- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-01-20 11:35:52+13:00
- Desc:
- Added annotations to deyoung_keizer_1992 model
- Permanent Source URI:
- https://models.cellml.org/workspace/deyoung_keizer_1992/rawfile/ca53e58197651359e51f889857d6b2765f5160ad/deyoung_keizer_1992.cellml
<?xml version='1.0'?>
<model name="deyoung_keizer_1992_version01" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>IP3-Mediated Ca2+ Release</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 is able to be integrated in OpenCell but is not currently valid CellML.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Ca<superscript>2+</superscript> is a ubiquitous intracellular secondary messenger, and evidence from several different cell types suggests that an important mode of signalling is through oscillations rather than the maintenance of a steady state level. The oscillatory behaviour of inositol 1,4,5-triphosphate (IP3)-mediated Ca<superscript>2+</superscript> release has been modelled by Gary W. De Young and Joel Keizer. Their 1992 paper is referenced fully below.
</para>
<para>
>A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca<superscript>2+</superscript> concentration, Gary W. De Young and Joel Keizer, 1992,
<emphasis>Proc. Natl. Acad. Sci. USA</emphasis>
, 89, 9895-9899.<ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=1329108&dopt=Abstract">PubMed ID: 1329108</ulink>
</para>
<para>
Several mechanisms have been proposed to explain oscillations of intracellular Ca<superscript>2+</superscript> concentration in cells. In this study, De Young and Keizer investigate the idea that a biphasic response of the IP3 receptor/channel to cytosolic Ca<superscript>2+</superscript> may alone be sufficient to induce Ca<superscript>2+</superscript> oscillations.
</para>
<para>
They constructed a simplified model of the IP3 receptor/channel by assuming that three equivalent and independent subunits are involved in Ca<superscript>2+</superscript> conduction. Each subunit has three binding sites: one for IP3, one for Ca<superscript>2+</superscript> activation, and one for Ca<superscript>2+</superscript> inactivation. Thus each subunit may exist in eight states with transitions governed by second-order (association) and first-order (dissociation) rate constants (see <xref linkend="fig_pathway_diagram"/> below). All three subunits must be in the state S<subscript>110</subscript> (one IP3 and one activating Ca<superscript>2+</superscript> bound) for the channel to be open and conducting.
</para>
<informalfigure float="0" id="fig_pathway_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>A schematic diagram of the kinetics of an IP3 receptor/channel subunit</title>
</objectinfo>
<imagedata fileref="deyoung_1992.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the kinetics of an IP<subscript>3</subscript> receptor/channel subunit.</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 prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="nanomolar">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="second"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="micromolar"/>
<unit exponent="-1" units="second"/>
</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 name="time" public_interface="out" units="second"/>
</component>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component cmeta:id="Ca_i" name="Ca_i">
<variable cmeta:id="id_000000001" name="Ca_i" public_interface="out" units="micromolar"/>
<variable name="J1" units="flux"/>
<variable name="J2" units="flux"/>
<variable initial_value="6.0" name="v1" units="first_order_rate_constant"/>
<variable initial_value="0.11" name="v2" units="first_order_rate_constant"/>
<variable initial_value="0.9" name="v3" units="second_order_rate_constant"/>
<variable initial_value="0.1" name="k3" units="micromolar"/>
<variable name="c1" public_interface="in" units="dimensionless"/>
<variable cmeta:id="id_000000002" name="Ca_ER" public_interface="in" units="micromolar"/>
<variable name="P_open" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math id="1" xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<ci>J1</ci>
<ci>J2</ci>
</apply>
</apply>
<apply id="J1_calculation">
<eq/>
