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* Theoretical Biology, Utrecht University, Utrecht, The Netherlands;
Aaron Diamond AIDS Research Center, The Rockefeller University, New York, NY 10016; and
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545
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Abstract |
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1% for CD4-CD45RA+ T cells. In SIV-infected monkeys with high viral loads, the turnover rates of T cells were increased 2-fold, and that of memory T cells 3-fold. The turnover of CD4+CD45RA+ naive T cells was increased 2-fold, whereas that of CD4-CD45RA+ naive T cells was marginally increased. B cells and NK cells also had increased turnover in SIV-infected macaques, averaging 3 and 2.5% per day, respectively. For all cell types studied here the daily turnover rate increased with the decrease of the CD4 count that accompanied SIV infection. As a consequence, the turnover rates of CD4+ T cells, CD4- T cells, B cells, and NK cells within each monkey are strongly correlated. This suggests that the cellular turnover of different lymphocyte populations is governed by a similar process which one could summarize as "generalized immune activation." Because the viral load and the CD4 T cell count are negatively correlated we cannot determine which of the two plays the most important role in this generalized immune activation. |
Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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One method of quantifying cellular turnover involves labeling dividing cells with the base analog 5-bromo-2'-deoxyuridine (BrdU),3 which can be administered via drinking water and substitutes for thymidine in newly synthesized DNA. BrdU+ cells can be easily detected by flow cytometry, and BrdU labeling has been widely used to study lymphocyte kinetics in animals (4, 14, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29). BrdU data (as depicted, see Fig. 2) can be described with three parameters. One characterizes the slope with which the fraction of labeled cells increases during BrdU labeling, another characterizes the loss rate of labeled cells after BrdU withdrawal, and the last defines the asymptotic fraction of labeled cells that would be approached if BrdU were given indefinitely. In a more methodological companion paper (30), we demonstrated that one can derive various mathematical models that allow one to estimate these three parameters from the data. In particular, we showed that the average turnover rate, which for a population at steady state is defined as the average death rate, is independent of the biological assumptions underlying a set of biologically reasonable mathematical models used for fitting BrdU data (30). In this study, we use one of these models to analyze BrdU labeling curves for a number of different lymphocyte populations.
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Materials and Methods |
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For defining B cells, an anti-CD20 Ab was used, giving a bright signal as shown in Fig. 1f. For NK cells, we used the CD3-CD8+CD16+ phenotype as an NK marker. Because CD16 Ag is also expressed on some monocytes, which are highly labeled with BrdU, it is necessary to gate the CD8+CD16+ population very tightly as shown in Fig. 1h. NK cells without CD16 expression were, therefore, not included in our study.
We use a simple population dynamical model developed by Mohri et al. (4) and report its parameters by converting them into average turnover rates (30). Briefly, the model considers activated cells, A, that have a source of s cells per day from elsewhere, and which proliferate and die at per cell rates 
and 
, respectively,
 | (1) |
Giving BrdU does not substantially perturb the lymphocyte dynamics, we assume that the various lymphocyte populations remain at steady state throughout the labeling study. Thus, without loss of generality, one can scale the steady state total number of cells to one, i.e., R + A = 1. Because at steady state the total number of activated cells remains constant, i.e., dA/dt = 0, one obtains for the source s = ( - )A.
Let L be the fraction of cells labeled with BrdU (L (0) = 0), and U the fraction of unlabeled cells. During the labeling period, unlabeled cells are lost by death and by proliferation. Assuming that during the labeling period the source yields labeled cells (30), and that labeling is 100% efficient so that upon division each progeny acquires label, one obtains from equation 1 (4, 29, 30),
 | (2) |
- )(1 - R) and U = 1 - L - R, this has the solution
 | (3) |
= 1 - R is the maximum that the fraction of labeled cells would approach if BrdU were given indefinitely. If labeling is <100% efficient we are overestimating during the labeling period (4, 29). However, the bone marrow aspirations suggested an adequate uptake of BrdU in proliferating cells (Fig. 1).
