- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:46:15+12:00
- Desc:
- committing version01 of sneyd_dufour_2002
- Permanent Source URI:
- https://models.cellml.org/workspace/sneyd_dufour_2002/rawfile/66978ca7c4ee191103c73ba0fbf6cb59befcf13b/sneyd_dufour_2002.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : sneyd_model_2002.xml
CREATED : 20th March 2002
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
The 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 James Sneyd and Jean-Francois Dufuor's 2002 dynamic model of the type-2 inositol triphosphate receptor.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
--><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="sneyd_dufour_2002_version01" name="sneyd_dufour_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Dynamic Model Of The Type-2 Inositol Triphosphate Receptor</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>
Oscillations and waves in the concentration of free intracellular calcium ions (Ca<superscript>2+</superscript>) are seen in many cell types and are known to be an important intra- and intercellular signalling system. It is therefore of interest to determine the mechanisms underlying such complex dynamic behaviour. One of the most important of these mechanisms is the inositol triphosphate receptor (IPR), which also functions as a Ca<superscript>2+</superscript> channel. Models of the IPR play a central role in models of Ca<superscript>2+</superscript> oscillations and waves. However, many models of this receptor do not agree with recent experimental data on the dynamic responses of the receptor.
</para>
<para>
In their 2002 dynamic model of the type-2 IPR, which is based on dynamic and steady-state experimental data, James Sneyd and Jean-Francois Dufour demonstrate that Ca<superscript>2+</superscript> binds to the receptor using saturating, not mass-action kinetics. Their model is similar to the Michaelis-Menten model of an enzyme-catalysed reaction (see <xref linkend="fig_simplified_diagram"/> below). The model assumes that the binding of IP<subscript>3</subscript> (denoted by p in the diagram below) and Ca<superscript>2+</superscript> is sequential , not independent, so Ca<superscript>2+</superscript> can bind to the activating site only after IP<subscript>3</subscript> has bound.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.pnas.org/cgi/content/abstract/99/4/2398">A dynamic model of the type-2 inositol triphosphate receptor</ulink>, James Sneyd and Jean-Francois Dufour, 2002, <ulink url="http://www.pnas.org/">
<emphasis>Proceedings of the National Academy of Sciences </emphasis>
</ulink>, 99, 2398-2403. (A <ulink url="http://www.pnas.org/cgi/reprint/99/4/2398.pdf">PDF</ulink> of the article is available to subscribers of the PNAS website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11842185&dopt=Abstract">PubMed ID: 11842185</ulink>
</para>
<para>
The raw CellML description of the dynamic model of the type-2 inositol triphosphate receptor can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_simplified_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>A simplified diagram of the IPR model</title>
</objectinfo>
<imagedata fileref="sneyd_2002.png"/>
</imageobject>
</mediaobject>
<caption>A simplified diagram of the IPR model, where R represents the free receptor, O is the open state of the channel, A is the activated state of the channel and I<subscript>1</subscript>, I<subscript>2</subscript>, and S are three inactive states.</caption>
</informalfigure>
</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="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="second" 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="second" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component cmeta:id="R" name="R">
<variable units="micromolar" public_interface="out" name="R"/>
<variable units="flux" public_interface="in" name="delta_R_rxn_1"/>
<variable units="flux" public_interface="in" name="delta_R_rxn_2"/>
<variable units="second" 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>
<apply>
<plus/>
<ci>delta_R_rxn_1</ci>
<ci>delta_R_rxn_2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="O" name="O">
<variable units="micromolar" public_interface="out" name="O"/>
<variable units="flux" public_interface="in" name="delta_O_rxn_2"/>
<variable units="flux" public_interface="in" name="delta_O_rxn_3"/>
<variable units="flux" public_interface="in" name="delta_O_rxn_4"/>
<variable units="second" 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>
<apply>
<plus/>
<ci>delta_O_rxn_2</ci>
<ci>delta_O_rxn_3</ci>
<ci>delta_O_rxn_4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S" name="S">
<variable units="micromolar" public_interface="out" name="S"/>
<variable units="flux" public_interface="in" name="delta_S_rxn_3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S</ci>
</apply>
<ci>delta_S_rxn_3</ci>
</apply>
</math>
</component>
<component cmeta:id="I_1" name="I_1">
<variable units="micromolar" public_interface="out" name="I_1"/>
<variable units="flux" public_interface="in" name="delta_I_1_rxn_1"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I_1</ci>
</apply>
<ci>delta_I_1_rxn_1</ci>
</apply>
</math>
</component>
<component cmeta:id="I_2" name="I_2">
<variable units="micromolar" public_interface="out" name="I_2"/>
