- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 16:14:31+12:00
- Desc:
- committing version03 of tolic_mosekilde_sturis_2000
- Permanent Source URI:
- https://models.cellml.org/workspace/tolic_mosekilde_sturis_2000/rawfile/2b9a9c1187fd52ae40399e0dd60f5d5010328ada/tolic_mosekilde_sturis_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : tolic_model_III_2000.xml
CREATED : 14th January 2003
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 a modified version of Tolic et al's original 2000 mathematical model of the insulin-glucose feedback system in pancreatic beta cells. The model has been altered to account for hyperglycemic conditions.
CHANGES:
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="tolic_mosekilde_sturis_2000_version03" name="tolic_mosekilde_sturis_2000_version03">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Insulin-Glucose Feedback System</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>
Endocrine systems often secrete hormones in pulses. Examples include the release of growth hormone and gonadotropins, and also the secretion of insulin from the pancreas, which are secreted over intervals of 1-3 hours and 80-150 minutes respectively. It has been suggested that relative to constant or stochastic signals, oscillatory signals are more effective at producing a sustained response in the target cells. In addition to the slow insulin oscillations, there are more rapid pulses that occur every 8-15 minutes. The mechanisms underlying both types of oscillations are not fully understood, however it is thought that the more rapid oscillations may arise from an intrapancreatic pacemaker mechanism. One possible explanation of the slow insulin oscillations, is an instability in the insulin-glucose feedback system. This hypothesis has been the subject of a number of studies, including some which have developed a mathematical model of the insulin-glucose feedback system.
</para>
<para>
In 2000, Iva Marija Tolic, Erik Mosekilde and Jeppe Sturis published a paper, based on a previously published mathematical model of the insulin-glucose feedback regulation. They hoped to identify a possible mechanism behind the efficiency of oscillatory insulin secretions. Analysis of the original model revealed that the slow oscillations of insulin secretion could arise from a Hopf bifurcation in the insulin-glucose feedback mechanism. The model included several feedback loops (see the figure below), including: glucose stimulating pancreatic beta cells to secrete insulin, insulin stimulating glucose uptake and inhibiting hepatic glucose production, and also positive feedback as glucose enhances its own uptake. The model includes two significant delays, reflecting the fact that the effect of insulin on glucose utilisation is dependent on the concentration of insulin in a slowly equilibrating intercellular compartment as opposed to the concentration of the plasma insulin. The other delay is due to the time lag between the appearance of insulin in the plasma and its inhibitory effect on hepatic glucose production.
</para>
<para>
In order to gain insight into certain features of the model, Tolic <emphasis>et al.</emphasis> simplified it (version 2). In addition, they developed a third version of the model which accounted for the effect of hyperglycemic conditions on glucose production (version 3).
</para>
<para>
Model simulations suggested to Tolic <emphasis>et al.</emphasis> that the interaction of the oscillatory insulin supply with the glucose receptors of the glucose utilising cells was of minimal importance. This was because the oscillations in the concentration of the intercellular insulin were small, and changes in the average glucose utilisation only depend weakly on amplitude. However, with their model they were able to resolve conflicting results from clinical studies. Different experimental conditions will influence hepatic glucose release. If hepatic glucose release is occurring near its maximum limit, an oscillatory insulin supply will be more effective at lowering the blood glucose level than a constant supply. However, if the insulin level is sufficiently high to cause the hepatic release of glucose to virtually disappear, the opposite is observed. For insulin concentrations close to the point of inflection of the insulin-glucose dose-response curve, an oscillatory and a constant insulin secretion produce similar effects.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-45CWWN9-J&_coverDate=12%2F07%2F2000&_alid=70282669&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6932&_sort=d&wchp=dGLbVlb-lSzBk&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=75f86c586e338b9e1febc2f0808c8e50">Modelling the Insulin-Glucose Feedback System: The Significance of Pulsatile Insulin Secretion</ulink>, Iva Marija Tolic, Erik Mosekilde and Jeppe Sturis, 2000, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6932&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c8e64d20ff203cda2255f4b6b7affe4f">
<emphasis>Journal of Theoretical Biology</emphasis>
</ulink>, 207, 361-375. (A PDF version of the article is available to subscribers of the Journal of Theoretical Biology website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11082306&dopt=Abstract">PubMed ID: 11082306</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>A simplified diagram of the model</title>
</objectinfo>
<imagedata fileref="tolic_2000.png"/>
</imageobject>
</mediaobject>
<caption>A simplified diagram of the model. There are three main variables: G which represents the amount of glucose in the intercellular space and in the plasma, Ip which represents the amount of insulin in the plasma, and Ii which is the amount of insulin in the intercellular space. The black arrows represent transmembrane glucose and insulin exchange. The green arrows represent positive feedback loops.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model.
