A model for AIDS pathogenesis

Modelling the course of an HIV infection: insights from ecology and evolution

The Human Immunodeficiency Virus (HIV) is one of the most threatening viral agents. This virus infects approximately 33 million people, many of whom are unaware of their status because, except for flu-like symptoms right at the beginning of the infection during the acute phase, the disease progresses more or less symptom-free for 5 to 10 years. During this asymptomatic phase, the virus slowly destroys the immune system until the onset of AIDS when opportunistic infections like pneumonia or Kaposi’s sarcoma can overcome immune defenses. Mathematical models have played a decisive role in estimating important parameters (e.g., virion clearance rate or life-span of infected cells). However, most models only account for the acute and asymptomatic latency phase and cannot explain the progression to AIDS. Models that account for the whole course of the infection rely on different hypotheses to explain the progression to AIDS. The aim of this study is to review these models, present their technical approaches and discuss the robustness of their biological hypotheses. Among the few models capturing all three phases of an HIV infection, we can distinguish between those that mainly rely on population dynamics and those that involve virus evolution. Overall, the modeling quest to capture the dynamics of an HIV infection has improved our understanding of the progression to AIDS but, more generally, it has also led to the insight that population dynamics and evolutionary processes can be necessary to explain the course of an infection.

Evolutionary dynamics of HIV at multiple spatial and temporal scales

Infectious diseases remain a formidable challenge to human health, and understanding pathogen evolution is crucial to designing effective therapeutics and control strategies. Here, we review important evolutionary aspects of HIV infection, highlighting the concept of selection at multiple spatial and temporal scales. At the smallest scale, a single cell may be infected by multiple virions competing for intracellular resources. Recombination and phenotypic mixing introduce novel evolutionary dynamics. As the virus spreads between cells in an infected individual, it continually evolves to circumvent the immune system. We discuss evolutionary mechanisms of HIV pathogenesis and progression to AIDS. Viral spread throughout the human population can lead to changes in virulence and the transmission of immune-evading variation. HIV emerged as a human pathogen due to selection occurring between different species, adapting from related viruses of primates. HIV also evolves resistance to antiretroviral drugs within a single infected host, and we explore the possibility for the spread of these strains between hosts, leading to a drug-resistant epidemic. We investigate the role of latency, drug-protected compartments, and direct cell-to-cell transmission on viral evolution. The introduction of an HIV vaccine may select for viral variants that escape vaccine control, both within an individual and throughout the population. Due to the strong selective pressure exerted by HIV-induced morbidity and mortality in many parts of the world, the human population itself may be co-evolving in response to the HIV pandemic. Throughout the paper, we focus on trade-offs between costs and benefits that constrain viral evolution and accentuate how selection pressures differ at different levels of selection.

A strong case for viral genetic factors in HIV virulence

HIV infections show great variation in the rate of progression to disease, and the role of viral genetic factors in this variation had remained poorly characterized until recently. Now a series of four studies [1-4] published within a year has filled this important gap and has demonstrated a robust effect of the viral genotype on HIV virulence.

On the intra-host dynamics of HIV-1 infections

An extension of a previously proposed theory for the pathogenesis of AIDS is presented and analyzed using a mathematical modelling approach. This theory is based on the observation that human immunodeficiency virus type 1 (HIV-1) predominantly infects and replicates in (CD4+)-T cells, and that the infection process within an infected individual is characterized by ongoing generation and selection of HIV variants with increasing reproductive capacity. This evolutionary process is considered to be the reason for the gradual loss of immunocompetence and the final destruction of the immune system observed in most patients. The extension presented here incorporates the effect of the permanently increasing susceptibility of (CD4+)-T cell clones, as a result of the evolutionary process. The presented model reproduces and possibly explains a wide variety of findings about the HIV infection process. Numerical results indicate that the effect of the initial dose is minimal, and restricted to the primary phase of infection. According to the model predictions the impact of the HIV evolutionary speed is crucial for the progression to disease. An important progression determinant is the initial infection rate, being a component of the viral reproductive capacity. An influential role in disease progression seems to be played by the initial (CD4+)-T cell count.

Statistical methods for HIV dynamic studies in AIDS clinical trials

Studies of HIV dynamics in AIDS research are very important for understanding pathogenesis of HIV infection and for assessing the potency of antiviral therapies. Since the viral dynamic results from clinical data were first published by Ho et al. and Wei et al., the study of HIV-1 dynamics in vivo has drawn a great attention from AIDS clinicians and researchers. Although the important findings from HIV dynamic studies have been published in many prestigious scientific journals, statistical methods for estimating viral dynamic parameters have not been paid enough attention by HIV dynamic investigators. The estimation methods in many viral dynamic studies are very crude and inefficient. In this paper, we review the statistical methods and mathematical models for HIV dynamic data analysis developed in recent years. We also address some practical issues and share our experiences in the design and analysis of viral dynamic studies. Some principles and guidelines for the design and analysis of viral dynamic studies are provided. The methodologies reviewed in this paper are also applicable to studies of other viruses such as hepatitis B virus or hepatitis C virus. We also pose some challenging statistical problems in this area in order to stimulate further study by the statistical research community.

