Sara van den Berg

142 Chapter 6 measuring the ions m/z 435 u (M+0) and m/z 436 u (M+1) in the gas chromatograph- mass spectrometer (GC/MS) (7890A GC System, 5975C inert XL EI/CI MSD with Triple- Axis Detector; Agilent Technologies). The tracer-to-tracee ratio (TTR) was then calculated, by dividing the enriched, deuterated ion (M+1) by the unenriched, naturally occurring ion (M+0). Correction for abundance sensitivity of the GC/MS The measured TTR of each sample was corrected for abundance sensitivity, that is the positive correlation observed between sample input and measured TTR at fixed theoretical TTR [25, 26]. In short, eight standards with different known enrichments ([M+1]/[M+0] = 0, 0.0016, 0.0031, 0.0063, 0.0126, 0.0255, 0.0523, and 0.01097) were measured on the GC/MS at different sample input (M+0), within the same time period as the samples (<3 months). A second-order polynomial was fitted to each standard (M0 versus M1), and the corrected TTR of each sample was calculated by linear interpolation between these polynomials [26]. All data were arcsin(sqrt) transformed before fitting different models to the data (see below). To allow for this transformation, any negative values had to be set to zero. Finally, the atom percent excess (APE) of each sample was calculated from the corrected TTR values (as APE = TTR/(1-TTR)) and presented in the paper. Data points that were out of range of the standards ( N = 317/1059) were excluded from the analysis and indicated by in red in Supplementary Figure 5,6 . Mathematical modelling to estimate T-cell production and loss rates We first fitted a simple label enrichment/decay curve to the urine enrichment data of each individual: during label intake ( t ≤ τ ): after label intake ( t > τ ): as described previously [22], where U(t) represents the fraction of 2 H 2 O in urine at time t (in days), f is the fraction of 2 H 2 O 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 used these best fits when analyzing the enrichment in the different T-cell populations. The estimated maximum level of 2 H enrichment in the granulocyte population of each individual 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. Because the granulocyte enrichment curves had not yet reached plateau after 5 weeks of labelling, we constrained the fits to the granulocyte data by imposing that all individuals have the same granulocyte turnover rate d and a fixed delay of bone marrow maturation ( ∆ ) of 5 days [27] in the following differential equation, describing the granulocyte dynamics for all individuals: