Numerical modelling of label-structured cell population growth using CFSE distribution data

The mathematical modelling of label-structured cell population dynamics leads to a hyperbolic partial differential equation in one space variable. The model contains fundamental parameters of cell turnover and label dilution that need to be estimated from the flow cytometry data on the kinetics of the CFSE label distribution. To this end a maximum likelihood approach is used. The Lax-Wendroff method is used to solve the corresponding initial-boundary value problem for the model equation. By fitting two original experimental data sets with the model we show its biological consistency and potential for quantitative characterization of the cell division and death rates, treated as continuous functions of the CFSE expression level.Once the initial distribution of the proliferating cell population with respect to the CFSE intensity is given, the distributed parameter modelling allows one to work directly with the histograms of the CFSE fluorescence without the need to specify the marker ranges. The label-structured model and the elaborated computational approach establish a quantitative basis for more informative interpretation of the flow cytometry CFSE systems.Understanding the dynamics of cell proliferation, differentiation and death is one of the central problems in immunology [1]. A cell population is an ensemble of individual cells, all of which contribute in a different way to the overall observed behavior [2]. A quantitative characterization of this heterogeneity is provided by flow cytometry. Flow cytometry is a technique based on the use of fluorescence activated cell sorter (FACS) for a quantitative single cell analysis of the suspensions of cells, which are labelled with fluorescent substance(s). Once the labelled cells are run through the cell sorter machine, the computer collects data on the fluorescence intensity for each cell [3]. The FACS is capable of analyzing up to a dozen parameters per cell at rates up to 105 cells per second. Therefore it represent