In the period shortly after BrdU administration has ended, division of labeled cells yields labeled daughter cells (4), because chromosomes with incorporated BrdU are segregated to both daughter cells. However, rapid clonal expansion represented by the source will yield unlabeled cells (30), due to dilution of BrdU to levels that are undetectable (32). Thus, one obtains from equation 1 that
 | (4) |
 | (5) |
From the model one can easily extract the quantities, + , characterizing the initial slope, or up slope, of the labeling curve, - characterizing the rate of decay of labeled cells after labeling has ended, or down slope, and the asymptote of the labeling curve. Thus, by fitting the model to the data, one can generally estimate the parameters , , and . However, different data sets have particular features which may require variants of this approach. For example, when the up and down slopes + and - are sufficiently similar, one can fit the data with a two parameter model fixing = 0. Similarly, whenever the data fail to suggest that a fraction of the cells remains unlabeled one can fit the data with a two parameter model fixing = 1. When both can be fixed one can fit the data with a one parameter model having only as a free parameter. Thus, we will fit the data with four models, i.e., the full three parameter "" model, two different two-parameter models, i.e., the "" and the "" model, and the one-parameter "" variant. For each variant we use the main result of the companion paper (30) and define the average turnover rate as 
= , where = 1 - R represents the fraction of activated cells, and is their rate of turnover. The resting cells are assumed to have a negligible turnover.
In adult monkeys, one expects that naive T cells are largely produced by the thymus and that they have little peripheral proliferation. Thus, for naive T cells the source s would be expected to reflect thymic output, and additionally one expects 
0. Because T cell maturation in the thymus follows a "conveyor belt"-type program (33), one expects labeled cells to continue appearing from the thymus after BrdU administration has been stopped. Thus the source of labeled cells is expected to be nonzero for a period of time after BrdU withdrawal. We decided to account for this by making the time at which BrdU administration ends, te, a free parameter. This is a correct procedure only in the case = 0. Otherwise extending te would allow additional labeled cells to be created by proliferation. Thus our "naive T cell model" (see Table III) maximally has three parameters (i.e., , , and te).
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remains very similar if a data set is fitted with any of the four models outlined above (see Fig. 1 in De Boer et al. (30)). We nevertheless prefer to fit each data set with the most appropriate model. The most appropriate model has sufficient parameters to explain the data, i.e., to allow for a good fit, but at the same time has no redundant parameters that hardly improve the quality of the fit. The quality of a fit is conventionally expressed as the "residual mean square", which is the residual sum of squares divided by the residual degrees of freedom, i.e., the difference between the number of data points and the number of free parameters (34). Thus, although adding a more or less redundant parameter to a model will obviously decrease the residual sum of squares, it will probably increase the residual mean square. Several conventional statistical procedures allow one to select the most appropriate model for a given data set. The partial F test compares two nested models by the difference between their residual sum of squares per additional parameter, divided by the residual mean square of the largest of the two models (34). Akaike’s Information Criterion is also based on the residual mean square but adds a penalty for the number of parameters (35). Because our estimate for the average turnover rate is fairly independent of the precise choice of the model, there is, for our special case, no reason to be conservative with selecting a more complicated model. Therefore, we opted for selecting the model with the lowest residual mean square. Technically, this corresponds to doing a partial F test and accepting the more complicated model whenever the F value is larger than one. We tested this approach by also doing a somewhat more conservative partial F test (i.e., testing whether F >1.6 corresponding to p <0.25). This yielded very similar results: in only 2 of the 120 fits, did we have to pick a simpler model, but as expected (30) we nevertheless obtained very similar estimates for the average turnover (not shown). Parameter estimates were obtained using the DNLS1 subroutine, from the Common Los Alamos Software Library, which is based on the Levenberg-Marquardt algorithm (36) for solving nonlinear least-squares problems. These parameters were used to calculate the predicted T cell population size. Ninety-five percent confidence intervals for the inferred parameters were then determined using a bootstrap method (37), where the residuals to the optimal fit were resampled 500 times.
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Results |
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Typical examples of the BrdU labeling in CD4+ and CD4- T cells from an SIV infected and an uninfected macaque are given in Fig. 2, a and b. The data from the infected monkey were best fitted with the three-parameter model, and those from the uninfected monkey with the one-parameter model. The turnover rate of CD4+ and CD4- T cells in uninfected rhesus macaques is 1% per day (Table I). The average turnover rate in SIV-infected macaques with a high viral load is increased 2-fold, and that in macaques with a low viral load is increased 1.5-fold. This confirms the previous interpretation of these data that SIV infection increases the cellular turnover in both CD4+ and CD4- T cells (4), but in this study the average increase remains <2-fold. Although the increase in the turnover rate is relatively small, these results are statistically significant because there is hardly any overlap in the average turnover rates of CD4 and CD8 cells in highly infected and uninfected macaques. An estimated 2-fold increase in cellular turnover of CD4+ T cells is in good agreement with some human data (5), but is lower than other human data (11, 13). Our estimated 2-fold increase in the turnover of CD8+ T cells is also lower than that reported for HIV-infected humans (5, 11, 13).