-->
<units name="mU">
<unit units="mole" prefix="pico" multiplier="6.67"/>
</units>
<units name="mg">
<unit units="gram" prefix="milli"/>
</units>
<units name="min">
<unit units="second" multiplier="60.0"/>
</units>
<units name="l">
<unit units="litre"/>
</units>
<units name="mg_per_min">
<unit units="mg"/>
<unit units="min" exponent="-1"/>
</units>
<units name="mg_per_l">
<unit units="mg"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="mU_per_l">
<unit units="mU"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="mU_per_min">
<unit units="mU"/>
<unit units="min" exponent="-1"/>
</units>
<units name="l_per_min">
<unit units="l"/>
<unit units="min" exponent="-1"/>
</units>
<units name="per_mU">
<unit units="mU" exponent="-1"/>
</units>
<component name="environment">
<variable units="min" public_interface="out" name="time"/>
<variable units="l" public_interface="out" name="Vp" initial_value="3.0"/>
<variable units="l" public_interface="out" name="Vi" initial_value="11.0"/>
<variable units="l" public_interface="out" name="Vg" initial_value="10.0"/>
<variable units="l_per_min" public_interface="out" name="E" initial_value="0.2"/>
</component>
<component name="plasma_insulin">
<variable units="mU" public_interface="out" name="Ip"/>
<variable units="min" name="tp" initial_value="6.0"/>
<variable units="mU_per_min" name="f1_G"/>
<variable units="mU_per_min" name="Rm" initial_value="210.0"/>
<variable units="mg_per_l" name="C1" initial_value="2000.0"/>
<variable units="mg_per_l" name="a1" initial_value="300.0"/>
<variable units="min" public_interface="in" name="time"/>
<variable units="l" public_interface="in" name="Vp"/>
<variable units="l" public_interface="in" name="Vi"/>
<variable units="l" public_interface="in" name="Vg"/>
<variable units="mU" public_interface="in" name="Ii"/>
<variable units="mg" public_interface="in" name="G"/>
<variable units="l_per_min" public_interface="in" name="E"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ip_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ip </ci>
</apply>
<apply>
<minus/>
<ci> f1_G </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> E </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> Ip </ci>
<ci> Vp </ci>
</apply>
<apply>
<divide/>
<ci> Ii </ci>
<ci> Vi </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Ip </ci>
<ci> tp </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="f1_G_calculation">
<eq/>
<ci> f1_G </ci>
<apply>
<divide/>
<ci> Rm </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<minus/>
<ci> C1 </ci>
<ci> G </ci>
</apply>
<ci> Vg </ci>
</apply>
<ci> a1 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intercellular_insulin">
<variable units="mU" public_interface="out" name="Ii"/>
<variable units="min" public_interface="out" name="ti" initial_value="100.0"/>
<variable units="min" public_interface="in" name="time"/>
<variable units="l" public_interface="in" name="Vp"/>
<variable units="l" public_interface="in" name="Vi"/>
<variable units="mU" public_interface="in" name="Ip"/>
<variable units="l_per_min" public_interface="in" name="E"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ii_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ii </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> E </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> Ip </ci>
<ci> Vp </ci>
</apply>
<apply>
<divide/>
<ci> Ii </ci>
<ci> Vi </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Ii </ci>
<ci> ti </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="glucose">
<variable units="mg" public_interface="out" name="G"/>
<variable units="mg_per_min" name="Gin" initial_value="216.0"/>
<variable units="mg_per_min" name="f2_G"/>
<variable units="mg_per_min" name="f3_G"/>
<variable units="mU_per_min" name="f4_Ii"/>
<variable units="dimensionless" name="f5_x3"/>
<variable units="mg_per_min" name="f6_G"/>
