Bulletin of Mathematical Biology

, Volume 68, Issue 5, pp 1011–1031 | Cite as

Estimating Lymphocyte Division and Death Rates from CFSE Data

  • Rob J. De BoerEmail author
  • Vitaly V. Ganusov
  • Dejan Milutinović
  • Philip D. Hodgkin
  • Alan S. Perelson
Original Article


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 rate Cell death rate CFSE Lymphocyte dynamics IL-2 


“anti-CD3 mAb”

monoclonal antibody (mAb) triggering T cell activation via the CD3 molecule associated with T cell antigen receptors

interleukin-2 (IL-2)

growth factor for T cells that is measured in “units/ml”, where 1 unit/ml is the concentration required to give 50% of the maximum response in the HT2 bioassay (Mosmann et al., 1986)


radioactively labeled 3H-thymidine that is incorporated in the DNA of dividing cells


nucleotide analog 5-bromo-2′-deoxyuridine also incorporated in the DNA of dividing cells


color dye “carboxyfluorescin diacetate succinimidyl ester” which is taken up in the cytosol of cells, and which dilutes twofold when cells divides


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Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • Rob J. De Boer
    • 1
    • 2
    Email author
  • Vitaly V. Ganusov
    • 1
  • Dejan Milutinović
    • 1
  • Philip D. Hodgkin
    • 3
  • Alan S. Perelson
    • 2
    • 4
  1. 1.Theoretical BiologyUtrecht UniversityUtrechtThe Netherlands
  2. 2.Santa Fe InstituteSanta FeUSA
  3. 3.The Walter and Eliza Hall Institute of Medical ResearchVictoriaAustralia
  4. 4.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

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