- Author:
- Ethan Choi <mcho099@aucklanduni.ac.nz>
- Date:
- 2010-01-05 10:01:29+13:00
- Desc:
- created model 2 from Nowak 1996.
The model runs in PCEnv and COR, however the model cannot be verified as the figures in the paper portray graphs that have variable parameters rather than the model itself.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/nowak_bangham_1996/rawfile/3306926d209adf36cc4c2e532f23e5c9f57d0646/nowak_1996b.cellml
<?xml version="1.0"?>
<!-- FILE : nowak_1996b.cellml
CREATED : 22th Dec 2009
LAST MODIFIED : 22th Dec 2009
AUTHOR : Ethan Choi
MODEL STATUS : This model conforms to the CellML 1.1 Specification. Runs in COR and PCEnv
DESCRIPTION : This file contains a CellML description of Nowak and Bangham's 1996 mathematical model for Population dynamics of immune responses to persistent viruses -->
<model name="nowak_1996b" cmeta:id="nowak_1996b" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<!-- documentation -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Population dynamics of immune responses to persistent viruses</title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This model has been built with the differential expressions in Nowak's 1996 paper for population dynamics of immune responses to persistent viruses and is known to run in PCEnv and COR. nowak_1996b is the 2nd model out of 3 outlined in the paper. The model cannot be verified as the paper figures portray graphs that cannot be rendered by PCEnv or COR due to the need for variable parameters, and also certain parameters are unspecified and left for the modeller to decide. Current parameterization portrays the interaction of uninfected cells x, infected cells y, free virus particles v, and CTL response z (model 2).</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>Abstract: Mathematical models, which are based on a firm understanding of biological interactions, can provide nonintuitive insights into the dynamics of host responses to infectious agents and can suggest new avenues for experimentation. Here, a simple mathematical approach is developed to explore the relation between antiviral immune responses, virus load, and virus diversity. The model results are compared to data on cytotoxic T cell responses and viral diversity in infections with the human T cell leukemia virus (HTLV-1) and the human immunodeficiency virus (HIV-1).</para>
<para>A Model for Circadian Rhythms in Drosophila Incorporating the Formation of a Complex between the PER and TIM Proteins, Leloup JC, Goldbeter A, 1998, <emphasis>Journal of Biological Rhythms</emphasis>, 272, 74-79 <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/8600540">PubMed ID: 8600540</ulink>
</para>
<informalfigure float="0" id="______">
<mediaobject>
<imageobject>
<objectinfo>
<title>Model Diagram</title>
</objectinfo>
<imagedata fileref="Nowak_1996.png"/>
</imageobject>
</mediaobject>
<caption>Image caption/description</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!-- units -->
<units name="day">
<unit multiplier="86400" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="day"/>
</units>
<!-- components -->
<component name="environment">
<variable name="time" public_interface="out" units="day"/>
</component>
<component name="uninfected" cmeta:id="uninfected">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#uninfected">This component stores information related to the uninfected cell population</rdf:Description>
<rdf:Description rdf:about="#x">uninfected cells</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="lambda" initial_value="1" units="first_order_rate_constant"/>
<variable name="d" initial_value="0.01" units="first_order_rate_constant"/>
<variable name="beta" public_interface="in" units="first_order_rate_constant"/>
<variable name="v" public_interface="in" units="dimensionless"/>
<variable name="x" cmeta:id="x" initial_value="100" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>lambda</ci>
<apply>
<times/>
<ci>d</ci>
<ci>x</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta</ci>
<ci>x</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="infected" cmeta:id="infected">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#infected">This component stores information related to the infected cell population</rdf:Description>
<rdf:Description rdf:about="#y">infected cells</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="beta" initial_value="0.02" public_interface="out" units="first_order_rate_constant"/>
<variable name="a" initial_value="0.5" units="first_order_rate_constant"/>
<variable name="p" initial_value="1" units="first_order_rate_constant"/>
<variable name="x" public_interface="in" units="dimensionless"/>
<variable name="v" public_interface="in" units="dimensionless"/>
<variable name="z" public_interface="in" units="dimensionless"/>
