- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 12:30:48+12:00
- Desc:
- committing version07 of bertram_arnot_zamponi_2002
- Permanent Source URI:
- https://models.cellml.org/workspace/bertram_arnot_zamponi_2002/rawfile/8413fc17c1454bc548aa4738bd7572fc7a9aa2c6/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
14/07/2007 - James Lawson
Removed reaction rate math from reaction elements, created backrate variable for all components describing reactions, added equations for backrate (=rate * -1) and delta variables, where reaction 0 describes transition from C1 to C2, delta C1 = rate, delta C2 = backrate.
- value of x_infinity unknown, therefore model can not be completed.
- this model also only represents the presynaptic cell. Postsynaptic cell needs to be coded and cells put in a network using imports.
15/07/05 - Received communication from Associate Professor Richard Bertram defining the variable x_infinity.
Added to model:
In component "sodium_current,"
Added two variables:
alpha_x and beta_x, both with units dimensionless.
Added three equations:
alpha_x = 0.2{units="dimensionless"} * (V + 40) / (1 - exp(-((V + 40)) / 10))
beta_x = 8 * exp(-((V + 65 / 18)))
x_infinity = alpha_x / (alpha_x + beta_x)
15/07/05 - Received communication from Associate Professor Richard Bertram defining the variable x_infinity.
Added to model:
In component "sodium_current,"
Added two variables:
alpha_x and beta_x, both with units dimensionless.
Added three equations:
alpha_x = 0.2{units="dimensionless"} * (V + 40) / (1 - exp(-((V + 40)) / 10))
beta_x = 8 * exp(-((V + 65 / 18)))
x_infinity = alpha_x / (alpha_x + beta_x)
Assumed that since 'n' (K+ current activation variable, defined in terms of alpha_n and beta_n similarly to x_infinity) has units = dimensionless, as so alpha_n and beta_n, x_infinity, alpha_x and beta_x should also have units = dimensionless.
Model now won't integrate, gets to second time step (as shown by CSV export) before it starts producing NaN results.
21/05/07 - James Lawson
Removed reaction components from model. Rebuilt model completely using differential expressions describing the rate of change over time of the probability of Ca++ channel opening. Changed units for C1, C2, C3 etc. from micromolar to dimensionless, since they are defining a probability, not a concentration. Added equation T = T_ * R, which describes transmitter concentration in the synaptic cleft. Used value of 4mM for T_, which corresponds to a superthreshold response of the post-synaptic cell. Also, changed values of kG?_minus, starting with a value of 0.00025, which corresponds to the beta1-gamma2 G-protein. Applied rule in paper: kG2_minus = kG_minus * 64, kG3_minus = kG2_minus * 64. kG_minus values for other G-proteins are: beta2-gamma2: 0.001, beta3-gamm2: 0.0005, beta4-gamma2: 0.01
Model unfortunately still does not integrate. Reason unknown. Model was originally built in Berkely-Madonna simulation software. Might be worthwhile asking Richard Bertram for the original model and have a look at it in the BM suite (can get free trial).
--><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#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" name="bertram_arnot_zamponi_2002_version01" cmeta:id="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 model was created by James Lawson on 21/05/07. The model has been rebuilt with the reaction components completely removed. kG_minus was altered to follow the rules defined in the paper: kG2_minus = 64 * kG_minus, kG3_minus = kG2_minus. The value used for kG_minus was 0.00025 and corresponded to the beta1-gamma2 G-proten. kG_minus values for other G-proteins are: beta2-gamma2: 0.001, beta3-gamm2: 0.0005, beta4-gamma2: 0.01</para>
<para>At present, this model is not able to reproduce the results in the publication. The postsynaptic cell model needs to be coded and the cells put in the network arrangement defined by the paper using CellML 1.1 imports. This work is pending the upgrade of the model repository to handle CellML 1.1 based models which use imports.</para>
<para>
ValidateCellML verifies this model as valid CellML, although unit inconsistencies are present.
