- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:21:53+12:00
- Desc:
- committing version01 of bertram_arnot_zamponi_2002
- Permanent Source URI:
- https://models.cellml.org/workspace/bertram_arnot_zamponi_2002/rawfile/1f727f9df5fe010424b5a8326545a3276a83e6ae/bertram_arnot_zamponi_2002.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE :bertram_model_2002.xml
CREATED : 6th November 2002
LAST MODIFIED : 20th April 2005
AUTHOR : Catherine Lloyd
Bioengineering Institute
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 Bertram, Arnot and Zamponi's 2002 analysis of the role of G Protein G-beta-gamma isoform specificity in synaptic signal processing.
CHANGES:
09/04/2003 - AAC - Added publication date information.
20/04/2005 - PJV - Made MathML id's unique
--><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="bertram_arnot_zamponi_2002_version01" name="bertram_arnot_zamponi_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>G-Protein Specificity In Synaptic Signalling</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Ca<superscript>2+</superscript> flux through voltage-gated channels plays a role in muscle contraction, gene expression, synaptic transmission, short- and long-term memory. Ca<superscript>2+</superscript> channels are regulated by many electrical, genetic and biochemical pathways, including G-protein signal transduction pathways. In their 2002 study, Richard Bertram, Michelle I. Arnot, and Gerald W. Zamponi focus on the direct regulation of N-type Ca<superscript>2+</superscript> channels by the G-beta-gamma subunits of activated G-proteins (see <xref linkend="fig_reaction_diagram"/> below). Ca<superscript>2+</superscript> ion binding to a low-affinity binding site induces vesicle fusion with the plasma membrane, followed by the release of transmitter by exocytosis. Transmitter binding to a presynaptic autoreceptor activates a G-protein, the G-beta-gamma subunit od which binds directly to an N-type Ca<superscript>2+</superscript> channel. Such binding puts channels into a reluctant state, reducing the net flow of Ca<superscript>2+</superscript> into the cell. Autoinhibition of transmitter release then occurs as the result of the G-protein-mediated inhibition of Ca<superscript>2+</superscript> channels. The resultant depolarisation results in the unbinding of G-beta-gamma from the channel.
</para>
<para>
The mathematical model developed by bertram <emphasis>et al.</emphasis> in this study was used to address two questions: 1) What is the role of G-protein-mediated autoinhibition on synaptic signalling processing; and 2) How is signal processing affected by different G-beta-gamma isoforms? The presynaptic model has equations for membrane potential, Ca<superscript>2+</superscript>-dependent transmitter release, transmitter binding to autoreceptors, and Ca<superscript>2+</superscript> influx through G-protein-regulated channels. This mathematical model has been translated into a CellML description which can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://jn.physiology.org/cgi/content/abstract/87/5/2612">Role for G Protein G-Beta-Gamma Isoform Specificity in Synaptic Signal Processing: A Computational Study</ulink>, Richard Bertram, Michelle I. Arnot, and Gerald W. Zamponi, 2002, <ulink url="http://jn.physiology.org/">
<emphasis>Journal of Neurophysiology</emphasis>
</ulink>, 87, 2612-2623. (<ulink url="http://jn.physiology.org/cgi/content/full/87/5/2612">Full text</ulink> and <ulink url="http://jn.physiology.org/cgi/reprint/87/5/2612.pdf">PDF</ulink> versions of the article are available for Journal Members on the Journal of Neurophysiology website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11976397&dopt=Abstract">PubMed ID: 11976397</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="reaction_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the presynaptic model.</caption>
</informalfigure>
<para>
G-protein autoinhibitory feedback on the presynaptic terminal acts like a high-pass filter, allowing only high-frequency signals to pass through the to the postsynaptic cell. Low-frequency signals are effectively filtered out. Model simulations in this study show how different G-beta-gamma isoforms have different filtering properties. They also emphasise that the different filtering characteristics associated with a specific G-beta-gamma subunit depend on many biophysical parameters, such as the unbinding rate of a transmitter molecule from the presynaptic autoreceptor. For example faster unbinding lowers the filter cut while slower unbinding raises it. This allows for great synapse-tot-synapse variability in the distinction between signal and background noise.
