Transport Models for Collective Dynamics in Biological Systems

Mathematical and Statistical Modeling of Human Lymphocyte Proliferation Using CFSE Data

Thomas Banks

North Carolina State University


CFSE analysis of proliferating cell populations is a tool of growing popularity for the study of cell division and division-linked changes in cell behavior. Partial differential equation (PDE) models are presented to describe lymphocyte dynamics in a CFSE proliferation assay. Previously poorly understood physical mechanisms accounting for dye dilution by division, auto fluorescence and label decay are included. A new class of division-dependent compartmental models allows one to separate proliferation and death rates from intracellular label dynamics. By fitting the new models to the commonly used histogram representation of the data, it is shown that these improvements result in models with a strong physical basis which are still fully capable of replicating the behavior observed in in vitro data. Some mathematical and statistical aspects of the corresponding inverse problems are discussed. The new models provide quantitative techniques that are useful for the comparison of CFSE proliferation assay data across different data sets and experimental conditions. Variability and uncertainty in data and modeling are discussed. The efforts involve joint investigations with W. C. Thompson and a team of immunologists in Barcelona led by A. Meyerhans.