Optimizing within-host viral fitness: infected cell lifespan and virion production rate

We explore how an infected cell's virion production rate can affect the relative fitness of a virus within a host. We perform an invasion analysis, based on an age-structured model of viral dynamics, to derive the within-host relative viral fitness. We find that for chronic infections, in the absence of trade-offs between viral life history stages, natural selection favors viral strains whose virion production rate maximizes viral burst size. We then show how various life history trade-offs such as that between virion production and immune system recognition and clearance of virally infected cells can lead to natural selection favoring production rates lower than the one that maximizes burst size. Our findings suggest that HIV replication rates should vary between cells with different life spans, as has been suggested by recent observation.

Use of a stochastic model to develop understanding of the impact of different patterns of antiretroviral drug use on resistance development

OBJECTIVE

To use a stochastic model to gain insights into the consequence for resistance development of different drug use patterns.

METHODS

We consider use of three drugs (A, B and C) where for each drug one and only one viral mutation is associated with ability to replicate (effective reproductive ratio, R > 1) in the presence of that drug as monotherapy. For drug A mutation is a, etc. We define eight populations of short-lived infected cells that live 1 day: Vo with no mutations a, b, c; Va with mutation a only, Vab with mutations a and b, etc. A random number generator was used to determine whether mutations occur in any one round of replication and to sample from a Poisson distribution to determine for each cell the number of cells of the same population created in the next generation, using the R operative at that time. Values of R depended on drug exposure, cost of resistance and availability of target cells.

RESULTS

Treatment strategies and the resulting percentage (over 100 runs) developing full "resistance" in 1500 days (Vabc not equal 0) were: (i) ABC 1500 days 0%; (ii) A 300 days, AB 300 days, ABC 900 days 100%; (iii) AB 300 days, ABC 1200 days 33%; (iv) ABC 2/3 1500 days 15%; (v) ABC 1/2 1500 days 100%; (vi) ABC 50 days, no drugs 50 days, for 1500 days 1%, where ABC 2/3 means on-drug for 2 days in every 3, ABC 1/2 represents on-drug for 1 day in every 2, and represents suboptimal adherence.

CONCLUSIONS

This model helps to develop understanding of key principles concerning development of resistance under different patterns of treatment use.

Modeling plasma virus concentration during primary HIV infection

During primary HIV infection the viral load in plasma increases, reaches a peak, and then declines. Phillips has suggested that the decline is due to a limitation in the number of cells susceptible to HIV infection, while other authors have suggested that the decline in viremia is due to an immune response. Here we address this issue by developing models of primary HIV-1 infection, and by comparing predictions from these models with data from ten anti-retroviral, drug-naive, infected patients. Applying nonlinear least-squares estimation, we find that relatively small variations in parameters are capable of mimicking the highly diverse patterns found in patient viral load data. This approach yields an estimate of 2.5 days for the average lifespan of productively infected cells during primary infection, a value that is consistent with results obtained by drug perturbation experiments. We find that the data from all ten patients are consistent with a target-cell-limited model from the time of initial infection until shortly after the peak in viremia. However, the kinetics of the subsequent fall and recovery in virus concentration in some patients are not consistent with the predictions of the target-cell-limited model. We illustrate that two possible immune response mechanisms, cytotoxic T lymphocyte destruction of infected target cells and cytokine suppression of viral replication, could account for declines in viral load data not predicted by the original target-cell-limited model. We conclude that some additional process, perhaps mediated by CD8+ T cells, is important in at least some patients.

Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials

In this paper, we introduce a novel application of hierarchical nonlinear mixed-effect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV-1 dynamics (HIV-1 RNA copies) after initiation of potent antiviral treatments and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixed-effect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV-1 RNA measurements and demonstrate the potential use of the models in clinical decision-making.

Evolutionary dynamics of HIV-induced subversion of the immune response

Human immunodeficiency virus (HIV) disease progression is characterized by a slow but steady decline in the number of CD4+ T cells. It results in the development of AIDS when the immune response collapses and the virus grows uncontrolled. Pathogenicity of HIV may be due to viral escape from cellular immune responses as well as virus-induced immune impairment. Here we discuss how the dynamic interactions between the virus population and the immune response may lead to the development of AIDS. In particular we argue that in vivo evolution of HIV may be the driving force successively weakening the immune system. This may lead to increased levels of viraemia as well as to the evolution of more virulent phenotypes which indicate progression to AIDS. These insights are important for understanding the disease process itself and for designing effective treatment regimes.

In vivo HIV-1 replicative capacity in early and advanced infection

OBJECTIVE

Previous studies on patients treated with potent antiretroviral therapy have shown that viral clearance rates do not tend to change between early and advanced HIV-1 infection. Our objective was to investigate whether the other major aspect of virus dynamics, viral replicative capacity, does change. In vitro work has indicated that the viral replicative, capacity increases but in vivo evidence has been lacking.