</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>
Role for G Protein G-Beta-Gamma Isoform Specificity in Synaptic Signal Processing: A Computational Study, Richard Bertram, Michelle I. Arnot, and Gerald W. Zamponi, 2002,
<emphasis>Journal of Neurophysiology</emphasis>
, 87, 2612-2623. <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="bertram_2002.png"/>
</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>
<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">
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<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>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_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" public_interface="in" name="i_app"/>
<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/>
<bvar>
<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="stimulus_protocol">
<variable units="microA_per_cm2" public_interface="out" name="Istim"/>
<variable units="millisecond" name="IstimStart" initial_value="10"/>
<variable units="millisecond" name="IstimEnd" initial_value="50000"/>
<variable units="microA_per_cm2" name="IstimAmplitude" initial_value="40"/>
<variable units="millisecond" name="IstimPeriod" initial_value="100"/>
<variable units="millisecond" name="IstimPulseDuration" initial_value="1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<ci>Istim</ci>
<piecewise>
<piece>
<ci>IstimAmplitude</ci>
<apply>
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<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<apply>
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<ci>time</ci>
<ci>IstimEnd</ci>
</apply>
<apply>
<leq/>
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<apply>
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<ci>IstimStart</ci>
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<apply>
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<apply>
<floor/>
<apply>
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<ci>IstimStart</ci>
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<ci>IstimPeriod</ci>
</apply>
</apply>
<ci>IstimPeriod</ci>
</apply>
</apply>
<ci>IstimPulseDuration</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn units="uA_per_mm2">0</cn>
</otherwise>
</piecewise>
</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/>
<ci> V </ci>
<cn cellml:units="millivolt"> 120.0 </cn>
</apply>
</apply>
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<apply>
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<ci>beta_x</ci>
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<cn cellml:units="dimensionless">18</cn>
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</math>
<variable units="dimensionless" name="alpha_x"/>
<variable units="dimensionless" name="beta_x"/>
</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">
<apply id="i_K_calculation">
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<ci> i_K </ci>
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<apply>
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<ci> n </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
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<ci> V </ci>
<cn cellml:units="millivolt"> 77.0 </cn>
</apply>
</apply>
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</math>
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<component name="potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
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<variable units="second" public_interface="in" name="time"/>
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<cn cellml:units="millivolt"> 80.0 </cn>
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<component name="leak_current">
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<cn cellml:units="millivolt"> 54.0 </cn>
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<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"/>
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</component>
<component name="calcium_concentration">
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<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="dimensionless" public_interface="in" name="O"/>
<variable units="millisecond" public_interface="in" name="time"/>
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<pi/>
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<ci> i_V </ci>
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<ci> V </ci>
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</component>
<component name="rate_constants">
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<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="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>
<apply id="T_is_t">
<eq/>
<ci>T</ci>
<ci>t</ci>
</apply>
</math>
<variable units="first_order_rate_constant" public_interface="out" name="kG_minus" initial_value="0.00025"/>
<variable units="first_order_rate_constant" public_interface="out" name="kG2_minus" initial_value="0.016"/>
<variable units="first_order_rate_constant" public_interface="out" name="kG3_minus" initial_value="1.024"/>
<variable units="millimolar" public_interface="in" name="t"/>
<variable units="millimolar" name="T"/>
</component>
<component name="C1">
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="dimensionless" public_interface="out" name="C1" initial_value="1"/>
<variable units="dimensionless" public_interface="in" name="C2"/>
<variable units="dimensionless" public_interface="in" name="C_G1"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_minus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C1</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta</ci>
<ci>C2</ci>
</apply>
<apply>
<times/>
<ci>kG_minus</ci>
