Modeling HIV-1 infection in the brain

Abstract

While highly active antiretroviral therapy (HAART) is successful in controlling the replication of Human Immunodeficiency Virus (HIV-1) in many patients, currently there is no cure for HIV-1, presumably due to the presence of reservoirs of the virus. One of the least studied viral reservoirs is the brain, which the virus enters by crossing the blood-brain barrier (BBB) via macrophages, which are considered as conduits between the blood and the brain. The presence of HIV-1 in the brain often leads to HIV associated neurocognitive disorders (HAND), such as encephalitis and early-onset dementia. In this study we develop a novel mathematical model that describes HIV-1 infection in the brain and in the plasma coupled via the BBB. The model predictions are consistent with data from macaques infected with a mixture of simian immunodeficiency virus (SIV) and simian-human immunodeficiency virus (SHIV). Using our model, we estimate the rate of virus transport across the BBB as well as viral replication inside the brain, and we compute the basic reproduction number. We also carry out thorough sensitivity analysis to define the robustness of the model predictions on virus dynamics inside the brain. Our model provides useful insight into virus replication within the brain and suggests that the brain can be an important reservoir causing long-term viral persistence.

Fig 1. The schematic diagram of the model representing HIV-1 infection in the brain.

The boxes represent a cell population, the solid arrows represent transport from one population to another, and the dashed arrows represent the cause for the corresponding events.

Fig 2. Model fit to the data.

Plasma viral load (solid line) and CSF viral load (dashed line) predicted by the selected model, i.e. Model 1, along with the experimental data (filled circle: plasma viral load; filled triangle: CSF viral load) from three monkeys [24, 25].

Fig 3. Sensitivity of parameter estimations to R0.

Local sensitivity of ${\displaystyle {\mathfrak{R}}_0}$ based on sensitivity index (left) and the partial rank correlation coefficients for global sensitivity of ${\displaystyle {\mathfrak{R}}_0}$ based on Latin Hypercube sampling (right).

Fig 4. Incoming infected macrophages entering the brain (φM*).

Model simulations of the total count of infected macrophages (φM*) entering the brain for 100 days post-infection.

Fig 5. Simulations of macrophages in the plasma and the CSF.

Model simulations over 100 days post-infection of infected macrophages (top row) and uninfected macrophages (bottom row) in the plasma (left column) and in the brain (right column).

Fig 6. Long-term model simulations.

Viral load (top left) for the plasma (solid line) and the brain (dashed line) along with the CD4+ T cell count (top right) and the total infected macrophages (bottom row) in the brain (bottom left) and in the plasma (bottom right).

Fig 7. Box-plots of the results of 200 simulations of the model from Latin hypercube sampling.

The sensitivity of the dynamics of plasma viral load (top) and the CSF viral load (bottom) based on 200 Latin Hypercube sampling. The black solid line represents the viral dynamics predicted by the model with median parameters estimated from three monkey data.

Fig 8. Partial rank correlation coefficients from the Latin hypercube sampling method.

PRCC values of the plasma (top, left) and the CSF (bottom, left) viral loads at weeks 1 (pre-peak), 2 (peak), 3 (post-peak), and 26 (set-point) post infection along with the PRCC values of the timing of the peak viral loads in the plasma (top right) and in the CSF (bottom right).