- Author:
- Ethan Choi <mcho099@aucklanduni.ac.nz>
- Date:
- 2010-02-17 11:56:07+13:00
- Desc:
- misuse of boolean operators on the f_function equation replaced with piecewise function.
- Permanent Source URI:
- http://models.cellml.org/workspace/rong_perelson_2009/rawfile/2ae52265aff215318d9b72fa23bff46467aff29f/rong_2009b.cellml
<?xml version="1.0"?>
<!-- FILE : rong_2009b.cellml
CREATED : 4th Feb 2010
LAST MODIFIED : 15th Feb 2010
AUTHOR : Ethan Choi
MODEL STATUS : This model conforms to the CellML 1.1 Specification. Runs in OpenCell
DESCRIPTION : This file contains a CellML description of Rong's 2009 mathematical model-->
<model name="rong_2009b" cmeta:id="rong_2009b" 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#" 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>Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy.</title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This CellML model has been built with the differential expressions in Rong and Perelson's 2009 paper for the model with programmed expansion and contraction of latently infected cells upon activation using equation set 4 from the paper (rong_2009b). This file is known to run in OpenCell and COR, and is set to the parameters in Table 1 and figure 3 in the paper. The model requires the use of a Normal and Uniform distribution on the variable f (causing it to occasionally spike randomly), but this feature has not been implemented in this CellML model (since we are still waiting for the publication of the 1.2 specification) and therefore we may need to return to this model later. Instead of a normal distribution, f has been manually set to spike from T_on (at day 50) to T_off only once to replicate one spike, and used to compare against the diagrams in the paper (figure 3) which it has replicated.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: Although potent combination therapy is usually able to suppress plasma viral loads in HIV-1 patients to below the detection limit of conventional clinical assays, a low level of viremia frequently can be detected in plasma by more sensitive assays. Additionally, many patients experience transient episodes of viremia above the detection limit, termed viral blips, even after being on highly suppressive therapy for many years. An obstacle to viral eradication is the persistence of a latent reservoir for HIV-1 in resting memory CD4(+) T cells. The mechanisms underlying low viral load persistence, slow decay of the latent reservoir, and intermittent viral blips are not fully characterized. The quantitative contributions of residual viral replication to viral and the latent reservoir persistence remain unclear. In this paper, we probe these issues by developing a mathematical model that considers latently infected cell activation in response to stochastic antigenic stimulation. We demonstrate that programmed expansion and contraction of latently infected cells upon immune activation can generate both low-level persistent viremia and intermittent viral blips. Also, a small fraction of activated T cells revert to latency, providing a potential to replenish the latent reservoir. By this means, occasional activation of latently infected cells can explain the variable decay characteristics of the latent reservoir observed in different clinical studies. Finally, we propose a phenomenological model that includes a logistic term representing homeostatic proliferation of latently infected cells. The model is simple but can robustly generate the multiphasic viral decline seen after initiation of therapy, as well as low-level persistent viremia and intermittent HIV-1 blips. Using these models, we provide a quantitative and integrated prospective into the long-term dynamics of HIV-1 and the latent reservoir in the setting of potent antiretroviral therapy.</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="rong_2009.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model.</caption>
</informalfigure>
<para>The original paper reference is cited below:</para>
<para>Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy, Rong L, Perelson A, 2009, <emphasis>PLoS Computational Biology</emphasis>, 5(issue 10): e1000533. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/19834532">PubMed ID: 19834532</ulink></para>
</sect1>
</article>
</documentation>
<!-- units -->
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<units name="per_day">
<unit exponent="-1" units="day"/>
</units>
<units name="ml">
<unit prefix="milli" units="litre"/>
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<unit exponent="-1" units="day"/>
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<!-- components -->
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<rdf:Description rdf:about="#uninfected">This component relates to the uninfected CD4+ T cell dynamics</rdf:Description>
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</rdf:RDF>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#latently_infected">This component relates to the latently infected CD4+ cell dynamics</rdf:Description>
<rdf:Description rdf:about="#L_0">Latently infected cells that cannot produce virus but are ready to do so once activated by antigens</rdf:Description>
</rdf:RDF>
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<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>eta</ci>
<apply>
<minus/>
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<ci>efficacy</ci>
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<ci>k</ci>
<ci>V</ci>
<ci>T</ci>
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<ci>d_0</ci>
<ci>L_0</ci>
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<times/>
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<ci>L_0</ci>
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<apply>
<times/>
<apply>
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<ci>f</ci>
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<ci>rho</ci>
<ci>L_a</ci>
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<rdf:Description rdf:about="#activated">This component relates to the latently infected CD4+ cell dynamics</rdf:Description>
<rdf:Description rdf:about="#f">f determines the times at which antigen is present at concentration sufficiently high to activate cells.</rdf:Description>
<rdf:Description rdf:about="#L_a">activated cells that undergo programmed clonal expansion and contraction.</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="a" public_interface="in" units="per_day"/>
<variable name="L_0" public_interface="in" units="per_ml"/>
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<variable name="rho" public_interface="in" units="per_day"/>
