A Division-Dependent Compartmental Model for Computing Cell Numbers in CFSE-based Lymphocyte Proliferation Assays

Abstract

Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,41,47,48]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,51,53]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.Key words: Cell proliferation, cell division number, CFSE, label structured population dynamics, partial differential equations, inverse problems. 1 Report Documentation Page

Infected hematopoietic stem cells and with integrated HBV DNA generate defective T cells in chronic HBV infection patients

“…Carboxyfluorescein diacetate succinimidyl ester (CFSE) is a fluorescent dye used to label cells, the proliferative activity of which can then be detected by flow cytometry. Using this method, cells may be traced through successive generations without the use of radioactivity . CFSE dilution was measured by flow cytometry for assessing T‐lymphocyte proliferation.…”

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay

“…The main feature of age-structured model is a non-local boundary condition which describes the fertility process in population in explicit form. As the reproduction of individuals in populations plays an important role in nature the age-structured models are widely studied and used in theoretical and applied researches of biological, demographical and ecological systems [9,12,13,16,17,22,23,26,29,[31][32][33][42][43][44]53]. This class of models is well adapted to simulation of the dynamical properties of experimental cultures of cell aggregations including the cell-division cycle with variable intermitotic time.…”

Quantifying CFSE label decay in flow cytometry data

“…$$\frac{\partial n_i}{\partial t}+\frac{\partial [v(t,x)n_i(t,x)]}{\partial x}=-({\alpha }_i(t)+{\beta }_i(t))n_i(t,x)+R_i(t,x),$$ with the generations linked through the division mechanism R i ( t , x ) as a source term (see [7, 12, 26]). Because each generation of cells is assigned to a particular compartment (indexed by i ) with unique proliferation and death rates, it is not necessary to estimate these rates in terms of the structure variable x , so that peak overlap and label decay no longer affect the accuracy of the estimated rates.…”