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or the model). Fitting with = 0 should not be interpreted as evidence against T cell proliferation in these monkeys (30). Because total cell numbers remain at steady state, the total production of cells should always balance the average death rate in Table I, even if = 0. Fitting with = 0 could mean that most of the proliferation in T cells occurs during a clonal expansion involving so many divisions that labeled cells dilute their BrdU and appear as an unlabeled source (30, 32). This is one of the reasons why one can only reliably estimate an average turnover rate from these data (30). Naive and memory T cells
Typical examples of BrdU labeling in naive and memory CD4+ and CD4- T cells from the SIV-infected macaque H1348 and uninfected macaque U1426 are given in Fig. 3. The labeling of the total T cell population from these same macaques was illustrated in Fig. 2.
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The turnover rate of naive and memory CD4+ T cells in uninfected macaques is 0.6 and 1.0% per day, respectively (Tables II and III). Our estimate that the turnover rate in memory CD4+ T cells is only 2-fold higher than that in naive CD4+ T cells is relatively low (5, 11, 13, 38). In the CD4- T cell population there seems to be no difference in turnover between the naive and memory cells (see Tables II and III). This is in disagreement with other data (5, 11, 38), and may be due to the poor characterization of naive and memory T cells by the mere absence or presence of the CD45RA Ag (39). If in rhesus monkeys the CD45RA+ subpopulation of T cells is contaminated with Ag-experienced cells having a higher turnover than true naive T cells, we may indeed be underestimating the difference in naive and memory T cell turnover.
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3-fold in both the CD4+ and the CD4- compartment (see Table II). In the CD4+ compartment, the naive T cell turnover is almost 2-fold increased in monkeys with a high viral load (see Table III). For CD4-CD45RA+ T cells there is hardly any increase in the average turnover in SIV-infected monkeys (see Table III). Most of the memory T cell data are again fitted best with models lacking proliferation (i.e., the and the models). B cells and NK cells
The average turnover of CD3-CD20+ "B cells" and CD3-CD8+CD16+ "NK cells" in the four uninfected monkeys is 2% per day (Table IV). This may be biased by the high turnover in monkey U1458, whom at week four has peak values of 55 and 29% BrdU+ B cells and NK cells, respectively. This monkey had an unexpectedly low CD4 count in the peripheral blood (4), and it was later found that he died of hepatic degeneration associated with cachexia and wasting due to loss of gastrointestinal tract function. Excluding U1458, we obtain daily turnover rates of 1.8 ± 0.6 and 1.6 ± 0.6, for the B cell and NK cell averages, respectively. The daily turnover rates of B cells and NK cells are increased to 3 and 2.5%, respectively, in infected monkeys with a high viral load. In infected monkeys with a low viral load, the turnover rate is actually smaller than that in uninfected monkeys (which could be due to the aberrant uninfected monkey U1458). Thus, SIV infection also increases the cellular turnover of B cells and NK cells, albeit to a lower extend than in T cells. This confirms earlier observations (40).
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model in which = 0). This would be in agreement with an interpretation of considerable B cell production by the bone marrow and/or by considerable clonal expansion (30). Conversely, the NK cell data require a nonzero proliferation in 11 of the 15 cases (see Table IV). The two typical examples depicted in Fig. 2 indeed confirm that the NK cell data tend to have different slopes during the labeling and delabeling period, whereas the two slopes of the B cells are similar. Therefore, the NK cell data seem to suggest that the maintenance of NK cells involves proliferation in the form of peripheral renewal (30). Immune activation
Decreasing the CD4 T cell count in the peripheral blood tends to increase cellular turnover for all cell types studied here (Figs. 4 and 5). Although, similar data have been published before for T cells (4, 5, 13, 18), these correlations might not reflect cause and effect because the CD4 T cell count is typically correlated negatively with the viral load (13, 18). For the current data we also find a negative relation between the viral load and the CD4 count (Fig. 6d). Different studies disagree on the relative contribution of the viral load and the CD4 T cell count on immune activation: Cohen Stuart et al. (18) find that both have a partial contribution, Lempicki et al. (13) find no true effect of CD4 T cell count, and Leng et al. (41) find that the CD4 T cell count has the largest contribution.
