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A Compuational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model
The CellML code.
<!-- FILE : MAPK_cascade_2001.xml
CREATED : 25th October 2001
LAST MODIFIED : 26th April 2005
AUTHOR : Catherine Lloyd
Department of Engineering Science
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 a study by Asthagiri
and Lauffenburger (2001) of the feedback effects on signal dynamics in the
mitogen-activated protein kinase (MAPK) cascade.
CHANGES:
22/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
25/02/2002 - CML - Altered connections after checking the model with the
validator.
18/07/2002 - CML - Added more metadata.
27/08/2002 - AAC - Corrected the initial value of variable 'k6_' in component
'adaptor_heterodimer_syn'.
09/04/2003 - AAC - Added publication date information.
26/04/2005 - PJV - Changed unit dimensions to make them consistent
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="asthagiri_lauffenburger_2001_version01" name="asthagiri_lauffenburger_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Feedback Effects On Signal Dynamics In A Mitogen-Activated Protein Kinase (MAPK) Cascade</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>
In 2001, Anand Asthagiri and Douglas Lauffenburger published a mathematical model which examined the mechanisms that govern MAPK pathway dynamics (see <xref linkend="fig_pathway_diagram" /> below). Their model builds upon the MAPK cascade model of Chi-Ying Huang and James Ferrell (1996). This earlier model focused on the steady-state effects of signaling, whereas more recently, it has been discovered that a signal's information content partly resides in its dynamics.
</para>
<para>
In their model, Anand Asthagiri and Douglas Lauffenburger concentrate on the role of negative feedback mechanisms in the generation of signal adaptation - a term referring to the reset of a signal to prestimulation levels. They assess how different modes of feedback affect the properties of MAPK signalling dynamics.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://pubs.acs.org/cgi-bin/abstract.cgi/bipret/2001/17/i02/abs/bp010009k.html">A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model</ulink>, Anand R. Asthagiri and Douglas A. Lauffenburger, 2001, <ulink url="http://pubs.acs.org/journals/bipret/index.html">
<emphasis>Biotechnol. Prog</emphasis>
</ulink>, 17, 227-239. (<ulink url="http://pubs.acs.org/cgi-bin/article.cgi/bipret/2001/17/i02/html/bp010009k.html">Full text</ulink> and PDF versions are available to subscribers on the ACS Publications website. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11312698&dopt=Abstract">PubMed ID: 11312698</ulink>
</para>
<para>
The raw CellML description of the MAPK cascade model with feedback effects can be downloaded in various formats as described in <xref linkend="sec_download_this_model" />. For an example of a more complete documentation of another real reaction pathway, see <ulink url="${HTML_EXMPL_BI_EGF_INTRO}">The Bhalla Iyengar EGF Pathway Model, 1999</ulink>.
</para>
<informalfigure float="0" id="fig_pathway_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>the conventional rendering of the MAPK cascade with feedback effects</title>
</objectinfo>
<imagedata fileref="../images/MAPK_cascade_2001/conventional_rendering.gif" />
</imageobject>
</mediaobject>
<caption>A rendering of the MAPK cascade with feedback effects. Species are represented by rounded rectangles, and reactions by arrows. The action of a catalyst on a reaction is represented by dashed lines.</caption>
</informalfigure>
<para>
In CellML, models are thought of as connected networks of discrete components. These components may correspond to physiologically separated regions or chemically distinct objects, or may be useful modelling abstractions. This model has 71 components representing chemically distinct objects (41 chemical species and 30 reactions) and one component defined for modelling convenience which stores the universal variable time. Because this model has so many components, its CellML rendering would be complex. For an example of a CellML rendering of a reaction pathway see <ulink url="${HTML_EXMPL_BI_EGF_INTRO}">The Bhalla Iyengar EGF Pathway Model, 1999</ulink>.
