Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division

Abstract

Since their invention in 1994, fluorescent dyes such as carboxyfluorescein diacetate succinimidyl ester (CFSE) are used for cell proliferation analysis in flow cytometry. Importantly, the interpretation of such assays relies on the assumption that the label is divided equally between the daughter cells upon cell division. However, recent experimental studies indicate that division of cells is not perfectly symmetric and there is unequal distribution of protein between sister cell pairs. The uneven partition of protein or mass to daughter cells can lead to an overlap in the generations of CFSE-labelled cells with straightforward consequences for the resolution of individual generations. Numerous mathematical models developed so far for the analysis of CFSE proliferation assay incorporate the premise that the CFSE fluorescence intensity is halved in the two daughter cells. Here, we propose a novel modelling approach for the analysis of the CFSE cell proliferation assays which are characterized by poorly resolved peaks of cell generations in flow cytometric histograms. We formulate a mathematical model in the form of a system of delay hyperbolic partial differential equations which provides a good agreement with the CFSE histograms time-series data and allows an analytical treatment. The model is a further generalization of the recently proposed class of division- and label-structured models as it considers an asymmetric cell division. In addition, the basic structure of the cell cycle, i.e. the resting and cycling cell compartments, is taken into account. The model is used to estimate fundamental parameters such as activation rate, duration of the cell cycle, apoptosis rate, CFSE decay rate and asymmetry factor in cell division of monoclonal T cells during cognate interaction with dendritic cells.

Existence and stability of periodic solutions of an impulsive differential equation and application to CD8 T-cell differentiation

“…Considering a CFSE-labelled lymphocyte population, Luzyanina et al (2013) built a system of delay hyperbolic partial differential equations structured by a continuous variable representing intracellular CFSE amount and allowing uneven distribution of CFSE between daughter cells. Each equation models the size of the population of lymphocytes that have undergone a given number of divisions.…”

Model-based assessment of the Role of Uneven Partitioning of Molecular Content on Heterogeneity and Regulation of Differentiation in CD8 T-cell Immune Responses

“…Less is known about the partitioning of molecular content in the course of subsequent cell divisions. However, partitioning of CFSE dye during lymphocyte proliferation has been mathematically studied [16,17], and these studies suggest that uneven partitioning, which does not result from cell polarisation, occurs at T-cell division.…”

Estimates and impact of lymphocyte division parameters from CFSE data using mathematical modelling

“…Whereas these models describe the evolution of cell numbers in each generation, derived from CFSE histograms, other models, called “label-structured models” deal directly with the fluorescence histogram [15–18], avoiding data pre-processing. Indeed pre-processing can introduce errors, as it is sometimes difficult to assign CFSE intensities to a division number [4].…”

“…Moreover, CFSE division in daughter cells could be asymmetric, and these models should overcome this difficulty [19]. Although these models have some similarities to the “age- and division-structured models” that are developed in this study, they deal with a different type of data (fluorescence and not cell numbers) [18]. …”