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Cytotoxic T lymphocytes and viral turnover in HIV type 1 infection
To understand the role of the immune system in limiting HIV type 1 replication, it is critical to know to what extent the rapid turnover of productively infected cells is caused by viral cytopathicity or by immunemediated lysis. We show that uncultured peripheral blood mononuclear cells of many patients contain cytotoxic T lymphocytes (CTL) that lyse target cells—at plausible peripheral blood mononuclear celltotarget ratios—with halflives of less than 1 day. In 23 patients with CD4 counts ranging from 10 to 900 per μl, the average rate of CTLmediated lysis corresponds to a target cell halflife of 0.7 day. We develop mathematical models to calculate the turnover rate of infected cells subjected to immunemediated lysis and viral cytopathicity and to estimate the fraction of cells that are killed by CTL as opposed to virus. The models provide new interpretations of drug treatment dynamics and explain why the observed rate of virus decline is roughly constant for different patients. We conclude that in HIV type 1 infection, CTLmediated lysis can reduce virus load by limiting virus production, with small effects on the halflife of infected cells.
Recent studies of HIV type 1 (HIV1) dynamics have shown that the initial rate of virus decline during drug treatment is approximately 30% per day, leading to the interpretation that productively infected cells have a halflife of about 2 days (1–6). There is little variation in this halflife, which ranges from about 1 to 4 days in patients with CD4 cell counts between 20 and 500 μl (Fig. 1). There is no correlation between the rate of viral turnover and CD4 cell count or virus load. The important question is whether the observed turnover rate of infected cells is caused by viral cytopathicity or immunemediated clearance mechanisms. If we postulate that cytotoxic T lymphocyte (CTL)mediated lysis determines the life span of a productively infected cell (7, 8), then it is surprising to find so little variation in the observed halflife of infected cells and no correlation with the disease stage (CD4 cell count) of a patient. On the other hand, if cell death is only due to viral cytopathicity, then immunemediated lysis can have no effect on reducing virus production. We will analyze whether CTLmediated lysis could be fast enough to account for the observed turnover rates, and we will develop a mathematical model to quantify the effect of CTL killing on infected cell halflife and virus production.
In HIV1infected patients, antiviral CTL arise early in infection (9–11) and are present within uncultured circulating peripheral blood mononuclear cells (PBMC) as a subset of CD8^{+} cells (12–27). The rate of CTLmediated killing should influence both the halflife of virusinfected cells and the amount of virus production. We determined the in vitro halflife of target cells [human leukocyte antigen (HLA) class I matched B cells which bear sufficient peptide for Tcell recognition] from assays of specific cytotoxicity by fresh PBMC. Fig. 2A shows timeresolved decay curves of target cells in the presence of PBMC from HIV1positive patient 84 (who has been infected for about 5 years and has currently a CD4 cell count of 540 per μl) at various PBMCtotarget ratios. From the slope of the decay curve, we can calculate the death rate of target cells. At a PBMCtotarget ratio of 64:1, the death rate of target cells corresponds to a halflife of 12 hr. Fig. 2B shows the halflives of target cells for different PBMCtotarget ratios.
Clearly, the above data are results from in vitro measurements, and it is uncertain how accurately they reflect the rate of CTLmediated lysis in vivo. We argue, however, that using uncultured PBMC and adding a small amount of target cells may provide conditions that are as close as possible to the in vivo situation. The fraction of cells infected with HIV1 and expressing HIV1 RNA in lymph nodes can be as high as 3–6% in asymptomatic subjects (28, 29), although this may vary depending on the lymphoid microenvironment (30). This implies an overall ratio of lymphocytes to infected target lymphocytes of at least 15–30:1. In patients with lower viral burden, the ratio will be higher. Therefore, by using PBMCtotarget ratios of 25:1 or larger, we may simulate the in vivo situation.
Although the above experiments were carried out with peptide pulsed B cell lines as targets, we have also measured the death rate of HIV1infected CD4 cells in the presence of uncultured PBMC from the HLAB8 positive patient SC3 (an asymptomatic individual who has been infected for at least 3 years and has a CD4 cell count of 440 per μl). Effector cells were freshly isolated PBMC; targets were B8matched C8166 cells used 48 hr after infection with 10 TCID_{50} of HIV IIIB. At a PBMCtotarget ratio of 64:1, we find 17% specific lysis after 8 hr, corresponding to a target cell halflife of 1.2 days. At a ratio of 32:1, we obtain a halflife of 2.4 days (Fig. 2C).
Results derived from published studies of fresh responses by many other workers (12–18) can also be used to calculate target cell halflives (Fig. 2D). In some patients, the halflife of target cells is less than 12 hr at PBMCtotarget ratios of 50:1 or greater. On the other hand, many HIV1infected individuals do not show strong responses and target cell halflife by CTL killing would exceed 48 hr.
