Explicit Kinetic Heterogeneity: Mathematical Models for Interpretation of Deuterium Labeling of Heterogeneous Cell Populations

Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three most common models, which are based on quite different biological assumptions, actually predict mathematically identical labeling curves with one parameter for the exponential up and down slope, and one parameter defining the maximum labeling level. By extending these previous models, we here propose a novel approach for the analysis of data from deuterium labeling experiments. We construct a model of “kinetic heterogeneity” in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a novel way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length.Author Summary: Understanding of cellular processes is impossible without quantitative estimates of how quickly cells in an organism divide and die. The most widely used approach to measure rates of cell turnover in humans is by labeling dividing cells with deuterium given in the form of deuterated glucose or heavy water. Surprisingly, quantitative estimates of the rates of cell turnover obtained from accumulation and decay of the labeled nucleotides in the cell population varied between different studies. We demonstrate that these differences were not likely to arise because of different mathematical models used in data fitting, since the previously used models have an identical mathematical structure. We extend these previous models to allow for cell populations with different rates of turnover and show how such a new explicit kinetic heterogeneity model can be applied to simulated and experimental data. The new model opens a new way of interpreting data from deuterium labeling experiments and will likely lead to new insights into how infections and/or treatments affect cell turnover in humans.