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D. C. Macallan et al.
Eur. J. Immunol. 2003. 33: 2316–2326
Measurement and modeling of human
T cell kinetics
Derek C. Macallan1, Becca Asquith2, Andrew J. Irvine1, Diana L. Wallace3,
Andrew Worth3, Hala Ghattas1, Yan Zhang1, George E. Griffin1, David F. Tough3
and Peter C. Beverley3
1
2
3
Department of Infectious Diseases, St George’s Hospital Medical School, London, GB
Department of Immunology, Wright-Fleming Institute, Imperial College, London, GB
Edward Jenner Institute for Vaccine Research, Compton, Newbury, GB
The ability to measure, describe and interpret T cell kinetics is pivotal in understanding normal lymphocyte homeostasis and diseases that affect T cell numbers. Following in vivo
labeling of dividing cells with 6,6-D2-glucose in eight healthy volunteers, peripheral blood T
cells were sorted by CD4, CD8 and CD45 phenotype. Enrichment of deuterium in DNA was
measured by gas chromatography-mass spectrometry. A novel model of T cell kinetics,
allowing for heterogeneity within T cell pools, was used to analyze data on acquisition and
loss of label and calculate proliferation and disappearance rates for each subpopulation.
Proliferation rates for CD45RO+CD8+ cells and CD45RO+CD4+ cells were 5.1% and 2.7% /
day, respectively (equivalent doubling times: 14 and 26 days). CD45RA+CD8+ lymphocytes
and CD45RA+CD4+ lymphocytes had slower proliferation rates, 0.5% and 0.6% / day,
respectively (doubling time about 4 months). Disappearance rates of labeled cells were similar for all cell types (7%–12% / day) and exceeded corresponding proliferation rates. This disparity may be understood conceptually in terms of either phenotypic heterogeneity (rapid
versus slow turnover pools), or history (recently divided cells are more likely to die). The new
kinetic model fits the data closely and avoids the need to postulate a large external source
of lymphocytes to maintain equilibrium.
Key words: T Lymphocyte / Cellular proliferation / Memory / Human
1 Introduction
Proper functioning of the adaptive immune system, with
the ability to rapidly up- and down-regulate T cell
responses, requires a T cell pool with both adequate
diversity, in terms of functional attributes and breadth of
antigenic specificity, and quantity, that is adequate numbers of cells in each subpopulation. Maintenance of the
diversity and quantity of T cell pools is critically dependent upon the kinetics of the cells that constitute those
pools, specifically the balance between proliferation and
disappearance rates for each cell subpopulation.
Understanding how proliferation and death rates are balanced to allow acute expansions within distinct populations and the incorporation of new memory cells without
loss of diversity or functional capability depends upon
adequate tools to measure in vivo kinetic behavior of T
cells. Bromodeoxyuridine (BrdU) labeling in murine and
[DOI 10.1002/eji.200323763]
Abbreviation: BrdU: Bromodeoxyuridine
0014-2980/03/0808-2316$17.50 + .50/0
Received
Revised
Accepted
14/11/02
8/5/03
4/6/03
ovine studies has contributed enormously to our understanding of T cell homeostasis [1]. In humans, disappearance rates of cells bearing chromosomal damage
induced by diagnostic or therapeutic irradiation have
confirmed heterogeneity within T cell pools; CD45RO+
cells disappear more rapidly than their CD45RA+ counterparts [2]. More recently, stable (non-radioactive) tracer
studies have directly measured T cell proliferation rates
in vivo in healthy individuals and in HIV infection, initial
studies yielding proliferation rates of about 0.9% and
0.5% / day for CD4 and CD8 cells, respectively, in
healthy subjects [3, 4].
