisecond" name="kbd"/>
<variable units="micrometre" public_interface="in" name="delta_r"/>
<variable units="micrometre2" public_interface="in" name="Ai2"/>
<variable units="micrometre3" public_interface="in" name="vol_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Dy_calculation">
<eq/>
<ci> Dy </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Dyi2 </ci>
<ci> kbd </ci>
</apply>
<apply>
<times/>
<ci> Dy </ci>
<ci> kfd </ci>
</apply>
</apply>
</apply>
<apply id="kfd_calculation">
<eq/>
<ci> kfd </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Ddy </ci>
<ci> Ai2 </ci>
</apply>
<apply>
<times/>
<ci> delta_r </ci>
<ci> vol_i </ci>
</apply>
</apply>
</apply>
<apply id="kbd_calculation">
<eq/>
<ci> kbd </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Ddy </ci>
<ci> Ai2 </ci>
</apply>
<apply>
<times/>
<ci> delta_r </ci>
<ci> vol_i </ci>
</apply>
</apply>
</apply>
<apply id="CaDy_calculation">
<eq/>
<ci> CaDy </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Dy </ci>
<ci> Cai </ci>
<ci> k1d </ci>
</apply>
<apply>
<times/>
<ci> CaDy </ci>
<ci> k2d </ci>
</apply>
</apply>
</apply>
<apply id="FDy_calculation">
<eq/>
<ci> FDy </ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> F0 </ci>
</apply>
<ci> FCaDy </ci>
</apply>
<ci> F0 </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_concentration">
<variable units="millimolar" public_interface="out" name="Ca0" initial_value="0.1"/>
<variable units="micrometre2" name="A0" initial_value="706.86"/>
<variable units="micrometre3" name="vol0"/>
<variable units="millimolar" name="Ca1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Ca"/>
<variable units="microA_per_cm2" public_interface="in" name="i_ex"/>
<variable units="millimolar" public_interface="in" name="CaBu"/>
<variable units="millimolar" public_interface="in" name="Bu"/>
<variable units="millimolar" public_interface="in" name="CaDy"/>
<variable units="millimolar" public_interface="in" name="Dy"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="per_millimolar_per_millisecond" public_interface="in" name="k1d"/>
<variable units="per_millisecond" public_interface="in" name="k2d"/>
<variable units="per_millimolar_per_millisecond" public_interface="in" name="k1b"/>
<variable units="per_millisecond" public_interface="in" name="k2b"/>
<variable units="per_millisecond" public_interface="in" name="kfc"/>
<variable units="per_millisecond" public_interface="in" name="kbc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca0_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca0 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> kbc </ci>
<ci> Ca1 </ci>
</apply>
<apply>
<times/>
<ci> k2b </ci>
<ci> CaBu </ci>
</apply>
<apply>
<times/>
<ci> k2d </ci>
<ci> CaDy </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci> i_Ca </ci>
<ci> i_ex </ci>
</apply>
<ci> A0 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> vol0 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> kfc </ci>
<ci> Ca0 </ci>
</apply>
<apply>
<times/>
<ci> k1b </ci>
<ci> Bu </ci>
<ci> Ca0 </ci>
</apply>
<apply>
<times/>
<ci> k1d </ci>
<ci> Dy </ci>
<ci> Ca0 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="joule_per_mole_kelvin" public_interface="out" name="R" initial_value="8.3144"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.15"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96485"/>
<variable units="micrometre" public_interface="out" name="delta_r"/>
<variable units="micrometre2" public_interface="out" name="Ai2"/>
<variable units="micrometre3" public_interface="out" name="vol_i" initial_value="1767.15"/>
<variable units="millivolt" public_interface="out" name="E_K" initial_value="-80.0"/>
<variable units="micrometre" name="diameter" initial_value="15.0"/>
<variable units="dimensionless" name="Nc" initial_value="6.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="delta_r_calculation">
<eq/>
<ci> delta_r </ci>
<apply>
<divide/>
<ci> diameter </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<minus/>
<ci> Nc </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="calcium_channel">
<component_ref component="calcium_channel_m_gate"/>
<component_ref component="calcium_channel_h_gate"/>
</component_ref>
<component_ref component="sodium_channel">
<component_ref component="sodium_channel_m_gate"/>
<component_ref component="sodium_channel_h_gate"/>
</component_ref>
<component_ref component="potassium_channel">
<component_ref component="potassium_channel_n_gate"/>
</component_ref>
<component_ref component="calcium_dependent_potassium_channel">
<component_ref component="calcium_dependent_potassium_channel_m_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="excitatory_synapse"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="potassium_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_dependent_potassium_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="excitatory_synapse" component_1="membrane"/>
<map_variables variable_2="i_sp" variable_1="i_sp"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_channel" component_1="membrane"/>
<map_variables variable_2="i_Ca" variable_1="i_Ca"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="sodium_channel" component_1="membrane"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="potassium_channel" component_1="membrane"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_dependent_potassium_channel" component_1="membrane"/>
<map_variables variable_2="i_SK" variable_1="i_SK"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="leak_channel" component_1="membrane"/>
<map_variables variable_2="i_l" variable_1="i_l"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_extrusion" component_1="membrane"/>
<map_variables variable_2="i_ex" variable_1="i_ex"/>
</connection>
<connection>
<map_components component_2="calcium_channel" component_1="model_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="buffered_calcium_diffusion" component_1="model_parameters"/>
<map_variables variable_2="delta_r" variable_1="delta_r"/>
<map_variables variable_2="Ai2" variable_1="Ai2"/>
<map_variables variable_2="vol_i" variable_1="vol_i"/>
</connection>
<connection>
<map_components component_2="calcium_indicator" component_1="model_parameters"/>
<map_variables variable_2="delta_r" variable_1="delta_r"/>
<map_variables variable_2="Ai2" variable_1="Ai2"/>
<map_variables variable_2="vol_i" variable_1="vol_i"/>
</connection>
<connection>
<map_components component_2="calcium_concentration" component_1="model_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="potassium_channel" component_1="model_parameters"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="calcium_dependent_potassium_channel" component_1="model_parameters"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="calcium_channel" component_1="calcium_concentration"/>
<map_variables variable_2="Ca0" variable_1="Ca0"/>
<map_variables variable_2="i_Ca" variable_1="i_Ca"/>
</connection>
<connection>
<map_components component_2="calcium_dependent_potassium_channel" component_1="calcium_concentration"/>
<map_variables variable_2="Ca0" variable_1="Ca0"/>
</connection>
<connection>
<map_components component_2="calcium_extrusion" component_1="calcium_concentration"/>
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Warashina and Ogura's 2004 mathematical model of stimulation-secretion coupling in a chromaffin cell.
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