Cell-density independent increased lymphocyte production and loss rates post-autologous HSCT

Lymphocyte numbers need to be quite tightly regulated. It is generally assumed that lymphocyte production and lifespan increase homeostatically when lymphocyte numbers are low and, vice versa, return to normal once cell numbers have normalized. This widely accepted concept is largely based on experiments in mice, but is hardly investigated in vivo in humans. Here we quantified lymphocyte production and loss rates in vivo in patients 0.5–1 year after their autologous hematopoietic stem cell transplantation (autoHSCT). We indeed found that the production rates of most T- and B-cell subsets in autoHSCT-patients were two to eight times higher than in healthy controls, but went hand in hand with a threefold to ninefold increase in cell loss rates. Both rates also did not normalize when cell numbers did. This shows that increased lymphocyte production and loss rates occur even long after autoHSCT and can persist in the face of apparently normal cell numbers.


Introduction
Under healthy conditions, the peripheral T-and B-cell populations are maintained at relatively constant numbers throughout life (Lin et al., 2016;Wertheimer et al., 2014). Homeostatic mechanisms are thought to regulate lymphocyte production and survival rates in a density-dependent manner. Indeed, studies in rodents have shown that lymphocyte division and lifespan increase in response to severe lymphopenic conditions (Freitas and Rocha, 2000). Robust peripheral proliferation of T-cells occurs both upon adoptive cell transfer into severely lymphocyte-depleted mice and in partially immune-depleted hosts in the absence of adoptive cell transfer, a phenomenon termed lymphopenia-induced proliferation (LIP) (Freitas and Rocha, 2000;Miller and Stutman, 1984;Bell et al., 1987;Neujahr et al., 2006). Similarly, rapid proliferation and extended survival of B-cells occur after adoptive cell transfer into B-cell deficient hosts and correlate with peripheral B-cell numbers (Gaudin et al., 2004).
By analogy, it is generally assumed that lymphopenic conditions induce alterations in lymphocyte dynamics in humans. However, in humans full recovery of the T-cell compartment following an autologous hematopoietic stem cell transplantation (autoHSCT) is notoriously slow, often taking several years (Heining et al., 2007;Ringhoffer et al., 2013;Bosch et al., 2012;Williams et al., 2007). On the basis of elevated frequencies of Ki-67 + cells, severe lymphopenia arising after HSCT and lymphocyte-depleting treatments has been associated with increased proliferation of naive and memory T-cells (Jones et al., 2013;Bouvy et al., 2013;Hazenberg et al., 2002;Alho et al., 2016). However, elevated frequencies of Ki-67 + cells were shown to decline within 3-6 months after cell depletion, despite the fact that patients were still deeply lymphopenic (Bouvy et al., 2013;Hazenberg et al., 2002;Alho et al., 2016). Furthermore, increased T-cell proliferation rates after allogeneic HSCT have been shown to correlate with the occurrence of graft-versus-host disease (GVHD) and infectious-disease-related complications (Hazenberg et al., 2002). Together, these observations question whether homeostatic mechanisms are induced to compensate for low lymphocyte numbers in humans undergoing HSCT. It remains unclear to what extent increased T-cell proliferation post-HSCT reflects a T-cell density-dependent response to lymphopenia, or an immune response triggered by therapy-related tissue damage, infectious complications or immune activation.
To elucidate whether lymphocyte production and death rates in humans are regulated in a density-dependent manner, we used in vivo deuterium labeling to quantify the production and loss rates of different T-and B-cell subsets in patients who received an autologous HSCT (autoHSCT), and had no signs of clinically manifested infections or GVHD. Twelve months after autoHSCT, absolute numbers of CD4 + T-cells and memory and natural effector B-cells in these patients were still lower than in healthy individuals, while CD8 + T-cell and naive B-cell numbers had already recovered to healthy control (HC) values. Deuterium labeling revealed that the production rates of most lymphocyte subsets, even those that had already reconstituted, were significantly higher in patients post-autoHSCT than in healthy individuals. These increased rates of T-and B-cell production could only be reconciled with the observed stable cell numbers over the study time if lymphocyte loss rates were also significantly increased. Our data therefore show that increased lymphocyte production and loss rates occur long after autoHSCT, and can even persist when a lymphocyte subset has already normalized.

