Computational analysis of CFSE proliferation assay

Abstract

CFSE based tracking of the lymphocyte proliferation using flow cytometry is a powerful experimental technique in immunology allowing for the tracing of labelled cell populations over time in terms of the number of divisions cells undergone. Interpretation and understanding of such population data can be greatly improved through the use of mathematical modelling. We apply a heterogeneous linear compartmental model, described by a system of ordinary differential equations similar to those proposed by Kendall. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set that we specifically analyze specifies the following characteristics of the kinetics of PHA-induced human T lymphocyte proliferation assay in vitro: (i) the total number of live cells, (ii) the total number of dead but not disintegrated cells and (iii) the number of cells divided j times. Following the maximum likelihood approach for data fitting, we estimate the model parameters which, in particular, present the CTL birth-and death rate "functions". It is the first study of CFSE labelling data which convincingly shows that the lymphocyte proliferation and death both in vitro and in vivo are division number dependent. For the first time, the confidence in the estimated parameter values is analyzed by comparing three major methods: the technique based on the variance-covariance matrix, the profile-likelihood-based approach and the bootstrap technique. We compare results and performance of these methods with respect to their robustness and computational cost. We show that for evaluating mathematical models of differing complexity the information-theoretic approach, based upon indicators measuring the information loss for a particular model (Kullback-Leibler information), provides a consistent basis. We specifically discuss methodological and computational difficulties in parameter identification with CFSE data, e.g., the loss of confidence in the parameter estimates starting around the 6-th division. Overall, our study suggests that the heterogeneity inherent in cell kinetics should be explicitly incorporated into the structure of mathematical models.

IL-2 Regulates Expansion of CD4+ T Cell Populations by Affecting Cell Death: Insights from Modeling CFSE Data

“…IL-2 only moderately affects the cell interdivision time, but reducing the IL-2 concentration increases the degree of stochasticity of the cell division. Interestingly, a recent study has also found dependence of the rate of cell death and proliferation on the division number for lymphocytes stimulated with PMA in vitro (21).…”

Novel Lipophilic Tracking Dyes for Monitoring Cell Proliferation

“…Alternatively, one can restrict the use of this probe to cell types which are quiescent, or in which cell division is unlikely to begin before dye equilibration has occurred. More recently, dynamic approaches to modeling the proliferation of CFSE stained cells have been investigated, making use of sophisticated statistical and calculus based formulae to assist in the interpretation of experimental data (Deenick et al, 2003;Hawkins et al, 2007;Liu et al, 2006;Luzyanina et al, 2007). Mathematical correction may also account for continued, slow rates of dye loss (after 24-48 hours) in populations where an unstimulated, non-dividing control sample is not possible (Matera et al, 2004;Ubezio et al, 2007).…”

Stretched cell cycle model for proliferating lymphocytes

“…Furthermore, mathematical models adopting this mechanical description (so-called "transition probability" or "compartment" models) remain popular and form the basis of many studies of lymphocyte and cancer kinetics in vitro and in vivo today (13)(14)(15)(16)(17)(18)(19)(20)(21).…”