# Cytotoxic T lymphocytes and viral turnover in HIV type1infection

^{*}RodneyE. Phillips,

^{*}CharlesR. Rinaldo,

^{†}LindaM. Wahl,

^{‡}Graham Ogg,

^{*}RobertM. May,

^{‡}AndrewJ. McMichael,

^{*}and MartinA. Nowak

^{‡}

^{§}

^{*}Molecular Immunology Group, Nuffield Department of Medicine, John Radcliffe Hospital, Oxford, OX3 9DU, United Kingdom;

^{†}Department of Pathology, University of Pittsburgh School of Medicine, Pittsburgh, PA 15213; and

^{‡}Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, United Kingdom

^{§}To whom reprint requests should be addressed. e-mail: ku.ca.xo.xav@kawon.

1996)

## Abstract

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 immune-mediated 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 cell-to-target ratios—with half-lives of less than 1 day. In 23 patients with CD4 counts ranging from 10 to 900 per μl, the average rate of CTL-mediated lysis corresponds to a target cell half-life of 0.7 day. We develop mathematical models to calculate the turnover rate of infected cells subjected to immune-mediated 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, CTL-mediated lysis can reduce virus load by limiting virus production, with small effects on the half-life of infected cells.

**Keywords:**virus dynamics, mathematical model, antiviral treatment, immune response

Recent studies of HIV type 1 (HIV-1) 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 half-life of about 2 days (1–6). There is little variation in this half-life, which ranges from about 1 to 4 days in patients with CD4 cell counts between 20 and 500 μl (Fig. (Fig.1).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 immune-mediated 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 half-life 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 immune-mediated lysis can have no effect on reducing virus production. We will analyze whether CTL-mediated 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 half-life and virus production.

**...**

In HIV-1-infected 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 CTL-mediated killing should influence both the
half-life of virus-infected cells and the amount of virus production.
We determined the *in vitro* half-life of target cells [human
leukocyte antigen (HLA) class I matched B cells which bear sufficient
peptide for T-cell recognition] from assays of specific cytotoxicity
by fresh PBMC. Fig. Fig.22*A* shows
time-resolved decay curves of target cells in the presence of PBMC from
HIV-1-positive patient 84 (who has been infected for about 5 years and
has currently a CD4 cell count of 540 per μl) at various
PBMC-to-target ratios. From the slope of the decay curve, we can
calculate the death rate of target cells. At a PBMC-to-target ratio of
64:1, the death rate of target cells corresponds to a half-life of 12
hr. Fig. Fig.22*B* shows the half-lives of target cells for
different PBMC-to-target ratios.

*A*) Time-resolved decay curve of peptide-sensitized target cells from HIV-1-infected, asymptomatic patient 84. The assays of fresh killing were performed

**...**

Clearly, the above data are results from *in vitro*
measurements, and it is uncertain how accurately they reflect the rate
of CTL-mediated 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 HIV-1 and expressing
HIV-1 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
PBMC-to-target 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
HIV-1-infected CD4 cells in the presence of uncultured PBMC from the
HLA-B8 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
B8-matched C8166 cells used 48 hr after infection with 10
TCID_{50} of HIV IIIB. At a PBMC-to-target ratio of 64:1, we
find 17% specific lysis after 8 hr, corresponding to a target cell
half-life of 1.2 days. At a ratio of 32:1, we obtain a half-life of 2.4
days (Fig. (Fig.22*C*).

Results derived from published studies of fresh responses by many other
workers (12–18) can also be used to calculate target cell half-lives
(Fig. (Fig.22*D*). In some patients, the half-life of target cells
is less than 12 hr at PBMC-to-target ratios of 50:1 or greater. On the
other hand, many HIV-1-infected individuals do not show strong
responses and target cell half-life by CTL killing would exceed 48 hr.

To explore a possible correlation between the rate of CTL-mediated
lysis and disease stage of a patient, we calculated the half-life 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. Fig.22*E* shows the calculated
half-life of target cells with respect to the strongest response among
the Gag-, Pol-, Nef-, or Tat-specific CTL in each patient. There is no
correlation between the CD4 count of a patient and the half-life of
target cells. At a PBMC-to-target ratio of 50:1, the average rate of
CTL-mediated lysis is 1.0 ± 0.57 per day, which corresponds to a
half-life of about 0.7 day. Note that the lack of correlation between
viral turnover and CD4 count (Fig. (Fig.1)1) is paralleled by a lack of
correlation between the fresh CTL response and CD4 count (Fig.
(Fig.22*E*).

In contrast to the anti-Gag, -Pol, -Nef, or -Tat responses, which are
mostly due to CTL activity, the anti-Env response is likely to contain
a large proportion of antibody-dependent cell cytotoxicity (25–27).
The calculated average rate of anti-Env-mediated lysis *in
vitro* is 1.24 ± 0.66 per day, corresponding to a half-life
of about 0.6 day. However, it is not clear how important
antibody-dependent 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 CTL-mediated lysis
can make a significant contribution to the turnover rate of
HIV-infected cells *in vivo*. If HIV directly kills
productively infected cells, does CTL-mediated 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 CTL-mediated 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 CTL-mediated 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. (Fig.3).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.

*y*

_{1}are newly infected cells that do not produce virus and are not killed by CTL,

*y*

_{2}are cells that can be killed by CTL, and

**...**

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 one-step 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 Table11 gives numerical values for the effect of CTL killing. For a cytopathic virus, the half-life 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 CTL-mediated 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 half-life. Responses equivalent to 10% lysis in 4 hr eliminate 99% of infected cells.

*T*

_{1/2}, and the fraction,

*F*, of cells killed by CTL according to model1

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 half-life 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. (Fig.4).4). Thus, the rate of
CTL-mediated 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 CTL-mediated
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 CTL-mediated
lysis.

There is one additional explanation for why CTL-mediated 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 CTL-mediated 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
CTL-mediated 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 CTL-mediated 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 CTL-mediated lysis. Clearly, the same argument
applies to model 2.

Fig. Fig.44 shows the slope of virus decline during drug therapy as a function of the rate of CTL-mediated lysis. For both model 1 with heterogeneity and model 2, we find that the virus decay slope is roughly constant provided that HIV-1 is cytopathic and would also kill cells in the absence of a CTL response. If HIV-1 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. (Fig.1)1) suggests that HIV-1 is cytopathic. Otherwise, one would have to argue that all individuals measured so far have a minimum CTL-mediated (or immune-mediated) 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 half-life of productively infected cells varies from 10 to 100 days in different individuals (32).

Our analysis reveals that also low levels of CTL-mediated 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 antigen-specific 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 T-cell 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 HIV-1 disease progression, the crucial question is to
what extent immune responses reduce virus load in infected patients
(34). Our results suggest that CTL-mediated 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, Xiao-Li Huang, Zheng Fan, Philip Goulder, Matt Collin, Ann Edwards, Paul Giangrande, Sebastian Bonhoeffer, Barbara Bittner, the staff of the Department of Genito-Urinary 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

Abbreviations: CTL, cytotoxic T lymphocyte(s); PMBC, peripheral blood mononuclear cell(s).

## References

**National Academy of Sciences**

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- Cytotoxic T lymphocytes and viral turnover in HIV
type1infectionCytotoxic T lymphocytes and viral turnover in HIV type1infectionProceedings of the National Academy of Sciences of the United States of America. Dec 24, 1996; 93(26)15323

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