Yates, Stark, Klein, Antia, Callard, 2007

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. This variant is a simple model of self-renewing memory CD4+ T cell homeostasis in the absence of HIV infection.

Model Structure

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.

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 runaway hypothesis. Using simple mathematical models of the dynamics of T cell homeostasis and proliferation Yates et al. demonstrate that the simplest formulation of this runaway mechanism is flawed, however. In particular, it is too fast, predicting that cells would die out in months, not years. In response, Yates et al. 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.

The original publication contains three different mathematical models:

  • The first is a simple model of self-renewing memory CD4+ T cell homeostasis in the absence of HIV infection;

  • The second model is an extension of this, and includes a description of HIV infection;

  • And the final model of memory CD4+ T cell dynamics in HIV infection includes both homeostatically activated, and antigen- or bystander-activated cells.

The CellML model presented here represents the first model of memory CD4+ T cell homeostasis (in the absence of HIV infection), and is summarised in the figure below. The other two models have also been coded in CellML and can be downloaded as version 1 variants 1 and 2 of the model.

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 complete 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. (A PDF version of the article is available on the PLoS Medicine website.) PubMed ID: 17518516

In addition, this study has been discussed in detail in a Perspectives article in PLoS Medicine by Rob J. De Boer: Time Scales of CD4+ T Cell Depletion in HIV Infection. A PDF version of the article is also available.