Heterogeneous T-cell reconstitution kinetics post-autoHSCT
To investigate whether lymphocyte production and loss depend on cell numbers during lymphopenia in humans, we quantified the production and loss rates of T-and B-cells in six patients who received an autoHSCT for the treatment of hematological malignancies. Patients were included in the study between 196 days and 420 days post-autoHSCT, received deuterated water ( 2 H 2 O) for 6 weeks, and were followed for approximately 1 year after start of the labeling period ( Figure 1).
Patient B withdrew from the study 10 weeks after the start of 2 H 2 O labeling due to infectious complications unrelated to participation in the study. All other patients had no complications that needed treatment during the study follow-up, which was supported by C-reactive protein (CRP) levels in the normal range ( Figure 2).
The sub-optimal T-cell recovery observed in the peripheral blood of patients post-autoHSCT ( Figure 3A) was largely due to the slow reconstitution of CD4 + T-cells ( Figure 3B). At the start of 2 H 2 O labeling, CD8 + T-cell numbers had reached normal levels in most patients, whereas CD4 + T-cell numbers remained below normal levels even 1.5 years post-autoHSCT. This resulted in an inverse CD4:CD8 ratio in all patients except for patient C ( Figure 3C), who experienced extremely slow CD8 + T-cell reconstitution ( Figure 3D). Naive (CD45RO -CD27 + ) CD4 + T-cell numbers remained below normal levels throughout the 2-year follow-up period, whereas memory (CD45RO + ) CD4 + T-cells reached the lower range of normal levels around 400 days post-autoHSCT ( Figure 3B). Naive and memory CD8 + T-cell numbers were at normal or supra-normal levels at the start of the study in all patients except for patient C ( Figure 3D). In line with cell numbers, for most patients the fractions of naive cells, central memory (CM, CD45RO + CD27 + ), effector memory (EM, CD45RO + CD27 -), and effector (CD45RO -CD27 -) T-cells differed from those in HCs and varied slightly over time ( Figure 3E and Because it is generally assumed that during lymphopenia the availability of growth and survival factors increases, which has in particular been shown for IL-7 plasma levels (van Gent et al., 2011;Sauce et al., 2012;Fry et al., 2001;Napolitano et al., 2001;Bolotin et al., 1999), we also determined plasma levels of IL-7 and IL-15 between 12 and 24 months post-autoHSCT. Despite the CD4 + T-cell lymphopenia observed in these patients, their plasma concentrations of IL-7 and IL-15 and several other cytokines were in the range of those of HCs ( Figure 2).

Increased CD4 + and CD8 + T-cell production rates post-autoHSCT
To investigate whether low CD4 + T-cell numbers were associated with increased T-cell production rates, we compared the level of deuterium enrichment in the DNA of the different T-cell subsets between patients and controls. Deuterium enrichment analysis showed a relatively high level of label incorporation in patients, despite the fact that the labeling period was 3 weeks shorter for patients than for controls ( Figure 4A). Using mathematical modeling (see Materials and methods section) we estimated the production rates of the different T-cell subsets (i.e. the number of new cells produced per day, coming from a source or peripheral cell division, divided by the number of resident cells in the population). We found that the production rates of naive and memory CD4 + T-cells were, respectively, six times and three times higher in patients than in controls. For naive and memory  Figure supplement 1. Absolute numbers (cells Â 10 9 per liter of blood) of leukocytes, neutrophils, lymphocytes, and monocytes in peripheral blood of autologous hematopoietic stem cell transplantation (autoHSCT) patients (patients A-F) over time after autoHSCT obtained by automated blood leukocyte differential count (leukodiff).
CD8 + T-cells, the estimated production rates were approximately eight and four times higher in patients compared to controls ( Figure 4B and Figure 4-source data 2), despite the fact that absolute CD8 + T-cell numbers had already recovered to healthy levels 12 months post-transplantation.
Increased proliferation of naive but not memory CD4 + and CD8 + T-cells T-cell production rates as measured by deuterium labeling may reflect proliferation (i.e. either occasional self-renewal or a continuous burst of cell division) of the subset of interest or an influx of cells from a source (e.g. by thymic output) or from another subset (e.g. through lymphocyte differentiation). To distinguish between these options, we first measured Ki-67 expression, a snapshot marker of recent proliferative activity which, in contrast to deuterium labeling, allows to distinguish between cell division and influx. The fraction of Ki-67 + cells within the naive CD4 + and CD8 + T-cell pools was significantly higher in patients compared to controls ( Figure 5A). For the memory T-cell subsets, in contrast, the fraction of Ki-67 + cells of patients did not differ significantly from those of controls ( Figure 5A). This suggests that the increased production rates of memory CD4 + and CD8 + T-cells may occur due to an increased influx from naive T-cells into the memory compartment, rather than increased T-cell division within the memory T-cell pools.
Besides increased cell division in the naive T-cell pool, increased naive T-cell production rates post-autoHSCT could in theory also be due to increased thymic output. T-cell receptor excision circles (TRECs) are commonly measured to estimate thymopoiesis. Because the average TREC content per T-cell declines with age (Douek et al., 1998;Hazenberg et al., 2000;Hazenberg et al., 2001), we measured TREC contents of naive T-cells from patients, cord blood (CB), and young (on average 23 years of age) and aged (on average 68 years of age) healthy individuals (Westera et al., 2015). The average TREC content of naive CD4 + T-cells in patients was approximately 10-fold higher   . T-cell reconstitution following autologous hematopoietic stem cell transplantation (autoHSCT). Absolute numbers (cells per milliliter) of (A) total CD3 + T-cells, (B) total, naive (CD27 + CD45RO -) and memory (CD45RO + ) CD3 + CD4 + T-cells, (D) total, naive (CD27 + CD45RO -) and memory (CD45RO + ) CD3 + CD8 + T-cells, and (C) the CD4:CD8 ratio over time for the duration of the study are depicted. Box plots represent the distribution of values for healthy controls (HCs) (N = 17 for CD3 + , CD4 + , CD8 + , and CD4:CD8 ratio, other N = 27, box = 25th to 75th percentile, black line=median, Figure 3 continued on next page than in aged controls, and not significantly different from that of young individuals and CB ( Figure 5B), even though all but one of the patients were more than 50 years of age. For naive CD8 + T-cells, the average TREC content in patients was in the range of young and aged controls ( Figure 5B). We also measured CD31 expression on naive CD4 + T-cells, as CD31 + CD4 + T-cells are known to be enriched in recent thymic emigrants (RTEs) (Kohler and Thiel, 2009;van den Broek et al., 2018). The fraction of CD31 + cells within the naive CD4 + T-cell population was slightly higher in patients than in aged controls and slightly lower than in young controls and CB ( Figure 5C and Figure 5-figure supplement 2). For naive T-cells, the combined Ki-67, TREC, and CD31 data suggest that the increased T-cell production rate post-HSCT is at least partially due to increased T-cell division. Since the increased average TREC contents and percentages of CD31 + cells may be a direct consequence of normal thymic output entering a smaller T-cell pool (Hazenberg et al., 2003), the contribution of thymic output to the increased T-cell production rate in these patients remains unclear.

