<?xml version="1.0"?>
<!-- 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>Understanding the slow depletion of memory CD4+ T cells in HIV infection</title>
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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. The original paper contains three different mathematical models and this particular CellML model represents the first model of self-renewing memory CD4+ T cell homeostasis in the absence of HIV infection.
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ABSTRACT: BACKGROUND: The asymptomatic phase of HIV infection is characterised by a slow decline of peripheral blood CD4(+) T cells. Why this decline is slow is not understood. One potential explanation is that the low average rate of homeostatic proliferation or immune activation dictates the pace of a "runaway" decline of memory CD4(+) T cells, in which activation drives infection, higher viral loads, more recruitment of cells into an activated state, and further infection events. We explore this hypothesis using mathematical models. METHODS AND FINDINGS: Using simple mathematical models of the dynamics of T cell homeostasis and proliferation, we find that this mechanism fails to explain the time scale of CD4(+) memory T cell loss. Instead it predicts the rapid attainment of a stable set point, so other mechanisms must be invoked to explain the slow decline in CD4(+) cells. CONCLUSIONS: A runaway cycle in which elevated CD4(+) T cell activation and proliferation drive HIV production and vice versa cannot explain the pace of depletion during chronic HIV infection. We summarize some alternative mechanisms by which the CD4(+) memory T cell homeostatic set point might slowly diminish. While none are mutually exclusive, the phenomenon of viral rebound, in which interruption of antiretroviral therapy causes a rapid return to pretreatment viral load and T cell counts, supports the model of virus adaptation as a major force driving depletion.
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<caption>A simple model of self-renewing memory CD4+ T cell homeostasis in the absence of HIV infection, with density-dependent rates of division (a and r), and death of resting cells (delta). d2 represents the rate of death of the dividing cells.</caption>
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<para>
The original paper reference is cited below:
</para>
<para>
Understanding the slow depletion of memory CD4+ T cells in HIV infection, Andrew Yates, Jaroslav Stark, Nigel Klein, Rustom Antia, and Robin Callard, 2007, <emphasis>PLoS Medicine</emphasis>, volume 4, issue 5, 948-955. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/17518516">PubMed ID: 17518516</ulink></para>
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Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.
</title><cmeta:comment><rdf:Description rdf:about="rdf:#733b907a-a2a2-4cbe-8637-d79873b3a762"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#f8aac214-79b5-4d71-9dee-b818504baee3"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Callard</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Robin</Given></rdf:Description><rdf:Description rdf:about="rdf:#a4cd6f17-2513-4684-af3b-f8f95025a584"><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#44cb3720-36a5-4fcb-bb66-b8ef1d12e18f"/></N></rdf:Description><rdf:Description rdf:about="rdf:#81fcdf29-28d4-4418-88e3-8a2577259a35"><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type><rdf:value xml:lang="en">c.lloyd@auckland.ac.nz</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#1d3ca92e-37ad-4dae-a0f8-25929b5e95d8"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type><rdf:_2><rdf:Description rdf:about="rdf:#9ed65789-1534-4b7f-8f5d-7ba0c254a232"/></rdf:_2><rdf:_5><rdf:Description rdf:about="rdf:#a3a2a133-0b9f-43b4-b016-f14d6b8fa9fa"/></rdf:_5><rdf:_1><rdf:Description rdf:about="rdf:#a4cd6f17-2513-4684-af3b-f8f95025a584"/></rdf:_1><rdf:_4><rdf:Description rdf:about="rdf:#95857dcc-9eff-4949-a326-d421b58abf33"/></rdf:_4><rdf:_3><rdf:Description rdf:about="rdf:#652cf41f-fa6a-4e50-80f3-0334a36b3bae"/></rdf:_3></rdf:Description><rdf:Description rdf:about="rdf:#982e8416-5826-4112-9dfe-ea0c525f0dfd"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-06-26T00:00:00+00:00</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#5dde4c38-d317-40be-a531-bfc54a9227b0"><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#cd28487e-fc1f-40a7-9a66-aeaa5f12b410"/></ORG><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#81fcdf29-28d4-4418-88e3-8a2577259a35"/></EMAIL><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#7eed3897-3e5e-417b-96e6-f82e7e2be5e3"/></N></rdf:Description><rdf:Description