<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> IP3-Mediated Ca2+ Release <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Bioengineering Institute, University of Auckland</shortaffil> </affiliation> </author> </articleinfo> <sect1 id="sec_structure"> Model Structure 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. 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, Proc. Natl. Acad. Sci. USA , 89, 9895-9899. (A PDF of the article is available to subscribers on the PNAS website.) PubMed ID: 1329108 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. 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 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. The raw CellML description of the IP3-mediated Ca <superscript>2+</superscript> release model can be downloaded in various formats as described in . <informalfigure float="0" id="fig_pathway_diagram"> <mediaobject> <imageobject> <objectinfo> A schematic diagram of the kinetics of an IP3 receptor/channel subunit </objectinfo> <imagedata fileref="deyoung_1992.png" /> </imageobject> </mediaobject> A schematic diagram of the kinetics of an IP <subscript>3</subscript> receptor/channel subunit. </informalfigure> </sect1> </documentation>
<rdf:RDF xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:j.0="http://imc.org/vCard/3.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/"> <rdf:Description rdf:about="http://www.cellml.org/Ca_ER"> <cmeta:comment> <rdf:Description rdf:about="rdf:#c7e7447a-77f3-43fa-87fd-ec0a9fa1f8f6"> <rdf:value>In their model, De Young and Keizer utilise the Ca2+ conservation condition to calculate the concentration of calcium ions in the endoplasmic reticulum (Ca_ER).</rdf:value> </rdf:Description> </cmeta:comment> <cmeta:comment> <rdf:Description rdf:about="rdf:#ad8345d6-c32a-4ec5-99af-a95703959255"> <rdf:value>De Young and Keize assumed that only the state S_110 (one IP3 and one activating Ca2+ bound) contributes to the conductance and that all three subunits must be in this state for the channel to be open. Thus the open probability is proportional to x^3_110.</rdf:value> </rdf:Description> </cmeta:comment> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0"> <cmeta:modification> <rdf:Description rdf:about="rdf:#fc301a38-a02f-4b0d-92d1-b81be7d2f1bb"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#9b0d3617-49f3-449d-a674-df54b20b59a4"> <vCard:N> <rdf:Description rdf:about="rdf:#1309919c-78c0-429e-b98f-89a03461383e"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology. 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> <dcterms:modified> <rdf:Description rdf:about="rdf:#faff940e-e1fc-4f3f-b71c-30d9a511ff6e"> <dcterms:W3CDTF>2007-06-05T09:34:14+12:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#0c3ffd4a-4825-47d3-83ff-33b8322d51cf"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#df88cf5f-f596-41a6-8634-7865d298770b"> <vCard:N> <rdf:Description rdf:about="rdf:#a51c52ea-6bfc-4a40-b12a-1c58f653446d"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> </rdf:Description> </cmeta:modifier> <rdf:value>Fixed link to diagram.</rdf:value> <dcterms:modified> <rdf:Description rdf:about="rdf:#22cf596c-7852-4e90-baad-f64fb2125d8e"> <dcterms:W3CDTF>2007-06-14T11:51:06+12:00</dcterms:W3CDTF> </rdf:Description> </dcterms:modified> </rdf:Description> </cmeta:modification> <dc:creator> <rdf:Description rdf:about="rdf:#0d964dd3-7ec6-430e-bab6-c5684a2b1cbf"> <vCard:N> <rdf:Description rdf:about="rdf:#7150953e-acf9-4165-a2b7-73ac5374bff3"> <vCard:Other>May</vCard:Other> <vCard:Family>Lloyd</vCard:Family> <vCard:Given>Catherine</vCard:Given> </rdf:Description> </vCard:N> <vCard:EMAIL> <j.0:internet