Supplemental Digital Contents
Supplemental Digital Content 1: Supplemental Methods
Mathematical modelingof urine and DNA enrichment data
We first fitted a simple label enrichment/decay curve to the urine enrichment data of each individual:
during label intake (t ≤ τ): U (t )  f (1  e  t )   e  t
after label intake (t >τ): U (t ) 
 f (1  e
 

)   e  e  (t  )
(Equation 1a)
(Equation 1b)
as described previously[1](Fig. S1 and Table S3), where U(t) represents the fraction of 2H2O in plasma at
time t (in days), f is the fraction of 2H2O in the drinking water, labelling was stopped at t = τ days, δ
represents the turnover rate of body water per day, and β is the plasma enrichment attained after the
boost of label by the end of day 0. We incorporated these best fits when analyzing the enrichment in the
different cell populations. Up- and down-labeling of the granulocyte population of each individual was
analyzed as described previously [1] (Fig. S1 and Table S4), to estimate the maximum level of label intake
that cells could possibly attain. The label enrichment data of all cell subsets were subsequently scaled by
the granulocyte asymptote of each individual [1].
Labeling data of the different T-cell subsets were fitted with a mathematical model that allowed
for kinetic heterogeneity between cells of the same population. Each kinetic sub-population i was
modelled to contain a fraction αiof cells with turnover rate pi. Because the population sizes hardly
changed, we considered a steady state for each kinetic sub-population (i.e., production equals loss), and
label enrichment of adenosine in the DNA of each sub-population i was modelled by the following
differential equation:
dl i
 pi cU (t ) i A  pi l i 
dt
(Equation 2a)
where li is the total amount of labelled adenosine in the DNA of sub-population i and A is the total
amount of adenosine in the cell population under investigation, c is an amplification factor that needs to
be introduced because the adenosine deoxyribose (dR) moiety contains multiple hydrogen atoms that
can be replaced by deuterium [1], and piis the average turnover rate of sub-population i. Basically,
labelled adenosines in sub-population i are gained when a deuterium atom is incorporated with
probability cU(t) in the DNA of cells that replicate at rate pi,and they are lost when cells of subpopulation i are lost at rate pi. For naive T cells this replication may occur both in the periphery and in the
thymus. Scaling this equation by the total amount of adenosine in the DNA of sub-population i, i.e.,
defining Li = li/(αiA), yields
dLi
 pi cU (t )  pi Li 
dt
(Equation 2b)
throughout the up- and down-labelling period, where Li represents the fraction of labelled adenosine dR
moieties in the DNA of sub-population i. The corresponding analytical solutions are
Li (t ) 

c
 f (1  e  pi t )  pi f (1  e  t )   pi (e  pi t  e  t )
  pi

(Equation 3a)
during label intake (t ≤ τ ), and
Li (t ) 

c
 f (e  pi (t  )  e  pi t )  pi f (e  (t  )  e  t )   pi (e  pi t  e  t )
  pi
after label intake (t>τ).

(Equation 3b)
The fraction of labelled DNA in the total T-cell population under investigation was subsequently derived
from L (t ) 
  L (t ) , and the average turnover rate p was calculated from p
i
i


i
pi  .
Because all enrichment data were expressed as fractions, labelling data were arcsin(sqrt) transformed
before the mathematical model was fitted to the data. As the number of kinetically different subpopulations within a cell population may not be known, one can increase the number of sub-populations
in the model until the estimated average turnover rate no longer markedly changes as previously
suggested [2-4]. Memory T-cell compartments were always better described with a model with at least
two kinetically different sub-populations. While the naive CD4+ T-cell dynamics were always described
well with a single exponential model, the naive CD8+ T-cell dynamics in untreated HIV-infected
individuals were significantly better described using a multi-exponential model (including two kinetically
different sub-populations).
