A new model for the estimation of cell proliferation dynamics using CFSE data

Abstract

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 [13, 43, 45], 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 γ 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.

Mathematical Models of Dividing Cell Populations: Application to CFSE Data

“…Thus, there seems to be an advantage in the direct mathematical modeling of CFSE histogram data. To this end, structured population models have been proposed [21,22,55,56,79]. Such partial differential equation (PDE) models have long been discussed in the context of cell populations [28] and can be structured by age [1,27,39,44], cyclin content [27], size [40,44,45,68] or DNA-content [26], or any number of other physiological variables [62].…”

“…The use of such a nonphysiological structure variable was suggested as early as 2000 for BrdU-based assays [30], and was first explored in the context of CFSE-based assays in [56]. More recent work [8,21,22,55,79] has consistently demonstrated that the label-structured PDE framework can accurately model the observed histogram data from a CFSE-based proliferation assay. The primary benefit of using such a model is the ability to treat CFSE histogram data directly.…”

“…The parameter x a accounts for the autofluorescence or natural brightness of unlabeled cells. The advection term in the equation above (with parameters c and k) models the slow decay of CFSE FI (as a result of the natural turnover of intracellular proteins within the cell) using a Gompertz decay process [21]. These two features (autofluorescence and label decay) are important mathematical structures describing the manner in which the intracellular dye is processed by cells.…”

“…The density n(t, x) can then be used to compute cell counts in terms of measured FI, to be compared directly to histogram data such as Figure 2. While the model (3.15) has been shown to very accurately fit CFSE histogram data [21,22], it cannot be used to compute quantities such as the number of cells having undergone a given number of divisions. As such, it is not (in the form above) directly comparable to the methods previously discussed.…”

“…As such, it is not (in the form above) directly comparable to the methods previously discussed. Also, though the structural dependence of the proliferation and death rate functions can be used to infer division-dependent characteristics [21,79], this interpretation is neither straightforward nor intuitive [74]. In order to alleviate these difficulties, a simple reformulation [23,46,74,79] of the model (3.15) can be used to describe the structured densities of subpopulations of cells corresponding to distinct generations, which interact through division.…”