<variable units="mg_per_min" name="f7_G"/>
<variable units="mg_per_l" name="C2" initial_value="144.0"/>
<variable units="mg_per_l" name="C3" initial_value="1000.0"/>
<variable units="mU_per_l" name="C4" initial_value="80.0"/>
<variable units="mU_per_l" name="C5" initial_value="26.0"/>
<variable units="mU_per_l" name="C6" initial_value="2.0"/>
<variable units="mU_per_l" name="C7" initial_value="2.0"/>
<variable units="mg_per_min" name="U0" initial_value="40.0"/>
<variable units="mg_per_min" name="Um" initial_value="940.0"/>
<variable units="mg_per_min" name="Ub" initial_value="72.0"/>
<variable units="dimensionless" name="beta" initial_value="1.77"/>
<variable units="mg_per_min" name="Rg" initial_value="180.0"/>
<variable units="per_mU" name="alpha" initial_value="0.29"/>
<variable units="per_mU" name="gamma" initial_value="5.0"/>
<variable units="per_mU" name="delta" initial_value="-2.4"/>
<variable units="mg_per_min" name="Sb" initial_value="20.0"/>
<variable units="mg_per_min" name="Sm" initial_value="140.0"/>
<variable units="min" public_interface="in" name="time"/>
<variable units="min" public_interface="in" name="ti"/>
<variable units="l" public_interface="in" name="Vg"/>
<variable units="l" public_interface="in" name="Vp"/>
<variable units="l" public_interface="in" name="Vi"/>
<variable units="l_per_min" public_interface="in" name="E"/>
<variable units="mU" public_interface="in" name="Ii"/>
<variable units="min" public_interface="in" name="x3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="G_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> G </ci>
</apply>
<apply>
<plus/>
<ci> Gin </ci>
<apply>
<times/>
<ci> f5_x3 </ci>
<ci> f6_G </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> f2_G </ci>
<apply>
<times/>
<ci> f3_G </ci>
<ci> f4_Ii </ci>
</apply>
<ci> f7_G </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="f2_G_calculation">
<eq/>
<ci> f2_G </ci>
<apply>
<times/>
<ci> Ub </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> G </ci>
</apply>
<apply>
<times/>
<ci> C2 </ci>
<ci> Vg </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="f3_G_calculation">
<eq/>
<ci> f3_G </ci>
<apply>
<divide/>
<ci> G </ci>
<apply>
<times/>
<ci> C3 </ci>
<ci> Vg </ci>
</apply>
</apply>
</apply>
<apply id="f4_Ii_calculation">
<eq/>
<ci> f4_Ii </ci>
<apply>
<plus/>
<ci> U0 </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Um </ci>
<ci> U0 </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<times/>
<ci> beta </ci>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ii </ci>
<apply>
<times/>
<ci> C4 </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> Vi </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> E </ci>
<ci> ti </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="f5_x3_calculation">
<eq/>
<ci> f5_x3 </ci>
<apply>
<divide/>
<ci> Rg </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<ci> alpha </ci>
<apply>
<divide/>
<ci> x3 </ci>
<apply>
<minus/>
<ci> Vp </ci>
<ci> C5 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="f6_G_calculation">
<eq/>
<ci> f6_G </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<divide/>
<ci> G </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> C3 </ci>
<ci> Vg </ci>
</apply>
<ci> C6 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="f7_G_calculation">
<eq/>
<ci> f7_G </ci>
<apply>
<plus/>
<ci> Sb </ci>
<apply>
<minus/>
<ci> Sm </ci>
<ci> Sb </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<ci> delta </ci>
<apply>
<divide/>
<ci> G </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> C3 </ci>
<ci> Vg </ci>
</apply>
<ci> C7 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delay">
<variable units="min" public_interface="out" name="x3"/>
<variable units="min" name="td" initial_value="36.0"/>
<variable units="min" name="x1"/>
<variable units="min" name="x2"/>
<variable units="min" public_interface="in" name="time"/>
