<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : heinze_model_1998.xml
CREATED : 20th July 2007
LAST MODIFIED : 20th July 2007
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Heinze et al's 1998 mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion.
CHANGES:
--><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="heinze_model_1998" name="heinze_keener_midgley_model_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion</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>
One of the quintessential characteristics of reproductive hormones is their pulsatile nature. Semi-regular pulses of gonadotropin releasing hormone (GnRH) are secreted from the hypothalamus at varying frequencies, usually about once an hour, and the hormone travels through the portal circulation to the pituitary where it stimulates the release of luteinizing hormone (LH). LH secretion is also often semi-regular and pulsatile, although the presence of high-frequency or continuous GnRH the GnRH-LH relationship is disrupted and LH synthesis is reduced in a process called desensitisation. In turn, reduced concentrations of LH delay follicular development, steroid production and ovulation.
</para>
<para>
The complexity of the GnRH-LH relationship lends itself to mathematical modelling, with the hope that a theoretical approach can further support experimental results. In the paper described here, Heinze <emphasis>et al.</emphasis> present a mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion. The model consists of a system of nonlinear differential equations and incorporates two different possible mechanisms to account for the observed disruption of the GnRH-LH relationship in the presence of continuous GnRH exposure.
</para>
<para>
The original publication contains three different mathematical models:
</para>
<itemizedlist>
<listitem>
<para>The first represents the core model which describes the basic dynamics of GnRH-receptor binding in the pituitary and the subsequent release of LH. It includes two different possible mechanisms to account for the observed disruption of the GnRH-LH relationship in the presence of continuous GnRH exposure:</para>
<listitem>
<para>a) a desensitised receptor, and</para>
</listitem>
<listitem>
<para>b) a limited, yet replenishable, pool of releasable LH</para>
</listitem>
</listitem>
<listitem>
<para>In the second model the constant addition of LH to the releasable pool is removed such that it becomes exhaustable.</para>
</listitem>
<listitem>
<para>Finally, in the third model the desensitised receptor is removed.</para>
</listitem>
</itemizedlist>
<para>
There was good agreement between experimental data and simulation results for all three models. Consideration of the latter two models revealed the desensitised receptor (model 2) had a significant effect on the LH levels. Furthermore, the LH replenishment mechanism also had a significant effect in three of the four scenarios tested.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="heinze_1998_version2_variant1.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the components and reactions involved in the first model of luteinizing hormone (LH) release. kfb, kdf, and kbd are kinetic constants, F, B, and D represent the free, bound, and desensitised states of the gonadotropin-releasing hormone (GnRH) receptor, while R represents releasable LH and B is bound LH. a1 determines the rate of basal LH secretion and a2 is the rate of LH secretion in the presence of bound receptor. There's no replenishment of releasable LH.</caption>
</informalfigure>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://ajpendo.physiology.org/cgi/content/abstract/275/6/E1061">A mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion</ulink>, K. Heinze, R. W. Keener, and A. R. Midgley, Jr., 1998, <ulink url="http://ajpendo.physiology.org/">
<emphasis>American Journal of Physiology</emphasis>
</ulink>, 275, E1061-E1071. (<ulink url="http://ajpendo.physiology.org/cgi/content/full/275/6/E1061">Full text</ulink> and <ulink url="http://ajpendo.physiology.org/cgi/reprint/275/6/E1061">PDF</ulink> versions of the article are available to journal subscribers on the <emphasis>American Journal of Physiology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=9843750&query_hl=1&itool=pubmed_docsum">PubMed ID: 9843750</ulink>
</para>
<para>
The CellML model presented here represents the second model. The other two models have also been coded in CellML and can be downloaded as version 1 and version 1 variant 2 of the model.