</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="minute">
<unit units="second" multiplier="60.0" />
</units>
<units base_units="yes" name="number" />
<units base_units="yes" name="cell" />
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<unit units="cell" exponent="-1" />
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</units>
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<unit units="mole" />
<unit units="litre" exponent="-1" />
</units>
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<unit units="minute" exponent="-1" />
</units>
<units name="first_order_rate_constant">
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</units>
<units name="second_order_rate_constant">
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<unit units="minute" exponent="-1" />
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<component name="global_variables">
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</component>
<component cmeta:id="R" name="R">
<variable units="number_per_cell" public_interface="out" name="R" initial_value="1.0" />
<variable units="number_per_cell_per_minute" public_interface="in" name="delta_R_ligand_receptor_binding" />
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</apply>
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<
CREATED : 25th October 2001
LAST MODIFIED : 26th April 2005
AUTHOR : Catherine Lloyd
Department of Engineering Science
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 a study by Asthagiri
and Lauffenburger (2001) of the feedback effects on signal dynamics in the
mitogen-activated protein kinase (MAPK) cascade.
CHANGES:
22/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
25/02/2002 - CML - Altered connections after checking the model with the
validator.
18/07/2002 - CML - Added more metadata.
27/08/2002 - AAC - Corrected the initial value of variable 'k6_' in component
'adaptor_heterodimer_syn'.
09/04/2003 - AAC - Added publication date information.
26/04/2005 - PJV - Changed unit dimensions to make them consistent
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="asthagiri_lauffenburger_2001_version01" name="asthagiri_lauffenburger_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Feedback Effects On Signal Dynamics In A Mitogen-Activated Protein Kinase (MAPK) Cascade</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>
In 2001, Anand Asthagiri and Douglas Lauffenburger published a mathematical model which examined the mechanisms that govern MAPK pathway dynamics (see <xref linkend="fig_pathway_diagram" /> below). Their model builds upon the MAPK cascade model of Chi-Ying Huang and James Ferrell (1996). This earlier model focused on the steady-state effects of signaling, whereas more recently, it has been discovered that a signal's information content partly resides in its dynamics.
</para>
<para>
In their model, Anand Asthagiri and Douglas Lauffenburger concentrate on the role of negative feedback mechanisms in the generation of signal adaptation - a term referring to the reset of a signal to prestimulation levels. They assess how different modes of feedback affect the properties of MAPK signalling dynamics.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://pubs.acs.org/cgi-bin/abstract.cgi/bipret/2001/17/i02/abs/bp010009k.html">A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model</ulink>, Anand R. Asthagiri and Douglas A. Lauffenburger, 2001, <ulink url="http://pubs.acs.org/journals/bipret/index.html">
<emphasis>Biotechnol. Prog</emphasis>
</ulink>, 17, 227-239. (<ulink url="http://pubs.acs.org/cgi-bin/article.cgi/bipret/2001/17/i02/html/bp010009k.html">Full text</ulink> and PDF versions are available to subscribers on the ACS Publications website. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11312698&dopt=Abstract">PubMed ID: 11312698</ulink>
</para>
<para>
The raw CellML description of the MAPK cascade model with feedback effects can be downloaded in various formats as described in <xref linkend="sec_download_this_model" />. For an example of a more complete documentation of another real reaction pathway, see <ulink url="${HTML_EXMPL_BI_EGF_INTRO}">The Bhalla Iyengar EGF Pathway Model, 1999</ulink>.
</para>
<informalfigure float="0" id="fig_pathway_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>the conventional rendering of the MAPK cascade with feedback effects</title>
</objectinfo>
<imagedata fileref="../images/MAPK_cascade_2001/conventional_rendering.gif" />
</imageobject>
</mediaobject>
<caption>A rendering of the MAPK cascade with feedback effects. Species are represented by rounded rectangles, and reactions by arrows. The action of a catalyst on a reaction is represented by dashed lines.</caption>
</informalfigure>
<para>
In CellML, models are thought of as connected networks of discrete components. These components may correspond to physiologically separated regions or chemically distinct objects, or may be useful modelling abstractions. This model has 71 components representing chemically distinct objects (41 chemical species and 30 reactions) and one component defined for modelling convenience which stores the universal variable time. Because this model has so many components, its CellML rendering would be complex. For an example of a CellML rendering of a reaction pathway see <ulink url="${HTML_EXMPL_BI_EGF_INTRO}">The Bhalla Iyengar EGF Pathway Model, 1999</ulink>.