Understanding T cell physiology from labeling data
depends critically upon the models used in interpretation. Recent development of such modeling approaches
has mostly occurred in the context of studies of T cell
kinetics in HIV infection [5]. The proposition that CD4+
lymphocytes have very high turnover rates was based on
rapid rises in CD4 numbers observed on initiation of antiretroviral therapy (HAART) [6] but indirect assessments
of CD4 population kinetics in HIV infection have been
conflicting: for example, major reductions in telomere
length were not found [7] but Ki67 expression was
© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Immunol. 2003. 33: 2316–2326
increased [8]. Initial studies using deuterium-labeled glucose and a simple single-compartment model in HIV
infection suggested that T cell turnover is increased by
about fourfold in the CD4 population and sixfold in the
CD8 population [4]. Subsequent analyses, however,
have relied upon more complex approaches.
Simple kinetic models based on the classical precursorproduct relationship apply well to homogenous pools of
molecules. However, cell kinetics are more complex
because cells are heterogeneous both in phenotype, i.e.
what type of cell, and in history, i.e. what has recently
happened to the cell. Evidence from several studies suggests that both kinds of heterogeneity may affect cell
kinetics [9–11]. This implies that a cell population cannot
be treated as kinetically homogeneous with a single turnover rate representing equal proliferation and death
rates. The inability to fit a model with a single ‘turnover
rate’ to T cell labeling data [12, 13] may be a manifestation of kinetic heterogeneity. Instead of a single turnover
rate, it is commonly found that the measured proliferation rate is less than the measured death rate despite the
population size remaining constant. Some have sought
to resolve this disparity by postulating non-proliferative
entry of cells from an external pool, mathematically represented by a ‘source’ term; such a model has recently
been described in the context of HIV infection [13]. However, there are difficulties in this approach, discussed
below, relating to the magnitude of the source term
derived and the nature of its physiologic correlate.
We have sought to address this issue by investigating
the kinetic behavior of T cells in healthy young volunteers
using short, 24-h, labeling studies with deuteriumlabeled glucose. T cells were sorted into major subpopulations (CD4 and CD8) and according to CD45 phenotype. As expected, we were unable to describe the measured data using a single-pool model with a single turnover rate. We therefore developed a new model and
applied it to the experimental data to describe labeling in
a pool at steady state without requiring equality of the
observed proliferation and disappearance rate constants
and without the need to invoke a source term. We demonstrate how such a model is consistent with the known
physiology of the immune system and suggest conceptual models on the basis of heterogeneity and history
that correlate with the mathematical model. Finally by
analyzing data in this way, we find we are able to draw
conclusions about the normal organization and regulation of T cell pools.
Measurement and modeling of human T cell kinetics
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2 Results
2.1 Labeling of lymphocyte populations
Cell turnover was assessed by quantitating the incorporation of deuterium from deuterated glucose into the
DNA of dividing cells [14, 15]. Eight healthy volunteers
received an infusion of deuterium-labeled glucose (6,6D2-glucose) for 24 h. Blood samples for estimation of
deuterium enrichment in DNA of lymphocyte populations
were taken on days 3, 4, 10 and 21 after commencement
of the infusion (taken as day 0), or on the closest possible days thereto, together with late samples ( G 21 d) in
three subjects. The percentage of labeled lymphocytes
in peripheral blood after labeling are shown in Fig. 1,
according to expression of CD4, CD8 and CD45. The
magnitude of labeling, or peak height, directly reflects
the proliferation rate; for both CD8+ and CD4+ lymphocytes this was considerably greater for CD45RA–
(CD45RO+) cells than their CD45RA+ counterparts. Kinetics were similar for CD8+CD45RO+ and CD4+CD45RO+
populations.
Preliminary studies (not shown) indicated that there was
a lag-time to peak labeling in peripheral blood and that
the peak had not been reached by 2 days post-infusion.
Current studies therefore included samples from either
the third or fourth post-labeling day or both. When both
were included, day 4 exceeded day 3 labeling in approximately half of the series, suggesting that peak labeling in
peripheral blood with this protocol occurs between
days 3 and 4, about 2.5 days after the end of the infusion. We assume that this lag is due to a delay between
division, which primarily occurs in lymph nodes and lymphoid organs, and release into blood, where labeled cells
are detected.