Each parameter (piandαi) was modeled as the sum of a population (fixed) parameter a  and a random
effect bi  allowing each parameter to be different from one patient to another:  i  a  bi . Each
random effect was assumed to be normally distributed with a variance to be estimated:
bi ~ N (0;  i2 ) .Hence, for each biological parameter, two parameters were estimated: one for the
average value and one for the variance of the random effect. Parameters were estimated using the R
package nlme for mixed effects models. Average lifespans were calculated from the average turnover
rates as 1/p.
References
1. Vrisekoop N, den Braber I, de Boer AB, Ruiter AF, Ackermans MT, van der Crabben SN,
et al.Sparse production but preferential incorporation of recently produced naive T
cells in the human peripheral pool. Proc Natl Acad Sci U S A 2008; 105(16):61156120.
2. Ganusov V, Borghans JAM, De Boer RJ. Explicit kinetic heterogeneity: mathematical
models for interpretation of deuterium labeling of heterogeneous cell populations.
In: 2010.
3. Westera L, Drylewicz J, den Braber I, Mugwagwa T, van dM, I, Kwast L, et al.Closing the
gap between T-cell life span estimates from stable isotope-labeling studies in mice
and humans. Blood 2013; 122(13):2205-2212.
4. De Boer RJ, Perelson AS, Ribeiro RM. Modelling deuterium labelling of lymphocytes with
temporal and/or kinetic heterogeneity. J R Soc Interface 2012; 9(74):2191-2200.
Supplemental Figure S1: 2H enrichment in urine and granulocytes of healthy individuals, and treatment-naive and cARTtreated HIV-infected individuals.The left panel represents the enrichment in urine and the right panel the enrichment in
granulocytes. The curves represent the best fits of the mathematical model to the experimental data (see Supplemental
Methods). The enrichment at day 7 of granulocytes for the third cART-treated HIV-infected patient was excluded for the fit to
have more consistent estimates with the other individuals (see Table S3). This leads to negligible differences in the estimates (at
the fifth digit).
Supplemental Figure S2: 2H enrichment of naive and memory T cells of healthy individuals.
Best fits of the percentage of labeled DNA in naive and memory CD4 + and CD8+ T cells of 5 healthy volunteers. The grey curves
show the best fit of the multi-exponential model to the full experimental dataset, including the long-term follow-up points (red
open symbols) whenever available. For reference, the average labeling curves(derived from the complete group of healthy
individuals) are plotted for each cell subset by the dashed grey curves. Label enrichment in the DNA of the different cell
populations was scaled between 0 and 100% by normalizing for the estimated maximum enrichment obtained in granulocytes
(see Supplemental Methods).
Supplemental Figure S3: 2H enrichment of naive and memory T cells of treatment-naive HIV-infected individuals.
The percentage of labeled DNA in naive and memory CD4+ and CD8+ T cells of 4 treatment-naive HIV-infected individuals. The
black curves show the best fit of the multi-exponential model to the experimental data. For reference, the average labeling
curves of healthy (dashed grey curves) and HIV-infected (dashed black curves) individuals are plotted for each cell subset. Label
enrichment in the DNA of the different cell populations was scaled between 0 and 100% by normalizing for the estimated
maximum enrichment obtained in granulocytes (see Supplemental Methods).
Supplemental Figure S4: 2H enrichment of naive and memory T cells of cART-treated HIV-infected individuals.
The percentage of labeled DNA in naive and memory CD4+ and CD8+ T cells of 3 cART-treated HIV-infected individuals. The black
curves show the best fit of the multi-exponential model to the experimental data. For reference, the average labeling curves of
healthy (dashed grey curves) and HIV-infected (dashed black curves) individuals are plotted for each cell subset. Label
enrichment in the DNA of the different cell populations was scaled between 0 and 100% by normalizing for the estimated
maximum enrichment obtained in granulocytes (see Supplemental Methods).