</para>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar" exponent="1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar_2_per_second">
<unit units="micromolar" exponent="2"/>
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="millivolt_per_millimolar">
<unit units="millivolt"/>
<unit units="millimolar" exponent="1"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_cm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="picoS">
<unit units="siemens" prefix="pico"/>
</units>
<units name="nanometre">
<unit units="metre" prefix="nano"/>
</units>
<units name="millijoule_per_mole_kelvin">
<unit units="joule" prefix="milli"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<!--
The presynaptic terminal is modelled with equations for membrane potential, Ca2+-dependent transmitter release, transmitter binding to autoreceptors and Ca2+ influx through G protein-regulated channels.
-->
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initail_value="-65.0"/>
<variable units="millijoule_per_mole_kelvin" public_interface="out" name="R" initial_value="8314.41"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96485.0"/>
<variable units="microF_per_cm2" name="Cm" initial_value="1.0"/>
<variable units="microA_per_cm2" name="i_app" initial_value="40.0"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K"/>
<variable units="microA_per_cm2" public_interface="in" name="i_leak"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
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<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_K </ci>
<ci> i_leak </ci>
<ci> i_app </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_Na"/>
<variable units="dimensionless" name="x_infinity"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="dimensionless" public_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<cn cellml:units="picoS"> 120.0 </cn>
<apply>
<power/>
<ci> x_infinity </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> n </ci>
</apply>
<apply>
<minus/>
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<cn cellml:units="millivolt"> 120.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_K"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" public_interface="out" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<apply>
<times/>
<cn cellml:units="picoS"> 36.0 </cn>
<apply>
<power/>
<ci> n </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 77.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="dimensionless" name="alpha_n"/>
<variable units="dimensionless" name="beta_n"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_n </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> n </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_n </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
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<eq/>
<ci> alpha_n </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.02 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 55.0 </cn>
</apply>
</apply>
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<minus/>
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<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 55.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_n_calculation">
<eq/>
<ci> beta_n </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.25 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 65.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="leak_current">
<variable units="microA_per_cm2" public_interface="out" name="i_leak"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_leak_calculation">
<eq/>
<ci> i_leak </ci>
<apply>
<times/>
<cn cellml:units="picoS"> 0.3 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 54.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transmitter_release">
<variable units="micromolar" public_interface="out" name="R"/>
<variable units="second_order_rate_constant" name="kr_plus" initial_value="0.15"/>
<variable units="first_order_rate_constant" name="kr_minus" initial_value="2.5"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="R_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> R </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> kr_plus </ci>
<ci> Ca </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> R </ci>
</apply>
</apply>
<apply>
<times/>
<ci> kr_minus </ci>
<ci> R </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_concentration">
<variable units="micromolar" public_interface="out" name="Ca"/>
<variable units="millimolar" name="Ca_ex" initial_value="2.0"/>
<variable units="micromolar" name="Ca_open"/>
<variable units="micromolar_2_per_second" name="Dc" initial_value="220.0"/>
<variable units="nanometre" name="r" initial_value="10.0"/>
<variable units="flux" name="sigma"/>
<variable units="microA_per_cm2" name="i_V"/>
<variable units="picoS" name="g_Ca" initial_value="1.2"/>
<variable units="millivolt_per_millimolar" name="P" initial_value="6.0"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="micromolar" public_interface="in" name="O"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_open_calculation">
<eq/>
<ci> Ca_open </ci>
<apply>
<divide/>
<ci> sigma </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Dc </ci>
<ci> r </ci>
<pi/>
</apply>
</apply>
</apply>
<apply id="sigma_calculation">
<eq/>
<ci> sigma </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -5.182 </cn>
<ci> i_V </ci>
</apply>
</apply>
<apply id="i_V_calculation">
<eq/>
<ci> i_V </ci>
<apply>
<times/>
<ci> g_Ca </ci>
<ci> P </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Ca_ex </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The following components describe all the reactants and products involved in the reactions.