2.2 Development of model for analysis and
interpretation
Kinetics of label incorporation and loss were interpreted
by fitting a mathematical model to the data: proportion of
labeled deoxyadenosine over time.
The amount of deoxyadenosine present in the DNA of a
population of cells can be considered as a pool of A mol
(Fig. 2). This amount will be proportional to the total
number of cells, being proportional to the quantity of
nuclear DNA. At steady state, the proliferation rate (p)
and the average disappearance rate (d) for the whole
pool are matched and A remains constant (Fig. 2). The
term p is defined as the proportion of cells undergoing
division per unit time and is expressed in %/day; d is
similarly defined for the number of cells disappearing
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Eur. J. Immunol. 2003. 33: 2316–2326
Fig. 1. Enrichment curves for lymphocyte subsets. Enrichment of deuterium in deoxyadenosine (mean ± SD of triplicate measurements) in lymphocyte populations following 24-h infusion of 6,6-D2-glucose. Values are expressed as proportion of labeled cells
relative to total cells in each subpopulation (equivalent to A*/(Ab) in the model in Fig. 2); lines represent best-fit curves.
from the pool and includes both death within and exit
from the pool, the latter either by trafficking or by phenotypic transformation.
During the labeling period, if a cell divides, then each of
the two new cells produced will contain one strand of
original DNA and one newly synthesized strand [16]. The
newly synthesized strands, equivalent to the number of
new cells, will contain labeled deoxyadenosine, the
quantity of which will depend upon the proportion of
deoxyadenosine triphosphate molecules that are
labeled. As the deoxyribose moiety of deoxyadenosine is
Eur. J. Immunol. 2003. 33: 2316–2326
Measurement and modeling of human T cell kinetics
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labeled cells (d*) and the amount of labeled deoxyadenosine (A*) (Fig. 1). Further divisions of a labeled cell do not
result in loss of label from the pool, thus d* only reflects
disappearance of cells from the pool [16]. Combining
these terms, the rate of change of labeled deoxyadenosine can be described as:
Where ; is the length of the labeling period.
Solving analytically yields:
Fig. 2. Model for interpretation of lymphocyte enrichment. In
a pool of cells that contains a total amount of deoxyadenosine, A (proportional to the total number of cells and
assumed to be constant), new cells are produced with an
average proliferation rate, p, and lost at rate d. If the pool is
at steady state, p=d. Infusion of labeled glucose results in
the accumulation of labeled deoxyadenosine, whose
amount is given by A*, at a rate determined by the adjusted
plasma glucose enrichment, b, and the average rate of proliferation, p. During and after labeling, labeled deoxyadenosine is lost from the lymphocyte pool at a rate d*. In general
d* will be greater than the average disappearance rate d.
primarily synthesized from glucose, the proportion of
labeling in deoxyadenosine is directly proportional to the
proportion of glucose molecules in plasma that are
labeled [14]; this is measured experimentally. However,
there is some dilution of deuterium between plasma glucose and deoxynucleotide triphosphates; this was taken
to be a constant 0.65, as previously described [14]. For
the purposes of modeling, these two factors are combined into a single factor b, the probability that an incorporated deoxyadenosine molecule will be labeled, which
represents the mean precursor enrichment for DNA synthesis.
during the labeling period
after the labeling period.
In this model no assumption of equality between p and
d* has been made; p represents the average proliferation
rate of the whole population, whereas d* refers only to
labeled cells (i.e. cells that divided during the labeling
period). For a kinetically heterogeneous population, even
one at steady state, these two rates will not be the same,
as discussed below.
The model was fitted to the experimental data expressed
as the percentage of labeled deoxyadenosine at each
time-point (Fig. 1), equal to A*/(Ab) in the above description. Values for p and d* were derived for each lymphocyte subset in each individual.
2.3 Proliferation rates of lymphocyte
subpopulations
The number of newly divided cells depends on the total
number of cells and the average rate of proliferation (p) of
these cells. The rate of increase of labeled deoxyadenosine (A*) is therefore given by bpA, where A is the total
amount of deoxyadenosine (Fig. 1).