<ci>C_G1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha</ci>
</apply>
<ci>kG_plus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable units="millisecond" public_interface="in" name="time"/>
</component>
<component name="C2">
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="dimensionless" public_interface="in" name="C1"/>
<variable units="dimensionless" public_interface="out" name="C2" initial_value="0"/>
<variable units="dimensionless" public_interface="in" name="C3"/>
<variable units="dimensionless" public_interface="in" name="C_G2"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG2_minus"/>
<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>C2</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha</ci>
<ci>C1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta</ci>
<ci>C3</ci>
</apply>
<apply>
<times/>
<ci>kG2_minus</ci>
<ci>C_G2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C2</ci>
<apply>
<plus/>
<ci>beta</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha</ci>
</apply>
<ci>kG_plus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="C3">
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="dimensionless" public_interface="in" name="C2"/>
<variable units="dimensionless" public_interface="out" name="C3" initial_value="0"/>
<variable units="dimensionless" public_interface="in" name="C4"/>
<variable units="dimensionless" public_interface="in" name="C_G3"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG3_minus"/>
<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>C3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha</ci>
<ci>C2</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>beta</ci>
<ci>C4</ci>
</apply>
<apply>
<times/>
<ci>kG3_minus</ci>
<ci>C_G3</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C3</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha</ci>
</apply>
<ci>kG_plus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="C4">
<variable units="first_order_rate_constant" public_interface="in" name="alpha"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta"/>
<variable units="dimensionless" public_interface="in" name="C3"/>
<variable units="dimensionless" public_interface="out" name="C4" initial_value="0"/>
<variable units="dimensionless" public_interface="in" name="O"/>
<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>C4</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha</ci>
<ci>C3</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>beta</ci>
<ci>O</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C4</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>beta</ci>
</apply>
<ci>alpha</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="O">
<variable units="dimensionless" public_interface="in" name="C1"/>
<variable units="dimensionless" public_interface="in" name="C2"/>
<variable units="dimensionless" public_interface="in" name="C3"/>
<variable units="dimensionless" public_interface="in" name="C4"/>
<variable units="dimensionless" public_interface="out" name="O"/>
<variable units="dimensionless" public_interface="in" name="C_G1"/>
<variable units="dimensionless" public_interface="in" name="C_G2"/>
<variable units="dimensionless" public_interface="in" name="C_G3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>O</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>C1</ci>
</apply>
<ci>C2</ci>
</apply>
<ci>C3</ci>
</apply>
<ci>C4</ci>
</apply>
<ci>C_G1</ci>
</apply>
<ci>C_G2</ci>
</apply>
<ci>C_G3</ci>
</apply>
</apply>
</math>
</component>
<component name="C_G1">
<variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
<variable units="dimensionless" public_interface="in" name="C1"/>
<variable units="dimensionless" public_interface="out" name="C_G1" initial_value="0"/>
<variable units="dimensionless" public_interface="in" name="C_G2"/>
<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>C_G1</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>beta_</ci>
<ci>C_G2</ci>
</apply>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C_G1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha_</ci>
</apply>
<ci>kG_minus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG_minus"/>
</component>
<component name="C_G2">
<variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
<variable units="dimensionless" public_interface="in" name="C2"/>
<variable units="dimensionless" public_interface="in" name="C_G1"/>
<variable units="dimensionless" public_interface="out" name="C_G2" initial_value="0"/>
<variable units="dimensionless" public_interface="in" name="C_G3"/>
<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>C_G2</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha_</ci>
<ci>C_G1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta_</ci>
<ci>C_G3</ci>
</apply>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C_G2</ci>
<apply>
<plus/>
<ci>beta_</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha_</ci>
</apply>
<ci>kG2_minus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG2_minus"/>
</component>
<component name="C_G3">
<variable units="first_order_rate_constant" public_interface="in" name="alpha_"/>
<variable units="first_order_rate_constant" public_interface="in" name="beta_"/>
<variable units="dimensionless" public_interface="in" name="C3"/>
<variable units="dimensionless" public_interface="in" name="C_G2"/>
<variable units="dimensionless" public_interface="out" name="C_G3" initial_value="0"/>
<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>C_G3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha_</ci>
<ci>C_G2</ci>
</apply>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C3</ci>
</apply>
</apply>
<apply>
<times/>
<ci>C_G3</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta_</ci>
</apply>