</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="minute">
<unit units="second" multiplier="60.0" />
</units>
<units base_units="yes" name="number" />
<units base_units="yes" name="cell" />
<units name="number_per_cell">
<unit units="number" />
<unit units="cell" exponent="-1" />
</units>
<units name="number_per_cell_per_minute">
<unit units="number_per_cell" />
<unit units="minute" exponent="-1" />
</units>
<units name="molar">
<unit units="mole" />
<unit units="litre" exponent="-1" />
</units>
<units name="flux">
<unit units="molar" />
<unit units="minute" exponent="-1" />
</units>
<units name="first_order_rate_constant">
<unit units="minute" exponent="-1" />
</units>
<units name="second_order_rate_constant">
<unit units="molar" exponent="-1" />
<unit units="minute" exponent="-1" />
</units>
<component name="global_variables">
<variable units="minute" public_interface="out" name="time" />
</component>
<component cmeta:id="R" name="R">
<variable units="number_per_cell" public_interface="out" name="R" initial_value="1.0" />
<variable units="number_per_cell_per_minute" public_interface="in" name="delta_R_ligand_receptor_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>R</ci>
</apply>
<ci>delta_R_ligand_receptor_binding</ci>
</apply>
</math>
</component>
<component cmeta:id="C" name="C">
<variable units="molar" public_interface="out" name="C" />
<variable units="flux" public_interface="in" name="delta_C_ligand_receptor_binding" />
<variable units="flux" public_interface="in" name="delta_C_receptor_dimerisation" />
<variable units="minute" 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</ci>
</apply>
<apply>
<plus />
<ci>delta_C_ligand_receptor_binding</ci>
<ci>delta_C_receptor_dimerisation</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C2" name="C2">
<variable units="molar" public_interface="out" name="C2" />
<variable units="flux" public_interface="in" name="delta_C2_receptor_dimerisation" />
<variable units="flux" public_interface="in" name="delta_C2_dimerised_receptor_activation" />
<variable units="minute" 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_receptor_dimerisation</ci>
<ci>delta_C2_dimerised_receptor_activation</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C_" name="C_">
<variable units="molar" public_interface="out" name="C_" />
<variable units="flux" public_interface="in" name="delta_C__dimerised_receptor_activation" />
<variable units="flux" public_interface="in" name="delta_C__receptor_adaptor_complex_syn" />
<variable units="flux" public_interface="in" name="delta_C__receptor_adaptors_complex_syn2" />
<variable units="minute" 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_</ci>
</apply>
<apply>
<plus />
<ci>delta_C__dimerised_receptor_activation</ci>
<ci>delta_C__receptor_adaptor_complex_syn</ci>
<ci>delta_C__receptor_adaptors_complex_syn2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="L" name="L">
<variable units="molar" public_interface="out" name="L" initial_value="3.0E-8" />
<variable units="flux" public_interface="in" name="delta_L_ligand_receptor_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>L</ci>
</apply>
<ci>delta_L_ligand_receptor_binding</ci>
</apply>
</math>
</component>
<component cmeta:id="A2_" name="A2_">
<variable units="molar" public_interface="out" name="A2_" />
<variable units="flux" public_interface="in" name="delta_A2__E0_E4__desyn" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>A2_</ci>
</apply>
<ci>delta_A2__E0_E4__desyn</ci>
</apply>
</math>
</component>
<component cmeta:id="E4_" name="E4_">
<variable units="molar" public_interface="out" name="E4_" />
<variable units="flux" public_interface="in" name="delta_E4__E0_E4__desyn" />
<variable units="flux" public_interface="in" name="delta_E4__E2_E4__desyn" />
<variable units="flux" public_interface="in" name="delta_E4__E4_activation" />
