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CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and division-linked changes in cell behavior. Recently, a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.

We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.

This paper discusses statistical and computational aspects of inverse or parameter estimation problems based on Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the topics addressed are mathematical model, statistical model and data assumptions, and some techniques (residual plots, sensitivity analysis, model comparison tests) for verifying these. The ideas are illustrated throughout with the popular logistic growth model of Verhulst and Pearl as well as with a recently developed population-level model of pneumococcal disease spread., Prepared in cooperation with the Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC and the Department of Mathematics and Statistics, Arizona State University, Tempe, AZ.

Background Fluorescently labeled ligands and flow cytometric methods allow quantification of receptor-ligand binding. Such methods require calibration of the fluorescence of bound ligands. Moreover, binding of unlabeled ligands can be calculated based on their abilities to compete with a labeled ligand. In this study, calibration parameters were determined for six fluorescently labeled N-formyl peptides that bind to receptors on neutrophils. Two of these ligands were then used to develop and validate competitive binding protocols for determining binding constants of unlabeled ligands. Methods Spectrofluorometric and flow cytometric methods for converting relative flow cytometric intensities to number of bound ligand/cell were extended to include peptides labeled with fluorescein, Bodipy, and tetramethylrhodamine. The validity of flow cytometric competitive binding protocols was tested using two ligands with different fluorescent properties that allowed determination of rate constants both directly and competitively for one ligand, CHO-NLFNYK-tetramethylrhodamine. Results Calibration parameters were determined for six fluorescently-labeled N-formyl peptides. Equilibrium dissociation constants for these ligands varied over two orders of magnitude and depended upon the peptide sequence and the molecular structure of the fluorescent tag. Kinetic rate constants for CHO-NLFNYK-tetramethylrhodamine determined directly or in competition with CHO-NLFNYK-fluorescein were statistically identical. Conclusions Combination of spectrofluorometric and flow cytometric methods allows convenient calculation of calibration parameters for a series of fluorescent ligands that bind to the same receptor site. Competitive binding protocols have been independently validated. Cytometry 45:102-114, 2001. © 2001 Wiley-Liss, Inc.