To explore a possible correlation between the rate of CTLmediated lysis and disease stage of a patient, we calculated the halflife of target cells in the presence of fresh PBMC from 23 patients with CD4 cell counts ranging from 10 to 900 per μl. CTL activity was determined against targets expressing five different HIV proteins: Gag, Pol, Env, Nef, or Tat (25). Fig. 2E shows the calculated halflife of target cells with respect to the strongest response among the Gag, Pol, Nef, or Tatspecific CTL in each patient. There is no correlation between the CD4 count of a patient and the halflife of target cells. At a PBMCtotarget ratio of 50:1, the average rate of CTLmediated lysis is 1.0 ± 0.57 per day, which corresponds to a halflife of about 0.7 day. Note that the lack of correlation between viral turnover and CD4 count (Fig. 1) is paralleled by a lack of correlation between the fresh CTL response and CD4 count (Fig. 2E).
In contrast to the antiGag, Pol, Nef, or Tat responses, which are mostly due to CTL activity, the antiEnv response is likely to contain a large proportion of antibodydependent cell cytotoxicity (25–27). The calculated average rate of antiEnvmediated lysis in vitro is 1.24 ± 0.66 per day, corresponding to a halflife of about 0.6 day. However, it is not clear how important antibodydependent cell cytotoxicity is in vivo in the presence of a vast excess of serum Ig, which would compete with the specific antibodies for Fc receptors.
Given these findings, we will now explore whether CTLmediated lysis can make a significant contribution to the turnover rate of HIVinfected cells in vivo. If HIV directly kills productively infected cells, does CTLmediated destruction play a role in the overall decay rate of infected cells? We develop a mathematical model to relate the expected lifetime of an infected cell to the rate of CTLmediated clearance mechanisms and virus cytopathicity and to calculate the amount of virus production inhibited by CTL. Consider a model with three compartments of infected cells representing different stages of the virus life cycle: y_{1} are newly infected cells, which are not yet producing free virus and are not targets for CTL killing; y_{2} are cells that are still not producing virus but can be killed by CTL, whereas y_{3} are cells that are producing free virus and can be killed by CTL.
There are different ways to specify the dynamics of the infected cell life cycle. In model 1, we assume that the transitions from y_{1} to y_{2} and from y_{2} to y_{3} occur at fixed times t_{1} and t_{2} in the life cycle of an infected cell. This means a cell gets invaded by virus at time t = 0. At time t_{1}, enough new viral proteins have been produced such that the cell becomes a potential target for CTLmediated killing. The death rate of a target cell due to CTL is given by α. At time t_{2}, the cell starts to produce free virus particles. This increases the death rate by an amount c, which is due to virus cytopathicity. Thus we have a stepwise model for cellular decay. Between time 0 and t_{1}, the death rate is 0; between times t_{1} and t_{2}, the death rate is α; after time t_{2}, the death rate is α + c. Another possibility (model 2) is to assume that the transitions occur at constant rates: y_{1} turns into y_{2} at rate a; y_{2} turns into y_{3} at rate b; and y_{3} cells die at rate c. As before, the CTL response eliminates y_{2} and y_{3} cells at rate α. Both models can be used to calculate the lifetime of infected cells, the average duration of virus production of a single cell, and the fraction of cells killed by CTL as opposed to virus (Fig. 3). Although it is likely that a cell becomes a target for CTL before onset of virus production (31), this assumption is not essential and can easily be reversed.
Between the two limiting cases, described by models 1 and 2, lies a spectrum of models where the transition from y_{1} to y_{2} (and from y_{2} to y_{3}) is not given by a simple onestep process with an exponential distribution and also does not occur after a fixed length of time. We considered a Poisson process, where a number, n, of events have to accumulate (at certain rates) before the transition occurs. If n = 1, we obtain model 1, and if n is very large, we obtain model 2. For intermediate values of n, the resulting decay is not strictly exponential but for practical purposes may be indistinguishable from an exponential decay.
Table 1 gives numerical values for the effect of CTL killing. For a cytopathic virus, the halflife of infected cells does not vary much in the presence of weak or strong CTL responses, but the fraction of infected cells killed by CTL and the amount of virus production inhibited by CTL can be greatly affected by the rate of CTLmediated lysis. For example, a response equivalent to 10% lysis in 4 hr can eliminate about 70% of infected cells; the remaining 30% is eliminated by virus cytopathic effects. For a noncytopathic virus, differences in CTL activity lead to large variation in infected cell halflife. Responses equivalent to 10% lysis in 4 hr eliminate 99% of infected cells.