</para>
</sect1>
</article>
</documentation>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="GnRH">
<dc:title>GnRH</dc:title>
<dcterms:alternative>gonadotropin-releasing hormone</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="F">
<dc:title>F</dc:title>
<dcterms:alternative>free gonadotropin-releasing hormone receptor</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="F" initial_value="1.0"/>
<variable units="second_order_rate_constant" public_interface="in" name="kfb"/>
<variable units="first_order_rate_constant" public_interface="in" name="kdf"/>
<variable units="dimensionless" public_interface="in" name="D"/>
<variable units="nanomolar" public_interface="in" name="GnRH"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<bvar>
<ci>time</ci>
</bvar>
<ci> F </ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> kdf </ci>
<ci> D </ci>
</apply>
<apply>
<times/>
<ci> kfb </ci>
<ci> F </ci>
<ci> GnRH </ci>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="D">
<dc:title>D</dc:title>
<dcterms:alternative>desensitized gonadotropin-releasing hormone receptor</dcterms:alternative>
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<variable units="first_order_rate_constant" public_interface="in" name="kdf"/>
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<rdf:Description rdf:about="B">
<dc:title>B</dc:title>
<dcterms:alternative>bound gonadotropin-releasing hormone receptor</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<ci> GnRH </ci>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="R">
<dc:title>R</dc:title>
<dcterms:alternative>releasable luteinizing hormone</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="ng_ml" public_interface="out" name="R" initial_value="2115.0"/>
<variable units="first_order_rate_constant" public_interface="in" name="a1"/>
<variable units="first_order_rate_constant" public_interface="in" name="a2"/>
<variable units="dimensionless" public_interface="in" name="B"/>
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</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="C">
<dc:title>C</dc:title>
<dcterms:alternative>total (cumulative) amount of extracellular luteinizing hormone secreted</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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</component>
<component name="model_parameters">
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<variable units="first_order_rate_constant" public_interface="out" name="kdf" initial_value="2.52"/>
<variable units="first_order_rate_constant" public_interface="out" name="kbd" initial_value="9.91"/>
<variable units="first_order_rate_constant" public_interface="out" name="a1" initial_value="0.0328"/>
<variable units="first_order_rate_constant" public_interface="out" name="a2" initial_value="0.0830"/>
</component>
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</connection>
<connection>
<map_components component_2="environment" component_1="F"/>
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<connection>
<map_components component_2="environment" component_1="D"/>
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<connection>
<map_components component_2="GnRH" component_1="F"/>
<map_variables variable_2="GnRH" variable_1="GnRH"/>
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<connection>
<map_components component_2="model_parameters" component_1="F"/>
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<map_variables variable_2="kfb" variable_1="kfb"/>
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<map_components component_2="B" component_1="D"/>
<map_variables variable_2="B" variable_1="B"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="D"/>
<map_variables variable_2="kbd" variable_1="kbd"/>
<map_variables variable_2="kdf" variable_1="kdf"/>
</connection>
<connection>
<map_components component_2="B" component_1="F"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="GnRH" component_1="B"/>
<map_variables variable_2="GnRH" variable_1="GnRH"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="B"/>
<map_variables variable_2="kbd" variable_1="kbd"/>
<map_variables variable_2="kfb" variable_1="kfb"/>
</connection>
<connection>
<map_components component_2="B" component_1="R"/>
<map_variables variable_2="B" variable_1="B"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="R"/>
<map_variables variable_2="a1" variable_1="a1"/>
<map_variables variable_2="a2" variable_1="a2"/>
</connection>
<connection>
<map_components component_2="B" component_1="C"/>
<map_variables variable_2="B" variable_1="B"/>
</connection>
<connection>
<map_components component_2="R" component_1="C"/>
<map_variables variable_2="R" variable_1="R"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="C"/>
<map_variables variable_2="a1" variable_1="a1"/>
<map_variables variable_2="a2" variable_1="a2"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#7cd17e43-ae09-4a9a-a024-d75274fc48ca">
<rdf:li>luteinizing hormone</rdf:li>
<rdf:li>gonadotropin-releasing hormone</rdf:li>
<rdf:li>hypothalamus</rdf:li>
<rdf:li>pituitary</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#6215fcf7-5422-431b-8261-e181232d5ea7">
<rdf:li rdf:resource="rdf:#2280a9f8-6bb2-4b9f-a26c-fcf8e3069e4e"/>
<rdf:li rdf:resource="rdf:#49acaa8c-3b64-4fe8-9be0-a69b0511a7b5"/>
<rdf:li rdf:resource="rdf:#f0f2783c-d0c8-4969-9d1d-cf06f0f0b73d"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#1b4e0baa-0aa0-4c2e-bae0-1b647e6c001b">
<vCard:Given>A</vCard:Given>
<vCard:Family>Midgley</vCard:Family>
<vCard:Other>R</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c63dce83-1a99-43c0-b0dd-e95bf8f04a48">
<dcterms:W3CDTF>2007-07-20T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f0f2783c-d0c8-4969-9d1d-cf06f0f0b73d">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
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Heinze et al's 1998 mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion.
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