Curves generated using the model described above
appeared to provide a good fit to the measured data
points (Fig. 1), whereas it was not possible to fit the data
with predictions from a single pool of equal proliferation
and death rate. The peak of the curve is seen at time ;
(1 day); proliferation rates thus allow for the fact that
some cell death may have occurred between division
(primarily in lymph node) and appearance in peripheral
blood.
Loss of labeled deoxyadenosine, by death, migration of
cells out of peripheral blood, or change of cell phenotype, is given by A*d*, the product of the rate of loss of
Best estimates for average proliferation rates are given in
Table 1 and illustrated in Fig. 3. In cases where it was not
possible to obtain a reliable fit to the data, no parameter
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Eur. J. Immunol. 2003. 33: 2316–2326
Table 1. Proliferation and disappearance rate constants for T cell populationsa)
a)
Errors on estimates of p and d* were determined by the asymptotic covariance matrix method. Abbreviations: n/f, not possible to
fit data; n/a, not applicable, only three data points.
b)
No detectable incorporation of label, proliferation rate, p, therefore taken to be zero.
c, d, e) Because of low incorporation it was not possible to obtain a good fit to data, so values for p were generated by curve fitting but
should be considered approximate estimates only.
f, g)
Significant differences for proliferation rate constant, p, for CD45RO+ versus CD45RA+ (probability X 0.05 by Wilcoxon signed
ranks test, 2-tailed).
h, i)
Significant differences for d* versus corresponding proliferation rate constant (probability X 0.05 by Wilcoxon signed ranks test,
2-tailed).
Eur. J. Immunol. 2003. 33: 2316–2326
Measurement and modeling of human T cell kinetics
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2.5 Whole-body lymphocyte turnover
Total appearance rates in blood for CD8+CD45RO+ and
CD4+CD45RO+ cells were estimated, using peripheral
blood lymphocyte counts and the relative proportions of
the different cell subtypes, and found to be approximately 7.4 and 7.1×106/l per day, respectively. For
CD45RA+ cells, production rates were significantly lower,
1.1 and 2.6×106/l per day for CD8 and CD4 cells, respectively. Taking individual blood volumes, predicted from
gender, weight and height [17], into account, total T cell
appearance in blood was calculated to be about 8×107
cells/day. If this production rate is typical of the whole
lymphoid population and if 2% of lymphocytes are in
blood at any one time [6], total T cell production is likely
to be of the order of 4×109 cells/day.
Fig. 3. Proliferation and disappearance rates of lymphocyte
subpopulations. Model estimates of p and d* for lymphocyte
subsets. Standard deviations of estimates are shown in
Table 1.
estimate is shown (Table 1). Mean proliferation rates for
CD8+CD45RO+ and CD4+CD45RO+ lymphocytes were
5.1% and 2.7% / day, equivalent to doubling times of 14
and 26 days, respectively. CD45RA+ cells had much
lower proliferation rates, 0.5% and 0.6% / day for CD8+
and CD4+ cells, respectively, consistent with longer doubling times of about 154 and 118 days, respectively
(probability X 0.05 versus corresponding CD45RO+ cells).
Exclusion of those estimates of p with a high coefficient
of variation did not substantially affect the conclusions.
2.4 Disappearance rates of lymphocyte
subpopulations
Disappearance rates for labeled cells, calculated using
the same model, yielded consistently higher values than
corresponding proliferation rates for all cell types
(Table 1). Mean disappearance rates for the four lymphocyte subpopulations ranged between 7% and 12% / day,
consistent with mean half-lives of between 6 and
10 days, although the inter-individual variation was far
greater than this and some values had large standard
deviations on the estimate of d*. The observation that the
disappearance rate of labeled cells (d*) is greater than
the average proliferation rate of cells (p) for all cell populations suggests that cells that proliferate are more likely
to be lost during the follow-up period.