<variable units="mU" public_interface="in" name="Ip"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="x1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x1 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="min"> 3.0 </cn>
<ci> td </ci>
</apply>
<apply>
<minus/>
<ci> Ip </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
<apply id="x2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x2 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="min"> 3.0 </cn>
<ci> td </ci>
</apply>
<apply>
<minus/>
<ci> x1 </ci>
<ci> x2 </ci>
</apply>
</apply>
</apply>
<apply id="x3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x3 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="min"> 3.0 </cn>
<ci> td </ci>
</apply>
<apply>
<minus/>
<ci> x2 </ci>
<ci> x3 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="plasma_insulin"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="Vg" variable_1="Vg"/>
<map_variables variable_2="Vi" variable_1="Vi"/>
<map_variables variable_2="E" variable_1="E"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intercellular_insulin"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="Vi" variable_1="Vi"/>
<map_variables variable_2="E" variable_1="E"/>
</connection>
<connection>
<map_components component_2="environment" component_1="glucose"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="Vg" variable_1="Vg"/>
<map_variables variable_2="Vi" variable_1="Vi"/>
<map_variables variable_2="E" variable_1="E"/>
</connection>
<connection>
<map_components component_2="environment" component_1="delay"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="glucose" component_1="plasma_insulin"/>
<map_variables variable_2="G" variable_1="G"/>
</connection>
<connection>
<map_components component_2="intercellular_insulin" component_1="plasma_insulin"/>
<map_variables variable_2="Ip" variable_1="Ip"/>
<map_variables variable_2="Ii" variable_1="Ii"/>
</connection>
<connection>
<map_components component_2="delay" component_1="plasma_insulin"/>
<map_variables variable_2="Ip" variable_1="Ip"/>
</connection>
<connection>
<map_components component_2="glucose" component_1="intercellular_insulin"/>
<map_variables variable_2="Ii" variable_1="Ii"/>
<map_variables variable_2="ti" variable_1="ti"/>
</connection>
<connection>
<map_components component_2="delay" component_1="glucose"/>
<map_variables variable_2="x3" variable_1="x3"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#6be7ae4f-c8d7-4528-b967-b9d2cf551ca4">
<rdf:li>insulin-glucose dynamics</rdf:li>
<rdf:li>beta cell</rdf:li>
<rdf:li>signal transduction</rdf:li>
<rdf:li>pulsatile secretion</rdf:li>
<rdf:li>Pancreatic Beta-Cell</rdf:li>
<rdf:li>metabolism</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
<rdf:li rdf:resource="rdf:#author3Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#2f4dd24d-f861-4a76-9ecb-06730dd9c3d6">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#tolic_mosekilde_sturis_2000_version03">
<dc:title>
A modified version of Tolic et al's original 2000 mathematical model of
the insulin-glucose feedback system in pancreatic beta cells. The model
has been altered to account for hyperglycemic conditions.
</dc:title>
<cmeta:bio_entity>Pancreatic Beta Cell</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#cad02067-9da6-4451-a432-4b9b726ec988"/>
<bqs:reference rdf:resource="rdf:#882f51f3-cb32-44e3-af8b-530fc18f9ae1"/>
<bqs:reference rdf:resource="rdf:#9ed07a75-ef54-4528-a3fb-9c0c4a0cd2e4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e5915965-df44-4349-b4bd-43ad2efb46e1">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b19b6570-a1be-4a9d-b31b-08ae12f11953">
<dcterms:W3CDTF>2003-01-14</dcterms:W3CDTF>
</rdf:Description>
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The University of Auckland, Bioengineering Institute
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