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<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>
<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>
<ulink url="http://www.pnas.org/cgi/content/abstract/89/20/9895">
A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca
<superscript>2+</superscript>
concentration
</ulink>
, Gary W. De Young and Joel Keizer, 1992,
<ulink url="http://www.pnas.org/">
<emphasis>Proc. Natl. Acad. Sci. USA</emphasis>
</ulink>
, 89, 9895-9899. (A
<ulink url="http://www.pnas.org/cgi/reprint/89/20/9895.pdf">PDF</ulink>
of the article is available to subscribers on the PNAS website.)
<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>
<para>
The raw CellML description of the IP3-mediated Ca
<superscript>2+</superscript>
release model can be downloaded in various formats as described in
<xref linkend="sec_download_this_model" />
.
</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>
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<rdf:value>In their model, De Young and Keizer utilise the Ca2+ conservation
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endoplasmic reticulum (Ca_ER).</rdf:value>
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<rdf:value>De Young and Keize assumed that only the state S_110 (one IP3 and
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all three subunits must be in this state for the channel to be
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The model runs in the PCEnv simulator and gives a nice curved output... But not the spiked output published in the original paper.</rdf:value>
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<rdf:value>Ca2+ feedback on the production of inositol 1,4,5-triphosphate (IP3) is described by the equation below, where alpha has a value between 0 and 1.</rdf:value>
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<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>signal transduction</rdf:li>
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<rdf:li>IP3 Receptor</rdf:li>
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<dc:title>Proceedings of the National Academy of Science, USA</dc:title>
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<bqs:first_page>9895</bqs:first_page>
<bqs:volume>89</bqs:volume>
<dc:title>A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca 2+ concentration</dc:title>
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<rdf:Description rdf:about="rdf:#33e862af-6f1a-4629-8913-c316c5475ba0">
<rdf:value>The binding kinetics of IP3 and the activation of the receptor by Ca2+ are rapid, ensuring rapid release of Ca2+ after an IP3 pulse. This allows the number of receptor subunit states in the model to be reduced by four. We can eliminate the four receptor subunit states with IP3 bound (S_111, S_100, S_101, S_100). This leaves the reduced system outlined below.</rdf:value>
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A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca 2+ concentration
C:\Users\thomp_000\Dropbox\Work Related\Annotated Models\deyoung_1992\deyoung_keizer_1992.cellml
Christopher Thompson
https://models.physiomeproject.org/exposure/cd65a6e4500cb8fae8eb0725c1a2db57/deyoung_keizer_1992.cellml/view
mitochondrial_model_1992
mitochondrial_model_1992
thompsct@umich.edu
Chemical concentration
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Chemical concentration flow rate
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calcium ion
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Endoplasmic reticulum
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Portion of cytosol
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A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
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Time domain
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Portion of cytosol
http://purl.org/sig/ont/fma/fma66836
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flux
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litre
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micromolar
micro
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second
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second_order_rate_constant
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constants
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Ca receptor binding constant (inhibition)
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IP3 receptor binding constant
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Ca receptor binding constant (inhibition)
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Ca receptor binding constant (activation)
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false
false
out
true
false
false
out
true
false
false
out
true
false
false
out
true
0.185
false
false
out
true
Volume ratio of endoplasmic reticulum and cytosol
false
false
in
true
IP3 receptor dissociation constant
false
false
in
true
IP3 receptor dissociation constant
false
false
in
true
Ca receptor dissociation constant (activation)
<math xmlns="http://www.w3.org/1998/Math/MathML" id="11" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="11">
<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>
environment
false
false
out
true
Time domain
fluxes
false
false
in
true
Cytosolic free Ca concentration
Chemical concentration
http://bhi.washington.edu/OPB#OPB_00340
false
false
out
true
Change in free Ca concentration from Ca binding to unbound subunits and dissociation of Ca from bound inhibition receptor.
false
false
out
true
false
false
out
true
false
false
out
true
false
false
in
true
Ca receptor binding constant (inhibition)
false
false
in
true
Ca receptor binding constant (activation)
false
false
in
true
Ca receptor dissociation constant (activation)
false
false
in
true
Ca receptor dissociation constant (activation)
false
false
in
true
Time domain
false
false
in
true
Proportion of IP3 receptor subunits with all receptors unbound.
false
false
in
true
Proportion of IP3 receptor subunits with Ca inactivation site bound.
false
false
in
true
Proportion of IP3 receptor subunits with Ca activation site bound.
false
false
in
true
Proportion of IP3 receptor subunits with Ca activation and deactivation sites bound.