<ci> J1 </ci>
<apply>
<times/>
<ci> c1 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> v1 </ci>
<ci> P_open </ci>
</apply>
<ci> v2 </ci>
</apply>
<apply>
<minus/>
<ci> Ca_ER </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply id="J2_calculation">
<eq/>
<ci> J2 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> v3 </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> k3 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Ca_ER" name="Ca_ER">
<variable cmeta:id="id_000000003" name="Ca_ER" public_interface="out" units="micromolar"/>
<variable initial_value="2.0" name="c0" units="micromolar"/>
<variable name="c1" public_interface="in" units="dimensionless"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math id="2" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_ER_calculation">
<eq/>
<ci> Ca_ER </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> c0 </ci>
<ci> Ca_i </ci>
</apply>
<ci> c1 </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="IP3" name="IP3">
<variable cmeta:id="id_000000004" name="IP3" public_interface="out" units="micromolar"/>
<variable initial_value="1.1" name="k4" units="micromolar"/>
<variable initial_value="0.5" name="alpha" units="dimensionless"/>
<variable initial_value="1.0" name="Ir" units="flux"/>
<variable initial_value="1.2" name="v4" units="first_order_rate_constant"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math id="3" xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>IP3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> v4 </ci>
<apply>
<divide/>
<apply>
<plus/>
<ci> Ca_i </ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha </ci>
</apply>
<ci> k4 </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> k4 </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Ir </ci>
<ci> IP3 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Not an essential part of the model so commented out
<component name="IP3_receptor" cmeta:id="IP3_receptor">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="IP3_receptor">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The IP3 receptor/Ca2+ channel is thought to be composed of four
identical subunits (S). Of the four conductance states, the third
is the most frequently achieved. De Young and Keizer construct a
simplified model of the IP3 receptor/channel by assuming three
equivalent and independent subunits are involved in conduction.
Each subunit has three binding sites (Siii). The first binds IP3,
the second is the Ca2+ activation site and the third is the Ca2+
inactivation site. The fraction of the subunits in the state Siii
is denoted by xiii.
</rdf:value>
</cmeta:comment>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">IP3_receptor</dc:title>
</rdf:Description>
</rdf:RDF>
<variable name="S_000" units="micromolar"/>
<variable name="S_100" units="micromolar"/>
<variable name="S_010" units="micromolar"/>
<variable name="S_001" units="micromolar"/>
<variable name="S_110" units="micromolar"/>
<variable name="S_011" units="micromolar"/>
<variable name="S_101" units="micromolar"/>
<variable name="S_111" units="micromolar"/>
<variable name="a1" public_interface="in" units="second_order_rate_constant"/>
<variable name="a2" public_interface="in" units="second_order_rate_constant"/>
<variable name="a3" public_interface="in" units="second_order_rate_constant"/>
<variable name="a4" public_interface="in" units="second_order_rate_constant"/>
<variable name="a5" public_interface="in" units="second_order_rate_constant"/>
<variable name="b1" public_interface="in" units="first_order_rate_constant"/>
<variable name="b2" public_interface="in" units="first_order_rate_constant"/>
<variable name="b3" public_interface="in" units="first_order_rate_constant"/>
<variable name="b4" public_interface="in" units="first_order_rate_constant"/>
<variable name="b5" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<variable name="IP3" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="4" cmeta:id="4">
<apply><eq/>
<ci> S_000 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> a5 </ci>
<ci> S_000 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b5 </ci>
<ci> S_010 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a1 </ci>
