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

Abstract

In this article we assess variability in cell proliferation dynamics observed for CD4+ and CD8+ T cells collected from two healthy donors. We review a recently developed class of models that incorporates the so-called "cyton model" for cell numbers into a conservation-based PDE model for cell population dynamics and describe a statistical model that relates CFSE-based ow cytometry data to such models. A parameter estimation scheme is summarized and then applied to a large body of data to assess experimental variability (variation in parameter estimates as identical experiments are replicated) and biological variability (di erences in parameter estimates obtained for di erent donors and cell types) in the context of these models. Variability in the data obtained from replicated experiments is also discussed. The results of this study indicate that many of the cyton model parameters for describing cell proliferation can be reliably estimated using our approach; however, they also show that substantial changes to our mathematical model and/or experimental procedures may be required to ensure identi ability of the remaining cell proliferation parameters.

Evaluating the Importance of Mitotic Asymmetry in Cyton-Based Models for Fse-Based Flow Cytometry Data

“…Note that when m = 1 2 , the expression for R i (t, x) given here simplifies such that the recruitment terms match those presented previously for the symmetric division models of Banks et al [2,3,4]. The initial conditions are given by…”

“…Here, we summarize a new class of cell proliferation models that incorporates aspects of the cyton model of Hawkins et al [14,15] and the separable PDE models of Schittler et al [20] and Hasenauer et al [13], as well as the possibility of asymmetric cell divisions as proposed by Bocharov et al [9] and Luzyanina et al [17]. These models extend the cyton-based division-and label-structured PDE models previously used by Banks et al [2,3,4] by including an additional parameter m that describes the degree to which cytoplasm apportionment during mitosis is asymmetric.…”

“…In the cyton model, n div i (t) and n die i (t) are rates (in cells/hr) at which cells in generation i divide and die, respectively. The cytons {(φ i , ψ i )} are used to compute {n div i (t)} and {n die i (t)}, which are in turn used to compute {N i (t)}, the numbers of cells present in each generation i at any given time t. Banks et al [2,3,4] and Kapraun [16] provide details of the cyton model, and use the same notation and symbols we use here.…”

“…As the success of the adaptive immune system in overcoming a perceived threat depends on the capacity of lymphocytes to proliferate, the ability to accurately predict cell proliferation dynamics in the presence of specific environmental stimuli has important implications for human health research in areas such as the treatment and prevention of infectious disease and immunosuppression for patients receiving organ and tissue transplants. Our recent efforts [2,3,4,6,7] have focused on estimating cell proliferation parameters and quantifying uncertainty in such estimates, but thus far we have always utilized mathematical models that are based upon the assumption of symmetric cell division. Here we consider how the incorporation of asymmetric cell division, which has been described as "almost an axiom of cell biology" [22], into our division-and label-structured partial differential equation models affects their ability to accurately describe data from CFSE dilution assays.…”

“…In previous publications [2,3,4], the authors have described methods for using CFSE-based flow cytometry data to determine T cell division and death rates (for cells having completed various numbers of divisions). In this manuscript, however, we focus on a new model in which the apportioning of CFSE during mitosis is not assumed to be even and consider whether such a model can describe one particular collection of data sets more accurately than a model based on symmetric (50-50) cell division.…”