<ci>kG3_minus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable units="first_order_rate_constant" public_interface="in" name="kG_plus"/>
<variable units="first_order_rate_constant" public_interface="in" name="kG3_minus"/>
</component>
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<connection>
<map_components component_2="membrane" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="sodium_current" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="potassium_current" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="leak_current" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="transmitter_release" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="calcium_concentration" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="rate_constants" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C1" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C2" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C3" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C4" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="O" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C_G1" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C_G2" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C_G3" component_1="environment"/>
<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"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_concentration" component_1="O"/>
<map_variables variable_2="O" variable_1="O"/>
</connection>
<connection>
<map_components component_2="calcium_concentration" component_1="transmitter_release"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
</connection>
<connection>
<map_components component_2="rate_constants" component_1="transmitter_release"/>
<map_variables variable_2="t" variable_1="T"/>
</connection>
<connection>
<map_components component_2="potassium_current_n_gate" component_1="potassium_current"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="C1" component_1="rate_constants"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="beta" variable_1="beta"/>
<map_variables variable_2="kG_plus" variable_1="kG_plus"/>
<map_variables variable_2="kG_minus" variable_1="kG_minus"/>
</connection>
<connection>
<map_components component_2="C1" component_1="C2"/>
<map_variables variable_2="C2" variable_1="C2"/>
<map_variables variable_2="C1" variable_1="C1"/>
</connection>
<connection>
<map_components component_2="C1" component_1="C_G1"/>
<map_variables variable_2="C_G1" variable_1="C_G1"/>
<map_variables variable_2="C1" variable_1="C1"/>
</connection>
<connection>
<map_components component_2="C2" component_1="rate_constants"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="beta" variable_1="beta"/>
<map_variables variable_2="kG_plus" variable_1="kG_plus"/>
<map_variables variable_2="kG2_minus" variable_1="kG2_minus"/>
</connection>
<connection>
<map_components component_2="C2" component_1="C3"/>
<map_variables variable_2="C3" variable_1="C3"/>
<map_variables variable_2="C2" variable_1="C2"/>
</connection>
<connection>
<map_components component_2="C2" component_1="C_G2"/>
<map_variables variable_2="C_G2" variable_1="C_G2"/>
<map_variables variable_2="C2" variable_1="C2"/>
</connection>
<connection>
<map_components component_2="C3" component_1="rate_constants"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="beta" variable_1="beta"/>
<map_variables variable_2="kG_plus" variable_1="kG_plus"/>
<map_variables variable_2="kG3_minus" variable_1="kG3_minus"/>
</connection>
<connection>
<map_components component_2="C3" component_1="C4"/>
<map_variables variable_2="C4" variable_1="C4"/>
<map_variables variable_2="C3" variable_1="C3"/>
</connection>
<connection>
<map_components component_2="C3" component_1="C_G3"/>
<map_variables variable_2="C_G3" variable_1="C_G3"/>
<map_variables variable_2="C3" variable_1="C3"/>
</connection>
<connection>
<map_components component_2="C4" component_1="rate_constants"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="beta" variable_1="beta"/>
</connection>
<connection>
<map_components component_2="C4" component_1="O"/>
<map_variables variable_2="O" variable_1="O"/>
<map_variables variable_2="C4" variable_1="C4"/>
</connection>
<connection>
<map_components component_2="O" component_1="C1"/>
<map_variables variable_2="C1" variable_1="C1"/>
</connection>
<connection>
<map_components component_2="O" component_1="C2"/>
<map_variables variable_2="C2" variable_1="C2"/>
</connection>
<connection>
<map_components component_2="O" component_1="C3"/>
<map_variables variable_2="C3" variable_1="C3"/>
</connection>
<connection>
<map_components component_2="O" component_1="C_G1"/>
<map_variables variable_2="C_G1" variable_1="C_G1"/>
</connection>
<connection>
<map_components component_2="O" component_1="C_G2"/>
<map_variables variable_2="C_G2" variable_1="C_G2"/>
</connection>
<connection>
<map_components component_2="O" component_1="C_G3"/>
<map_variables variable_2="C_G3" variable_1="C_G3"/>
</connection>
<connection>
<map_components component_2="C_G1" component_1="rate_constants"/>
<map_variables variable_2="alpha_" variable_1="alpha_"/>
<map_variables variable_2="beta_" variable_1="beta_"/>
<map_variables variable_2="kG_plus" variable_1="kG_plus"/>
<map_variables variable_2="kG_minus" variable_1="kG_minus"/>
</connection>
<connection>
<map_components component_2="C_G1" component_1="C_G2"/>
<map_variables variable_2="C_G2" variable_1="C_G2"/>
<map_variables variable_2="C_G1" variable_1="C_G1"/>
</connection>
<connection>
<map_components component_2="C_G2" component_1="rate_constants"/>
<map_variables variable_2="alpha_" variable_1="alpha_"/>
<map_variables variable_2="beta_" variable_1="beta_"/>
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