<ci> S_000 </ci>
<ci> IP3 </ci>
</apply>
</apply>
<apply><times/>
<ci> b1 </ci>
<ci> S_100 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a4 </ci>
<ci> S_000 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b4 </ci>
<ci> S_001 </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_001 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> a5 </ci>
<ci> S_001 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b5 </ci>
<ci> S_011 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a3 </ci>
<ci> S_001 </ci>
<ci> IP3 </ci>
</apply>
</apply>
<apply><times/>
<ci> b3 </ci>
<ci> S_101 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b4 </ci>
<ci> S_001 </ci>
</apply>
</apply>
<apply><times/>
<ci> a4 </ci>
<ci> S_000 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_100 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> a5 </ci>
<ci> S_100 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b5 </ci>
<ci> S_110 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b1 </ci>
<ci> S_100 </ci>
</apply>
</apply>
<apply><times/>
<ci> a1 </ci>
<ci> S_000 </ci>
<ci> IP3 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a2 </ci>
<ci> S_100 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b2 </ci>
<ci> S_101 </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_101 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> a5 </ci>
<ci> S_101 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b5 </ci>
<ci> S_111 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b3 </ci>
<ci> S_101 </ci>
</apply>
</apply>
<apply><times/>
<ci> a3 </ci>
<ci> S_001 </ci>
<ci> IP3 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b2 </ci>
<ci> S_101 </ci>
</apply>
</apply>
<apply><times/>
<ci> a2 </ci>
<ci> S_100 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_010 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> b5 </ci>
<ci> S_010 </ci>
</apply>
</apply>
<apply><times/>
<ci> a5 </ci>
<ci> S_000 </ci>
<ci> Ca_i </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a1 </ci>
<ci> S_000 </ci>
<ci> IP3 </ci>
</apply>
</apply>
<apply><times/>
<ci> b1 </ci>
<ci> S_100 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a4 </ci>
<ci> S_000 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b4 </ci>
<ci> S_001 </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_011 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> b5 </ci>
<ci> S_011 </ci>
</apply>
</apply>
<apply><times/>
<ci> a5 </ci>
<ci> S_001 </ci>
<ci> Ca_i </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a3 </ci>
<ci> S_001 </ci>
<ci> IP3 </ci>
</apply>
</apply>
<apply><times/>
<ci> b3 </ci>
<ci> S_101 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b4 </ci>
<ci> S_001 </ci>
</apply>
</apply>
<apply><times/>
<ci> a4 </ci>
<ci> S_000 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_110 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> b5 </ci>
<ci> S_110 </ci>
</apply>
</apply>
<apply><times/>
<ci> a5 </ci>
<ci> S_100 </ci>
<ci> Ca_i </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b1 </ci>
<ci> S_100 </ci>
</apply>
</apply>
<apply><times/>
<ci> a1 </ci>
<ci> S_000 </ci>
<ci> IP3 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a2 </ci>
<ci> S_100 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply><times/>
<ci> b2 </ci>
<ci> S_101 </ci>
</apply>
</apply>
</apply>
<apply><eq/>
<ci> S_111 </ci>
<apply><plus/>
<apply><minus/>
<apply><times/>
<ci> b5 </ci>
<ci> S_111 </ci>
</apply>
</apply>
<apply><times/>
<ci> a5 </ci>
<ci> S_101 </ci>
<ci> Ca_i </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b3 </ci>
<ci> S_101 </ci>
</apply>
</apply>
<apply><times/>
<ci> a3 </ci>
<ci> S_001 </ci>
<ci> IP3 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> b2 </ci>
<ci> S_101 </ci>
</apply>
</apply>
<apply><times/>
<ci> a2 </ci>
<ci> S_100 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</math>
</component> -->
<component cmeta:id="id_000000008" name="receptor_dissociation_constants">
<variable initial_value="0.13" name="d1" public_interface="out" units="micromolar"/>
<variable initial_value="1.049" name="d2" public_interface="out" units="micromolar"/>
<variable initial_value="943.4" name="d3" public_interface="out" units="nanomolar"/>