<variable units="flux" public_interface="in" name="delta_I_2_rxn_5"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I_2</ci>
</apply>
<ci>delta_I_2_rxn_5</ci>
</apply>
</math>
</component>
<component cmeta:id="A" name="A">
<variable units="micromolar" public_interface="out" name="A"/>
<variable units="flux" public_interface="in" name="delta_A_rxn_4"/>
<variable units="flux" public_interface="in" name="delta_A_rxn_5"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>A</ci>
</apply>
<apply>
<plus/>
<ci>delta_A_rxn_4</ci>
<ci>delta_A_rxn_5</ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="reaction_rate_constants">
<variable units="first_order_rate_constant" public_interface="out" name="phi_1"/>
<variable units="first_order_rate_constant" public_interface="out" name="phi_2"/>
<variable units="first_order_rate_constant" public_interface="out" name="phi_2b"/>
<variable units="second_order_rate_constant" public_interface="out" name="phi_3"/>
<variable units="first_order_rate_constant" public_interface="out" name="phi_4"/>
<variable units="first_order_rate_constant" public_interface="out" name="phi_4b"/>
<variable units="first_order_rate_constant" public_interface="out" name="phi_5"/>
<variable units="second_order_rate_constant" name="k_1a" initial_value="0.64"/>
<variable units="first_order_rate_constant" public_interface="out" name="k_1b" initial_value="0.04"/>
<variable units="second_order_rate_constant" name="k_2a" initial_value="37.4"/>
<variable units="first_order_rate_constant" name="k_2b" initial_value="1.4"/>
<variable units="second_order_rate_constant" name="k_3a" initial_value="0.11"/>
<variable units="first_order_rate_constant" public_interface="out" name="k_3b" initial_value="29.8"/>
<variable units="second_order_rate_constant" name="k_4a" initial_value="4.0"/>
<variable units="first_order_rate_constant" name="k_4b" initial_value="0.54"/>
<variable units="first_order_rate_constant" name="l_2a" initial_value="1.7"/>
<variable units="first_order_rate_constant" public_interface="out" name="l_2b" initial_value="0.8"/>
<variable units="second_order_rate_constant" name="l_4a" initial_value="1.7"/>
<variable units="second_order_rate_constant" name="l_4b" initial_value="2.5"/>
<variable units="first_order_rate_constant" name="l_6a" initial_value="4707.0"/>
<variable units="first_order_rate_constant" name="l_6b" initial_value="11.4"/>
<variable units="micromolar" name="L_1" initial_value="0.12"/>
<variable units="micromolar" name="L_3" initial_value="0.025"/>
<variable units="micromolar" name="L_5" initial_value="54.7"/>
<variable units="micromolar" name="c"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="phi_1_calculation">
<eq/>
<ci> phi_1 </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_1a </ci>
<ci> L_1 </ci>
</apply>
<ci> l_2a </ci>
</apply>
<ci> c </ci>
</apply>
<apply>
<plus/>
<ci> L_1 </ci>
<apply>
<times/>
<ci> c </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> L_1 </ci>
<ci> L_3 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="phi_2_calculation">
<eq/>
<ci> phi_2 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_2a </ci>
<ci> L_3 </ci>
</apply>
<apply>
<times/>
<ci> l_4a </ci>
<ci> c </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> L_3 </ci>
<apply>
<times/>
<ci> c </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> L_3 </ci>
<ci> L_1 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="phi_2b_calculation">
<eq/>
<ci> phi_2b </ci>
<apply>
<divide/>
<apply>
<plus/>
<ci> k_2b </ci>
<apply>
<times/>
<ci> l_4b </ci>
<ci> c </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> c </ci>
<ci> L_5 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="phi_3_calculation">
<eq/>
<ci> phi_3 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> k_3a </ci>
<ci> L_5 </ci>
</apply>
<apply>
<plus/>
<ci> c </ci>
<ci> L_5 </ci>
</apply>
</apply>
</apply>
<apply id="phi_4_calculation">
<eq/>
<ci> phi_4 </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_4a </ci>
<ci> L_5 </ci>
</apply>
<ci> l_6a </ci>
</apply>
<ci> c </ci>
</apply>
<apply>
<plus/>
<ci> c </ci>
<ci> L_5 </ci>
</apply>
</apply>
</apply>
<apply id="phi_4b_calculation">
<eq/>
<ci> phi_4b </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_1a </ci>
<ci> L_1 </ci>
</apply>
<ci> l_2a </ci>
</apply>
<ci> c </ci>
</apply>
<apply>
<plus/>
<ci> c </ci>
<ci> L_1 </ci>
</apply>
</apply>
</apply>
<apply id="phi_5_calculation">
<eq/>
<ci> phi_5 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> L_1 </ci>
<apply>
<plus/>
<ci> k_4b </ci>
<ci> l_6b </ci>
</apply>
<ci> c </ci>
</apply>
<apply>
<plus/>
<ci> c </ci>
<ci> L_1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="reaction1">
<variable units="micromolar" public_interface="in" name="R"/>
<variable units="micromolar" public_interface="in" name="I_1"/>
<variable units="first_order_rate_constant" public_interface="in" name="phi_1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1b"/>
<variable units="first_order_rate_constant" public_interface="in" name="l_2b"/>
<variable units="flux" public_interface="out" name="delta_R_rxn_1"/>
<variable units="flux" public_interface="out" name="delta_I_1_rxn_1"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="R">
<role stoichiometry="1" direction="forward" delta_variable="delta_R_rxn_1" role="reactant"/>
</variable_ref>
<variable_ref variable="I_1">
