Bulletin of Mathematical Biology

, Volume 70, Issue 1, pp 21–44

Modeling T Cell Proliferation and Death in Vitro Based on Labeling Data: Generalizations of the Smith–Martin Cell Cycle Model

Original Article

DOI: 10.1007/s11538-007-9239-4

Cite this article as:
Lee, H.Y. & Perelson, A.S. Bull. Math. Biol. (2008) 70: 21. doi:10.1007/s11538-007-9239-4


The fluorescent dye carboxyfluorescein diacetate succinimidyl ester (CFSE) classifies proliferating cell populations into groups according to the number of divisions each cell has undergone (i.e., its division class). The pulse labeling of cells with radioactive thymidine provides a means to determine the distribution of times of entry into the first cell division. We derive in analytic form the number of cells in each division class as a function of time based on the distribution of times to the first division. Choosing the distribution of time to the first division to fit thymidine labeling data for T cells stimulated in vitro under different concentrations of IL-2, we fit CFSE data to determine the dependence of T cell kinetic parameters on the concentration of IL-2. As the concentration of IL-2 increases, the average cell cycle time is shortened, the death rate of cells is decreased, and a higher fraction of cells is recruited into division. We also find that if the average cell cycle time increases with division class then the qualify of our fit to the data improves.


CFSEThymidineT cellIL-2Smith–Martin cell cycle model

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  1. 1.Theoretical Biology & BiophysicsLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Biostatistics and Computational Biology, School of Medicine and DentistryUniversity of RochesterRochesterUSA