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.