Understanding the slow depletion of memory CD4+ T cells in HIV infection
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
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 second model of self-renewing memory CD4+ T cell homeostasis in the presence of HIV infection.
Model Structure
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.
model diagram
A simple model of self-renewing memory CD4+ T cell homeostasis which includes HIV infection. Activated dividing cells are infected with HIV at a rate proportional to the viral load which, in turn, is proportional to the infected cell count (Z), and an infectivity parameter (p) models the effciency of the infection process.
The original paper reference is cited below:
Understanding the slow depletion of memory CD4+ T cells in HIV infection, Andrew Yates, Jaroslav Stark, Nigel Klein, Rustom Antia, and Robin Callard, 2007, PLoS Medicine, volume 4, issue 5, 948-955. PubMed ID: 17518516
$\frac{d x}{d \mathrm{time}}=2.0ry-ax(1.0-\frac{x}{\mathrm{kappa}})+\mathrm{d1}x\frac{x}{\mathrm{kappa}}$
$\frac{d y}{d \mathrm{time}}=ax(1.0-\frac{x}{\mathrm{kappa}})-(r+\mathrm{d2})y+pzy\mathrm{d2}=\frac{-(99.0a\mathrm{d1})+ar+\mathrm{d1}r}{a-\mathrm{d1}}$
$\frac{d z}{d \mathrm{time}}=pzy-vz$
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.17518516Understanding the slow depletion of memory CD4+ T cells in HIV infection (Model 2)The University of Auckland, Bioengineering InstituteModel has been checked in COR and PCEnv. The units have been corrected and the equations fixed according to the author's original source code.Understanding the slow depletion of memory CD4+ T cells in HIV infection49489552007-05-22JamesLawsonRichard2008-09-02T13:36:14+12:00CatherineLloydMayc.lloyd@auckland.ac.nzimmunologyimd2nologyhivHIVcell cyclecd4+ t cellCD4+ T cellviral dynamicsPLoS Medicineydividing CD4+ T cells
Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.
keywordxresting memory CD4+ T cellsCatherineLloydMay500100002007-09-17T17:09:55+12:00NigelKleinzHIV-infected CD4+ T cellsThis is a CellML description of Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.The University of AucklandThe Bioengineering InstituteFixed error where 'd2' had somehow replaced 'mu' in 'multiplier' within the CellML and in the documentation.RustomAntia2007-06-26T00:00:00+00:00JaroslavStarkCatherine LloydRobinCallardCatherine LloydAndrewYates