N a iv e
M e m o ry
CD8
0 .0 1
0 .0 1
0 .0 1
0 .0 0 1
0 .0 0 1
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 1
0 .0 0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
0 .0 0 0 0 1
0 .0 0 0 0 1
0 .0 0 0 0 1
1
1
1
0 .1
0 .1
0 .1
0 .0 1
0 .0 1
0 .0 1
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
1
1
0 .1
0 .1
0 .1
0 .0 1
0 .0 1
0 .0 1
y
a
re
a
e
-t
tr
T
n
R
A
c
H
h
d
lt
te
H
d
te
a
y
IV
h
H
h
te
e
d
a
lt
H
d
te
a
re
-t
T
R
A
c
u
y
IV
h
H
d
a
e
te
tr
n
-t
T
R
A
c
e
re
a
a
h
d
te
lt
H
IV
h
H
lt
d
a
e
te
h
a
e
tr
n
u
a
0 .0 0
re
0 .0 0
-t
0 .0 0
T
0 .2 5
0 .0 0
R
0 .2 5
A
0 .2 5
c
0 .5 0
0 .2 5
IV
0 .7 5
0 .5 0
H
1 .0 0
0 .7 5
0 .5 0
IV
1 .0 0
0 .7 5
0 .5 0
IV
1 .0 0
0 .7 5
IV
1 .0 0
IV
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
d
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
e
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
te
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
h
1
0 .1
0 .0 1
y
 fa s t
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
a
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
e
0 .0 0 1
0 .0 0 0 1
0 .0 0 0 0 1
1
p s lo w
1
0 .1
0 .0 1
u
p fa s t
0 .1
0 .1
0 .0 1
0 .0 0 1
tr
0 .1
0 .1
CD8
1
1
n
1
1
p
CD4
u
CD4
Supplemental Figure S5:95% confidence intervals on the
individual parameters of the model
Parameter results of the best fit of the model with two kinetically different sub-populations to the data, where αfast is the size of
the fast sub-population, pfast its turnover rate,pslow the turnover rate of the slower sub-population and p the average turnover
rate. Red horizontal lines represent the median average turnover rate for each group in each subset.
Supplemental Table S1:Expected in vivo lifespan of human CD4+ T cells in HIV –infected individuals.
Subset
Total CD4+ T-cells
Naive CD4+ T cells
Memory CD4+ T cells
Reference
Patient group
N
Lifespan
(d)Median:Range
Label
administration
duration (d)
Remarks
Hellerstein et al. 1999
untreated
7
34:27-50
2
Maximal enrichment only
Kovacs et al. 2005
untreated
9
5
5
Delabeling curve only
McCune et al. 2000
untreated
11
32:22-67
1-2
Mohri et al. 2001
untreated
7
45:26-100
7
Computed as 1/p
Hellerstein et al.
2003*
untreated
5
177
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
untreated
3
130:87-800
63
Deuterated water
Hellerstein et al. 1999
treated
5
25:13-34
2
Maximal enrichment only
Hellerstein et al.
2003*
Long-term ARV
6
177
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
McCune et al. 2000
Short-term HAART
7
28:13-45
1-2
Maximal enrichment only
McCune et al. 2000
Long-term HAART
8
119:63-556
1-2
Maximal enrichment only
Ribeiro et al. 2002
Short-term HAART
5
61:43-133
7
Computed as 1/(d*fA)
Ribeiro et al. 2002
Long-term HAART
3
101:86-130
7
Computed as 1/(d*fA)
Hegedus et al. 2014
untreated
10
250:120-485
10hours
Hellerstein et al.
2003*
untreated
5
452
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
untreated
4
618:416-1667
63
Deuterated water
Hellerstein et al.
2003*
Long-term ARV
6
755
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
treated
3
769:135-1667
63
Deuterated water
Hegedus et al. 2014
untreated
10
42:19-66
10hours
Hellerstein et al.
2003*
untreated
5
91
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
untreated
4
53:34-104
63
Deuterated water
Hellerstein et al.
2003*
Long-term ARV
6
112
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
treated
3
76:63-104
63
Deuterated water
Maximal enrichment only
Median:IQR
Median:IQR
* the fraction of labeled DNA fwasvisually estimated from Figure 2 in Hellerstein et al. 2003
Supplemental Table S2:Expected in vivo lifespan of human CD8+ T cells in HIV –infected individuals.