<variable name="d4" public_interface="out" units="nanomolar"/>
<variable initial_value="82.34" name="d5" public_interface="out" units="nanomolar"/>
<variable name="a5" public_interface="in" units="second_order_rate_constant"/>
<variable name="b5" public_interface="in" units="first_order_rate_constant"/>
<variable name="a2" public_interface="in" units="second_order_rate_constant"/>
<variable name="b2" public_interface="in" units="first_order_rate_constant"/>
<variable name="a3" public_interface="in" units="second_order_rate_constant"/>
<variable name="b3" public_interface="in" units="first_order_rate_constant"/>
<variable name="a4" public_interface="in" units="second_order_rate_constant"/>
<variable name="b4" public_interface="in" units="first_order_rate_constant"/>
<variable cmeta:id="id_000000007" initial_value="15.0" name="IP3_cold" units="nanomolar"/>
<variable initial_value="" name="K_d2" units="nanomolar"/>
<variable initial_value="" name="K_d1" units="nanomolar"/>
<math id="5" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d1_calculation">
<eq/>
<ci> d1 </ci>
<apply>
<minus/>
<ci> K_d1 </ci>
<ci> IP3_cold </ci>
</apply>
</apply>
</math>
<math id="5A" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d2_calculation">
<eq/>
<ci>d2</ci>
<apply>
<divide/>
<ci>b2</ci>
<ci>a2</ci>
</apply>
</apply>
</math>
<math id="5B" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d3_calculation">
<eq/>
<ci>d3</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>K_d2</ci>
<ci>IP3_cold</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>d2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>d1</ci>
<ci>d2</ci>
</apply>
</apply>
</apply>
</math>
<math id="5C" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d4_calculation">
<eq/>
<ci>d4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>d1</ci>
<ci>d2</ci>
</apply>
<ci>d3</ci>
</apply>
</apply>
</math>
<math id="5D" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d5_calculation">
<eq/>
<ci>d5</ci>
<apply>
<divide/>
<ci>b5</ci>
<ci>a5</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="probability_of_an_open_IP3_receptor_channel" name="probability_of_an_open_IP3_receptor_channel">
<variable name="P_open" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_000000006" name="Ca_i" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_000000005" name="IP3" public_interface="in" units="micromolar"/>
<variable name="d1" public_interface="in" units="micromolar"/>
<variable name="d2" public_interface="in" units="micromolar"/>
<variable name="d3" public_interface="in" units="nanomolar"/>
<variable name="d5" public_interface="in" units="nanomolar"/>
<math id="6" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="P_open_calculation">
<eq/>
<ci> P_open </ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> IP3 </ci>
<ci> d2 </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> IP3 </ci>
</apply>
<apply>
<times/>
<ci> IP3 </ci>
<ci> d2 </ci>
</apply>
<apply>
<times/>
<ci> d1 </ci>
<ci> d2 </ci>
</apply>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> d3 </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> d5 </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="x_000">
<variable name="x_000" public_interface="out" units="micromolar"/>
<variable name="V1" public_interface="in" units="flux"/>
<variable name="V3" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math id="7" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="x_000_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x_000</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci> V1 </ci>
</apply>
<ci> V3 </ci>
</apply>
</apply>
</math>
</component>
<component name="x_001">
<variable name="x_001" public_interface="out" units="micromolar"/>
<variable name="V1" public_interface="in" units="flux"/>
<variable name="V4" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math id="8" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="x_001_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x_001</ci>
</apply>
<apply>
<minus/>
<ci> V1 </ci>
<ci> V4 </ci>
</apply>
</apply>
</math>
</component>
<component name="x_010">
<variable name="x_010" public_interface="out" units="micromolar"/>
