<?xml version="1.0"?>
<!--
This CellML file was generated on 19/04/2010 at 1:40:15 at p.m. using:
COR (0.9.31.1371)
Copyright 2002-2010 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<title>Modelling the Insulin-Glucose Feedback System: The Significance of Pulsatile Insulin Secretion</title>
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<firstname>Catherine</firstname>
<surname>Lloyd</surname>
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<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
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<section id="sec_status">
<title>Model Status</title>
<para>
This model runs in OpenCell and COR to recreate the published results (Figure 1). The units are consistent throughout. This describes the original Insulin-Glucose feedback model described in equations 1-11.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A mathematical model of the insulin-glucose feedback regulation in man is used to examine the effects of an oscillatory supply of insulin compared to a constant supply at the same average rate. We show that interactions between the oscillatory insulin supply and the receptor dynamics can be of minute significance only. It is possible, however, to interpret seemingly conflicting results of clinical studies in terms of their different experimental conditions with respect to the hepatic glucose release. If this release is operating near an upper limit, an oscillatory insulin supply will be more efficient in lowering the blood glucose level than a constant supply. If the insulin level is high enough for the hepatic release of glucose to nearly vanish, the opposite effect is observed. For insulin concentrations close to the point of inflection of the insulin-glucose dose-response curve an oscillatory and a constant insulin infusion produce similar effects.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Modelling the Insulin-Glucose Feedback System: The Significance of Pulsatile Insulin Secretion, Iva Marija Tolic, Erik Mosekilde and Jeppe Sturis, 2000, <emphasis>Journal of Theoretical Biology</emphasis>, 207, 361-375. <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">
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<title>A simplified diagram of the model</title>
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<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>
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<times/>
<ci>C3</ci>
<ci>Vg</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f4_Ii</ci>
<apply>
<plus/>
<ci>U0</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Um</ci>
<ci>U0</ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>beta</ci>
</apply>
<apply>
<ln/>
<apply>
<times/>
<apply>
<divide/>
<ci>Ii</ci>
<ci>C4</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<ci>Vi</ci>
</apply>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>E</ci>
<ci>ti</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f5_x3</ci>
<apply>
<divide/>
<ci>Rg</ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<ci>alpha</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>x3</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mU_per_min">1</cn>
</apply>
<ci>Vp</ci>
</apply>
<ci>C5</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delay">
<variable initial_value="104.5878705" name="x3" public_interface="out" units="min"/>
<variable initial_value="36" name="td" units="min"/>
<variable initial_value="110.420253" name="x1" units="min"/>
<variable initial_value="112.7601171" name="x2" units="min"/>
<variable name="time" public_interface="in" units="min"/>
<variable name="Ip" public_interface="in" units="mU"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x1</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>td</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<ci>Ip</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mU_per_min">1</cn>
</apply>
<ci>x1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x2</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>td</ci>
</apply>
<apply>
<minus/>
<ci>x1</ci>
<ci>x2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x3</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>td</ci>
</apply>
<apply>
<minus/>
<ci>x2</ci>
<ci>x3</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="plasma_insulin" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="Vg" variable_2="Vg"/>
<map_variables variable_1="Vi" variable_2="Vi"/>
<map_variables variable_1="E" variable_2="E"/>
</connection>
<connection>
<map_components component_1="intercellular_insulin" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="Vi" variable_2="Vi"/>
<map_variables variable_1="E" variable_2="E"/>
</connection>
<connection>
<map_components component_1="glucose" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="Vg" variable_2="Vg"/>
<map_variables variable_1="Vi" variable_2="Vi"/>
<map_variables variable_1="E" variable_2="E"/>
</connection>
<connection>
<map_components component_1="delay" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="plasma_insulin" component_2="glucose"/>
<map_variables variable_1="G" variable_2="G"/>
</connection>
<connection>
<map_components component_1="plasma_insulin" component_2="intercellular_insulin"/>
<map_variables variable_1="Ip" variable_2="Ip"/>
<map_variables variable_1="Ii" variable_2="Ii"/>
</connection>
<connection>
<map_components component_1="plasma_insulin" component_2="delay"/>
<map_variables variable_1="Ip" variable_2="Ip"/>
</connection>
<connection>
<map_components component_1="intercellular_insulin" component_2="glucose"/>
<map_variables variable_1="Ii" variable_2="Ii"/>
<map_variables variable_1="ti" variable_2="ti"/>
</connection>
<connection>
<map_components component_1="glucose" component_2="delay"/>
<map_variables variable_1="x3" variable_2="x3"/>
</connection>
</model>