rdf:about="rdf:#1472577d-da63-41ff-afe3-5b4e1d598199"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">17518516</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#f215639c-9a6d-440c-84cb-6b6cbbb6677a"/></JournalArticle></rdf:Description><rdf:Description rdf:about="rdf:#bb4d98c2-4389-4097-8456-807289e59fb5"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="rdf:#74c191d5-df1a-4aae-8d4a-e748d3b6685d"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lawson</Family><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Richard</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">James</Given></rdf:Description><rdf:Description rdf:about="rdf:#ea5eea5c-1851-4d7b-bc10-288bb9782023"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-09-17T17:06:32+12:00</W3CDTF></rdf:Description><rdf:Description rdf:about="x"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">resting memory CD4+ T cells</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">x</title></rdf:Description><rdf:Description rdf:about="rdf:#9ed65789-1534-4b7f-8f5d-7ba0c254a232"><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#6fb109b7-79ce-49a3-a5f7-1083f2d4cdcd"/></N></rdf:Description><rdf:Description rdf:about="rdf:#59f268dc-70fe-4d69-a01f-b824efe25bf5"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Antia</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Rustom</Given></rdf:Description><rdf:Description rdf:nodeID="n3"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n1"/></boundIntervals></rdf:Description><rdf:Description rdf:about="rdf:#f538febf-2c10-45f2-bffd-17bf54850981"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">PLoS Medicine</title></rdf:Description><rdf:Description rdf:about="rdf:#cd28487e-fc1f-40a7-9a66-aeaa5f12b410"><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The Bioengineering Institute</Orgunit><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname></rdf:Description><rdf:Description rdf:about="rdf:#d5ac2592-bb6f-4c4d-b15a-60270ffd0b93"><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#a832aa07-24f2-4942-8103-35ee88329f34"/></creator><rdf:value xml:lang="en">This CellML file has been checked in COR and PCEnv. The units are consistent and the model runs to give the published results. However, by using the author's original source code it does mean this model now slightly varies from the published version.</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#c6cd5fad-3cdd-485e-8b40-2c11ddd7a975"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#ac3cb885-f91c-43ec-97ed-53402a1bec94"/></subject></rdf:Description><rdf:Description rdf:about="rdf:#a65956ea-caa9-4270-8219-7ec680fdd3e0"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given></rdf:Description><rdf:Description rdf:about="rdf:#701c754d-e4ad-4093-aad9-15d5f46d3d8d"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#a65956ea-caa9-4270-8219-7ec680fdd3e0"/></N></rdf:Description><rdf:Description rdf:about="rdf:#aa80bb34-4fca-4257-bf19-c5c2e7b6b101"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_8 xml:lang="en">viral dynamics</rdf:_8><rdf:_7 xml:lang="en">cell cycle</rdf:_7><rdf:_6 xml:lang="en">CD4+ T cell</rdf:_6><rdf:_2 xml:lang="en">hiv</rdf:_2><rdf:_5 xml:lang="en">imd2nology</rdf:_5><rdf:_1 xml:lang="en">immunology</rdf:_1><rdf:_4 xml:lang="en">cd4+ t cell</rdf:_4><rdf:_3 xml:lang="en">HIV</rdf:_3></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#5dde4c38-d317-40be-a531-bfc54a9227b0"/></creator><cmeta:modification><rdf:Description rdf:about="rdf:#65b61c60-a1ea-4efa-bdb7-babc13f1dc96"/></cmeta:modification><cmeta:modification><rdf:Description rdf:about="rdf:#04eca01e-25c5-41fd-81f8-cb22897aa487"/></cmeta:modification><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#982e8416-5826-4112-9dfe-ea0c525f0dfd"/></created><publisher xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">The University of Auckland, Bioengineering Institute</publisher><cmeta:comment><rdf:Description rdf:about="rdf:#d5ac2592-bb6f-4c4d-b15a-60270ffd0b93"/></cmeta:comment></rdf:Description><rdf:Description rdf:nodeID="n2"><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">600</endingValue></rdf:Description><rdf:Description rdf:about="rdf:#65b61c60-a1ea-4efa-bdb7-babc13f1dc96"><cmeta:modifier><rdf:Description rdf:about="rdf:#ad6e8b47-e1a9-46ab-86fe-82556ed7c1ff"/></cmeta:modifier><modified xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#10c4eb30-78d7-4991-a0cd-a0cb9d42061a"/></modified><rdf:value xml:lang="en">Fixed error where 'd2' had somehow replaced 'mu' in 'multiplier' within the CellML and in the documentation.</rdf:value></rdf:Description></rdf:RDF></model>