<variable name="V2" public_interface="in" units="flux"/>
<variable name="V3" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math id="9" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="x_010_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x_010</ci>
</apply>
<apply>
<minus/>
<ci> V3 </ci>
<ci> V2 </ci>
</apply>
</apply>
</math>
</component>
<component name="x_011">
<variable name="x_011" public_interface="out" units="micromolar"/>
<variable name="x_000" public_interface="in" units="micromolar"/>
<variable name="x_001" public_interface="in" units="micromolar"/>
<variable name="x_010" public_interface="in" units="micromolar"/>
<math id="8a" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="x_011_eq">
<eq/>
<ci>x_011</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> x_000 </ci>
<ci> x_001 </ci>
<ci> x_010 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fluxes">
<variable name="V1" public_interface="out" units="flux"/>
<variable name="V2" public_interface="out" units="flux"/>
<variable name="V3" public_interface="out" units="flux"/>
<variable name="V4" public_interface="out" units="flux"/>
<variable name="x_000" public_interface="in" units="micromolar"/>
<variable name="x_001" public_interface="in" units="micromolar"/>
<variable name="x_011" public_interface="in" units="micromolar"/>
<variable name="x_010" public_interface="in" units="micromolar"/>
<variable name="Ca_i" public_interface="in" units="micromolar"/>
<variable name="a4" public_interface="in" units="second_order_rate_constant"/>
<variable name="d4" public_interface="in" units="nanomolar"/>
<variable name="a5" public_interface="in" units="second_order_rate_constant"/>
<variable name="d5" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<math id="10" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V1_calculation">
<eq/>
<ci> V1 </ci>
<apply>
<times/>
<ci> a4 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> x_000 </ci>
</apply>
<apply>
<times/>
<ci> d4 </ci>
<ci> x_001 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="V2_calculation">
<eq/>
<ci> V2 </ci>
<apply>
<times/>
<ci> a4 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> x_010 </ci>
</apply>
<apply>
<times/>
<ci> d4 </ci>
<ci> x_011 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="V3_calculation">
<eq/>
<ci> V3 </ci>
<apply>
<times/>
<ci> a5 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> x_000 </ci>
</apply>
<apply>
<times/>
<ci> d5 </ci>
<ci> x_010 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="V4_calculation">
<eq/>
<ci> V4 </ci>
<apply>
<times/>
<ci> a5 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Ca_i </ci>
<ci> x_001 </ci>
</apply>
<apply>
<times/>
<ci> d5 </ci>
<ci> x_011 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="constants">
<variable initial_value="400.0" name="a1" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="" name="b1" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.2" name="a2" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="" name="b2" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="400.0" name="a3" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="" name="b3" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.2" name="a4" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="" name="b4" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="20.0" name="a5" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="" name="b5" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.185" name="c1" public_interface="out" units="dimensionless"/>
<variable name="d1" public_interface="in" units="micromolar"/>
<variable name="d3" public_interface="in" units="nanomolar"/>
<variable name="d4" public_interface="in" units="nanomolar"/>
<math id="11" xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="b1_calculation">
<eq/>
<ci> b1 </ci>
<apply>
<times/>
<ci> d1 </ci>
<ci> a1 </ci>
</apply>
</apply>
<apply id="b3_calculation">
<eq/>
<ci> b3 </ci>
<apply>
<times/>
<ci> d3 </ci>
<ci> a3 </ci>
</apply>
</apply>
<apply id="b4_calculation">
<eq/>
<ci> b4 </ci>
<apply>
<times/>
<ci> d4 </ci>
<ci> a4 </ci>
</apply>
</apply>
</math>
</component>
<!--
"Time" is passed from the "environment" component to most other components.