<role stoichiometry="1" direction="forward" delta_variable="delta_I_1_rxn_1" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> phi_1 </ci>
<ci> R </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> l_2b </ci>
<ci> k_1b </ci>
</apply>
<ci> I_1 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction2">
<variable units="micromolar" public_interface="in" name="R"/>
<variable units="micromolar" public_interface="in" name="O"/>
<variable units="first_order_rate_constant" public_interface="in" name="phi_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="phi_2b"/>
<variable units="micromolar" name="p"/>
<variable units="flux" public_interface="out" name="delta_R_rxn_2"/>
<variable units="flux" public_interface="out" name="delta_O_rxn_2"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="R">
<role stoichiometry="1" direction="forward" delta_variable="delta_R_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="O">
<role stoichiometry="1" direction="forward" delta_variable="delta_O_rxn_2" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> phi_2 </ci>
<ci> R </ci>
<ci> p </ci>
</apply>
</apply>
<apply>
<times/>
<ci> phi_2b </ci>
<ci> O </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="micromolar" public_interface="in" name="S"/>
<variable units="micromolar" public_interface="in" name="O"/>
<variable units="second_order_rate_constant" public_interface="in" name="phi_3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_3b"/>
<variable units="flux" public_interface="out" name="delta_S_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_O_rxn_3"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="O">
<role stoichiometry="1" direction="forward" delta_variable="delta_O_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="S">
<role stoichiometry="1" direction="forward" delta_variable="delta_S_rxn_3" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> phi_3 </ci>
<ci> O </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_3b </ci>
<ci> S </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction4">
<variable units="micromolar" public_interface="in" name="A"/>
<variable units="micromolar" public_interface="in" name="O"/>
<variable units="first_order_rate_constant" public_interface="in" name="phi_4"/>
<variable units="first_order_rate_constant" public_interface="in" name="phi_4b"/>
<variable units="flux" public_interface="out" name="delta_A_rxn_4"/>
<variable units="flux" public_interface="out" name="delta_O_rxn_4"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="O">
<role stoichiometry="1" direction="forward" delta_variable="delta_O_rxn_4" role="reactant"/>
</variable_ref>
<variable_ref variable="A">
<role stoichiometry="1" direction="forward" delta_variable="delta_A_rxn_4" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> phi_4 </ci>
<ci> O </ci>
</apply>
</apply>
<apply>
<times/>
<ci> phi_4b </ci>
<ci> A </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction5">
<variable units="micromolar" public_interface="in" name="A"/>
<variable units="micromolar" public_interface="in" name="I_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="phi_5"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1b"/>
<variable units="first_order_rate_constant" public_interface="in" name="l_2b"/>
<variable units="flux" public_interface="out" name="delta_A_rxn_5"/>
<variable units="flux" public_interface="out" name="delta_I_2_rxn_5"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="A">
<role stoichiometry="1" direction="forward" delta_variable="delta_A_rxn_5" role="reactant"/>
</variable_ref>
<variable_ref variable="I_2">
<role stoichiometry="1" direction="forward" delta_variable="delta_I_2_rxn_5" role="product"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> phi_5 </ci>
<ci> A </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> l_2b </ci>
<ci> k_1b </ci>
</apply>
<ci> I_2 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<connection>
<map_components component_2="environment" component_1="R"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="O"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="S"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="I_1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="I_2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="reaction_rate_constants" component_1="reaction1"/>
<map_variables variable_2="phi_1" variable_1="phi_1"/>
<map_variables variable_2="k_1b" variable_1="k_1b"/>
<map_variables variable_2="l_2b" variable_1="l_2b"/>
</connection>
<connection>
<map_components component_2="reaction_rate_constants" component_1="reaction2"/>
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<connection>
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Added publication date information.
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This is the CellML description of Sneyd and Dufour's 2002 dynamic
model of type-2 inositol triphosphate receptor. The dynamic
properties of this receptor are essential for the control of
intracellular calcium, including the generation of calcium
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The Sneyd-Dufour 2002 dynamic model of the type-2 inositol triphosphate
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A dynamic model of the type-2 inositol triphosphate receptor
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The University of Auckland, Bioengineering Institute
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