-->
<component cmeta:id="C1" name="C1">
<variable units="micromolar" public_interface="out" name="C1" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C1_rxn0"/>
<variable units="flux" public_interface="in" name="delta_C1_rxn6"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C1</ci>
</apply>
<apply>
<plus/>
<ci>delta_C1_rxn0</ci>
<ci>delta_C1_rxn6</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C2" name="C2">
<variable units="micromolar" public_interface="out" name="C2" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn0"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn1"/>
<variable units="flux" public_interface="in" name="delta_C2_rxn7"/>
<variable units="millisecond" public_interface="in" name="time"/>
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<ci>delta_C2_rxn1</ci>
<ci>delta_C2_rxn7</ci>
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<variable units="micromolar" public_interface="out" name="C3" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C3_rxn1"/>
<variable units="flux" public_interface="in" name="delta_C3_rxn2"/>
<variable units="flux" public_interface="in" name="delta_C3_rxn8"/>
<variable units="millisecond" public_interface="in" name="time"/>
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<ci>delta_C3_rxn2</ci>
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<component cmeta:id="C4" name="C4">
<variable units="micromolar" public_interface="out" name="C4" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C4_rxn2"/>
<variable units="flux" public_interface="in" name="delta_C4_rxn3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<ci>C4</ci>
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<apply>
<plus/>
<ci>delta_C4_rxn2</ci>
<ci>delta_C4_rxn3</ci>
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</apply>
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</component>
<component cmeta:id="O" name="O">
<variable units="micromolar" public_interface="out" name="O" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_O_rxn3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci>time</ci>
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<ci>O</ci>
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<ci>delta_O_rxn3</ci>
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<component cmeta:id="C_G1" name="C_G1">
<variable units="micromolar" public_interface="out" name="C_G1" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C_G1_rxn6"/>
<variable units="flux" public_interface="in" name="delta_C_G1_rxn4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci>time</ci>
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<ci>C_G1</ci>
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<apply>
<plus/>
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<ci>delta_C_G1_rxn4</ci>
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</apply>
</math>
</component>
<component cmeta:id="C_G2" name="C_G2">
<variable units="micromolar" public_interface="out" name="C_G2" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C_G2_rxn4"/>
<variable units="flux" public_interface="in" name="delta_C_G2_rxn7"/>
<variable units="flux" public_interface="in" name="delta_C_G2_rxn5"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci>time</ci>
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<ci>delta_C_G2_rxn7</ci>
<ci>delta_C_G2_rxn5</ci>
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</apply>
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</component>
<component cmeta:id="C_G3" name="C_G3">
<variable units="micromolar" public_interface="out" name="C_G3" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_C_G3_rxn5"/>
<variable units="flux" public_interface="in" name="delta_C_G3_rxn8"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<apply>
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<bvar>
<ci>time</ci>
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<ci>C_G3</ci>
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<apply>
<plus/>
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<ci>delta_C_G3_rxn8</ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe the kinetics and reactions of the model.
-->
<component name="rate_constants">
<variable units="first_order_rate_constant" public_interface="out" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="out" name="alpha_"/>
<variable units="first_order_rate_constant" public_interface="out" name="beta"/>
<variable units="first_order_rate_constant" public_interface="out" name="beta_"/>
<variable units="first_order_rate_constant" public_interface="out" name="kG_plus"/>
<variable units="dimensionless" name="a"/>
<variable units="second_order_rate_constant" name="ka_plus" initial_value="200.0"/>
<variable units="first_order_rate_constant" name="ka_minus" initial_value="0.0015"/>
<variable units="millimolar" name="T" initial_value="1.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="rate_constants_alpha_calculation">
<eq/>
<ci> alpha </ci>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant"> 0.45 </cn>
<apply>
<exp/>
<apply>
<divide/>
<ci> V </ci>
<cn cellml:units="millivolt"> 22.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_calculation">
<eq/>
<ci> alpha_ </ci>
<apply>
<divide/>
<ci> alpha </ci>
<cn cellml:units="dimensionless"> 8.0 </cn>
</apply>
</apply>
<apply id="beta_calculation">
<eq/>
<ci> beta </ci>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant"> 0.015 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 14.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha__calculation">
<eq/>
<ci> beta_ </ci>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 8.0 </cn>
</apply>
</apply>
<apply id="da_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> a </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> ka_plus </ci>
<ci> T </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> a </ci>
</apply>
</apply>