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<variable name="T_off" initial_value="54" units="day"/>
<variable name="T_on" initial_value="50" units="day"/>
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<eq/>
<ci>f</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>T_off</ci>
<ci>time</ci>
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<apply>
<lt/>
<ci>time</ci>
<ci>T_on</ci>
</apply>
</piece>
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<rdf:Description rdf:about="#productively_infected">This component relates to the productively infected cells' dynamics</rdf:Description>
<rdf:Description rdf:about="#T_star">productively infected cells that can produce virus particles (T* in the paper).</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="eta" public_interface="in" units="dimensionless"/>
<variable name="efficacy" public_interface="in" units="dimensionless"/>
<variable name="k" public_interface="in" units="ml_per_day"/>
<variable name="V" public_interface="in" units="per_ml"/>
<variable name="T" public_interface="in" units="per_ml"/>
<variable name="delta" initial_value="1" units="per_day"/>
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<variable name="T_star" cmeta:id="T_star" initial_value="0.3" public_interface="out" units="per_ml"/>
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<ci>T_star</ci>
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<plus/>
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<times/>
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<minus/>
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<ci>eta</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>efficacy</ci>
</apply>
<ci>k</ci>
<ci>V</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
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<ci>delta</ci>
<ci>T_star</ci>
<ci>T_star</ci>
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</apply>
<apply>
<times/>
<ci>a_L</ci>
<ci>L_a</ci>
</apply>
</apply>
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</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#viral_load">This component relates to the HIV population size</rdf:Description>
<rdf:Description rdf:about="#V">total viral load.</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable name="p_v" initial_value="2000" units="per_day"/>
<variable name="T_star" public_interface="in" units="per_ml"/>
<variable name="c" initial_value="23" units="per_day"/>
<variable name="V" cmeta:id="V" initial_value="50" public_interface="out" units="per_ml"/>
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<ci>p_v</ci>
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<apply>
<times/>
<ci>c</ci>
<ci>V</ci>
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</apply>
</apply>
</math>
</component>
<component name="drug_efficacy" cmeta:id="drug_efficacy">
<variable name="efficacy" cmeta:id="efficacy" initial_value="0.85" public_interface="out" units="dimensionless"/>
</component>
<!-- connections -->
<connection>
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<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="latently_infected"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="activated"/>
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</connection>
<connection>
<map_components component_1="environment" component_2="productively_infected"/>
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</connection>
<connection>
<map_components component_1="environment" component_2="viral_load"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="uninfected" component_2="latently_infected"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="k" variable_2="k"/>
</connection>
<connection>
<map_components component_1="uninfected" component_2="productively_infected"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="k" variable_2="k"/>
</connection>
<connection>
<map_components component_1="uninfected" component_2="viral_load"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="latently_infected" component_2="viral_load"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="productively_infected" component_2="viral_load"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="T_star" variable_2="T_star"/>
</connection>
<connection>
<map_components component_1="latently_infected" component_2="activated"/>
<map_variables variable_1="L_0" variable_2="L_0"/>
<map_variables variable_1="a" variable_2="a"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="L_a" variable_2="L_a"/>
<map_variables variable_1="f" variable_2="f"/>
</connection>
<connection>
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<map_variables variable_1="eta" variable_2="eta"/>
</connection>
<connection>
<map_components component_1="activated" component_2="productively_infected"/>
<map_variables variable_1="L_a" variable_2="L_a"/>
<map_variables variable_1="a_L" variable_2="a_L"/>
</connection>
<connection>
<map_components component_1="drug_efficacy" component_2="uninfected"/>
<map_variables variable_1="efficacy" variable_2="efficacy"/>
</connection>
<connection>
<map_components component_1="drug_efficacy" component_2="latently_infected"/>
<map_variables variable_1="efficacy" variable_2="efficacy"/>
</connection>
<connection>
<map_components component_1="drug_efficacy" component_2="productively_infected"/>
<map_variables variable_1="efficacy" variable_2="efficacy"/>
</connection>
<!-- metadata -->
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy</dc:title>
<cmeta:comment rdf:parseType="Resource">
<rdf:value>This is the CellML description of Rong and Perelson's 2009 mathematical model for latently infected cell activation in HIV-infected patients on potent therapy</rdf:value>
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<cmeta:bio_entity>CD4+ T cell</cmeta:bio_entity>
<!-- Keywords -->
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<rdf:li>dynamics</rdf:li>
<rdf:li>HAART</rdf:li>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy</dc:title>
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<dcterms:W3CDTF>2009-10-16</dcterms:W3CDTF>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">PLoS Computation Biology</dc:title>
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<bqs:first_page>1</bqs:first_page>
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<!-- OpenCell metadata -->
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<rdf:Description rdf:nodeID="n3">
<endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">300</endingValue>
<pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">100000</pointDensity>
</rdf:Description>
</rdf:RDF>
</model>