3 Discussion
Our investigation of T cell kinetics in healthy young
adults has revealed several key points. Firstly, data from
in vivo labeling studies may be modeled using a simple
approach allowing for heterogeneity within T cell subpopulations. Secondly, in all human cell types studied
using this model, the measured disappearance rate
exceeded the measured proliferation rate (discussed
below). Thirdly, using such a model, normal division rates
and total production rates for T cell subpopulations
defined by their CD4, CD8 and CD45 phenotype may be
described and compared. Fourthly, despite marked differences in proliferation rates, similar disappearance
rates were observed for labeled cells within both
CD45RO+ and CD45RA+ cell populations.
The model we have employed (Fig. 2) encompasses heterogeneity in the T cell pool by allowing the proliferation
rate (p) and the disappearance rate (d*) to differ; the logic
of this approach is that p represents the average proliferation rate of the whole population, whereas the measured disappearance rate, d*, refers only to the loss of
labeled cells (i.e. cells that divided during the labeling
period). For a kinetically heterogeneous population, even
at steady state, these two rates will differ as cells that
label may have different death rates to those that do not.
It is commonly assumed that disparity between measured proliferation and death rates is not compatible with
a population at steady state. In some models, this perceived problem is ‘solved’ by the introduction of a term
describing an alternative source of new cells that may be
labeled, unlabeled or a mix of both labeled and unlabeled cells [13, 18]. A similar approach has been proposed for quantification of BrdU labeling studies [19].
Although a small source of cells that divide but fail to
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label during labeling is conceivable, models of labeling in
HIV infection allowed for labeling in the source term,
even after discontinuation of infusion, and arrived at a
value for source input of about 10-times the proliferation
rate of cells within the pool [13]. The physiological correlate of such a large source is difficult to define and its
magnitude implies that the focus of our attention on ‘proliferation’ has been misplaced, as the influx of cells from
an external source is by far the greater term. A subsequent development of this model subdivides cells into
resting and activated states, with terms for the transition
between states and the proliferation rate within the activated cell pool but retains the source term and the concept of homogeneity within pools [20].
We have not introduced a source term, arguing instead
that different death and proliferation rates are a natural
feature of a heterogeneous population [21]. Our model
does not disprove the presence of a relatively small influx
of cells from an external source. Indeed, over a longer
time-frame, thymic output is thought to make a major
contribution to the maintenance of T cell populations;
certainly there is evidence that thymic output is pivotal in
determining the extent of immune reconstitution following stem cell transplantation and treatment of HIV infection [22, 23]. However, the majority of daily turnover of T
cell pools seems to occur by proliferation of cells within
those pools rather than input from other pools.
In this study, observed disappearance rates exceeded
observed proliferation rates for all defined T cell populations. We take disappearance of label as being primarily
indicative of cell death, either within the circulation or by
migration of cells to lymph nodes prior to death [24].
Redistribution may be an important factor in T cell kinetics in HIV infection, where homing of CD4 cells to lymph
nodes may precede apoptosis [24], but is less likely to
account for disappearance of labeled cells in this study,
as lymphocytes at all sites are labeled and no late reappearance of label seems to occur in peripheral blood. We
have not explicitly included phenotype switching in this
model. A cell leaving a pool by phenotype switching
would be included in the term d*. Conversion of
CD45RA+ to CD45RO+ might contribute to the rapid
apparent disappearance rate of CD45RA+ cells, discussed below; CD45 RO+ to CD45RA+ reversion probably also occurs but is unlikely to contribute significantly
in the short time-frame considered.
At steady state, the number of new cells produced must
equal the number of cells that die. How can such a situation arise when there is a disparity between proliferation
and death rates? The approach of adding a large source
term [13], discussed above, is illustrated in Fig. 4a for
comparison but is not consistent with our model.
