- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:32:09+12:00
- Desc:
- committing version01 of kesmir_deboer_1999
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/kesmir_deboer_1999/rawfile/11b77e367d0e516a8c2fbf273eca2d7b9fe79541/kesmir_deboer_1999.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : kesmir_model_1999.xml
CREATED : 4th December 2003
LAST MODIFIED : 4th December 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Kesmir and De Boer's 1999 mathematical model on germinal centre kinetics and termination.
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="kesmir_deboer_1999_version01" name="kesmir_deboer_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Kinetics of Germinal Centre Reactions</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>
Affinity maturation during the humoral immune response to T cell-dependent Ag occurs in germinal centres (GCs). GCs are highly dynamic areas where B lymphocytes rapidly divide and somatic cells mutate and are selected for. Ag is stored in the form of immune complexes on follicular dendritic cells. Ag is the main selective agent during a GC reaction as mutated B cells have to bind Ag to avoid apoptosis. Following this AG-based selection of B cells, the B cells have to interact with the GC T cells in order to improve their chance of survival.
</para>
<para>
In this current study, Kesmir and De Boer extend previous mathematical models of GC reactions by including:
<itemizedlist>
<listitem>
<para>the cell division history of the centroblasts;</para>
</listitem>
<listitem>
<para>the Ag uptake by centrocytes; and</para>
</listitem>
<listitem>
<para>T cell dynamics.</para>
</listitem>
</itemizedlist>
Focusing on GC kinetics, rather than affinity maturation, the authors show that:
<itemizedlist>
<listitem>
<para>the main effect of T cells on GC kinetics is confined to the early stages of the GC reaction;</para>
</listitem>
<listitem>
<para>the duration of the reaction is largely determined by Ag availability and only slightly by the availability of T cell help; and</para>
</listitem>
<listitem>
<para>both the Ag concentration and the half-life of the immune complexes have a negligible effect on the GC kinetics.</para>
</listitem>
</itemizedlist>
A schematic of the model can be seen in <xref linkend="fig_cell_diagram"/> below.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.jimmunol.org/cgi/content/abstract/163/5/2463">A Mathematical Model on Germinal Center Kinetics and Termination</ulink>, Can Kesmir and Rob J. De Boer, 1999, <ulink url="http://www.jimmunol.org/">
<emphasis>The Journal of Immunology</emphasis>
</ulink>, 163, 2463-2469. (<ulink url="http://www.jimmunol.org/cgi/content/full/163/5/2463">Full text (HTML)</ulink> and <ulink url="http://www.jimmunol.org/cgi/reprint/163/5/2463.pdf">PDF</ulink> versions of the article are available on the <emphasis>The Journal of Immunology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10452981&dopt=Abstract">PubMed ID: 10452981</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="kesmir_1999.png"/>
</imageobject>
</mediaobject>
<caption>The model GC reaction.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units base_units="yes" name="cells_per_GC"/>
<units name="day">
<unit units="second" exponent="-1" multiplier="86400.0"/>
</units>
<units name="first_order_rate_constant">
<unit units="day" exponent="-1"/>
</units>
<component name="environment">
<variable units="day" public_interface="out" name="time"/>
</component>
<component cmeta:id="B0" name="B0">
<rdf:RDF>
<rdf:Description rdf:about="B0">
<dc:title>B0</dc:title>
<dcterms:alternative>centroblast 0 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B0" initial_value="3.0"/>
<variable units="dimensionless" public_interface="in" name="pr"/>
<variable units="first_order_rate_constant" public_interface="in" name="mu"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="CT_"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B0</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> pr </ci>
<ci> mu </ci>
<ci> CT_ </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B0 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B0 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B1" name="B1">
<rdf:RDF>
<rdf:Description rdf:about="B1">
<dc:title>B1</dc:title>
<dcterms:alternative>centroblast 1 division</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B1"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B0"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B0</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B1 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B1 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B2" name="B2">
<rdf:RDF>
<rdf:Description rdf:about="B2">
<dc:title>B2</dc:title>
<dcterms:alternative>centroblast 2 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B2"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B1"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B2 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B2 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B3" name="B3">
<rdf:RDF>
<rdf:Description rdf:about="B3">
<dc:title>B3</dc:title>
<dcterms:alternative>centroblast 3 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B3"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B2"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B3</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B2</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B3 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B3 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B4" name="B4">
<rdf:RDF>
<rdf:Description rdf:about="B4">
<dc:title>B4</dc:title>
<dcterms:alternative>centroblast 4 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B4"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B3"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B4</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B3</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B4 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B4 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B5" name="B5">
<rdf:RDF>
<rdf:Description rdf:about="B5">
<dc:title>B5</dc:title>
<dcterms:alternative>centroblast 5 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B5"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B4"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B5</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B4</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B5 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B5 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B6" name="B6">