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Although one could argue that a CD4+ T cell homeostatic response to low CD4 T cell counts could up-regulate cellular turnover in various cell types, it seems more likely that the common factor correlated with the CD4 T cell count is a global immune activation associated with viral Ags and/or other infections (11, 13, 18, 41, 42, 43, 44). Supporting evidence for this is the rapid decrease in cellular turnover in patients on anti-retroviral therapy long before the CD4 T cell counts have normalized (11, 13, 31).
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Discussion |
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, of the CD4+ and CD8+ T cell populations (4). However, the death rate estimated in Ref. 4 applied only to the subpopulation of activated CD4+ and CD8+ T cells, and not the entire population (30, 45).
The estimates of the average turnover rate, , provided in Tables I-III have somewhat narrower 95% confidence limits than the previously published estimates of . The reason for this is 2-fold. First, the average turnover rate is sensitive to events in both activated and resting cell populations and hence depends less on the detailed assumptions made about these subpopulations. Because activation and division of resting cells acts as a source of proliferating cells various tradeoffs among parameters can occur when matching experimental data. Because the average turnover rate hardly changes when these tradeoffs occur (30), we obtain better confidence limits on its estimate. Second, we use a statistical procedure to fit each data set with a model having the minimal number of parameters required to explain the data. This also narrows the confidence limits (30). These two improvements enable us to draw more reliable conclusions about T lymphocyte turnover in SIV- and SIV+ macaques, and to analyze data on additional subsets of cells.
The nature of the source is clearly of biological interest. The data that we obtain from BrdU labeling cannot fully define the source. However, we have previously shown (29) that we can replace the source by a population of resting cells that upon activation enters the proliferating compartment. Our published detailed analysis of this model shows that if the resting cells are truly resting, or if they divide very slowly compared with the rate of division of the activated cells, then one recovers a model with a constant source. In addition, we have recently analyzed 2H-glucose labeling data in humans using models with a constant source (31) and with models without a source but with a resting population that becomes activated (46, 47) and have shown that both models yield the same estimates for activated cell death rates. Finally, we have argued that BrdU dilution by clonal expansion provides an explanation for the source of unlabeled cells after BrdU withdrawal (32), and have shown that under these different interpretations our procedure of fitting an average turnover rate yields similar estimates (30). Thus, we have reasonable confidence that the nature of the source will not change our conclusions about the proliferating pool of cells.
We have found that monkeys with low CD4+ T cell counts tend to have higher average turnover rates in CD45RA+ "naive" and CD45RA- "memory" CD4+ and CD4- T cell populations, in CD3-CD20+ B cells, and in CD3-CD8+CD16+ NK cells. Thus, the turnover rates in the various populations are correlated positively, which suggest that generalized immune activation is driving the increased turnover. Moreover, because CD4+ T cell counts and viral loads are negatively correlated, increased immune activation could also be due to increased viral loads. In this data, the increase in average cellular turnover rates caused by SIV infection is typically <2-fold. This level of increase in cellular turnover is in good agreement with telomere data showing little effect of HIV infection on the average telomere length in naive and memory CD4+ T cells (17, 48), and with TCR rearrangement excision circle data showing a decrease in the TCR rearrangement excision circles per naive T cell in response to a small increase in the division rate (49).
Our estimated 2-fold increase in cellular turnover with SIV infection is smaller than estimates in HIV-1-infected humans obtained with the Ki67 mAb (5, 11, 13), or with 2H-glucose labeling (10, 31). Because the average turnover rate depends on the CD4+ T cell count (see Fig. 4), this is probably due to differences in the disease stage of the subjects in the various studies. Human patients with high CD4+ T cell counts have low fractions of Ki67+ T cells (8), whereas patients with low counts have high fractions of Ki67+ T cells (5, 11). Importantly, Ki67 data from Chakrabarti et al. (50) show that rhesus macaques naturally have a high percentage of T cells in division, i.e., 7% of the CD4+ T cells are Ki67+ and 7.8% of the CD8+ T cells, and that these percentages increase 2- to 3-fold upon SIV infection (50). Thus, the difference between the two studies in the fold-increase caused by the infection, i.e., 6-fold in humans and 2-fold in macaques, could be largely due to our higher estimated average turnover rate in healthy macaques. Additionally, there could be a methodological problem with Ki67. The Ki67 mAb labels cells during the late G1, M, and S phases of the cell cycle (51). However, nondividing activated cells remaining in the G1 phase may be Ki67+ (52, 53). In contrast to normal individuals, a large fraction of the CD4+CD45RO+Ki67+ T cells in HIV-infected patients are in the G1 phase of the cell cycle (53). Another study found that both in healthy controls and in HIV-1-infected patients, >40% of the Ki67+CD4+ T cells express CTLA-4, suggesting that these cells were not proliferating, whereas only 20% of the Ki67+CD8+ T cells were CTLA-4+ (41). To resolve this discrepancy between Ki67 measurements and cellular proliferation we need a method of translating Ki67 measurements into the corresponding proliferation rates. The excellent positive correlation between the fraction of Ki67+ cells and the estimated proliferation rate of CD4+ and CD8+ T cells in HIV-1-infected patients and healthy human controls labeled with 2H-glucose (31), suggests that such a translation is feasible.