Fig. 4. Models consistent with disparity of proliferation and
disappearance rates. Our mathematical analysis is consistent with both (b) and (c) but not the ‘source’ model (a),
which is shown for comparison only. (a) Source model. The
disparity between p and d is matched by entry of cells at rate
s. (b) Two-pool model. The total lymphocyte pool consists of
a large slow-turnover pool, constituting a proportion, m, of
the total, and a small fast-turnover population, (1–m) of the
total, whose proliferation and death rates are indicated by
suffixes s and f. Both pools contribute to the measured proliferation rate in proportion to their respective sizes: p = mps
+ (1–m)pf. Similarly, disappearance from the slow pool is the
product of the number of labeled cells (mps) and the disappearance rate-constant (ds); for the fast pool, the product of
(1–m)pf and df. The disappearance rate, d*, is the sum of
these divided by the total number of labeled cells [mps +
(1–m)pf ]. During the labeling phase, a greater proportion of
cells become labeled in the faster pool, as pf G ps; in consequence, these cells have a disproportionate effect on the
unlabeling kinetics. (c) Activation-induced cell death model.
The resting pool comprises a proportion (m) of all cells.
Recently divided cells, comprising (1–m), may divide again,
at rate p1, but are more likely to die than resting cells: d1 G d0.
Labeled cells are therefore preferentially lost. As above, p is
given by the sum of labeling in the two pools and d*, assuming the term for reversion between pools to be small, is the
sum of the products of the death rates, d0 and d1, for resting
and recently divided pools, respectively, and the corresponding proportions of labeled cells, mp0 and (1–m)p1,
divided by the total number of labeled cells.
Eur. J. Immunol. 2003. 33: 2316–2326
In the model presented here, we argue that a measured
death rate that exceeds the measured proliferation rate
is a natural feature of labeling a heterogeneous lymphocyte population [23]. We suggest two ways of conceptualizing this. Firstly heterogeneity may be related to the
intrinsic programmed characteristics of the cell: Fastversus slow-turnover cells. According to this concept, for
each subpopulation, overall proliferation and death rates
will be matched, maintaining stability (Fig. 4b). The measured enrichment of label is the sum of labeling in both
fast and slow turnover compartments. However,
because fast-turnover cells incorporate a greater proportion of label during the infusion, they are overrepresented in the labeled pool and thus have a disproportionate influence on the observed disappearance
rate. Although illustrated for two pools in Fig. 4b, ‘turnover’ will be a continuous, not a dichotomous, variable
and there will therefore be multiple pools of higher and
lower turnover rates in the physiological setting.
Alternatively, such heterogeneity may be a consequence
of the recent division history of the cell: Has this cell
recently divided? According to this approach, proliferation and death are not independent but rather occur as
temporally linked events (Fig. 4c). Such a link may operate to prevent excessive expansion of a dividing clone
and may occur as a consequence of regulatory events
within the cell. For example, in acute EBV infection, rapidly dividing cells show down-regulation of the antiapoptotic factor bcl-2 [25]. In the same disease state, we
have directly demonstrated rapid death of proliferating
cells [26]. Alternatively, such a link between proliferation
and disappearance may be mediated by intercellular signaling via molecules such as Fas/Fas-ligand. The latter
process would be consistent with mathematical models
proposed to explain how density-dependent factors may
maintain diversity within the immune system [27]. Where
death is positively related to the age of a cell, the converse would be true; thus were one able to label erythrocytes in this manner, the measured death rate would be
less than the proliferation rate in the short term, as younger cells tend to live longer than older cells, and d* would
be less than d.
In either case, proliferation would be expected to be
linked with expression of markers of cell death. In one
preliminary study of monocyte-depleted PBMC in a single individual 3 days post-labeling, Annexin-V+ cells had
labeling rates three-times higher than Annexin-V– cells,
demonstrating that such currently apoptotic cells were
more likely to have divided 3 days ago than those that
were not currently apoptotic.
The above argument suggests that the measured average disappearance rate, d*, will depend upon the dura-
Measurement and modeling of human T cell kinetics
2323
tion of labeling. With longer labeling periods, it has been
suggested that p and d* will tend to converge [21]. Long
labeling periods may saturate subpopulations that are
rapidly turning over, and lead to an underestimate of proliferation rate and this may be a disadvantage of 7-day or
longer labeling protocols. The 24-h labeling period
described here more closely resembles a ‘pulse-chase’
experiment and allows the labeling and unlabeling of
fast-turnover cells to become apparent.
