Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model is known to run in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent. The published paper contains four different mathematical models. This particular CellML model represents the fourth model - which includes a description of the infectious spread of the virus amongst CD4+ T cells and incorporates alternative target cells which are do not react against HIV, such as T cells with other specificities and antigen presenting cells and it also describes CD8+ CTL dynamics during HIV infection.
Model Structure
ABSTRACT: Recent experimental data have shown that HIV-specific CD4 T cells provide a very important target for HIV replication. We use mathematical models to explore the effect of specific CD4 T cell infection on the dynamics of virus spread and immune responses. Infected CD4 T cells can provide antigen for their own stimulation. We show that such autocatalytic cell division can significantly enhance virus spread, and can also provide an additional reservoir for virus persistence during anti-viral drug therapy. In addition, the initial number of HIV-specific CD4 T cells is an important determinant of acute infection dynamics. A high initial number of HIV-specific CD4 T cells can lead to a sudden and fast drop of the population of HIV-specific CD4 T cells which results quickly in their extinction. On the other hand, a low initial number of HIV-specific CD4 T cells can lead to a prolonged persistence of HIV-specific CD4 T cell help at higher levels. The model suggests that boosting the population of HIV-specific CD4 T cells can increase the amount of virus-induced immune impairment, lead to less efficient anti-viral effector responses, and thus speed up disease progression, especially if effector responses such as CTL have not been sufficiently boosted at the same time.
The original paper reference is cited below:
Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?, Dominik Wodarz and Dean H. Hamer, 2007, Mathematical Biosciences PubMed ID: 17379260
A schematic diagram describing the mathematical model.
$\frac{d T}{d \mathrm{time}}=\mathrm{lambda}-\mathrm{delta}T+\mathrm{gamma}Tv$
$\frac{d I}{d \mathrm{time}}=\mathrm{gamma}Tv-\mathrm{alpha}I+pI(z+w)$
$\frac{d x}{d \mathrm{time}}=rxv(1.0-\frac{x+y}{k})-dx+\mathrm{beta}xv$
$\frac{d y}{d \mathrm{time}}=\mathrm{beta}xv+ryv(1.0-\frac{x+y}{k})-ay+py(z+w)$
$\frac{d v}{d \mathrm{time}}=\mathrm{eta}(y+I)-uv$
$\frac{d w}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_9}-\mathrm{xi}w+\mathrm{phi}w$
$\frac{d \mathrm{m\_9}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_8}-\mathrm{rho}\mathrm{m\_9}$
$\frac{d \mathrm{m\_8}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_7}-\mathrm{rho}\mathrm{m\_8}$
$\frac{d \mathrm{m\_7}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_6}-\mathrm{rho}\mathrm{m\_7}$
$\frac{d \mathrm{m\_6}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_5}-\mathrm{rho}\mathrm{m\_6}$
$\frac{d \mathrm{m\_5}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_4}-\mathrm{rho}\mathrm{m\_5}$
$\frac{d \mathrm{m\_4}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_3}-\mathrm{rho}\mathrm{m\_4}$
$\frac{d \mathrm{m\_3}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_2}-\mathrm{rho}\mathrm{m\_3}$
$\frac{d \mathrm{m\_2}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_1}-\mathrm{rho}\mathrm{m\_2}$
$\frac{d \mathrm{m\_1}}{d \mathrm{time}}=2.0\mathrm{rho}\mathrm{m\_0}-\mathrm{rho}\mathrm{m\_1}$
$\frac{d \mathrm{m\_0}}{d \mathrm{time}}=-(\mathrm{rho}\mathrm{m\_0})$
$\frac{d z}{d \mathrm{time}}=\mathrm{xi}w+cx(y+I)\frac{z}{\mathrm{epsilon}x+1.0}-bz$
This is a CellML description of Wodarz and Hamer's 2007 mathematical model of infection dynamics in HIV-specific CD4+ T cells.Catherine LloydInfection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus (Model 4)The University of Auckland, Bioengineering Instituteuninfected HIV-specific CD4+ T cellsxThe University of AucklandThe Bioengineering Institutesusceptible non-specific target T cellsTCatherine LloydHIVimmunologyCD4+ T cellviral dynamicsInfection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?
Wodarz and Hamer's 2007 mathematical model of infection dynamics in HIV-specific CD4+ T cells.
infected non-specific target T cellsIMayCatherineLloydadded units and fixed one equation.effector T cellsw2007-09-06T13:44:15+12:002007-00-00 00:0017379260MayCatherineLloydkeywordfree virus particlesvDominikWodarzThis model runs in PCEnv to recreate the published results.effector and effector memory CD8+ T cellsz2007-07-16T00:00:00+00:00infected HIV-specific CD4+ T cellsyc.lloyd@auckland.ac.nzHDeanHamerMathematical Biosciences