<variable name="y" cmeta:id="y" initial_value="0" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta</ci>
<ci>x</ci>
<ci>v</ci>
</apply>
<apply>
<times/>
<ci>a</ci>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<ci>p</ci>
<ci>y</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="virus" cmeta:id="virus">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#virus">This component stores information related to the population of free virus particles</rdf:Description>
<rdf:Description rdf:about="#v">free virus particles</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="k" initial_value="1" units="first_order_rate_constant"/>
<variable name="u" initial_value="1" units="first_order_rate_constant"/>
<variable name="y" public_interface="in" units="dimensionless"/>
<variable name="v" cmeta:id="v" initial_value="10" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k</ci>
<ci>y</ci>
</apply>
<apply>
<times/>
<ci>u</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CTL" cmeta:id="CTL">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#CTL">This component stores information related to the virus specific cytotoxic T lymphocytes (CTLs)</rdf:Description>
<rdf:Description rdf:about="#z">magnitude of the CTL response</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="c" initial_value="1" units="first_order_rate_constant"/>
<variable name="b" initial_value="0.05" units="first_order_rate_constant"/>
<variable name="y" public_interface="in" units="dimensionless"/>
<variable name="z" cmeta:id="z" initial_value="1" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>c</ci>
<ci>y</ci>
<ci>z</ci>
</apply>
<apply>
<times/>
<ci>b</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- connections -->
<connection>
<map_components component_1="environment" component_2="uninfected"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="infected"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="virus"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="CTL"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="uninfected" component_2="virus"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<connection>
<map_components component_1="infected" component_2="uninfected"/>
<map_variables variable_1="x" variable_2="x"/>
<map_variables variable_1="beta" variable_2="beta"/>
</connection>
<connection>
<map_components component_1="infected" component_2="virus"/>
<map_variables variable_1="v" variable_2="v"/>
<map_variables variable_1="y" variable_2="y"/>
</connection>
<connection>
<map_components component_1="infected" component_2="CTL"/>
<map_variables variable_1="z" variable_2="z"/>
<map_variables variable_1="y" variable_2="y"/>
</connection>
<!-- metadata -->
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<rdf:Description rdf:about="">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Choi</vCard:Family>
<vCard:Given>Ethan</vCard:Given>
</vCard:N>
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<rdf:value>mcho099@aucklanduni.ac.nz</rdf:value>
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</vCard:EMAIL>
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
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<dcterms:W3CDTF>2009-12-22</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#mpwal_1996b">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Population dynamics of immune responses to persistent viruses</dc:title>
<cmeta:comment rdf:parseType="Resource">
<rdf:value>This is the CellML description of Nowak and Bangham's 1996 mathematical model (model 2) for population dynamics of immune responses to persistent viruses.</rdf:value>
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Ethan Choi</vCard:FN>
</dc:creator>
</cmeta:comment>
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<dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<rdf:value>
<rdf:li>Immunology </rdf:li>
<rdf:li>antiviral immune response</rdf:li>
<rdf:li>virus load</rdf:li>
<rdf:li>viral diversity</rdf:li>
<rdf:li>mutation</rdf:li>
<rdf:li>CTL</rdf:li>
<rdf:li>HTLV-1</rdf:li>
<rdf:li>HIV-1</rdf:li>
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<vCard:Given>Martin</vCard:Given>
<vCard:Other>A.</vCard:Other>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Population dynamics of immune responses to persistent viruses</dc:title>
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<dcterms:W3CDTF>1996-04-05</dcterms:W3CDTF>
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<bqs:Journal rdf:parseType="Resource">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Science</dc:title>
</bqs:Journal>
<bqs:volume>272</bqs:volume>
<bqs:first_page>74</bqs:first_page>
<bqs:last_page>79</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!-- PCEnv specific metadata -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#nowak_1996b">
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</model>