It should be noted that the model that we have used differs significantly from one-compartment source models
used by other groups [13, 14] (even in the case where the
source is assumed to be the output of resting cells or
cells that are slowly turning over). Our model is more akin
to recent two-compartment models [16]. A twocompartment model is not suitable for analyzing our
data-set as it requires far more data points.
We have confirmed that surface markers, such as CD45,
define kinetically distinct populations; in data reported in
the literature, where CD45RA+ and CD45RO+ subpopulations have not been separated, the reported rate must
therefore represent a composite value. Similarly, other
surface markers may define kinetically distinct populations and such possibilities are currently being investigated.
In this study we have been able to define proliferation
rates for normal lymphocytes in healthy human subjects
according to their expression of CD4, CD8 and CD45
isoforms. Mean doubling times of 14 and 26 days were
estimated for CD8+CD45RO+ and CD4+CD45RO+ cells,
respectively, whilst corresponding CD45RA+ cells had
significantly slower doubling times, about 5 and
4 months, respectively (Table 1; probability X 0.05). The
daily production rates we obtained, taking the size of cell
populations into account, were very similar to those cited
elsewhere for healthy individuals studied using the same
technique [4]. Such data apply to a healthy European
population but might not apply in other genetic and environmental contexts; for example, studies of T cell subpopulations have shown marked differences in the proportions of naive- and memory-phenotype T cells
between Ethiopian and European cohorts [28].
Immune memory is thought to reside primarily in cells of
CD45RO+ phenotype. This study confirms that such
‘memory’ cells have a faster rate of turnover than ‘naive’
cells, as previously described in human in vivo labeling
studies [4], in murine studies using BrdU [1], and in
human studies based on disappearance of radiationinduced chromosomal damage, where turnover rates in
CD45RO+ cells were eight-times those in CD45RA+ cells
[2]. However, the absolute rates found using chromo-
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D. C. Macallan et al.
somal analysis were considerably slower than the rates
found here; this disparity might arise from differences in
the population of cells studied, exclusion of early celldeath events in the radiation studies or pathological
effects on irradiated cells.
Interestingly, death rates of all populations studied were
quite similar, despite wide variation in proliferation rates.
Proliferating CD45RA+ cells therefore appear to have
similar death rates to their CD45RO+ counterparts. Such
cells might represent true primed cells with a revertant
CD45RA+ phenotype [29] that have retained a high turnover; separation by other surface markers may help
resolve this question.
The approach described in this report is constrained by
several practical aspects. The small number of subjects,
and limited number of data points per subject, limit the
extent of modeling and the number of variables that can
be estimated. It is assumed that the death rate before the
peak, 3- or 4-day, time-point is equal to that after this
time; underestimation of the early death rate would lead
to underestimation of p. Simpler labeling protocols may
be possible and the use of alternative DNA precursors
may make experiments easier to perform [15]. Furthermore, unlike FACS-based techniques using reagents
such as BrdU, this approach does not allow one to identify the label in individual cells.
In summary, we have investigated normal T cell kinetics
using a kinetic approach that allows the described proliferation and disappearance rates to differ. Observed disappearance rates were consistently higher than corresponding proliferation rates; such disparity is consistent
with the known physiology of the immune system. Application to normal data has demonstrated several key
characteristics of T cell homeostasis; utilization of this
approach to model kinetic data in disease states is likely
to prove a useful tool to further dissect abnormalities of
lymphocyte kinetic behavior.
4 Materials and methods
4.1 Subjects
Subjects (four male, four female; mean age 25 years,
range 19–34) gave written informed consent under protocols approved by the Local Research Ethics Committee. The mean peripheral blood lymphocyte count was
1.9 × 109/l (range 0.9–2.8).
