Mathematical Biosciences and Engineering, 2012, 9(4): 699-736. doi: 10.3934/mbe.2012.9.699

Primary: 49N45, 92C37, 97M10; Secondary: 35F16, 35L40.

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A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

1. Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212
2. Center for Research in Scientific Computation, and Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212
3. ICREA Infection Biology Lab, Department of Experimental and Health Sciences, Univ. Pompeu Fabra, 08003 Barcelona

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 [30,31,32,37,38,42,48,49]. 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 [18,19,52,54]. 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.
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