Heterogeneous B-cell reconstitution kinetics post-autoHSCT
Next, we studied the changes in B-cell dynamics following autoHSCT. Although total CD19 + B-cell numbers and naive (IgM + CD27 -) B-cell numbers had already reached normal or even supra-normal levels by day 200 post-autoHSCT, Ig class-switched (IgM -CD27 + ) and IgM + (IgM + CD27 + ) memory B-cell numbers in most patients were still below, or in the lower range of, those of HCs throughout the study period ( Figure 6A and B and Figure 6-figure supplement 1).

Increased production rates of B-cells post-autoHSCT
We analyzed the deuterium enrichment of the different B-cell subsets to study whether B-cell production rates were increased for subsets which were still low in cell numbers ( Figure 7A). The production rates of Ig switched-memory B-cells and IgM + memory B-cells were 3.5 times and 5 times higher than in controls, respectively ( Figure 7B and Figure 7-source data 1). Also the production rate of naive B-cells, a population that had already reconstituted to supra-normal levels, remained significantly higher than in HCs ( Figure 7B, Figure 7-source data 1).
Because B-cell production may depend on peripheral B-cell division and on de novo bone marrow output, we measured Ki-67 expression and kappa-deleting recombination excision circles (KRECs), in an attempt to estimate bone marrow output. The percentages of dividing, that is, Ki-67 + , cells within IgM + and Ig class-switched memory B-cells were significantly higher in patients than in healthy individuals ( Figure 7C). In contrast, the fraction of Ki-67 + cells within the naive B-cell subset was similar between patients and controls ( Figure 7C). Although naive B-cell peripheral division rates were not increased post-autoHSCT, their production rates were two times higher than in controls. The division history (measured as number of cell divisions) of the naive B-cell subsets in patients tended to be lower than in controls (although not significantly), suggesting that the output of naive B-cells from the bone marrow rather than their peripheral proliferation rate was increased after autoHSCT ( Figure 7D). Source data 1. T-cell numbers and percentages in blood of patients and healthy controls. Figure supplement 1. T-cell subset distribution per autologous hematopoietic stem cell transplantation (autoHSCT) patient over time. Figure supplement 2. Gating strategy for TruCount analysis and cell sorting. Figure supplement 3. Total daily production of T-and B-cell subsets, calculated as average production rate s N þ p N À Á Â (absolute number of cells per liter of blood) Â (five liter blood) Â 50, assuming that 2% of lymphocytes reside in the blood (Ponchel et al., 2011).  (Westera et al., 2015). Dotted lines correspond to the end of the labeling period (black for autoHSCT patients and gray for HCs). Label enrichment was scaled between 0% and 100% by normalizing for the maximum enrichment in granulocytes (see Source code 1. Modeling in R and raw data. Source data 1. Estimates of urine and granulocyte parameters and their corresponding 95% confidence limits for deuterium enrichment. Source data 2. Estimates of average daily production rates for T-cell subsets of autoHSCT patients.    (Westera et al., 2015). For Patient A and Patient E, TREC content was measured the first day of the study (t 0 ) as well as the last study visit (t end ). For Patient D, TREC content was not successfully measured due to limited material. (C) CD31 expression was measured within naive CD4 + T-cells in autoHSCT patients, CB, and HCs (Westera et al., 2015). For changes in CD31 expression and absolute numbers of CD31 + cells over time, see    Increased lymphocyte production rates are counteracted by increased lymphocyte loss rates The increased lymphocyte production rates that we observed in patients after autoHSCT may at first sight suggest that, also in humans, lymphocyte production is regulated in a density-dependent  (Westera et al., 2015). Dotted lines correspond to the end of the labeling period (black for autoHSCT patients and gray for HCs). Label enrichment was scaled between 0% and 100% by normalizing for the maximum enrichment in granulocytes (Figure 4-source data 1). (B) Estimates of the per cell production rates of naive, Ig class-switched memory, and IgM + memory B-cells in autoHSCT patients and HCs (Westera et al., 2015). For individual fits and estimates, see Source data 1. Estimates of average daily production rates for B cell subsets of autoHSCT patients. manner. The observation that lymphocyte production rates were also elevated for subsets for which cell numbers had already normalized, however, challenges this interpretation. Another observation challenging this interpretation is that for most subsets, lymphocyte numbers increased very little over time, despite the significant increase in lymphocyte production. This suggests that lymphocyte loss rates were also significantly increased after autoHSCT.
To estimate the average loss rates of all lymphocyte subsets (i.e. the number of cells lost per day, by cell death, migration, or differentiation, divided by the number of resident cells in the population), we used the average lymphocyte production rates estimated from the deuterium labeling experiments and an exponential function to describe the changes in cell numbers of each lymphocyte subset over time. For most T-and B-cell subsets, the average loss rate was approximately three to five times higher post-autoHSCT than in healthy individuals (Figure 8 and Figure 8-source data 1). For naive CD8 + T-cells the average loss rate was even 9.5 times higher in patients than in healthy individuals ( Figure 8 and Figure 8-source data 1). Thus, despite the fact that production rates are clearly increased in patients post-autoHSCT, this increased production goes hand in hand with increased lymphocyte loss rates, thereby challenging the view that it reflects a homeostatic response to low lymphocyte numbers.