<rdf:RDF>
<rdf:Description rdf:about="B6">
<dc:title>B6</dc:title>
<dcterms:alternative>centroblast 6 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B6"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B5"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B6</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B5</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B6 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B6 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="B7" name="B7">
<rdf:RDF>
<rdf:Description rdf:about="B7">
<dc:title>B7</dc:title>
<dcterms:alternative>centroblast 7 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B7"/>
<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
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<variable units="cells_per_GC" public_interface="in" name="B6"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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</bvar>
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<times/>
<ci> rho </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
</apply>
<ci>B6</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> rho </ci>
<ci> B7 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B7 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF>
<rdf:Description rdf:about="B8">
<dc:title>B8</dc:title>
<dcterms:alternative>centroblast 8 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B8"/>
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<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
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<variable units="cells_per_GC" public_interface="in" name="B7"/>
<variable units="day" public_interface="in" name="time"/>
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<ci> alpha_B </ci>
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<ci> B8 </ci>
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</math>
</component>
<component cmeta:id="B9" name="B9">
<rdf:RDF>
<rdf:Description rdf:about="B9">
<dc:title>B9</dc:title>
<dcterms:alternative>centroblast 9 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="B9"/>
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<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
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<ci> rho </ci>
<apply>
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<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
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<ci>B8</ci>
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<times/>
<ci> rho </ci>
<ci> B9 </ci>
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<apply>
<times/>
<ci> delta_B </ci>
<ci> B9 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
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<rdf:RDF>
<rdf:Description rdf:about="B10">
<dc:title>B10</dc:title>
<dcterms:alternative>centroblast 10 divisions</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<variable units="dimensionless" public_interface="in" name="alpha_B"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta_B"/>
<variable units="cells_per_GC" public_interface="in" name="B9"/>
<variable units="day" public_interface="in" name="time"/>
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</bvar>
<ci>B10</ci>
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<times/>
<ci> rho </ci>
<apply>
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<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> alpha_B </ci>
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<ci>B9</ci>
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<ci> rho </ci>
<ci> B10 </ci>
</apply>
<apply>
<times/>
<ci> delta_B </ci>
<ci> B10 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C" name="C">
<rdf:RDF>
<rdf:Description rdf:about="C">
<dc:title>C</dc:title>
<dcterms:alternative>centrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="C"/>
<variable units="first_order_rate_constant" name="d" initial_value="2.0"/>
<variable units="first_order_rate_constant" public_interface="in" name="rho"/>
<variable units="first_order_rate_constant" public_interface="in" name="mu"/>
<variable units="cells_per_GC" public_interface="in" name="B10"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<diff/>
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<ci>time</ci>
</bvar>
<ci>C</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> d </ci>
<ci> rho </ci>
<ci> B10 </ci>
</apply>
<apply>
<times/>
<ci> mu </ci>
<ci> C </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="C_" name="C_">
<rdf:RDF>
<rdf:Description rdf:about="C_">
<dc:title>C_</dc:title>
<dcterms:alternative>Ag-bound centrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="C_"/>
<variable units="first_order_rate_constant" public_interface="in" name="mu"/>
<variable units="cells_per_GC" public_interface="in" name="CA"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
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<bvar>
<ci>time</ci>
</bvar>
<ci>C_</ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> mu </ci>
<ci> CA </ci>
</apply>
<apply>
<times/>
<ci> mu </ci>
<ci> C_ </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="M" name="M">
<rdf:RDF>
<rdf:Description rdf:about="M">
<dc:title>M</dc:title>
<dcterms:alternative>memory or Ab forming cell compartment</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_GC" public_interface="out" name="M"/>
<variable units="dimensionless" public_interface="in" name="pr"/>
<variable units="first_order_rate_constant" public_interface="in" name="mu"/>
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A Mathematical Model on Germinal Center Kinetics and Termination
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The University of Auckland, Bioengineering Institute
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Kesmir and De Boer's 1999 mathematical model on germinal centre kinetics and termination.
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<rdf:Description rdf:about="rdf:#508153de-b5bc-4746-baa7-f388ef43281b">
<vCard:ORG rdf:resource="rdf:#ff0d6dfd-8bac-4bcc-a629-4dabcccb78a7"/>
<vCard:EMAIL rdf:resource="rdf:#ec5e29db-8266-4606-a210-756845598a5c"/>
<vCard:N rdf:resource="rdf:#0888c0ce-7b6a-4635-b52d-55e7e8dc2f4c"/>
</rdf:Description>
</rdf:RDF>
</model>
