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Stochastic Models of Lymphocyte Proliferation and Death

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  • Anton Zilman
  • Vitaly V Ganusov
  • Alan S Perelson

Abstract

Quantitative understanding of the kinetics of lymphocyte proliferation and death upon activation with an antigen is crucial for elucidating factors determining the magnitude, duration and efficiency of the immune response. Recent advances in quantitative experimental techniques, in particular intracellular labeling and multi-channel flow cytometry, allow one to measure the population structure of proliferating and dying lymphocytes for several generations with high precision. These new experimental techniques require novel quantitative methods of analysis. We review several recent mathematical approaches used to describe and analyze cell proliferation data. Using a rigorous mathematical framework, we show that two commonly used models that are based on the theories of age-structured cell populations and of branching processes, are mathematically identical. We provide several simple analytical solutions for a model in which the distribution of inter-division times follows a gamma distribution and show that this model can fit both simulated and experimental data. We also show that the estimates of some critical kinetic parameters, such as the average inter-division time, obtained by fitting models to data may depend on the assumed distribution of inter-division times, highlighting the challenges in quantitative understanding of cell kinetics.

Suggested Citation

  • Anton Zilman & Vitaly V Ganusov & Alan S Perelson, 2010. "Stochastic Models of Lymphocyte Proliferation and Death," PLOS ONE, Public Library of Science, vol. 5(9), pages 1-14, September.
    • Handle: RePEc:plo:pone00:0012775
    DOI: 10.1371/journal.pone.0012775
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    Cited by:

    1. Mohammad Soltani & Cesar A Vargas-Garcia & Duarte Antunes & Abhyudai Singh, 2016. "Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-23, August.
    2. Tom Serge Weber & Irene Jaehnert & Christian Schichor & Michal Or-Guil & Jorge Carneiro, 2014. "Quantifying the Length and Variance of the Eukaryotic Cell Cycle Phases by a Stochastic Model and Dual Nucleoside Pulse Labelling," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-17, July.
    3. Michael Gabel & Tobias Hohl & Andrea Imle & Oliver T Fackler & Frederik Graw, 2019. "FAMoS: A Flexible and dynamic Algorithm for Model Selection to analyse complex systems dynamics," PLOS Computational Biology, Public Library of Science, vol. 15(8), pages 1-23, August.
    4. Zack W Jones & Rachel Leander & Vito Quaranta & Leonard A Harris & Darren R Tyson, 2018. "A drift-diffusion checkpoint model predicts a highly variable and growth-factor-sensitive portion of the cell cycle G1 phase," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-20, February.
    5. Vitaly V Ganusov & Jeremy Auerbach, 2014. "Mathematical Modeling Reveals Kinetics of Lymphocyte Recirculation in the Whole Organism," PLOS Computational Biology, Public Library of Science, vol. 10(5), pages 1-15, May.

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