Dynamics of HIV infection of CD4+ T cells
Ethan
Choi
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model has been built with the differential expressions in Perelson, Kirschner and de Boer's 1993 paper for the 3rd model (perelson_1993c); where the administration (at time tau) of azidothymidine (AZT) is modeled via blocking viral replication (N) on the initial perelson_1993b model (decaying s_V). This file is known to run in OpenCell and COR, and is set to the parameters in Table 1 of the paper. By changing the the parameters, the model will replicate all panels in figures 12. Note that in the paper, some figure diagrams are scaled logarithmically.
Model Structure
ABSTRACT: We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors. The latter gives more realistic predictions than the model with a constant source.
model diagram
Schematic diagram of the model.
The original paper reference is cited below:
Dynamics of HIV infection of CD4+ T cells, Perelson, Kirschner, Boer, Mathematical Biosciences, 114, 81-125. PubMed ID: 8096155
This component relates to the uninfected CD4+ T cell dynamics
Uninfected CD4+ T cell population size
rate of supply of CD4+ T cells from precursors, as a function of viral load
$\frac{d T}{d \mathrm{time}}=\mathrm{s\_V}-\mathrm{mu\_T}T+rT(1-\frac{T+\mathrm{T\_1}+\mathrm{T\_2}}{\mathrm{T\_max}})-\mathrm{k\_1}VT\mathrm{s\_V}=\frac{\mathrm{theta}s}{\mathrm{theta}+V}$
This component relates to the latently infected CD4+ helper cell dynamics
Latently infected CD4+ helper cell population size (T* in the paper)
$\frac{d \mathrm{T\_1}}{d \mathrm{time}}=\mathrm{k\_1}VT-\mathrm{mu\_T}\mathrm{T\_1}-\mathrm{k\_2}\mathrm{T\_1}$
This component relates to the actively infected CD4+ helper cell dynamics
actively infected CD4+ helper cell population size (T** in the paper)
$\frac{d \mathrm{T\_2}}{d \mathrm{time}}=\mathrm{k\_2}\mathrm{T\_1}-\mathrm{mu\_b}\mathrm{T\_2}$
This component relates to the HIV population size
concentration of free infectious viral particles
$\frac{d V}{d \mathrm{time}}=N\mathrm{mu\_b}\mathrm{T\_2}-\mathrm{k\_1}VT-\mathrm{mu\_V}V$
This component calculates the total CD4+ T cell
Total CD4+ T-cell population
$\mathrm{T\_tot}=T+\mathrm{T\_1}+\mathrm{T\_2}$
This component calculates the total CD4+ T cell
Time of AZT administration (1096 days = 3 years)
Initial N value before AZT administration
New N value after AZT administration
Number of free virus produced by lysing a CD4+ cell
$N=\begin{cases}\mathrm{N\_initial} & \text{if $\mathrm{time}< \mathrm{tau}$}\\ \mathrm{N\_AZT} & \text{if $\mathrm{time}\ge \mathrm{tau}$}\end{cases}$
Dynamics of HIV infection of CD4+ T cells (Model 3)
Choi
Ethan
mcho099@aucklanduni.ac.nz
The University of Auckland
Auckland Bioengineering Institute
2010-01-13
Dynamics of HIV infection of CD4+ T cells
This is the CellML description of Perelson, Kirschner, and Boer's 1993 mathematical model for the dynamics of HIV infection of CD4+ T cells
Ethan Choi
CD4+ T cell
keyword
Immunology
CD4 T cell
HIV
dynamics
AZT
8096155
Perelson
Alan
S
Kirschner
Denise
E
de Boer
Rob
Dynamics of HIV infection of CD4+ T cells
1993-03
Mathematical Biosciences
114
81
125
3650
100000