<variable units="flux" public_interface="in" name="delta_E4__E5_activation" />
<variable units="flux" public_interface="in" name="delta_E4__E0_E4__syn" />
<variable units="flux" public_interface="in" name="delta_E4__E2_E4__syn" />
<variable units="flux" public_interface="in" name="delta_E4__E4__P4_binding" />
<variable units="flux" public_interface="in" name="delta_E4__E4__E5_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E4_</ci>
</apply>
<apply>
<plus />
<ci>delta_E4__E0_E4__desyn</ci>
<ci>delta_E4__E2_E4__desyn</ci>
<ci>delta_E4__E4_activation</ci>
<ci>delta_E4__E5_activation</ci>
<ci>delta_E4__E0_E4__syn</ci>
<ci>delta_E4__E2_E4__syn</ci>
<ci>delta_E4__E4__P4_binding</ci>
<ci>delta_E4__E4__E5_binding</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="E0_E4_" name="E0_E4_">
<variable units="molar" public_interface="out" name="E0_E4_" />
<variable units="flux" public_interface="in" name="delta_E0_E4__E0_E4__syn" />
<variable units="flux" public_interface="in" name="delta_E0_E4__E0_E4__desyn" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E0_E4_</ci>
</apply>
<apply>
<plus />
<ci>delta_E0_E4__E0_E4__syn</ci>
<ci>delta_E0_E4__E0_E4__desyn</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="E1_" name="E1_">
<variable units="molar" public_interface="out" name="E1_" />
<variable units="flux" public_interface="in" name="delta_E1__E1_activation" />
<variable units="flux" public_interface="in" name="delta_E1__E2_activation" />
<variable units="flux" public_interface="in" name="delta_E1__E1__P1_binding" />
<variable units="flux" public_interface="in" name="delta_E1__E1__E2_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E1_</ci>
</apply>
<apply>
<plus />
<ci>delta_E1__E1_activation</ci>
<ci>delta_E1__E2_activation</ci>
<ci>delta_E1__E1__P1_binding</ci>
<ci>delta_E1__E1__E2_binding</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="E1" name="E1">
<variable units="molar" public_interface="out" name="E1" initial_value="1.0" />
<variable units="flux" public_interface="in" name="delta_E1_E1__inactivation" />
<variable units="flux" public_interface="in" name="delta_E1_E0__E1_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E1</ci>
</apply>
<apply>
<plus />
<ci>delta_E1_E1__inactivation</ci>
<ci>delta_E1_E0__E1_binding</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A1" name="A1">
<variable units="molar" public_interface="out" name="A1" initial_value="1.0" />
<variable units="flux" public_interface="in" name="delta_A1_adaptor_heterodimer_syn" />
<variable units="flux" public_interface="in" name="delta_A1_receptor_adaptor_complex_syn" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>A1</ci>
</apply>
<apply>
<plus />
<ci>delta_A1_adaptor_heterodimer_syn</ci>
<ci>delta_A1_receptor_adaptor_complex_syn</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A2" name="A2">
<variable units="molar" public_interface="out" name="A2" initial_value="1.0" />
<variable units="flux" public_interface="in" name="delta_A2_adaptor_heterodimer_syn" />
<variable units="flux" public_interface="in" name="delta_A2_receptor_adaptors_complex_syn1" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>A2</ci>
</apply>
<apply>
<plus />
<ci>delta_A2_adaptor_heterodimer_syn</ci>
<ci>delta_A2_receptor_adaptors_complex_syn1</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="E0_" name="E0_">
<variable units="molar" public_interface="out" name="E0_" />
<variable units="flux" public_interface="in" name="delta_E0__receptor_adaptors_complex_syn1" />
<variable units="flux" public_interface="in" name="delta_E0__receptor_adaptors_complex_syn2" />
<variable units="flux" public_interface="in" name="delta_E0__E1_activation" />
<variable units="flux" public_interface="in" name="delta_E0__E0_E4__syn" />
<variable units="flux" public_interface="in" name="delta_E0__E0__E1_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E0_</ci>
