The Fat Tail Problem

Abstract

DNA deuterium labeling provides a minimally invasive technique for studying cell population dynamics over prolonged periods. However, interpreting labeling data is sometimes complicated by the persistent high labeling fractions at late time points, here called the ”fat-tail” phenomenon. In this study, we systematically evaluated three kinetic models aimed at addressing this phenomenon: the Gamma-Distributed Death Rate (GDDR) model, the Gamma-Distributed Lifespan (GDLS) model, and the Non-Exponential Death Model. Through comparative analyses, we found that the general 2-dimensional kinetic heterogeneity model that is often used to fit deuterium labeling data effectively reproduced curves predicted by the more complex GDDR model, indicating that gamma distributed death rates do not resolve the problem. Additionally, while kinetically distinct, the GDLS model showed no significant practical advantage over the GDDR model when fitting artificially generated realistic noisy datasets. The Non-Exponential Death Model approached a fit of the one population model by making the transition rate of the first subpopulation very fast, and was unable to to describe experimental data that were well described with the 2-dimensional kinetic heterogeneity model. We propose future modeling directions, including time-dependent death rates, maturation delays, and stochastic models, emphasizing that increased complexity does not inherently resolve the fat-tail issue. Our findings underscore the importance of selecting biologically realistic model refinements to improve the interpretation of DNA deuterium labeling studies of immune cell turnover.