Eur. J. Immunol. 2003. 33: 2316–2326
4.2 In vivo labeling protocol
Labeling consisted of primed constant intravenous infusion for 24 h of 6,6-D2-glucose, 1 g/kg body-weight in 1 l
0.45% saline (Cambridge Isotopes, MA, USA), as previously described [14, 15]. During the infusion, the diet
consisted of small, low-energy meals; blood samples
were taken approximately 4-hourly for estimation of
plasma glucose enrichment. Blood samples for estimation of deuterium enrichment in DNA were taken on
days 3, 4, 10 and 21 after commencement of the infusion. In some subjects, it was not possible to take blood
on these days and blood was taken on the closest possible day as shown. Late samples ( G day 21) were taken in
three subjects (day 69 in subject 1, day 43 in subject 5
and day 42 in subject 7) and for such subjects the whole
disappearance curve was included in modeling.
4.3 Cell sorting
PBMC isolated from 50 ml of heparinized fresh blood
samples by Ficoll-Paque (Pharmacia, St Albans, GB)
density gradient centrifugation (after which PBMC were
resuspended at 1×107/ml in PBS + 0.2% BSA) were
stained with CD3–RPE (Serotec Ltd, Oxford, GB), then
sorted into CD3+ and CD3– fractions using a MoFlo cytometer (Cytomation, CO, USA). CD3+ cells were further
stained with biotinylated antibody against CD8 (Serotec)
+ streptavidin–allophycocyanin (Sav–APC, PharMingen,
San Diego, CA, USA) together with CD45RA–RPE–CY5
(Serotec) and sorted into CD8+CD45RA+, CD8–CD45RA+,
CD8+CD45RA– and CD8–CD45RA– subsets. In Sects. 2
and 3, CD45RA– cells are referred to as being CD45RO+
and CD8–CD3+ cells are referred to as being CD4+.
4.4 Analysis of deuterium enrichment
Enrichment of deuterium in DNA was assayed as previously described [14, 15]. DNA from sorted cell subsets
was extracted and digested enzymatically to deoxynucleosides. Deoxyadenosine, purified by C-18 solidphase extraction column chromatography, was converted to its aldononitrile acetate derivative by reaction
with hydroxylamine/pyridine (1% w/v, 100°C, 45 min)
and acetic anhydride (room temperature, 30 min). The
resulting derivative was analyzed by gas chromatography-mass spectrometry (GCMS), monitoring ions
m/z 198 and 200 by positive chemical ionization in selective ion mode (HP-225 column, HP 6890/5973 GCMS;
Hewlett Packard, Bracknell, GB) [15]. Abundancematched samples were analyzed in triplicate alongside a
standard curve derivatized concurrently. Plasma glucose
enrichment was measured using the same derivatization
(m/z 328 and 330). Typical reproducibility of the M+2/
Eur. J. Immunol. 2003. 33: 2316–2326
M+0 ratio was ±0.02%. The mean plasma glucoseenrichment value for the duration of the infusion was calculated from the area under the curve of the glucose
enrichment versus time profile.
4.5 Fitting of model to data
The model was fitted to the experimental data using nonlinear least squares regression (Levenberg-Marquardt
method) to estimate the parameters p and d*. The errors
on the estimates of p and d* were determined by the
asymptotic covariance matrix method. To allow for the
fact that GCMS analytic variance was greater on some
samples, particularly those of very low abundance, each
data point was weighted by the inverse of its variance
(three repeats). Where proliferation is expressed as doubling time or disappearance as half-life, these were calculated as ln2/p and ln2/d*, respectively. All data are
expressed as mean ± 1 SD.
Acknowledgements: We acknowledge helpful discussion
and comments on the manuscript by Prof Charles Bangham
and Dr Angela McLean. This work was supported by the
Edward Jenner Institute for Vaccine Research (publication
number 54). D. C. M. was supported by a Fellowship from
Serono International S.A., and a Medical Research CouncilGlaxo-Wellcome Clinician Scientist Fellowship. B. A. was
supported by the Wellcome Trust (ref: 054451).
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Correspondence: Derek C. Macallan, Department of Infectious Diseases, St George’s Hospital Medical School, Cranmer Terrace, London, SW17 0RE, GB
Fax: +44–20–8725–3487
e-mail: macallan — sghms.ac.uk