Theoretical implications of cellular immune reactions against helper lymphocytes infected by an immune system retrovirus

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.

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.

Dynamics of HIV infection of CD4+ T cells

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.(ABSTRACT TRUNCATED AT 400 WORDS)

A mathematical model of vaccination against HIV to prevent the development of AIDS

Vaccination and post-exposure immunization against the human immunodeficiency viruses (HIV-1 and HIV-2) faces the problem of the extensive genetic and antigenic variability of these viruses. This raises the question of what fraction of all possible antigen strains of the virus must be recognized by the immune response to a vaccine to prevent development of acquired immunodeficiency disease (AIDS). The success of a vaccine can depend on the variability of the target epitopes. The different HIV variants must be suppressed faster than new escape mutants can be produced. In this paper the antigenic variation of HIV during an individual infection is described by a stochastic process. The central assumption is that antigenic drift is important for the virus to survive immunological attack and to establish a persistent infection that leads to the development of AIDS after a long incubation period. The mathematical analysis reveals that the fraction of antigenic variants recognized by the immune response, that is induced by a successful immunogen, must exceed 1-1/R, where R is the diversification rate of the virus population. This means that if each HIV strain can produce, on average, five new escape mutants, then more than 80% of the possible variants must be covered by the immunogen. A generic result of the model is that, no matter how immunogenic a vaccine is, it will fail if it does not enhance immune attack against a sufficiently large fraction of strains. Furthermore, it is shown that the timing of the application of post-exposure immunization is important.

Model-based analysis of CD4+ lymphocyte dynamics in HIV-infected individuals. II. Evaluation of the model based on clinical observations

The recently developed mathematical model of CD4+ lymphocyte depletion in HIV-infected individuals is evaluated using a comparison with available clinical data. The data used for such an evaluation are to be extrapolated from the published clinical observations as these data sets are not homogeneous covering only parts of HIV infection duration. An additional complication is due to the uncertainty of exact infection onset. Based on these considerations, several different reference data sets are generated from the available clinical data and the range of applicability of the mathematical model and its modifications is then investigated. As a result of such quantitative confrontation, it can be concluded that the appropriate setting of cell interaction parameters in the model can result in a fairly good coincidence of the simulated HIV infection dynamics with reference data sets. Perspectives and limitations of such an approach are also discussed.

[HIV-1 antigenemia and T-cell activation in HIV-1 infected patients]

In order to study a supposed association between T-cell activation in vivo and HIV-1-antigenemia in HIV-1-infected patients, the detection of p24-antigen in sera was correlated to serum levels of beta-2-microglobulin and C1q-binding immune complexes. Anti-p24-antibodies and the urinary excretion of neopterin were also analysed. In 24 of 80 patients (30%) p24-antigen could be detected, and in 15 of 59 (25.4%) there was a loss of anti-p24-antibodies. Tests revealed elevated serum levels of beta-2-microglobulin in 58 of 80 patients (72.5%), elevated levels of C1q-binding immune complexes in 15 of 66 (22.7%), and increased excretion of neopterin in 52 of 60 (86.7%). Detection of p24-antigen, loss of anti-p24-antibodies, serum levels of beta-2-microglobulin, and urinary excretion of neopterin were significantly correlated to advanced stages of HIV-1 infection. Patients with p24-antigen in the serum showed significantly more frequently elevated serum levels of beta-2-microglobulin and no significant association with increased urinary excretion of neopterin. Because of the high proportion of patients with elevated serum levels of beta-2-microglobulin and increased excretion of urinary neopterin in the absence of detectable p24-antigen in serum, we could not correlate HIV-1-antigenemia to T-cell activation in vivo.

Stability analysis of simple models for immune cells interacting with normal pathogens and immune system retroviruses

A mathematical analysis is presented for several simple dynamical systems that might be considered as crude descriptions for the situation when an immune system retrovirus, immune cells, and normal autonomously replicating pathogens interact. By stability analysis of the steady-state solutions, the destabilizing effect of the immune system retrovirus is described. The qualitative behavior of the solutions depending on the system parameters is analyzed in terms of trajectories moving in a phase space in which the axes are defined by the population numbers of the interacting biological entities.