<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : yates_model_2007.xml
CREATED : 10th December 2003
LAST MODIFIED : 10th December 2003
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 Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.
CHANGES:
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<title>Modelling the Slow Depletion of Memory CD4+ T Cells in HIV Infection</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
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<section id="sec_status">
<title>Model Status</title>
<para>
This CellML version of the model has been checked in COR and PCEnv. The units are consistent and the original source code was used to fix the CellML model such that it now runs to recreate the published results. This variant is a model of memory CD4+ T cell dynamics in HIV infection and includes both homeostatically activated, and antigen- or bystander-activated cells
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
This mathematical model of CD4+ T cell depletion in HIV infection has recently been used to investigate one potential mechanism for how HIV slowly weakens the body's immune system. HIV infection is characterised by the extensive depletion of CD4+ T cells. During the acute phase of the infection, the virus efficiently targets effector-memory CD4+ T cells. This depletion of memory CD4+ T cells continues, very slowly, during the chronic phase of the infection, resulting overall in a significant loss of CD4+ T cells.
</para>
<para>
It is not fully understood why the decline in peripheral CD4+ T cells during the chronic phase of the HIV infection is so slow. Since the virus preferentially infects activated cells, and the body's response to the virus and the T cell depletion is to in turn activate more T cells to respond and compensate, generating more target cells, the authors suggest that this produces a feedback loop that may cause the slow erosion of T cells. The authors refer to this theory of T cell activation, infection, HIV production, immune activation and homeostatic compensation as the <emphasis>runaway</emphasis> hypothesis. Using simple mathematical models of the dynamics of T cell homeostasis and proliferation Yates <emphasis>et al.</emphasis> demonstrate that the simplest formulation of this <emphasis>runaway</emphasis> mechanism is flawed, however. In particular, it is too fast, predicting that cells would die out in months, not years. In response, Yates <emphasis>et al.</emphasis> suggest several other possible mechanisms that could underlie the slow virus-induced CD4+ T cell depletion, and they capture the dynamics of these mechanisms in several, simple mathematical models. One possible explanation could be that the virus slowly evolves and adapts to evade the host immune system over the course of the infection.
</para>
<para>
The original publication contains three different mathematical models:
</para>
<itemizedlist>
<listitem>
<para>The first is a simple model of self-renewing memory CD4+ T cell homeostasis in the absence of HIV infection;</para>
</listitem>
<listitem>
<para>The second model is an extension of this, and includes a description of HIV infection;</para>
</listitem>
<listitem>
<para>And the final model of memory CD4+ T cell dynamics in HIV infection includes both homeostatically activated, and antigen- or bystander-activated cells.</para>
</listitem>
</itemizedlist>
<para>
The CellML model presented here represents the third, complete model of memory CD4+ T cell homeostasis which includes HIV infection and homeostatically and antigen- or bystander-activated cells, and it is summarised in the figure below. The other two models have also been coded in CellML and can be downloaded as version 1 and version 1 variant 1 of the model.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
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<title>model diagram</title>
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<caption>An extension of the model of memory CD4+ T cell dynamics in HIV infection to include both homeostatically activated (y) and antigen- or bystander-activated cells (w). Resting memory cells (x) can undergo homeostatic proliferation at a rate a they can be antigen- or bystander-activated at a rate a* and undergo fold expansion f in the process. These cells are infected with HIV at a rate pz, die at a rate gamma1, or return to resting memory state at a rate mu.</caption>
</informalfigure>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://medicine.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pmed.0040177">Understanding the slow depletion of memory CD4+ T cells in HIV infection</ulink>, Andrew Yates, Jaroslav Stark, Nigel Klein, Rustom Antia, and Robin Callard, 2007, <ulink url="http://medicine.plosjournals.org/perlserv/?request=index-html&issn=1549-1676">
<emphasis>PLoS Medicine</emphasis>
</ulink>, volume 4, issue 5, 948-955. (A <ulink url="http://medicine.plosjournals.org/archive/1549-1676/4/5/pdf/10.1371_journal.pmed.0040177-S.pdf">PDF</ulink> version of the article is available on the <emphasis>PLoS Medicine</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17518516&query_hl=1&itool=pubmed_docsum">PubMed ID: 17518516</ulink>
</para>
<para>
In addition, this study has been discussed in detail in a Perspectives article in <emphasis>PLoS Medicine</emphasis> by Rob J. De Boer: <ulink url="http://medicine.plosjournals.org/perlserv/?request=get-document&doi=10.1371%2Fjournal.pmed.0040193">Time Scales of CD4+ T Cell Depletion in HIV Infection</ulink>. A <ulink url="http://medicine.plosjournals.org/archive/1549-1676/4/5/pdf/10.1371_journal.pmed.0040193-S.pdf">PDF</ulink> version of the article is also available.
</para>
</sect1>
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Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.
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