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 first model of self-renewing memory CD4+ T cell homeostasis in the absence 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 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.
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
$\frac{d x}{d \mathrm{time}}=2.0ry-ax(1.0-\frac{x}{\mathrm{kappa}})+\mathrm{d1}x\frac{x}{\mathrm{kappa}}$
$\frac{d y}{d \mathrm{time}}=ax(1.0-\frac{x}{\mathrm{kappa}})-(r+\mathrm{d2})y$
$\mathrm{d2}=\frac{-(99.0a\mathrm{d1})+ar+\mathrm{d1}r}{a-\mathrm{d1}}$
The Bioengineering InstituteThe University of AucklandCatherineLloydMayJaroslavStarkThis 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.17518516
Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.
5000.1100000xresting memory CD4+ T cellsAndrewYatesJamesLawsonRichard2007-06-26T00:00:00+00:00NigelKleinUnderstanding the slow depletion of memory CD4+ T cells in HIV infection (Model 1)The University of Auckland, Bioengineering Institutekeyword2008-09-02T13:34:09+12:002007-05-222007-09-17T17:06:32+12:00This is a CellML description of Yates et al.'s 2007 mathematical model of the slow depletion of memory CD4+ T cells in HIV infection.RustomAntiaRobinCallardhivcd4+ t cellimmunologyHIVimd2nologyCD4+ T cellcell cycleviral dynamicsPLoS Medicinec.lloyd@auckland.ac.nzUnderstanding the slow depletion of memory CD4+ T cells in HIV infection9559484Catherine LloydChecked the model in COR and PCEnv, corrected the units and used the author's original source code to get the model running.Catherine LloydCatherineLloydMayydividing CD4+ T cellsFixed error where 'd2' had somehow replaced 'mu' in 'multiplier' within the CellML and in the documentation.