rdf:about="rdf:#00e4410d-ab85-45fa-915f-2f8decd2918a"> <rdf:value>c.lloyd@auckland.ac.nz</rdf:value> </j.0:internet> </vCard:EMAIL> <vCard:ORG> <rdf:Description rdf:about="rdf:#ed97a0d5-8b10-4fc9-aeb7-d16ad3d2cbef"> <vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit> <vCard:Orgname>The University of Auckland</vCard:Orgname> </rdf:Description> </vCard:ORG> </rdf:Description> </dc:creator> <dcterms:created> <rdf:Description rdf:about="rdf:#11b77776-7e3e-4452-8103-eb0ee57e6bed"> <dcterms:W3CDTF>2007-05-18T00:00:00+00:00</dcterms:W3CDTF> </rdf:Description> </dcterms:created> <cmeta:comment> <rdf:Description rdf:about="rdf:#bef61b22-ec44-4905-8258-1cc9711bd1db"> <rdf:value></rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#b9f14777-1f34-4146-962a-f46ef362b77a"> <vCard:FN></vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/IP3"> <cmeta:comment> <rdf:Description rdf:about="rdf:#880256f5-3165-4875-a8dd-7c62054baa36"> <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> </rdf:Description> </cmeta:comment> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/x_011"> <dc:title>x_011</dc:title> <dcterms:alternative>IP3 receptor/channel subunit with an occupied Ca2+ inactivation binding site</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#mitochondrial_model_1992"> <bqs:reference> <rdf:Description rdf:about="rdf:#346e473e-e6b9-4526-aa07-ca35cc79fb31"> <dc:subject> <rdf:Description rdf:about="rdf:#a803213b-d551-486f-82d5-a098a59f73fb"> <rdf:value> <rdf:Bag rdf:about="rdf:#59a69767-7842-4332-b9c0-a1fd502cf3c4"> <rdf:li>calcium dynamics</rdf:li> <rdf:li>electrophysiology</rdf:li> <rdf:li>signal transduction</rdf:li> <rdf:li>ip3 receptor</rdf:li> <rdf:li>IP3 Receptor</rdf:li> </rdf:Bag> </rdf:value> <bqs:subject_type>keyword</bqs:subject_type> </rdf:Description> </dc:subject> </rdf:Description> </bqs:reference> <bqs:reference> <rdf:Description rdf:about="rdf:#0f182932-7b2c-4005-bb19-558e9f8cb9e7"> <bqs:JournalArticle> <rdf:Description rdf:about="rdf:#8279b5b4-917b-45f3-9464-03d1fda3688a"> <bqs:last_page>9899</bqs:last_page> <dcterms:issued> <rdf:Description rdf:about="rdf:#73f6218d-f1f6-4ebc-882b-6c095d51551c"> <dcterms:W3CDTF>1992-10-15</dcterms:W3CDTF> </rdf:Description> </dcterms:issued> <bqs:Journal> <rdf:Description rdf:about="rdf:#87b5dced-3171-44e3-a868-766d9876bcb8"> <dc:title>Proceedings of the National Academy of Science, USA</dc:title> </rdf:Description> </bqs:Journal> <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> <dc:creator> <rdf:Seq rdf:about="rdf:#2faff9c3-2816-4201-9df0-b95ab7092547"> <rdf:li> <bqs:Person rdf:about="rdf:#af1d72c9-ce72-46ee-98e0-f994d5f2405d"> <vCard:N> <rdf:Description rdf:about="rdf:#f969f77c-aa8c-49d9-9bb8-37133ec48199"> <vCard:Other>W</vCard:Other> <vCard:Family>De Young</vCard:Family> <vCard:Given>Gary</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> <rdf:li> <bqs:Person rdf:about="rdf:#88a9666b-d7ed-41b8-9502-8e601349ae0e"> <vCard:N> <rdf:Description rdf:about="rdf:#d5303080-28ff-48b7-9013-aa6b05d08853"> <vCard:Family>Keizer</vCard:Family> <vCard:Given>Joel</vCard:Given> </rdf:Description> </vCard:N> </bqs:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </bqs:JournalArticle> <bqs:Pubmed_id>1329108</bqs:Pubmed_id> </rdf:Description> </bqs:reference> <cmeta:comment> <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> <dc:creator> <rdf:Description rdf:about="rdf:#c0eeae3b-cf1e-4daf-9e58-b50ee1ca7a3d"> <vCard:FN></vCard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <cmeta:bio_entity>IP3 Receptor</cmeta:bio_entity> <dc:title>The De Young-Keizer 1992 model of oscillatory calcium release through the IP3 stimulated channel</dc:title> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/x_010"> <dc:title>x_010</dc:title> <dcterms:alternative>IP3 receptor/channel subunit with an occupied Ca2+ activation binding site</dcterms:alternative> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/Ca_i"> <cmeta:comment> <rdf:Description rdf:about="rdf:#d0dac9a5-f369-4d28-8877-4f3b869c076c"> <rdf:value>Cytoplasmic oscillations in Ca2+ concentration are described by the equation below where Ca_i is the cytosolic free Ca2+ concentration, J1 is the outward flux of Ca2+ and J2 is the inward flux of Ca2+.