Discussion
From a homeostatic viewpoint, a response to low lymphocyte numbers could take the form of increased lymphocyte production or decreased lymphocyte loss. Based on the observation that severe lymphopenia in mice is associated with increased peripheral proliferation (Freitas and Rocha, 2000;Miller and Stutman, 1984;Bell et al., 1987;Fry et al., 2001), it is widely believed that lymphocyte production rates are increased when cell numbers are low, and normalize when cell numbers do. We have previously shown that naive T-cell production rates do not increase to compensate for the at least 10-fold declined thymic output in elderly individuals (Westera et al., 2015). This could be due to the relatively small degree of naive T-cell loss observed during healthy aging. Under more severe conditions of lymphopenia in humans, high frequencies of proliferating lymphocytes have been observed, but these have been linked to immune activation and clinical events, for example, GVHD and opportunistic infections (Hazenberg et al., 2002). Thus, there is little evidence that lymphocyte numbers regulate cell production and loss rates in humans.  (Westera et al., 2015). Average loss rates were calculated (see Figure 8-source data 1) using the estimated average production rates and the corrected cell numbers (Figure 8-figure supplements 1 and 2)    Our deuterium labeling study shows that in patients receiving an autoHSCT, in the absence of GVHD, clinically manifested infections, and transplantation-related complications, the production rates of most T-and B-cell subsets were significantly increased 12 months after transplantation. Increased lymphocyte production rates during lymphopenia have generally been interpreted as evidence for a density-dependent response to low lymphocyte numbers (Jones et al., 2013;Bouvy et al., 2013;Alho et al., 2016;Havenith et al., 2012;Bouvy et al., 2016). We did two additional observations, however, that suggested that these increased lymphocyte production rates post-autoHSCT were not simply reflecting a homeostatic response to low cell numbers. First, T-and B-cell production rates did not normalize when cell numbers did. Second, not only lymphocyte production but also lymphocyte loss rates were significantly increased post-autoHSCT. Alternatively, the observed increased lymphocyte production rates post-autoHSCT could reflect an overrepresentation of young lymphocytes within the lymphocyte pool, in analogy with lymphocytes in the developing immune system of children, where especially in the first year T-cells have relatively high proliferation rates (van Gent et al., 2009). Likewise, in mice it has been shown that newly generated naive and memory T-cells have higher production and loss rates than their established counterparts (Gossel et al., 2017;Rane et al., 2018;Reynaldi et al., 2019). Finally, despite the fact that the patients in our study were included up to 12 months post-transplantation and were selected on the basis of being in good health, we cannot exclude the possibility that the increased proliferation and loss rates observed post-autoHSCT may reflect HSCT-related complications, such as the impact of initial chemotherapy and conditioning-therapy or subclinical infections and inflammation, which may have gone unnoticed. In fact, the increased lymphocyte production rates may even have been a response to increased lymphocyte loss rates, which themselves may have been induced by the transplantation. Lymphocyte production would then be modulated in an effort to normalize lymphocyte numbers. Whatever the underlying explanation, the ongoing dysregulation of lymphocyte dynamics in itself is an important observation. It shows that normalized cell numbers cannot be taken as an indication that homeostasis has been restored.
The observation that lymphocyte loss rates were increased post-autoHSCT is quite remarkable in light of the widely held view that homeostatic mechanisms could take the form of increased lymphocyte survival. This concept is supported by the observation that the availability of pro-survival and anti-apoptotic factors, such as IL-7 (Ponchel et al., 2011;Barata et al., 2019;Lundströ m et al., 2012), typically increases during lymphopenia. In our cohort, we found no evidence for increased lL-7 plasma levels, consistent with the observation that lymphocyte loss rates in these patients were not decreased. It remains unclear why IL-7 plasma levels were not increased in our cohort. A possible explanation could be that IL-7 production was hampered by transplantation-related damage to, for example, stromal cells or intestinal epithelial cells, which are an important source of IL-7 (Barata et al., 2019;Lundströ m et al., 2012;Kim et al., 2011). We found that lymphocyte loss rates were up to 10-fold increased after autoHSCT. Although in the current study we did not take into account markers of cell death, the estimated increased cell loss rates are in line with previous human studies on T-cell survival after allogenic HSCT, which consistently reported that the fraction of pro-apoptotic cells increases following transplantation (Alho et al., 2016;Brugnoni et al., 1999;Lin et al., 2000;Poulin et al., 2003). Although this suggests that intervention with lymphocyte survival after HSCT may aid lymphocyte reconstitution, other factors apart from increased cell death may have contributed to the loss of cells from the peripheral blood. Excessive lymphocyte differentiation and/or increased migration to the tissues would also increase cell loss rates. Further studies should address whether lymphocyte reconstitution occurs at similar rates in blood and tissues in order to clarify whether lymphocyte recruitment to the tissues may be a key factor influencing the loss of lymphocytes from the blood following autoHSCT.