The above models also provide new insights into the dynamics of virus decline after drug treatment. Before drug treatment, the virus population is at steady state and infected cells, y_{1}, are produced at a constant rate, β (which depends on the abundance of infectable cells, virus load, cytokine levels, etc.). The effect of drug treatment is to reduce β to zero. Reverse transcriptase inhibitors prevent the infection of new cells, whereas protease inhibitors render virus particles, which are being produced from already infected cells, noninfectious. Therefore reverse transcriptase inhibitors bring β to (almost) 0 as soon as they achieve a high enough concentration within the patient, whereas protease inhibitors allow for a short time infection of new cells by virus particles that have been produced before the drug was given (5, 6). If the free virus halflife is short, then the difference is negligible. In both models 1 and 2, this leads to an (approximately) exponential decline in plasma virus, v, after an initial shoulder. In model 1, the slope of the exponential decay is given by α + c (Fig. 4). Thus, the rate of CTLmediated killing should influence the rate of free virus decline. In model 2, however, the slope of the exponential decline is given by the smallest value among a, α + b, and α + c, which means that the slowest step in the life cycle of an infected cell (including the effect of α) determines the rate of virus decline during drug treatment. If the time between infection of the cell and expressing enough viral protein to become a target for CTL is rate limiting, then the observed exponential slope of virus decline is given by a and does not depend on the rate of CTLmediated killing. Even if a is larger than b or c, it is still possible that in most patients a is smaller than b + α and c + α, and therefore again the observed rate of virus decline reflects the initial phase of the viral life cycle and is unaffected by CTLmediated lysis.
There is one additional explanation for why CTLmediated killing may not affect the rate of virus decline during drug therapy. It is natural to assume that in a given patient infected cells are exposed to different rates of CTLmediated lysis. This can be a consequence of spatial heterogeneity (31), cell tropism, or antigenic variation. Therefore, rather than assuming a fixed average rate, α, of CTLmediated lysis for all cells, it may be better to consider a distribution of different α values. In the simplest model, we assume that in each patient, there is a small and variable fraction h of cells not exposed to CTL killing. Using the framework of model 1 and assuming that a fraction, h, of cells has death rate c and the remaining 1 − h cells have death rate c + α, we find that virus decay in treatment studies is given by [(1 − h)/(α + c)]exp[−α(t_{2} − t_{1}) − (α + c)(T − t_{2})] + (h/c)exp[−c(T − t_{2})]. For a patient with a weak CTL response (α ≈ 0), the slope is c; for a patient with a strong CTL response (α ≫ c), the slope is again dominated by c. Therefore, if a small fraction of infected cells (less than 5–10%) escape from CTL surveillance, the resulting virus decay slopes are independent of the average rate of CTLmediated killing in this patient. The intuitive reason behind this explanation is that virus dynamics experiments measure the turnover rate of cells that produce most of the plasma virus. But cells that are killed by CTL produce less plasma virus than cells that are not killed by CTL. Therefore, the virus decay slope will be biased toward the decay rate of cells that have escaped from CTLmediated lysis. Clearly, the same argument applies to model 2.
Fig. 4 shows the slope of virus decline during drug therapy as a function of the rate of CTLmediated lysis. For both model 1 with heterogeneity and model 2, we find that the virus decay slope is roughly constant provided that HIV1 is cytopathic and would also kill cells in the absence of a CTL response. If HIV1 were noncytopathic, there should be much smaller decay rates in patients with weak or absent CTL responses. The lack of extensive variation in virus decay slopes following drug therapy (Fig. 1) suggests that HIV1 is cytopathic. Otherwise, one would have to argue that all individuals measured so far have a minimum CTLmediated (or immunemediated) clearance rate of infected cells that corresponds to a target cell lysis of 5–10% in 4 hr, which seems unlikely.
For comparison, in infections with the hepatitis B virus, which is considered to be noncytopathic, the halflife of productively infected cells varies from 10 to 100 days in different individuals (32).
Our analysis reveals that also low levels of CTLmediated lysis can account for elimination of large fractions of infected cells. Therefore, it will be important to improve the sensitivity of ex vivo CTL measurements, either by longer CTL assays (8–24 hr) or direct staining and quantitation of antigenspecific CTL in PBMC samples (33). The more conventional assays involving culture, and sometimes cloning, of CTL probably measure a different parameter made up of the frequency of memory CTL and the effectiveness of Tcell help for CTL development. These memory cells are the source of the effector CTL measured in fresh PBMC, but the relationship between the two is complex.
With respect to HIV1 disease progression, the crucial question is to what extent immune responses reduce virus load in infected patients (34). Our results suggest that CTLmediated lysis is sufficiently fast to eliminate a large fraction of productively infected cells and thereby greatly reduce virus production. In addition, CD8^{+} T cells also release cytokines (35–37) that can block virus entry into cells (38–43). Both mechanisms are likely to reduce virus load and therefore slow down the rate of disease progression (44).
Acknowledgments
We thank Rolf Zinkernagel, XiaoLi Huang, Zheng Fan, Philip Goulder, Matt Collin, Ann Edwards, Paul Giangrande, Sebastian Bonhoeffer, Barbara Bittner, the staff of the Department of GenitoUrinary Medicine at the Radcliffe Infirmary, and Haemophilia Centre, Churchill Hospital, Oxford, and the Pittsburgh, PA portion of the Multicenter AIDS Cohort Study. This work was supported by the Wellcome Trust, the Medical Research Council (U.K.) and the National Institutes of Health.
Footnotes

↵ To whom reprint requests should be addressed. email: nowak{at}vax.ox.ac.uk.

1996)

Abbreviations: CTL, cytotoxic T lymphocyte(s); PMBC, peripheral blood mononuclear cell(s).
 Copyright © 1996, The National Academy of Sciences of the USA
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