Original Article

Bulletin of Mathematical Biology

, Volume 74, Issue 2, pp 300-326

First online:

Evaluation of Multitype Mathematical Models for CFSE-Labeling Experiment Data

  • Hongyu MiaoAffiliated withDepartment of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry Email author 
  • , Xia JinAffiliated withDepartment of Medicine, University of Rochester School of Medicine and DentistryDepartment of Microbiology and Immunology, University of Rochester School of Medicine and Dentistry
  • , Alan S. PerelsonAffiliated withTheoretical Biology and Biophysics Group, MS-K710, Los Alamos National Laboratory
  • , Hulin WuAffiliated withDepartment of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry

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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.


CFSE-labeling Cell cycle Age-dependent multitype branching process Cyton model Smith–Martin model Differential equation model Agent-based model Hybrid optimization Parameter estimation