</rdf:value> </rdf:Description> </cmeta:comment> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/x_000"> <dc:title>x_000</dc:title> <dcterms:alternative>IP3 receptor/channel subunit with 3 unoccupied binding sites</dcterms:alternative> </rdf:Description> </rdf:RDF>
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
mitochondrial_model_1992
Chemical concentration
Chemical concentration flow rate
calcium ion
Endoplasmic reticulum
Portion of cytosol
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.
Ca concentration in the endoplasmic reticulum.
Cytosolic free Ca concentration
Total Ca concentration in the cytosol
Volume ratio of endoplasmic reticulum and cytosol
Time domain
<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>
Outward flux of Ca from Cytosol
Cytosol intake of Ca
IP3 receptor/Ca channel open probability.
Activation constant for ATP-Ca pump
Max Ca channel flux
Ca leak flux constant
Max Ca uptake
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>Ca_i</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> </apply> <apply> <power /> <ci>k3</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn> </apply> </apply> </apply> </apply>
Flow of calcium from cytosol to endoplasmic reticulum
Flow of calcium from cytosol to endoplasmic reticulum across Ca-IP3 channel.
Flow of calcium from endoplasmic reticulum to cytosol
Flow of calcium from endoplasmic reticulum to cytosol across Ca-IP3 receptor.
Concentration of IP3 in the cytosol.
IP3 loss rate constant
Dissociation constant for Ca stimulation of IP3 production.
Maximum rate of IP3 production.
IP3 Ca channel
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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>
IP3 receptor binding constant
Ca receptor binding constant (inhibition)
Ca receptor binding constant (activation)
IP3 receptor dissociation constant
Ca receptor dissociation constant (activation)
<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>
Change in free Ca concentration from Ca binding to unbound subunits and dissociation of Ca from bound inhibition receptor.
Proportion of IP3 receptor subunits with all receptors unbound.
Proportion of IP3 receptor subunits with Ca inactivation site bound.
Proportion of IP3 receptor subunits with Ca activation site bound.
Proportion of IP3 receptor subunits with Ca activation and deactivation sites bound.
<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>
Ca receptor dissociation constant (inhibition)
<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>
<apply id="d1_calculation"> <eq /> <ci>d1</ci> <apply> <minus /> <ci>K_d1</ci> <ci>IP3_cold</ci> </apply> </apply> <apply id="d2_calculation"> <eq /> <ci>d2</ci> <apply> <divide /> <ci>b2</ci> <ci>a2</ci> </apply> </apply> <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> <apply id="d4_calculation"> <eq /> <ci>d4</ci> <apply> <divide /> <apply> <times /> <ci>d1</ci> <ci>d2</ci> </apply> <ci>d3</ci> </apply> </apply> <apply id="d5_calculation"> <eq /> <ci>d5</ci> <apply> <divide /> <ci>b5</ci> <ci>a5</ci> </apply> </apply>
<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>
<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>
<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>
<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>