Consistent with previous reports (Bosch et al., 2012;Alho et al., 2016;Storek et al., 2008), we found that 12 months post-autoHSCT, CD4 + T-cell numbers were below the normal range while CD8 + T-cells recovered more rapidly. Deuterium labeling in patients revealed that the average production rates of most T-cell subsets were significantly increased following autoHSCT. This increase was especially evident for naive T-cells. The high percentage of Ki-67 + naive T-cells post-autoHSCT suggests that increased naive T-cell production is to a large extent explained by increased peripheral T-cell proliferation. Memory T-cell production rates based on deuterium enrichment were also higher in patients compared to controls, while Ki-67 expression suggested that memory CD4 + and CD8 + T-cell proliferation rates were not significantly increased 0.5-1 year after autoHSCT in line with previous reports (Malphettes et al., 2003). This seeming contradiction may be explained by the fact that Ki-67, a snapshot marker, may be less sensitive to detect differences in T-cell proliferation than long-term in vivo deuterium labeling. Alternatively, the increased production rate of memory T-cells post-autoHSCT may be due to increased transition of naive T-cells into the memory T-cell population. In line with this, in mice it has been demonstrated that naive T-cells adoptively transferred into immunodeficient animals can acquire a memory phenotype after antigen independent stimulation and division (Cho et al., 2000;Goldrath et al., 2000).
If a significant part of cell production in a certain lymphocyte subset (e.g. the memory subset) is indeed due to an influx from another lymphocyte subset (e.g. the naive subset), the increased production rates that we observed may reflect either a true increase in cell production or a normal influx of cells entering a smaller lymphocyte population. To distinguish between these options, for each lymphocyte subset and each individual, we also calculated the total number of cells produced per day (i.e. coming from a source and/or from peripheral cell division), by multiplying the average production rate of each lymphocyte subset with the median cell number of that subset, and compared these values to those in HCs (Westera et al., 2015; Figure 3-source data 1 and Figure 4-source data 2). We found that total daily lymphocyte production was as high as in HCs for naive CD4 + T-cells and higher than in HCs for all other lymphocyte subsets, suggesting that the increased lymphocyte production rates post-autoHSCT truly reflected increased T-cell proliferation and/or an increased influx from another lymphocyte compartment.
Measuring thymopoiesis and the contribution of RTEs to the naive T-cell pool after HSCT is not straightforward. Although increased TREC contents at first sight seem suggestive for increased thymic output, T-cells bearing TRECs may in fact be overrepresented in the peripheral T-cell pool posttransplantation when cell numbers are low (Hazenberg et al., 2003). Hence, for naive CD4 + T-cells, whose numbers had not yet normalized, increased average TREC contents may incorrectly be interpreted as evidence for increased thymic output. The finding that the average TREC content of naive CD4 + T-cells following autoHSCT was higher than in age-matched controls provides no evidence that thymic output following transplantation was higher than in HCs, but does imply that the thymus had become functional again within 12 months after intense conditioning for autoHSCT. The fact that the average TREC content of naive CD4 + T -cells, but not that of naive CD8 + T-cells, was higher in patients than in healthy individuals may reflect differences in the degree of depletion of naive CD4 + and CD8 + T -cells. Alternatively, it might reflect differences in the way CD4 + and CD8 + T-cells are generated. In support of the latter explanation, repertoire analyses in patients receiving an autoHSCT for the treatment of autoimmune diseases have suggested that CD4 + T-cells largely arise de novo, since most CD4 + T-cell clones post-autoHSCT were not present at baseline, while CD8 + T-cells mainly expand from cells that were already circulating pre-transplantation (Muraro et al., 2005;Muraro et al., 2014;Dubinsky et al., 2010).
To study in a population other than T-cells whether lymphocyte production and loss rates in humans are regulated in a density-dependent manner, we quantified the production and loss rates of different B-cell subsets. In line with previous reports (Burns et al., 2003;Avanzini et al., 2005;Bemark et al., 2012), we found that 12 months after transplantation, naive B-cell numbers had reconstituted to healthy (or even higher than healthy) control values, while Ig class-switched and IgM + memory B-cells had not yet fully recovered. The delayed reconstitution of Ig class-switched and IgM + memory B-cells has typically been attributed to treatment-related damage to secondary lymphoid organs, which may hamper the formation of germinal centers essential for somatic hypermutation and isotype switching (Avanzini et al., 2005). Also for naive, Ig class-switched, and IgM + memory B-cells, we found that not only production rates but also cell loss rates were increased 12 months post-autoHSCT, further supporting our conclusion that increased lymphocyte production rates do not simply reflect a homeostatic response to low lymphocyte numbers.
In brief, our findings show that despite the slow reconstitution of lymphocytes in autoHSCT patients, lymphocyte production rates are increased. Since this increased production goes hand in hand with increased cell loss and does not normalize when cell numbers do, it is not simply due to a homeostatic response to low cell numbers. Future studies should address whether the dynamics of lymphocytes after autoHSCT normalize in the long run, what drives the increase in lymphocyte production and loss rates during immune reconstitution, and to what extent immune reconstitution in the tissues occurs.

