A structured population model of cell differentiation

Marie Doumic, Anna Marciniak-Czochra, Benoît Perthame, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential equations of transport type. Specifically, it consists of a structured population equation with a nonlinear feedback loop. This models the signaling process due to cytokines, which regulate the differentiation and proliferation process. We compare the continuous model to its discrete counterpart, a multicompartmental model of a discrete collection of cell subpopulations recently proposed by Marciniak-Czochra et al. [Stem Cells Dev., 18(2009), pp. 377-386] to investigate the dynamics of the hematopoietic system. We obtain uniform bounds for the solutions, characterize steady state solutions, and analyze their linearized stability. We show how persistence or extinction might occur according to values of parameters that characterize the stem cells' self-renewal. We also perform numerical simulations and discuss the qualitative behavior of the continuous model vis à vis the discrete one.

Original languageBritish English
Pages (from-to)1918-1940
Number of pages23
JournalSIAM Journal on Applied Mathematics
Issue number6
StatePublished - 2011


  • Cell differentiation
  • Stability analysis
  • Stem cells
  • Structured population dynamics
  • Transport equation


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