- Author:
- neilstephen2001 <npar276@aucklanduni.ac.nz>
- Date:
- 2021-01-24 21:37:35+13:00
- Desc:
- adding OMEX archives to workspace
- Permanent Source URI:
- http://models.cellml.org/workspace/7f1/rawfile/110f9ba31e34b7499c8d02e13a6b9984351c0e8f/keener_2001/model/keener_2001.cellml
<?xml version="1.0" encoding="UTF-8"?>
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Diffusion Induced Oscillatory Insulin Secretion</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 contains partial differentials and as such can not currently be solved by existing CellML tools.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Insulin is secreted from pancreatic beta cells in an oscillatory fashion. In his 2001 paper (cited below), James Keener examines a mathematical model for
<emphasis>in vitro</emphasis>
insulin secretion from pancreatic beta cells in a one-dimensional chemical flow reactor, where the reaction region is represented by the volume occupied by the cells (see
<xref linkend="fig_cell_diagram" />
below). Glucose enters the cell through GLUT-1 and GLUT-2 transporters. Once inside the cell, intracellular glucose is metabolised, and this process activates insulin secretion via exocytosis of insulin containing granules. In the extracellular medium, insulin activates GLUT-1 transporters and inactivates GLUT-2 transporters.
</para>
<para>In order to model the reactions, a steady flow of solution along the one-dimensional reactor is assumed, with insulin cells confined to a one-dimensional region. Keener found that the oscillations occur as a result of an important interplay between flow rate of the reactor and insulin diffusion. Without diffusion, the oscillations are eliminated.</para>
<para>The complete original paper reference is cited below:</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WC7-4593YHR-R&_user=140507&_coverDate=07%2F31%2F2001&_rdoc=2&_fmt=summary&_orig=browse&_srch=%23toc%236731%232001%23999369995%23288659!&_cdi=6731&_sort=d&_docanchor=&wchp=dGLbVzz-lSztb&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=ab655a0002a58212a7c8f4893876257a">Diffusion Induced Oscillatory Insulin Secretion</ulink>
, James P. Keener, 2001,
<ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6731&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=2670d6bf58ba6625cf8c13344d6a4cb5">
<emphasis>Bulletin of Mathematical Biology</emphasis>
</ulink>
, 63, 625-641. (A PDF version of the article is available to subscribers on the Bulletin of Mathematical Biology website.)
<ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11497161&dopt=Abstract">PubMed ID: 11497161</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell_diagram</title>
</objectinfo>
<imagedata fileref="keener_2001.png" />
</imageobject>
</mediaobject>
<caption>A schematic diagram representing the model of glucose uptake, glucose metabolism and insulin secretion by pancreatic beta cells. Red lines represent the inactivation of GLUT-2 transporters by extracellular insulin, blue arrows represent the activation of GLUT-1 transporters by extracellular insulin and the activation of insulin secretion by glucose metabolism.</caption>
</informalfigure>
<para>
The raw CellML descriptions of the model can be downloaded in various formats as described in
<xref linkend="sec_download_this_model" />
.
</para>
</sect1>
</article>
</documentation>
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<unit units="millimolar" />
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<rdf:Description rdf:about="keener_2001.cellml#environment.rho">
<dcterms:description>volume fraction of insulin-secreting cells in bed</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_glucose.G_i">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_0">
<semsim:physicalPropertyOf rdf:resource="#entity_0" />
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>concentration of intracellular glucose</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#environment.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
</rdf:Description>
<rdf:Description rdf:about="#GLUT_2_transporter.K2">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_21">
<semsim:physicalPropertyOf rdf:resource="#entity_0" />
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>glucose dissociation constant of GLUT-2 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#GLUT_1_transporter.Ki">
<bqbiol:isPropertyOf rdf:resource="keener_2001.cellml#entity_4" />
<dcterms:description>insulin dissociation constant of GLUT-1 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#extracellular_glucose.R2">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_6">
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00593" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>rate of glucose uptake by GLUT-2 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#insulin.D_I">
<dcterms:description>diffusivity of insulin</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#insulin_secretion.Rs">
<dcterms:description>rate of insulin secretion</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#glucose_metabolism.Rm">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_11">
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00593" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>rate of glucose metabolism</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#insulin_inhibition.J_infinity">
<dcterms:description>steady state function of insulin secretion inactivation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#glucose_metabolism.Vm">
<dcterms:description>maximum rate of glucose metabolism</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#glucose_metabolism.Vm">
<dcterms:description>maximum rate of glucose metabolism</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_glucose.R1">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_2">
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00593" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>rate of glucose uptake by GLUT-1 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#insulin_secretion.Vs">
<dcterms:description>maximum rate of insulin secretion</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#insulin.I">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_7">
<semsim:physicalPropertyOf rdf:resource="#entity_4" />
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>concentration of insulin</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#environment.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#insulin_inhibition.K_inh">
<bqbiol:isPropertyOf rdf:resource="keener_2001.cellml#entity_4" />
<dcterms:description>insulin dissociation constant of insulin secretion inhibition</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#GLUT_1_transporter.G">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_18">
<semsim:physicalPropertyOf rdf:resource="#entity_2" />
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>concentration of extracellular glucose</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#glucose_metabolism.rho">
<dcterms:description>volume fraction of insulin-secreting cells in bed</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#insulin.x">
<dcterms:description>length of bed of insulin-secreting cells</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#extracellular_glucose.D_G">
<dcterms:description>diffusivity of glucose</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_glucose.R2">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_3">
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00593" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>rate of glucose uptake by GLUT-2 receptors</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#glucose_metabolism.G_i">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_13">
<semsim:physicalPropertyOf rdf:resource="#entity_0" />
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>concentration of intracellular glucose</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#entity_1">
<bqbiol:is rdf:resource="http://identifiers.org/fma/FMA:85704" />
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#GLUT_2_transporter.G_i">
<bqbiol:isPropertyOf rdf:resource="keener_2001.cellml#entity_0" />
<dcterms:description>concentration of intracellular glucose</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#insulin_secretion.Ks">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_25">
<semsim:physicalPropertyOf rdf:resource="#entity_0" />
<semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>glucose dissociation constant of insulin secretion</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="keener_2001.cellml#insulin_inhibition.J">
<dcterms:description>insulin secretion inactivation variable</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#GLUT_1_transporter.time">
<bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
</rdf:Description>
</rdf:RDF>
</model>
