Estimating Lymphocyte Division and Death Rates from CFSE Data

Abstract

The division tracking dye, carboxyfluorescin diacetate succinimidyl ester (CFSE) is currently the most informative labeling technique for characterizing the division history of cells in the immune system. Gett and Hodgkin [Nat. Immunol. 1:239-244, 2000] have pioneered the quantitative analysis of CFSE data. We confirm and extend their data analysis approach using simple mathematical models. We employ the extended Gett and Hodgkin [Nat. Immunol. 1:239-244, 2000] method to estimate the time to first division, the fraction of cells recruited into division, the cell cycle time, and the average death rate from CFSE data on T cells stimulated under different concentrations of IL-2. The same data is also fitted with a simple mathematical model that we derived by reformulating the numerical model of Deenick et al. [J. Immunol. 170:4963-4972, 2003]. By a non-linear fitting procedure we estimate parameter values and confidence intervals to identify the parameters that are influenced by the IL-2 concentration. We obtain a significantly better fit to the data when we assume that the T cell death rate depends on the number of divisions cells have completed. We provide an outlook on future work that involves extending the Deenick et al. [J. Immunol. 170:4963-4972, 2003] model into the classical Smith-Martin model, and into a model with arbitrary probability distributions for death and division through subsequent divisions.

Cell division curtails helper phenotype plasticity and expedites helper T‐cell differentiation

“…: 0.5 h). 27,51 Although individual stochastic simulations were diverse, the average behaviour of the stochastic model was similar to that of the deterministic model (as was to be expected).…”

“…We implemented cell division in our model by dividing all molecules over two daughter cells, and subsequently considering one of these cells. On the basis of published division times estimated from in vitro T-cell cultures, a reasonable time to first division is about 70 h, whereas the time to complete subsequent divisions is about 10 h. 23,27 In our model, cell division reduces the time to cytokine expression by several days (Figure 3). This is due to DNA demethylation during cell division: DNA replication generates more nonmethylated DNA, which dilutes the amount of methylated DNA.…”

“…22,23 Here, we extend an established model for master transcription factors with epigenetic processes to investigate the differentiation, memory formation and plasticity of helper T cells. Helper T-cell differentiation has been studied extensively using mathematical models, 9,10,[24][25][26][27][28][29][30][31] but to the best of our knowledge, this is the first attempt to combine genetic and epigenetic levels of regulation in mechanistic models for cellular differentiation. Using analytical and numerical approaches, we show that cell division during clonal expansion markedly increases the speed of differentiation into functional helper T cells.…”

A new model to simulate and analyze proliferating cell populations in BrdU labeling experiments

“…To model the number of cells that have divided a certain number of times, we make use of an established division-structured population model [3,5], and extend it to a finite number of subsequent time intervals. This is important since BrdU labeling experiments comprise at least two, but possibly more, time intervals with different labeling conditions (e.g., uplabeling and delabeling phase), as will be exemplified later.…”

“…For several cases there exist analytical solutions for this ODE system, which have been reported elsewhere [3,5]. Moreover, several extensions for this model are available, for example if cell types [8] or age structure [9] are of importance, which allows to generalize the model class to cover a wide range of biological systems.…”