W. David Wick

How Many Human Immunodeficiency Virus Type 1-Infected Target Cells Can a Cytotoxic T-Lymphocyte Kill?

ABSTRACT The antiviral role of CD8+ cytotoxic T lymphocytes (CTLs) in human immunodeficiency virus type 1 (HIV-1) infection is poorly understood. Specifically, the degree to which CTLs reduce viral replication by killing HIV-1-infected cells in vivo is not known. Here we employ mathematical models of the infection process and CTL action to estimate the rate that CTLs can kill HIV-1-infected cells from in vitro and in vivo data. Our estimates, which are surprisingly consistent considering the disparities between the two experimental systems, demonstrate that on average CTLs can kill from 0.7 to 3 infected target cells per day, with the variability in this figure due to epitope specificity or other factors. These results are compatible with the observed decline in viremia after primary infection being primarily a consequence of CTL activity and have interesting implications for vaccine design.

Biologically-Directed Modeling Reflects Cytolytic Clearance of SIV-Infected Cells In Vivo in Macaques

The disappointing outcomes of cellular immune-based vaccines against HIV-1 despite strong evidence for the protective role of CD8+ T lymphocytes (CTLs) has prompted revisiting the mechanisms of cellular immunity. Prior data from experiments examining the kinetics of Simian Immunodeficiency Virus (SIV) clearance in infected macaques with or without in vivo CD8 depletion were interpreted as refuting the concept that CTLs suppress SIV/HIV by direct killing of infected cells. Here we briefly review the biological evidence for CTL cytolytic activity in viral infections, and utilize biologically-directed modeling to assess the possibility of a killing mechanism for the antiviral effect of CTLs, taking into account the generation, proliferation, and survival of activated CD4+ and CD8+ T lymphocytes, as well as the life cycle of the virus. Our analyses of the published macaque data using these models support a killing mechanism, when one considers T lymphocyte and HIV-1 lifecycles, and factors such as the eclipse period before release of virions by infected cells, an exponential pattern of virion production by infected cells, and a variable lifespan for acutely infected cells. We conclude that for SIV/HIV pathogenesis, CTLs deserve their reputation as being cytolytic.

Predicting the Impact of Blocking Human Immunodeficiency Virus Type 1 Nef In Vivo

ABSTRACT Human immunodeficiency virus type 1 (HIV-1) Nef is a multifunctional protein that confers an ability to evade killing by cytotoxic T lymphocytes (CTLs) as well as other advantages to the virus in vivo. Here we exploited mathematical modeling and related statistical methods to estimate the impact of Nef activity on viral replication in vivo in relation to CTLs. Our results indicate that downregulation of major histocompatibility complex class I (MHC-I) A and B by wild-type Nef confers an advantage to the virus of about 82% in decreased CTL killing efficiency on average, meaning that abolishing the MHC-I downregulation function of Nef would increase killing by more than fivefold. We incorporated this estimate, as well as prior estimates of replicative enhancement by Nef, into a previously published model of HIV-1 and CTLs in vivo (W. D. Wick, O. O. Yang, L. Corey, and S. G. Self, J. Virol. 79:13579-13586, 2005), generalized to permit CTL recognition of multiple epitopes. A sequence database analysis revealed that 92.9% of HIV-1 epitopes are A or B restricted, and a previous study found an average of about 19 epitopes recognized (M. M. Addo et al., J. Virol. 77:2081-2092, 2003). We combined these estimates in the model in order to predict the impact of inhibiting Nef function in the general (chronically infected) population by a drug. The predicted impact on viral load ranged from negligible to 2.4 orders of magnitude, depending on the effects of the drug and the CTL dynamical scenario assumed. We conclude that inhibiting Nef could make a substantial reduction in disease burden, lengthening the time before the necessity of undertaking combination therapy with other antiretroviral drugs.