Patient characteristics
Six patients who received an autoHSCT for the treatment of a hematologic malignancy were enrolled in the study after having provided written informed consent. Following repeated subcutaneous injections with granulocyte-colony stimulating factor (G-CSF), stem cells were obtained by leukapheresis of peripheral blood. Patients received a non T-cell depleted graft; the average number of CD34 + cells transplanted was 5.03 Â 10 6 cells/kg (median, 4.12; range, 1.82-12.38). Patients were included in the study between 196 and 420 days after autoHSCT, and had no signs of transplantation-related complications, severe infections (HIV, HBV, and HCV), other liver diseases, active uncontrolled infections (such as infectious mononucleosis), inadequate liver or kidney function, or cardiovascular disease before and during the study. Additional inclusion criteria were: fully transfusion independent at start of the study, hemoglobin level !6 mmol/l, and platelet count !50 Â 10 9 /L. Any use of medication during the study was unrelated to the malignancy and the HSCT (Figure 1). In order to compare the phenotypes of the B-and T-cell compartments of patients to those of age-matched healthy individuals, we used data from healthy individuals from a previous study (Westera et al., 2015), additional blood samples were collected from healthy volunteers not following the labeling protocol after having provided informed consent. This study was approved by the medical ethical committee of the University Medical Center Utrecht and conducted in accordance with the Helsinki Declaration.