BrdU labeling was recently applied to human HIV-1-infected patients (14). Because the authors fit a phenomenological model to the data, the comparison to our results is difficult. First, the authors find that during the delabeling phase the loss of the labeled fraction is biphasic, and therefore fit two exponential slopes. These slopes are interpreted as the death rates of two distinct subpopulations. However, from the more mechanistic models derived in this study and before (4, 29, 30) we know that the down slope reflects the difference between the rates of death and proliferation, rather than the death rate alone. This complicates matters substantially because the result that the phenomenological death rate is not affected by therapy (14) could mean that both proliferation (13) and death decrease during therapy, and that their difference remains similar. Second, the authors find that the percentage of labeled cells correlates positively with the plasma viral load, and that it decreases with treatment (14). This percentage attained after 30 min in vivo pulse labeling with BrdU should be proportional to what we call the average turnover rate. The higher the average turnover within a population the higher the fraction of labeled cells after a pulse labeling. Such an interpretation would allow for an agreement between the results because we find that the average turnover rate of various cell types correlates negatively with CD4+ T cell counts, which are inversely related to the plasma viral load.
If SIV/HIV infection increases the cellular turnover in various cell types, the obvious question is why are only the CD4+ T cell counts depleted by these lentiviruses. However, this question should be addressed carefully because HIV-1 infection differentially affects various lymphocyte subpopulations. For instance, the total CD8+ T cell population increases, but the naive CD8+ T cell subcompartment is depleted by HIV-1 infection (15, 16). There is evidence that the Th2-type immune activation caused by chronic helminth infections leads to decreased CD4+ T cell counts and increased CD8+ T cell counts (54), and the chronic immune activation associated with rheumatoid arthritis exhausts the T cell repertoire (without depleting naive or memory CD4+ T cell, however) (2). It remains unclear whether these other systems can be extrapolated to HIV-1 infection. Moreover, these observations still fail to explain why CD4+ T cells would be more vulnerable to chronic activation than other cell types. One obvious difference between CD4+ T cells and other cell types in HIV infection is that HIV infects CD4+ T cells, which as a consequence may die, or be cleared by the immune response. However, because only a small fraction, i.e., 0.1% or less, of all CD4+ T cells are productively infected at any given time (55, 56, 57), this explanation remains unsatisfying (58, 59) and needs further quantitative elaboration.
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Acknowledgments |
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mir, and Ruy Ribeiro for helpful discussions. We thank Cas Kruitwagen for statistical advice. |
Footnotes |
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2 Address correspondence and reprint requests to Dr. Rob J. De Boer, Theoretical Biology, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands. E-mail address: R.J.DeBoer{at}bio.uu.nl
3 Abbreviations used in this paper: BrdU, 5-bromo-2'-deoxyuridine, d-1, per day.
Received for publication January 28, 2002. Accepted for publication December 23, 2002.
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S. Moir, A. Malaspina, O. K. Pickeral, E. T. Donoghue, J. Vasquez, N. J. Miller, S. R. Krishnan, M. A. Planta, J. F. Turney, J. S. Justement, et al. Decreased Survival of B Cells of HIV-viremic Patients Mediated by Altered Expression of Receptors of the TNF Superfamily J. Exp. Med., September 6, 2004; 200(5): 587 - 600. [Abstract] [Full Text] [PDF]
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R. J. De Boer, D. Homann, and A. S. Perelson Different Dynamics of CD4+ and CD8+ T Cell Responses During and After Acute Lymphocytic Choriomeningitis Virus Infection J. Immunol., October 15, 2003; 171(8): 3928 - 3935. [Abstract] [Full Text] [PDF]
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, the uninfected monkey U1426. Parameters in a: 
