Evaluation of multitype mathematical models for CFSE-labeling experiment data

Abstract

Carboxy-fluorescein diacetate succinimidyl ester (CFSE) labeling is an important experimental tool for measuring cell responses to extracellular signals in biomedical research. However, changes of the cell cycle (e.g., time to division) corresponding to different stimulations cannot be directly characterized from data collected in CFSE-labeling experiments. A number of independent studies have developed mathematical models as well as parameter estimation methods to better understand cell cycle kinetics based on CFSE data. However, when applying different models to the same data set, notable discrepancies in parameter estimates based on different models has become an issue of great concern. It is therefore important to compare existing models and make recommendations for practical use. For this purpose, we derived the analytic form of an age-dependent multitype branching process model. We then compared the performance of different models, namely branching process, cyton, Smith-Martin, and a linear birth-death ordinary differential equation (ODE) model via simulation studies. For fairness of model comparison, simulated data sets were generated using an agent-based simulation tool which is independent of the four models that are compared. The simulation study results suggest that the branching process model significantly outperforms the other three models over a wide range of parameter values. This model was then employed to understand the proliferation pattern of CD4+ and CD8+ T cells under polyclonal stimulation.

Figure 1

A schematic illustration of the branching process model with death and quiescence.

Figure 2

Fit the branching process model (2.10) (solid) and the Cyton model (dashed) to raw data (circle) in log₁₀ scale for CD4+ cells under PHA stimulation.

Figure 3

Fit the branching process model (2.10) (solid) and the Cyton model (dashed) to raw data (circle) in log₁₀ scale for CD8+ cells under PHA stimulation.