In vivo deuterium labeling
In vivo deuterium labeling was performed as previously described with small adaptations (Westera et al., 2015). Briefly, patients received an oral ramp-up dose of 7.5 ml of heavy water ( 2 H 2 O, 99.8% enriched, Cambridge Isotope Laboratories) per kilogram body water on the first day of the study, and drank a daily maintenance dose of 1.25 ml 2 H 2 O per kilogram body water for 6 weeks. To reduce the study burden, the labeling period of autoHSCT patients was 3 weeks shorter than the labeling period we used in our previous study in HCs (Westera et al., 2015). Thanks to the use of the multi-exponential model, these different labeling periods for autoHSCT patients and HCs should not affect the estimated dynamic parameters (Westera et al., 2013). Blood was withdrawn four times during the labeling period and six times during the de-labeling period, with the last withdrawal approximately 1 year after the start of 2 H 2 O administration. Urine samples were collected during the first 13 weeks of the study and stored at À20˚C until analysis. For deuterium labeling, data from HCs from a previous study (Westera et al., 2015) were used. The age of the autoHSCT patients included in the current study (median age of 54 years, see Figure 1B) was not completely matched with that of the HCs studied before (median age of 22 years for young and 68 years for aged controls). Since lymphocyte dynamics hardly change with age (Westera et al., 2015), the comparisons in our study should not be affected by the relatively small age differences between patients and HCs.

DNA isolation
Genomic DNA was isolated from sorted B-and T-cell subsets, total peripheral blood mononuclear cells, and granulocytes using the Reliaprep Blood gDNA Miniprep System (Promega, Madison, WI, USA) and stored at À20˚C before processing for TREC analysis or gas chromatography/mass spectrometry (GC/MS).

TREC analysis
In sorted naive CD4 + and CD8 + T-cell samples, signal joint TREC numbers and DNA input were quantified with a ViiA 7 Real-Time PCR System (Applied Biosystems) as previously described (Hazenberg et al., 2000;Goldrath et al., 2000). Values are the mean of two qPCR measurements of a given DNA sample.

KREC analysis
For quantification of B-cell replication history, the KREC assay in sorted naive B-cells was performed as described previously (Muraro et al., 2005). In short, genomic DNA was used as template for Taq-Man-based real-time quantitative PCR of the albumin control gene, intronRSS-Kde coding joints from rearranged IGK loci, and intronRSS-Kde signal joints on KRECs. The difference in Ct values between the intronRSS-Kde coding joints and signal joints from the same sample was used to calculate B-cell replication history with technical correction Ct values obtained with the U698-DB01 control cell line (Muraro et al., 2005) as follows (Muraro et al., 2014): Ct signal joint À Ct coding joint À Á sample À Ct signal joint À Ct coding joint À Á

U698ÀDB01
The frequencies of cells containing an intronRSS-Kde coding joint were calculated as follows (Muraro et al., 2014):

Multiplex immunoassay
Plasma samples were obtained from heparinized blood at different time points and stored at À80˚C. Plasma levels of CRP (C-reactive protein), APRIL (A proliferation-inducing ligand or TNFSF13), FAS-L (FAS ligand or CD95L), IL-7 (Interleukin 7), IL-15 (Interleukin 15), and IL-8 (Interleukin eight or CXCL8) were measured by a multiplex immunoassay using Luminex xMAP technology (xMAP, Luminex, Austin, TX, USA). The assay was performed as previously described (Dubinsky et al., 2010). Biorad FlexMAP3D (Biorad laboratories, Hercules, USA) and xPONENT software version 4.2 (Luminex) were used for acquisition and data was analyzed by five-parametric curve fitting using Bio-Plex Manager software, version 6.1.1 (Biorad). Samples were measured without any previous freezethaw cycle. Samples of HCs were acquired at the same days as patient samples to take into account the effect of storage on the different plasma markers.