</apply>
<apply>
<plus />
<ci>delta_E0__receptor_adaptors_complex_syn1</ci>
<ci>delta_E0__receptor_adaptors_complex_syn2</ci>
<ci>delta_E0__E1_activation</ci>
<ci>delta_E0__E0_E4__syn</ci>
<ci>delta_E0__E0__E1_binding</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C_A1" name="C_A1">
<variable units="molar" public_interface="out" name="C_A1" />
<variable units="flux" public_interface="in" name="delta_C_A1_receptor_adaptor_complex_syn" />
<variable units="flux" public_interface="in" name="delta_C_A1_E0_E4__desyn" />
<variable units="flux" public_interface="in" name="delta_C_A1_receptor_adaptors_complex_syn1" />
<variable units="minute" 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_A1</ci>
</apply>
<apply>
<plus />
<ci>delta_C_A1_receptor_adaptor_complex_syn</ci>
<ci>delta_C_A1_E0_E4__desyn</ci>
<ci>delta_C_A1_receptor_adaptors_complex_syn1</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="P1" name="P1">
<variable units="molar" public_interface="out" name="P1" />
<variable units="flux" public_interface="in" name="delta_P1_E1__inactivation" />
<variable units="flux" public_interface="in" name="delta_P1_E1__P1_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
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<apply>
<plus />
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<variable units="molar" public_interface="out" name="E2_" />
<variable units="flux" public_interface="in" name="delta_E2__E2_activation" />
<variable units="flux" public_interface="in" name="delta_E2__E3_activation" />
<variable units="flux" public_interface="in" name="delta_E2__E2__P2_binding" />
<variable units="flux" public_interface="in" name="delta_E2__E2_E4__syn" />
<variable units="flux" public_interface="in" name="delta_E2__E2_E4__desyn" />
<variable units="flux" public_interface="in" name="delta_E2__E2__E3_binding" />
<variable units="minute" public_interface="in" name="time" />
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<eq />
<apply>
<diff />
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<ci>E2_</ci>
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<apply>
<plus />
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<ci>delta_E2__E3_activation</ci>
<ci>delta_E2__E2__P2_binding</ci>
<ci>delta_E2__E2_E4__syn</ci>
<ci>delta_E2__E2_E4__desyn</ci>
<ci>delta_E2__E2__E3_binding</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="E2" name="E2">
<variable units="molar" public_interface="out" name="E2" initial_value="1.0" />
<variable units="flux" public_interface="in" name="delta_E2_E2__inactivation" />
<variable units="flux" public_interface="in" name="delta_E2_E1__E2_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E2</ci>
</apply>
<apply>
<plus />
<ci>delta_E2_E2__inactivation</ci>
<ci>delta_E2_E1__E2_binding</ci>
</apply>
</apply>
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</component>
<component cmeta:id="P2" name="P2">
<variable units="molar" public_interface="out" name="P2" initial_value="1.0" />
<variable units="flux" public_interface="in" name="delta_P2_E2__inactivation" />
<variable units="flux" public_interface="in" name="delta_P2_E2__P2_binding" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>P2</ci>
</apply>
<apply>
<plus />
<ci>delta_P2_E2__inactivation</ci>
<ci>delta_P2_E2__P2_binding</ci>
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</apply>
</math>
</component>
<component cmeta:id="E1_P1" name="E1_P1">
<variable units="molar" public_interface="out" name="E1_P1" />
<variable units="flux" public_interface="in" name="delta_E1_P1_E1__P1_binding" />
<variable units="flux" public_interface="in" name="delta_E1_P1_E1__inactivation" />
<variable units="minute" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>E1_P1</ci>
</apply>
<apply>
<plus />
<ci>delta_E1_P1_E1__P1_binding</ci>
<