On Modeling HIV and T Cells In Vivo: Assessing Causal Estimators in Vaccine Trials

The first efficacy trials—named STEP—of a T cell vaccine against HIV/AIDS began in 2004. The unprecedented structure of these trials raised new modeling and statistical challenges. Is it plausible that memory T cells, as opposed to antibodies, can actually prevent infection? If they fail at prevention, to what extent can they ameliorate disease? And how do we estimate efficacy in a vaccine trial with two primary endpoints, one traditional, one entirely novel (viral load after infection), and where the latter may be influenced by selection bias due to the former? In preparation for the STEP trials, biostatisticians developed novel techniques for estimating a causal effect of a vaccine on viral load, while accounting for post-randomization selection bias. But these techniques have not been tested in biologically plausible scenarios. We introduce new stochastic models of T cell and HIV kinetics, making use of new estimates of the rate that cytotoxic T lymphocytes—CTLs; the so-called killer T cells—can kill HIV-infected cells. Based on these models, we make the surprising discovery that it is not entirely implausible that HIV-specific CTLs might prevent infection—as the designers explicitly acknowledged when they chose the endpoints of the STEP trials. By simulating thousands of trials, we demonstrate that the new statistical methods can correctly identify an efficacious vaccine, while protecting against a false conclusion that the vaccine exacerbates disease. In addition to uncovering a surprising immunological scenario, our results illustrate the utility of mechanistic modeling in biostatistics.

Impaired Viral Entry Cannot Explain Reduced CD4+ T Cell Susceptibility to HIV Type 1 in Certain Highly Exposed Individuals

Rare individuals report repeated unprotected HIV-1 sexual exposures, yet remain seronegative for years. We investigated the possibility that reduced in vitro CD4(+) T cell susceptibility to HIV-1 infection protects such highly exposed seronegative (ES) individuals. Susceptibility to three R5-tropic HIV-1 isolates, regardless of inoculating dose, was remarkably similar between 81 ES and 33 low-risk controls. In 94% (99/105) of donors, we observed a 1.36 log-unit range in HIV-1(JR-CSF) production, with similar results for HIV-1(1192). The median frequency of intracellular Gag(+) T cells after single-round infection was similar in ES (5.2%) and controls (7.2%), p = 0.456. However, in repeated testing, CD4(+) T cells from two controls (6.1%) and four ES (4.9%) exhibited a 10- to 2500-fold reduction in HIV-1 production and required 5- to 12-fold greater HIV-1(1192) and HIV-1(JR-CSF) inocula to establish infection (TCID(50)). Reduced viral entry cannot explain the low producer phenotype; no differences in CCR5 receptor density or beta-chemokine production were observed. In conclusion, we have identified a remarkably narrow range of HIV-1 susceptibility in seronegative donors regardless of risk activity, which can be applied as a benchmark to assess vaccine-induced antiviral effector activities. However, CD4(+) T cells from a subset of individuals demonstrated reduced HIV-1 susceptibility unexplained by impaired entry, lending support to the possibility that cellular restriction of HIV-1 may account for continued seronegativity in some of those having repeated sexual exposure. Identifying the host-virus interactions responsible for diminished in vitro susceptibility may contribute to the development of novel therapeutic strategies.

Simulating an HIV Infection In Vivo

When the HIV and CTL models are combined, we have gone beyond familiar textbook examples of biological modeling. Although mathematics provides insights into the predictions of the model (described in subsequent chapters), to some extent we must rely on computer simulation.

Derivation of the Escape Formula

We will consider a variety of mutations in the HIV genome, denoted in formulas by the index “m”.

The Nef-Deletion Threshold Formulas

We derive the results stated in Chapter 9. The Nef-maintenance condition follows from the Escape Formula as usual (escape is impossible if \(\mbox{ REA}_{m} < \mbox{ LOF}_{m}\)) and can be derived from re-arranging the definition of REA to read

Afterword: The RV144 Trial and the Current Status of HIV Vaccine Research

\displaystyle\begin{array}{rcl} \mbox{ REA}_{m}& = & 1 - \left (\,{ \sum _{e=2}^{E}\,f\,\kappa _{e}\,C_{e}/\delta \over \sum _{e=1}^{E}\,\kappa _{e}\,C_{e}/\delta } \,\right ) \\ & = & 1 - f\, \times \,\mbox{ FOE}.{}\end{array}