Measurement of deuterium enrichment in DNA and body water
Deuterium enrichment in DNA from granulocytes, sorted cells, and total peripheral blood mononuclear cells (t=0) was measured according to the method described by Burns et al., 2003. with minor modifications (Westera et al., 2015). Briefly, DNA was enzymatically hydrolyzed into deoxyribonucleotides and derivatized to penta-fluoro-triacetate (PFTA) before injection (DB-17MS column, Agilent Technologies) into the gas chromatograph (7890A GC System, Agilent Technologies  (Avanzini et al., 2005) on log 10-transformed enrichment data. Deuterium enrichment in urine was analyzed on the same GC/MS system (using a PoraPLOT Q 25 Â 0.32 column, Varian) by electron impact ionization as previously described (Bemark et al., 2012). Values are the mean of two GCMS measurements of a given derivative sample.

Quantification of lymphocyte dynamics by mathematical modeling of urine and DNA enrichment data and cell numbers
Mathematical models were fitted to the urine and DNA enrichment data as previously described (van Gent et al., 2011). The estimated maximum level of 2 H enrichment in the granulocyte population of each patient was considered to be the maximum level of label incorporation that cells could possibly attain and was used to scale the enrichment data of the other cell subsets. As cell numbers may not be constant over time during the lymphocyte reconstitution phase, we adapted the commonly used mathematical model for deuterium labeling in T-and B-cells by releasing the steadystate assumption. For naive T-and B-cells (N), we allow cells to be produced by the thymus for T-cells and the bone marrow for B-cells at rate s, proliferate at a rate p N , and are lost at a rate d N .
For the other lymphocyte subsets (X), we write that they proliferate at a rate p X and are lost at a rate d X .
The total amount of labeled DNA (L) can be modeled by the following differential equations: where U t ð Þ is the fraction of deuterium in body water at time t (in days), and c is an amplification factor as previously described (van Gent et al., 2011;Westera et al., 2013). We can derive the equations for the fraction of labeled DNA (defined by l ¼ L=X) using the quotient rule of differentiation: Because of parameter identifiability issues, we were not able to estimate both s and p N in Equation 5. We therefore made the simplifying assumption that the per cell production rate (i.e. the number of new cells produced per day, coming from the source or peripheral cell division, divided by the number of resident cells in the population) s N þ p N À Á was not time-dependent, such that Equation 6 could also be used for naive T-and B-cells. To account for potential kinetic heterogeneity in each subpopulation (Westera et al., 2013), we used a multi-exponential model in which each subpopulation i contains a fraction a i of cells with production rate p i per day, and made the simplifying assumption that these fractions a i are not time-dependent. The average per cell production rate p of each subpopulation was subsequently calculated as p X ¼ P i a i p i (Vrisekoop et al., 2008;Ganusov et al., 2010). All subsets, except naive CD4 + and CD8 + T-cells, were significantly better described by two subpopulations. For naive CD4 + and CD8 + T-cells, only one was needed.
Equation 6 shows that deuterium enrichment data will give information only on the per cell proliferation rates p X . To estimate the loss rates of the different lymphocyte subsets (i.e. the number of cells lost per day, by cell death, migration or differentiation, divided by the number of resident cells in the population) (d X ) we made use of cell number data. As leukocyte counts in blood are known to vary, for example, due to diurnal rhythms, we first used a linear regression model to describe the total leukocyte numbers for each individual. To obtain cell numbers, the number of leukocytes according to this regression line was multiplied by the fraction of cells in each subset. We then fitted an exponential function to these 'normalized' cell numbers for each subset and individual: where X 0 is the cell number at the time of inclusion in the study and p X was fixed to the estimated values from the deuterium analyses. Best fits of deuterium enrichment in body water and granulocytes are shown in Figure 4-figure supplement 1 and the corresponding parameter estimates are given in Figure 4-source data 1. Individual enrichment data and best fits are shown in

Statistical analyses
For each individual urine and granulocyte enrichment levels were simultaneously used to estimate their respective parameters and for each lymphocyte subset deuterium enrichment data and normalized cell numbers were simultaneously used to estimate their production and loss rates. Deuterium enrichment data were arcsin-sqrt transformed and normalized cell numbers were log10-transformed before parameter estimation. 95% confidence limits were determined by bootstrap analysis on the residuals. Parameter estimation was performed using a maximum likelihood approach using R (Sauce et al., 2012). Estimated medians of enrichment data, median values of longitudinal data, or values of single measurements were compared between two groups using Mann-Whitney tests (GraphPad Software, Inc) or multiple groups using Kruskal-Wallis with Dunn's correction. Differences with a p-value <0.05 were considered significant.