<apply>
<times/>
<ci> ka_minus </ci>
<ci> a </ci>
</apply>
</apply>
</apply>
<apply id="kG_plus_calculation">
<eq/>
<ci> kG_plus </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant"> 3.0 </cn>
<ci> a </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 680.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 320.0 </cn>
<ci> a </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="reaction0">
<variable units="micromolar" public_interface="in" name="C1"/>
<variable units="micromolar" public_interface="in" name="C2"/>
<variable units="flux" public_interface="out" name="delta_C1_rxn0"/>
<variable units="flux" public_interface="out" name="delta_C2_rxn0"/>
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C1">
<role stoichiometry="1" direction="forward" delta_variable="delta_C1_rxn0" role="reactant"/>
</variable_ref>
<variable_ref variable="C2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C2_rxn0" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci>alpha</ci>
<ci>C1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>beta</ci>
<ci>C2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction1">
<variable units="micromolar" public_interface="in" name="C2"/>
<variable units="micromolar" public_interface="in" name="C3"/>
<variable units="flux" public_interface="out" name="delta_C2_rxn1"/>
<variable units="flux" public_interface="out" name="delta_C3_rxn1"/>
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C2_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="C3">
<role stoichiometry="1" direction="forward" delta_variable="delta_C3_rxn1" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci>alpha</ci>
<ci>C2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci>beta</ci>
<ci>C3</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction2">
<variable units="micromolar" public_interface="in" name="C3"/>
<variable units="micromolar" public_interface="in" name="C4"/>
<variable units="flux" public_interface="out" name="delta_C3_rxn2"/>
<variable units="flux" public_interface="out" name="delta_C4_rxn2"/>
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C3">
<role stoichiometry="1" direction="forward" delta_variable="delta_C3_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="C4">
<role stoichiometry="1" direction="forward" delta_variable="delta_C4_rxn2" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci>alpha</ci>
<ci>C3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci>beta</ci>
<ci>C4</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="micromolar" public_interface="in" name="C4"/>
<variable units="micromolar" public_interface="in" name="O"/>
<variable units="flux" public_interface="out" name="delta_C4_rxn3"/>
<variable units="flux" public_interface="out" name="delta_O_rxn3"/>
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C4">
<role stoichiometry="1" direction="forward" delta_variable="delta_C4_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="O">
<role stoichiometry="1" direction="forward" delta_variable="delta_O_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>C4</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci>beta</ci>
<ci>O</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction4">
<variable units="micromolar" public_interface="in" name="C_G1"/>
<variable units="micromolar" public_interface="in" name="C_G2"/>
<variable units="flux" public_interface="out" name="delta_C_G1_rxn4"/>
<variable units="flux" public_interface="out" name="delta_C_G2_rxn4"/>
<variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C_G1">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G1_rxn4" role="reactant"/>
</variable_ref>
<variable_ref variable="C_G2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G2_rxn4" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci>alpha_</ci>
<ci>C_G1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_</ci>
<ci>C_G2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction5">
<variable units="micromolar" public_interface="in" name="C_G2"/>
<variable units="micromolar" public_interface="in" name="C_G3"/>
<variable units="flux" public_interface="out" name="delta_C_G2_rxn5"/>
<variable units="flux" public_interface="out" name="delta_C_G3_rxn5"/>
<variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C_G2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G2_rxn5" role="reactant"/>
</variable_ref>
<variable_ref variable="C_G3">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G3_rxn5" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci>alpha_</ci>
<ci>C_G2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci>beta_</ci>
<ci>C_G3</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction6">
<variable units="micromolar" public_interface="in" name="C1"/>
<variable units="micromolar" public_interface="in" name="C_G1"/>
<variable units="flux" public_interface="out" name="delta_C1_rxn6"/>
<variable units="flux" public_interface="out" name="delta_C_G1_rxn6"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" name="kG_minus" initial_value="0.00025"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C1">
<role stoichiometry="1" direction="forward" delta_variable="delta_C1_rxn6" role="reactant"/>
</variable_ref>
<variable_ref variable="C_G1">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G1_rxn6" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kG_minus</ci>
<ci>C_G1</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction7">
<variable units="micromolar" public_interface="in" name="C2"/>
<variable units="micromolar" public_interface="in" name="C_G2"/>
<variable units="flux" public_interface="out" name="delta_C2_rxn7"/>
<variable units="flux" public_interface="out" name="delta_C_G2_rxn7"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" name="kG2_minus" initial_value="0.01"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C2_rxn7" role="reactant"/>
</variable_ref>
