A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

Abstract

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and delabelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU þ cells are expected to divide into BrdU þ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU þ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU þ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virusinfected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU þ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations.

Temporal fate mapping reveals age-linked heterogeneity in naive T lymphocytes in mice

“…Division and death are normally quantified by following the accumulation and loss of cells labeled in vivo with BrdU or deuterium from heavy water or deuterated glucose, taken up by dividing cells during administration of label and diluted following its withdrawal (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). These experiments are typically performed over days to weeks and collectively have revealed that cell populations initially assumed to be homogenous may in fact comprise multiple subpopulations dividing and dying at different rates (kinetic heterogeneity) and/or that cells that are quiescent or have recently divided may have different susceptibilities to death (temporal heterogeneity).…”

A new model to simulate and analyze proliferating cell populations in BrdU labeling experiments

“…In this phase, separated peaks occur, but only at very low label intensities. These may, in real experiments, well lay below the detection threshold and thus not appear in the data [4]. …”

“…With this recursive definition and X (0) = 0, we arrive at $X\left(i\right)MathClass-rel={MathClass-op\; \sum }_{lMathClass-rel=1}^i{2}^{MathClass-bin-j}{U}_j$ for the label content after i divisions. Note: The special case of $p_{text\mathsf{\text{eff}}}^{\left(k\right)}\left(x\right)MathClass-rel=\delta \left(xMathClass-bin-\mu \right)$ represents a uniform labeling value as used in previous models [4]. …”

“…The fraction of labeled cells or the mean fluorescence intensity is the maximum information that is used by existing models to infer proliferation parameters from BrdU data [1,4,7]. This means that the detailed information, how many cells contain how much label, is available in the data but not exploited in these models.…”

“…Existing models for BrdU-labeling [1,4,7] assume a uniform value of label uptake. Thus they fail to reproduce a realistic label distribution, since a uniform labeling value would result in sharp peaks each corresponding uniquely to a certain number of undergone divisions.…”