-->
<connection>
<map_components component_1="Ca_i" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="IP3" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x_000" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x_001" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x_010" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="fluxes" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_i" component_2="Ca_ER"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
</connection>
<connection>
<map_components component_1="Ca_i" component_2="probability_of_an_open_IP3_receptor_channel"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="P_open" variable_2="P_open"/>
</connection>
<connection>
<map_components component_1="Ca_i" component_2="constants"/>
<map_variables variable_1="c1" variable_2="c1"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="constants"/>
<map_variables variable_1="c1" variable_2="c1"/>
</connection>
<connection>
<map_components component_1="IP3" component_2="Ca_i"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection>
<map_components component_1="probability_of_an_open_IP3_receptor_channel" component_2="IP3"/>
<map_variables variable_1="IP3" variable_2="IP3"/>
</connection>
<connection>
<map_components component_1="receptor_dissociation_constants" component_2="constants"/>
<map_variables variable_1="a2" variable_2="a2"/>
<map_variables variable_1="a3" variable_2="a3"/>
<map_variables variable_1="a4" variable_2="a4"/>
<map_variables variable_1="a5" variable_2="a5"/>
<map_variables variable_1="b2" variable_2="b2"/>
<map_variables variable_1="b3" variable_2="b3"/>
<map_variables variable_1="b4" variable_2="b4"/>
<map_variables variable_1="b5" variable_2="b5"/>
<map_variables variable_1="d1" variable_2="d1"/>
<map_variables variable_1="d3" variable_2="d3"/>
<map_variables variable_1="d4" variable_2="d4"/>
</connection>
<connection>
<map_components component_1="receptor_dissociation_constants" component_2="probability_of_an_open_IP3_receptor_channel"/>
<map_variables variable_1="d1" variable_2="d1"/>
<map_variables variable_1="d2" variable_2="d2"/>
<map_variables variable_1="d3" variable_2="d3"/>
<map_variables variable_1="d5" variable_2="d5"/>
</connection>
<connection>
<map_components component_1="receptor_dissociation_constants" component_2="fluxes"/>
<map_variables variable_1="d4" variable_2="d4"/>
<map_variables variable_1="d5" variable_2="d5"/>
</connection>
<connection>
<map_components component_1="x_000" component_2="x_011"/>
<map_variables variable_1="x_000" variable_2="x_000"/>
</connection>
<connection>
<map_components component_1="x_001" component_2="x_011"/>
<map_variables variable_1="x_001" variable_2="x_001"/>
</connection>
<connection>
<map_components component_1="x_010" component_2="x_011"/>
<map_variables variable_1="x_010" variable_2="x_010"/>
</connection>
<connection>
<map_components component_1="x_000" component_2="fluxes"/>
<map_variables variable_1="x_000" variable_2="x_000"/>
<map_variables variable_1="V1" variable_2="V1"/>
<map_variables variable_1="V3" variable_2="V3"/>
</connection>
<connection>
<map_components component_1="x_001" component_2="fluxes"/>
<map_variables variable_1="x_001" variable_2="x_001"/>
<map_variables variable_1="V1" variable_2="V1"/>
<map_variables variable_1="V4" variable_2="V4"/>
</connection>
<connection>
<map_components component_1="x_010" component_2="fluxes"/>
<map_variables variable_1="x_010" variable_2="x_010"/>
<map_variables variable_1="V2" variable_2="V2"/>
<map_variables variable_1="V3" variable_2="V3"/>
</connection>
<connection>
<map_components component_1="x_011" component_2="fluxes"/>
<map_variables variable_1="x_011" variable_2="x_011"/>
</connection>
<connection>
<map_components component_1="fluxes" component_2="Ca_i"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection>
<map_components component_1="fluxes" component_2="constants"/>
<map_variables variable_1="a4" variable_2="a4"/>
<map_variables variable_1="a5" variable_2="a5"/>
</connection>
<rdf:RDF>
<rdf:Description rdf:about="#Ca_i">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/chebi/CHEBI:39124"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000001">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/chebi/CHEBI:39124"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000002">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/chebi/CHEBI:39124"/>
</isVersionOf>
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/fma/FMA:63842"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#Ca_ER">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/chebi/CHEBI:39124"/>
</isVersionOf>
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/fma/FMA:63842"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000003">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/chebi/CHEBI:39124"/>
</isVersionOf>
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/fma/FMA:63842"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#IP3">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000004">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#probability_of_an_open_IP3_receptor_channel">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000005">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000006">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000007">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
<rdf:Description rdf:about="#id_000000008">
<isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
<rdf:Description rdf:about="http://identifiers.org/go/GO:0005220"/>
</isVersionOf>
</rdf:Description>
</rdf:RDF>
</model>