<variable_ref variable="C_G2">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G2_rxn7" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kG2_minus</ci>
<ci>C_G2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction8">
<variable units="micromolar" public_interface="in" name="C3"/>
<variable units="micromolar" public_interface="in" name="C_G3"/>
<variable units="flux" public_interface="out" name="delta_C3_rxn8"/>
<variable units="flux" public_interface="out" name="delta_C_G3_rxn8"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" name="kG3_minus" initial_value="0.0005"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="C3">
<role stoichiometry="1" direction="forward" delta_variable="delta_C3_rxn8" role="reactant"/>
</variable_ref>
<variable_ref variable="C_G3">
<role stoichiometry="1" direction="forward" delta_variable="delta_C_G3_rxn8" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kG3_minus</ci>
<ci>C_G3</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="potassium_current">
<component_ref component="potassium_current_n_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="reaction0" component_1="C1"/>
<map_variables variable_2="C1" variable_1="C1"/>
<map_variables variable_2="delta_C1_rxn0" variable_1="delta_C1_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction6" component_1="C1"/>
<map_variables variable_2="C1" variable_1="C1"/>
<map_variables variable_2="delta_C1_rxn6" variable_1="delta_C1_rxn6"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="C2"/>
<map_variables variable_2="C2" variable_1="C2"/>
<map_variables variable_2="delta_C2_rxn0" variable_1="delta_C2_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="C2"/>
<map_variables variable_2="C2" variable_1="C2"/>
<map_variables variable_2="delta_C2_rxn1" variable_1="delta_C2_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction7" component_1="C2"/>
<map_variables variable_2="C2" variable_1="C2"/>
<map_variables variable_2="delta_C2_rxn7" variable_1="delta_C2_rxn7"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="C3"/>
<map_variables variable_2="C3" variable_1="C3"/>
<map_variables variable_2="delta_C3_rxn1" variable_1="delta_C3_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="C3"/>
<map_variables variable_2="C3" variable_1="C3"/>
<map_variables variable_2="delta_C3_rxn2" variable_1="delta_C3_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction8" component_1="C3"/>
<map_variables variable_2="C3" variable_1="C3"/>
<map_variables variable_2="delta_C3_rxn8" variable_1="delta_C3_rxn8"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="C4"/>
<map_variables variable_2="C4" variable_1="C4"/>
<map_variables variable_2="delta_C4_rxn2" variable_1="delta_C4_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="C4"/>
<map_variables variable_2="C4" variable_1="C4"/>
<map_variables variable_2="delta_C4_rxn3" variable_1="delta_C4_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="O"/>
<map_variables variable_2="O" variable_1="O"/>
<map_variables variable_2="delta_O_rxn3" variable_1="delta_O_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction6" component_1="C_G1"/>
<map_variables variable_2="C_G1" variable_1="C_G1"/>
<map_variables variable_2="delta_C_G1_rxn6" variable_1="delta_C_G1_rxn6"/>
</connection>
<connection>
<map_components component_2="reaction4" component_1="C_G1"/>
<map_variables variable_2="C_G1" variable_1="C_G1"/>
<map_variables variable_2="delta_C_G1_rxn4" variable_1="delta_C_G1_rxn4"/>
</connection>
<connection>
<map_components component_2="reaction4" component_1="C_G2"/>
<map_variables variable_2="C_G2" variable_1="C_G2"/>
<map_variables variable_2="delta_C_G2_rxn4" variable_1="delta_C_G2_rxn4"/>
</connection>
<connection>
<map_components component_2="reaction7" component_1="C_G2"/>
<map_variables variable_2="C_G2" variable_1="C_G2"/>
<map_variables variable_2="delta_C_G2_rxn7" variable_1="delta_C_G2_rxn7"/>
</connection>
<connection>
<map_components component_2="reaction5" component_1="C_G2"/>
<map_variables variable_2="C_G2" variable_1="C_G2"/>
<map_variables variable_2="delta_C_G2_rxn5" variable_1="delta_C_G2_rxn5"/>
</connection>
<connection>
<map_components component_2="reaction5" component_1="C_G3"/>
<map_variables variable_2="C_G3" variable_1="C_G3"/>
<map_variables variable_2="delta_C_G3_rxn5" variable_1="delta_C_G3_rxn5"/>
</connection>
<connection>
<map_components component_2="reaction8" component_1="C_G3"/>
<map_variables variable_2="C_G3" variable_1="C_G3"/>
<map_variables variable_2="delta_C_G3_rxn8" variable_1="delta_C_G3_rxn8"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C3"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C4"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="O"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C_G1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C_G2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="C_G3"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<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="potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="leak_current"/>
<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="environment" component_1="transmitter_release"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="rate_constants"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="potassium_current" component_1="sodium_current"/>
<map_variables variable_2="n" variable_1="n"/>
</connection>
<connection>
<map_components component_2="leak_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_leak" variable_1="i_leak"/>
</connection>
<connection>
<map_components component_2="calcium_concentration" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="rate_constants" component_1="membrane"/>
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Role for G Protein G-beta-gamma Isoform Specificity in Synaptic
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