Modeling HIV quasispecies evolutionary dynamics

Abstract

Background: During the HIV infection several quasispecies of the virus arise, which are able to use different coreceptors, in particular the CCR5 and CXCR4 coreceptors (R5 and X4 phenotypes, respectively). The switch in coreceptor usage has been correlated with a faster progression of the disease to the AIDS phase. As several pharmaceutical companies are starting large phase III trials for R5 and X4 drugs, models are needed to predict the co-evolutionary and competitive dynamics of virus strains.

Results: We present a model of HIV early infection which describes the dynamics of R5 quasispecies and a model of HIV late infection which describes the R5 to X4 switch. We report the following findings: after superinfection (multiple infections at different times) or coinfection (simultaneous infection by different strains), quasispecies dynamics has time scales of several months and becomes even slower at low number of CD4+ T cells. Phylogenetic inference of chemokine receptors suggests that viral mutational pathway may generate a large variety of R5 variants able to interact with chemokine receptors different from CXCR4. The decrease of CD4+ T cells, during AIDS late stage, can be described taking into account the X4-related Tumor Necrosis Factor dynamics.

Conclusion: The results of this study bridge the gap between the within-patient and the inter-patients (i.e. world-wide) evolutionary processes during HIV infection and may represent a framework relevant for modeling vaccination and therapy.

Figure 1

Representation of the interactions between cells and/or cells and viruses. Representation of the interactions between cells and/or cells and viruses. HIV strains infect CD4+ T cells that become infected and produce new viruses. At the same time HIV peptides are presented via APC cells to T-Helper cells that become activated. Activated CD4+ T cells trigger B and CD8+ cells reactions: the first release antibodies that bind to the antigen while the latter directly remove infected CD4+ T cells. '+' and '-' signs indicate cell/virus production or removal.

Figure 2

Schematic description of the model for the switching from R5 to X4 viral phenotype. Schematic description of the model for the switching from R5 to X4 viral phenotype. Naïve T-cells, U, are generated at constant rate N_U and removed at rate δ^U. They give birth to differentiated, uninfected T-cells, T. These in turn are removed at constant rate δ^T and become infected as they interact with the virus. Infected T-cells, I, die at rate δ^I and contribute to the budding of viral particles, V, that are cleared out at rate c. As soon as the X4 phenotype arise, the production of the TNF starts, proportional to the X4 concentration and contribute to the clearance of naïve T-cells, via the δFU MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWF0oazdaqhaaWcbaGaemOrayeabaGaemyvaufaaaaa@30CD@ parameter.

Figure 3

Typical time evolution of the T cell abundance in the R5 model. Typical time evolution of the T cell abundance in the R5 model for short-term (a) and long-term behavior (b). We set μ = 10^-5 with N = 5. In the inset, the y-axis on the left reports the abundance of virus strains at time t = 50 in plot (a) and t = 2000 in plot (b); the y-axis on the right shows the interaction strength (dashed line) between T cells and virus phenotypes (x-axis).

Figure 4

Viral counts, V, during a superinfection scenario. Viral counts, V, during a superinfection scenario. We set N = 5 and no mutation is considered, thus μ = 0. (a) A slow mounting of the second viral infection (□), having time scale of several months, is observed. In (b) a compromised immune system is considered. The time for the second strain to reach the same abundance of the first-infecting strain (◇) is greater than in (a).

Figure 5

Speciation of virus quasispecies. Speciation of virus quasispecies and uninfected T cells dynamics after competitive superinfection at four different times: t = 0 (a), t = 4.5 (b), t = 5.25 (c) and t = 5.75 (d). Virus strain 15 is present at time t = 0, while strain 5 is inoculated at time t = 1. Mutation rate μ = 10^-4 and non-uniform interaction strength as in Figure 3. The dashed line represents the abundances of T cells targeting each viral phenotype, represented as vertical stems.

Figure 6

R5 to X4 switch. Time evolution of the concentrations of uninfected T-cells (◇) and viruses (+), during R5 to X4 switch, occurring at time t ≈ 900. After the appearance of the X4 phenotype a continuous slow decline in CD4+ T-cells level leads to AIDS phase (CD4 counts below 200 cells/ml). We set μ ≈ 0.001.

Figure 7

CD4+ T-cells concentration during HIV-1 super-infection. CD4+ T-cells concentration during HIV-1 super-infection by a R5 viral strain. Different signs represent: evolution without superinfection, (◇); superinfection occurring at time t = 100 and 400, (+) and (□), respectively. For a superinfection event occurring after the R5 to X4 switching the dynamics is qualitatively the same as for a single infection, (◇). If the second delayed infection occurs before the R5 to X4 switching, the time of appearance of X4 viruses may be shorter, when the superinfecting strain is closer to the X4 phenotypes, (+, □). Parameters as in Figure 6.

Figure 8

Maximum likelihood phylogeny. The maximum likelihood phylogeny under the JTT+F+Γ model of evolution for the set of human and mouse (mouse sequences are labelled with "-M") chemokine receptors. We have considered only the external loop regions. The scale bar refers to the branch lengths, measured in expected numbers of amino acid replacements per site.