Subset
Total CD8+ T-cells
Naive CD8+ T cells
Memory CD8+ T cells
Reference
Patient group
N
Lifespan
(d)Median:Range
Label
administration
duration (d)
Remarks
Hellerstein et al. 1999
untreated
7
34:23-48
2
Maximal enrichment only
Kovacs et al. 2005
untreated
9
21
5
Delabeling curve only
McCune et al. 2000
untreated
11
37:21-77
1-2
Mohri et al. 2001
untreated
7
42:28-100
7
Computed as 1/p
Hellerstein et al. 2003*
untreated
5
146
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Hellerstein et al. 1999
treated
5
26:13-30
2
Maximal enrichment only
Hellerstein et al. 2003*
Long-term ARV
6
317
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
McCune et al. 2000
Short-term HAART
7
27:13-63
1-2
Maximal enrichment only
McCune et al. 2000
Long-term HAART
8
200:67-370
1-2
Maximal enrichment only
Ribeiro et al. 2002
Short-term HAART
5
102:40-201
7
Computed as 1/(d*fA)
Ribeiro et al. 2002
Long-term HAART
2
137:94-180
7
Computed as 1/(d*fA)
Hegedus et al. 2014
untreated
10
144:62-303
10hours
Hellerstein et al. 2003*
untreated
5
253
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
untreated
4
271:256-588
63
Deuterated water
Hellerstein et al. 2003*
Long-term ARV
6
493
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
treated
3
1250:1111-5000
63
Deuterated water
Hegedus et al. 2014
untreated
10
46:13-40
10hours
Hellerstein et al. 2003*
untreated
5
123
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
untreated
4
43:29-81
63
Deuterated water
Hellerstein et al. 2003*
Long-term ARV
6
253
63
Deuterated water
lifespan computed as 1/k
in f=1-exp(-k*63)
Our study
treated
3
137:20-164
63
Deuterated water
* the fraction of labeled DNA fwasvisually estimated from Figure 2 in Hellerstein et al. 2003
Maximal enrichment only
Median:IQR
Median:IQR
Supplemental Table S3: Parameter estimates of the urine enrichment curves of healthy volunteers, and treatment-naive and
cART-treated HIV-infected individuals.
Healthy
Treatment-naive
cART-treated
A
B
C
D
E
A
B
C
D
A
B
C
f
0.0010
0.0011
0.0012
0.0017
0.0020
0.0007
0.0010
0.0009
0.0012
0.0178
0.0184
0.0165
δ
0.0610
0.0822
0.0705
0.1204
0.1338
0.1080
0.0735
0.1221
0.0811
0.0708
0.0647
0.0837
β
0.0086
0.0071
0.0082
0.0073
0.0059
0.0053
0.0087
0.0102
0.0178
0.0066
0.0062
0.0072
where f represents the fraction of 2H2O in the drinking water, δ is the turnover rate of body water per day, and β represents the
baseline urine enrichment attained after the boost of label by the end of day 0.
Supplemental Table S4: Parameter estimates of the granulocyte enrichment curves of healthy volunteers, and treatmentnaive and cART-treated HIV-infected individuals.
Healthy
Treatment-naive
cART-treated
A
B
C
D
E
A
B
C
D
A
B
Ca
pc
0.4105
0.4813
0.3729
0.3195
0.4237
0.5265
0.3391
0.5390
0.4174
0.3703
0.4116
0.4276
d
0.0938
0.1016
0.0751
0.0853
0.1052
0.0994
0.0790
0.1196
0.0937
0.0840
0.0922
0.0821
cb
4.3763
4.7372
4.9654
4.2543
4.0275
5.2968
4.2924
4.5067
4.4546
4.4083
4.4642
5.2086
where d represents the loss rate of labeled granulocytes per day, p the average production rate of granulocytes per day, and c
the amplification factor. a Obtained by leaving out the enrichment at day 7. bc was computed assuming p=d.