A novel statistical analysis and interpretation of flow cytometry data

Abstract

A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+ T and CD8+ T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.

Analysis of variability in estimates of cell proliferation parameters for cyton-based models using CFSE-based flow cytometry data

“…As in [4], we incorporate the cyton model for cell numbers into the division-and label-structured model framework described previously by replacing the sink and source terms in the right-hand sides of (3.1) with terms involving the cyton-based rates to obtain Like (3.1), the model given by (3.12) may be properly described as a division-and label-structured population model, as it makes use of structure variables for division number (or generation) and CFSE label content (which is proportional to CFSE-wavelength FI) . Also, as described in [12,19] and summarized in [4], the factorable form of the solutions { ( , )} and the technique for converting these to corresponding solutions {̃ ( ,̃ )} via convolution integrals (cf.…”

“…Long-standing results indicate that the partitioning of cytoplasm to two daughter cells during mitosis is not even [21], and a recent review [10] suggests that incorporating the assumption of asymmetric cell division into mathematical models for cell proliferation will "improve assessment of T cell performance parameters from CFSE-based proliferation assays." Nevertheless, we follow the convention of earlier work [4,12,16,18,19,22] in making the simplifying assumption that CFSE is evenly distributed during cell division.…”

“…Here, we summarize a class of models originally proposed in [22] and further developed in [7] and [4]. We then identify the speci c model to be considered for the purposes of our variability study.…”

“…Also, as described in [12,19] and summarized in [4], the factorable form of the solutions { ( , )} and the technique for converting these to corresponding solutions {̃ ( ,̃ )} via convolution integrals (cf. (3.8)) makes it possible to obtain numerical solutions very quickly when the model parameters are given [4,12]. This model has been shown to yield a reasonably good t to summary histogram data such as that presented in Figures 1 through 8, provided that the model parameters are chosen "optimally" [4].…”

“…It should explicitly noted that data sets formed in this way do not represent truly longitudinal data because measurements corresponding to each time point were made using distinct cell cultures (wells). In this type of in vitro experiment (see, for example, [16], [14], [18], and [4]) it is tacitly assumed that the populations of cells in each well are identical (up until the moment cells are harvested from a particular well) in that they include the same numbers of total cells in the same proportions (according to cell type). This assumption allows one to interpret time series data sets formed as described above as having come from longitudinal observations.…”