- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-05-14 23:21:38+12:00
- Desc:
- committing version03 of bertram_arnot_zamponi_2002
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/bertram_arnot_zamponi_2002/rawfile/b821641253a45428a36c0c905a927a6374f157d2/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 - 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.
--><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 model has been altered from version 01 by James Lawson on 14/05/07. The math in reaction elements has been moved up a level and is now the child of the component, not the reaction element. Backrates have been added and delta variables defined. </para>
<para>Communication from Richard Bertram giving the equations for the function x_infinity has allowed completion of the presynaptic model - James Lawson, 15/05/07. </para>
<para>This version (03) now runs in PCEnv but gives NaN outputs (as shown in CSV export) and therefore will not integrate.
</para>
<para>The next version of this model will have the reaction elements removed entirely</para>
<para>Additionally, 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>
</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/>
<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="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>
</apply>
<apply>
<eq/>
<ci>x_infinity</ci>
<apply>
<divide/>
<ci>alpha_x</ci>
<apply>
<plus/>
<ci>alpha_x</ci>
<ci>beta_x</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_x</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="dimensionless">40</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="dimensionless">40</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_x</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">65</cn>
<cn cellml:units="dimensionless">18</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</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">
<eq/>
<ci> i_K </ci>
<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">
<apply id="n_diff_eq">
<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>
<apply id="alpha_n_calculation">
<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>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<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>
<error xmlns="http://www.cellml.org/tools/mathml-input/error#" column="45" problem="syntax error"/>
<apply>
<eq/>
<ci>Ca</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>O</ci>
<ci>Ca_open</ci>
</apply>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
</apply>
</math>
</component>
<!--
The following components describe all the reactants and products involved in the reactions.
-->
<component name="C1" cmeta:id="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 name="C2" cmeta:id="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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C2</ci>
</apply>
<apply>
<plus/>
<ci>delta_C2_rxn0</ci>
<ci>delta_C2_rxn1</ci>
<ci>delta_C2_rxn7</ci>
</apply>
</apply>
</math>
</component>
<component name="C3" cmeta:id="C3">
<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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C3</ci>
</apply>
<apply>
<plus/>
<ci>delta_C3_rxn1</ci>
<ci>delta_C3_rxn2</ci>
<ci>delta_C3_rxn8</ci>
</apply>
</apply>
</math>
</component>
<component name="C4" cmeta:id="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>
</bvar>
<ci>C4</ci>
</apply>
<apply>
<plus/>
<ci>delta_C4_rxn2</ci>
<ci>delta_C4_rxn3</ci>
</apply>
</apply>
</math>
</component>
<component name="O" cmeta:id="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">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>O</ci>
</apply>
<ci>delta_O_rxn3</ci>
</apply>
</math>
</component>
<component name="C_G1" cmeta:id="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">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_G1</ci>
</apply>
<apply>
<plus/>
<ci>delta_C_G1_rxn6</ci>
<ci>delta_C_G1_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component name="C_G2" cmeta:id="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">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_G2</ci>
</apply>
<apply>
<plus/>
<ci>delta_C_G2_rxn4</ci>
<ci>delta_C_G2_rxn7</ci>
<ci>delta_C_G2_rxn5</ci>
</apply>
</apply>
</math>
</component>
<component name="C_G3" cmeta:id="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>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_G3</ci>
</apply>
<apply>
<plus/>
<ci>delta_C_G3_rxn5</ci>
<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 role="reactant" direction="forward" delta_variable="delta_C1_rxn0" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C2">
<role role="product" direction="forward" delta_variable="delta_C2_rxn0" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>delta_C1_rxn0</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C2_rxn0</ci>
<ci>rate</ci>
</apply>
</math>
</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 role="reactant" direction="forward" delta_variable="delta_C2_rxn1" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C3">
<role role="product" direction="forward" delta_variable="delta_C3_rxn1" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha</ci>
<ci>C2</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta</ci>
<ci>C3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C2_rxn1</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C3_rxn1</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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 role="reactant" direction="forward" delta_variable="delta_C3_rxn2" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C4">
<role role="product" direction="forward" delta_variable="delta_C4_rxn2" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>alpha</ci>
<ci>C3</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>beta</ci>
<ci>C4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C3_rxn2</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C4_rxn2</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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 role="reactant" direction="forward" delta_variable="delta_C4_rxn3" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="O">
<role role="product" direction="forward" delta_variable="delta_O_rxn3" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>C4</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>beta</ci>
<ci>O</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C4_rxn3</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_O_rxn3</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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 role="reactant" direction="forward" delta_variable="delta_C_G1_rxn4" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C_G2">
<role role="product" direction="forward" delta_variable="delta_C_G2_rxn4" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>alpha_</ci>
<ci>C_G1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_</ci>
<ci>C_G2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C_G1_rxn4</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C_G2_rxn4</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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 role="reactant" direction="forward" delta_variable="delta_C_G2_rxn5" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C_G3">
<role role="product" direction="forward" delta_variable="delta_C_G3_rxn5" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>alpha_</ci>
<ci>C_G2</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>beta_</ci>
<ci>C_G3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C_G2_rxn5</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C_G3_rxn5</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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 role="reactant" direction="forward" delta_variable="delta_C1_rxn6" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C_G1">
<role role="product" direction="forward" delta_variable="delta_C_G1_rxn6" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kG_minus</ci>
<ci>C_G1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C1_rxn6</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C_G1_rxn6</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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 role="reactant" direction="forward" delta_variable="delta_C2_rxn7" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="C_G2">
<role role="product" direction="forward" delta_variable="delta_C_G2_rxn7" stoichiometry="1"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
</role>
</variable_ref>
</reaction>
<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>
<apply>
<eq/>
<ci>backrate</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>kG_plus</ci>
<ci>C2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kG2_minus</ci>
<ci>C_G2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_C2_rxn7</ci>
<ci>rate</ci>
</apply>
<apply>
<eq/>
<ci>delta_C_G2_rxn7</ci>
<ci>backrate</ci>
</apply>
</math>
<variable units="flux" name="backrate"/>
</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"/>
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Bertram, Arnot and Zamponi's 2002 analysis of the role of G Protein
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