<math xmlns="http://www.w3.org/1998/Math/MathML" id="10" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="10">
<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>
probability_of_an_open_IP3_receptor_channel
false
false
in
true
Cytosolic free Ca concentration
Chemical concentration
http://bhi.washington.edu/OPB#OPB_00340
false
false
in
true
Concentration of IP3 in the cytosol.
Chemical concentration
http://bhi.washington.edu/OPB#OPB_00340
false
false
out
true
IP3 receptor/Ca channel open probability.
false
false
in
true
IP3 receptor dissociation constant
false
false
in
true
Ca receptor dissociation constant (inhibition)
false
false
in
true
IP3 receptor dissociation constant
false
false
in
true
Ca receptor dissociation constant (activation)
<math xmlns="http://www.w3.org/1998/Math/MathML" id="6" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="6">
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.0</cn>
</apply>
</apply>
</math>
receptor_dissociation_constants
15.0
false
false
true
Chemical concentration
http://bhi.washington.edu/OPB#OPB_00340
false
false
true
Chemical concentration
http://bhi.washington.edu/OPB#OPB_00340
false
false
true
Chemical concentration
http://bhi.washington.edu/OPB#OPB_00340
false
false
in
true
Ca receptor binding constant (inhibition)
false
false
in
true
IP3 receptor binding constant
false
false
in
true
Ca receptor binding constant (inhibition)
false
false
in
true
Ca receptor binding constant (activation)
false
false
in
true
false
false
in
true
false
false
in
true
false
false
in
true
0.13
false
false
out
true
IP3 receptor dissociation constant
1.049
false
false
out
true
Ca receptor dissociation constant (inhibition)
943.4
false
false
out
true
IP3 receptor dissociation constant
false
false
out
true
Ca receptor dissociation constant (activation)
82.34
false
false
out
true
Ca receptor dissociation constant (activation)
<math xmlns="http://www.w3.org/1998/Math/MathML" id="5" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="5">
<apply id="d1_calculation">
<eq />
<ci>d1</ci>
<apply>
<minus />
<ci>K_d1</ci>
<ci>IP3_cold</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="5A">
<apply id="d2_calculation">
<eq />
<ci>d2</ci>
<apply>
<divide />
<ci>b2</ci>
<ci>a2</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="5B">
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>d2</ci>
</apply>
</apply>
<apply>
<times />
<ci>d1</ci>
<ci>d2</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="5C">
<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 xmlns="http://www.w3.org/1998/Math/MathML" id="5D">
<apply id="d5_calculation">
<eq />
<ci>d5</ci>
<apply>
<divide />
<ci>b5</ci>
<ci>a5</ci>
</apply>
</apply>
</math>
x_000
false
false
in
true
false
false
in
true
false
false
in
true
Time domain
false
false
out
true
Proportion of IP3 receptor subunits with all receptors unbound.
<math xmlns="http://www.w3.org/1998/Math/MathML" id="7" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="7">
<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>
x_001
false
false
in
true
Change in free Ca concentration from Ca binding to unbound subunits and dissociation of Ca from bound inhibition receptor.
false
false
in
true
false
false
in
true
Time domain
false
false
out
true
Proportion of IP3 receptor subunits with Ca inactivation site bound.
<math xmlns="http://www.w3.org/1998/Math/MathML" id="8" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="8">
<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>
x_010
false
false
in
true
false
false
in
true
false
false
in
true
Time domain
false
false
out
true
Proportion of IP3 receptor subunits with Ca activation site bound.
<math xmlns="http://www.w3.org/1998/Math/MathML" id="9" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="9">
<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>
x_011
false
false
in
true
Proportion of IP3 receptor subunits with all receptors unbound.
false
false
in
true
Proportion of IP3 receptor subunits with Ca inactivation site bound.
false
false
in
true
Proportion of IP3 receptor subunits with Ca activation site bound.
false
false
out
true
Proportion of IP3 receptor subunits with Ca activation and deactivation sites bound.
<math xmlns="http://www.w3.org/1998/Math/MathML" id="8a" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="8a">
<apply id="x_011_eq">
<eq />
<ci>x_011</ci>
<apply>
<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
<apply>
<plus />
<ci>x_000</ci>
<ci>x_001</ci>
<ci>x_010</ci>
</apply>
</apply>
</apply>
</math>