METHODS

As an in vivo measure of the viral replicative capacity, we studied the rate of rebound of plasma HIV RNA level during a 1-week therapy interruption in previously untreated patients who had received 2 weeks of antiretroviral therapy.

RESULTS

Such therapy in five previously drug-naive patients with high CD4 lymphocyte counts (mean, 611 x 10(6)/l) and five patients with low counts (mean, 49 x 10(6)/l) led to a mean 2.2 log10 copies/ml decrease in plasma HIV-1 levels (from 5-6 log10 copies/ml) in 2 weeks. This was similar in the two groups. Interruption of therapy for the ensuing week resulted in a stable HIV-1 level for approximately 2 days followed by a rebound towards pretherapy level, which was much more marked in the patients with low CD4 cell counts (estimated mean rise 2.22 log10 versus 1.06 log10 copies/ml; P < 0.02). After restarting therapy, HIV RNA levels returned to pre-interruption levels.

CONCLUSIONS

These findings need confirmation, but the ability of HIV-1 to replicate in vivo appears to increase during HIV-1 infection. This increased replicative capacity, for which there are several potential explanations, may be the cause of gradual CD4 lymphocyte depletion.

Dynamics of cytotoxic T-lymphocyte exhaustion

We examine simple mathematical models to investigate the circumstances under which the dynamics of cytotoxic T-lymphocyte (CTL) activation and differentiation may result in the loss of virus specific CD8+ cells, a process known as CTL exhaustion. We distinguish between two general classes of viruses: (i) viruses infecting cells that are not involved in the immune response; and (ii) viruses infecting antigen presenting cells (APCs) and helper cells. The models specify host and viral properties that lead to CTL exhaustion and indicate that this phenomenon is only likely to be observed with viruses infecting APCs and helper cells. Moreover, it is found that for such viruses, a high rate of replication and a low degree of cytopathogenicity promote the exhaustion of the CTL response. In addition, a high initial virus load and a low CD4+ cell count promote the occurrence of CTL exhaustion. These conclusions are discussed with reference to empirical data on lymphocytic choriomeningitis virus and on human immunodeficiency virus.

Stochastic modeling of the dynamics of CD4+ T-cell infection by HIV and some Monte Carlo studies

In this paper, we develop a stochastic model for the interaction between CD4+ T cells and the human immunodeficiency virus (HIV) virus by taking into account the basic biological mechanism as described in [1-4]. We studied this stochastic model through extensive Monte Carlo simulations. Our results show that, in some cases, there is a positive probability that the virus will be eliminated by the process. We have also shown that, at the earlier stage of the infection, the probability distributions of the CD4+ T cells and free HIV are skewed; however, these distributions will eventually converge to the Gaussian distributions after several years. A real-data example is given to illustrate the application of our model.

Analysis of a model for the pathogenesis of AIDS

According to a previously proposed mathematical model, the pathogenesis of acquired immunodeficiency syndrome (AIDS) could be explained by two phenomena: direct human immunodeficiency virus (HIV) infection of CD4+ T-cell populations and ongoing generation and selection of HIV mutants with increasing replicative capacity. In the present paper, the results obtained with this model are described in more detail. For different values of biologically interpretable parameters, the model predicts very different patterns of CD4+ T-cell decline after primary infection. With the assumption of a variability of 10% to 25% of three parameters between infected individuals, the model yields a realistic distribution curve of the incubation period to AIDS.

Gene therapy of T helper cells in HIV infection: mathematical model of the criteria for clinical effect

This paper presents a mathematical analysis of the criteria for gene therapy of T helper cells to have a clinical effect on HIV infection. The analysis indicates that for such a therapy to be successful, it must protect the transduced cells against HIV-induced death. The transduced cells will not survive as a population if the gene therapy only blocks the spread of virus from transduced cells that become infected. The analysis also suggests that the degree of protection against disease-related cell death provided by the gene therapy is more important than the fraction cells that is initially transduced. If only a small fraction of the cells can be transduced, transduction of T helper cells and transduction of haematopoietic progenitor cells will result in the same steady-state level of transduced T helper cells. For gene therapy to be efficient against HIV infection, our analysis suggests that a 100% protection against viral escape must be obtained. The study also suggests that a gene therapy against HIV infection should be designed to give the transduced cells a partial but not necessarily total protection against HIV-induced cell death, and to avoid the production of viral mutants insensitive to the gene therapy.

Reduction of HIV concentration during acute infection: independence from a specific immune response

After infection with the human immunodeficiency virus (HIV), the concentration of the virus in the person's plasma increases. The subsequent decrease in concentration a few weeks later was though to result from an HIV-specific immune response. This purported causal relation is investigated with a model of the dynamics of early HIV infection that incorporates no increase in the rate of removal of free virions or virus-infected cells. A pattern of changes in virus concentration similar to that observed in patients is predicted by the model. Thus, the reduction in virus concentration during acute infection may not reflect the ability of the HIV-specific immune response to control virus replication.