- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-01-06 12:06:19+13:00
- Desc:
- Removed old version of the model. Also fixed RDF such that the metadata displays correctly, changed the link name to the model image, corrected the citation information to match the paper, and removed a redundant variable ("p") from nowak_1996a.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/nowak_bangham_1996/rawfile/54f6daaaef53eb31b27cb8f4cb660e8c76712f08/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 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:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="nowak_1996b" cmeta:id="nowak_1996b" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<!-- 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>Auckland 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. The units have been checked and they are consistent. This particular CellML model is the 2nd model out of the 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>Population dynamics of immune responses to persistent viruses, Nowak, MA and Bangham, CR, 1996, <emphasis>Science</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>Schematic diagram of a model for virus-CTL interaction.</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 -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description rdf:about="">
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Choi</vCard:Family>
<vCard:Given>Ethan</vCard:Given>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>mcho099@aucklanduni.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2009-12-22</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#nowak_1996b">
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<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>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>8600540</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Nowak</vCard:Family>
<vCard:Given>Martin</vCard:Given>
<vCard:Other>A</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Bangham</vCard:Family>
<vCard:Given>Charles</vCard:Given>
<vCard:Other>R</vCard:Other>
<vCard:Other>M</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
Population dynamics of immune responses to persistent viruses
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1996-04-05</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>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">
<simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:nodeID="n1"/>
</simulation>
</rdf:Description>
<rdf:Description rdf:nodeID="n1">
<boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:nodeID="n2"/>
</boundIntervals>
</rdf:Description>
<rdf:Description rdf:nodeID="n3">
<endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">10</endingValue>
<pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">10000</pointDensity>
</rdf:Description>
<rdf:Description rdf:nodeID="n2">
<rdf:first>
<rdf:Description rdf:nodeID="n3"/>
</rdf:first>
<rdf:rest>
<rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
</rdf:rest>
</rdf:Description>
</rdf:RDF>
</model>
