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Interpreting CFSE Obtained Division Histories of B Cells in Vitro with Smith–Martin and Cyton Type Models

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Abstract

The fluorescent dye carboxyfluorescin 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 using the cyton approach that utilizes independent stochastic distributions for the time to divide and the time to die. We confirm that our analytic form for the number of cells in each division class is consistent with the numerical solution of a set of delay differential equations representing the generalized Smith–Martin model with cell death rates depending on the division class. Choosing the distribution of time to the first division to fit thymidine labeling data for B cells stimulated in vitro with lipopolysaccharide (LPS) and either with or without interleukin-4 (IL-4), we fit CFSE data to determine the dependence of B cell kinetic parameters on the presence of IL-4. We find when IL-4 is present, a greater proportion of cells are recruited into division with a longer average time to first division. The most profound effect of the presence of IL-4 was decreased death rates for smaller division classes, which supports a role of IL-4 in the protection of B cells from apoptosis.

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Authors and Affiliations

  1. Department of Biostatistics and Computational Biology, School of Medicine and Dentistry, University of Rochester, Rochester, NY, 14642, USA

    Ha Youn Lee & Hulin Wu

  2. Walter and Eliza Hall Institute of Medical Research, Victoria, Australia

    Edwin Hawkins & Philip D. Hodgkin

  3. Department of Medicine, Division of Nephrology, Department of Microbiology and Immunology, University of Rochester, Rochester, NY, 14642, USA

    Martin S. Zand

  4. Department of Microbiology and Immunology, University of Rochester, Rochester, NY, 14642, USA

    Tim Mosmann

  5. Theoretical Biology & Biophysics, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Alan S. Perelson

Authors
  1. Ha Youn Lee
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  2. Edwin Hawkins
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  3. Martin S. Zand
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  4. Tim Mosmann
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  5. Hulin Wu
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  6. Philip D. Hodgkin
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  7. Alan S. Perelson
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Correspondence to Ha Youn Lee.

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Lee, H.Y., Hawkins, E., Zand, M.S. et al. Interpreting CFSE Obtained Division Histories of B Cells in Vitro with Smith–Martin and Cyton Type Models. Bull. Math. Biol. 71, 1649–1670 (2009). https://doi.org/10.1007/s11538-009-9418-6

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  • DOI: https://doi.org/10.1007/s11538-009-9418-6

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