Acta Biotheoretica

, Volume 63, Issue 4, pp 381–395 | Cite as

Travelling Waves of Cell Differentiation

Regular Article


The paper is devoted to modelling of cell differentiation in an initially homogeneous cell population. The mechanism which provides coexistence of two cell lineages in the initially homogeneous cell population is suggested. If cell differentiation is initiated locally in space in the population of undifferentiated cells, it can propagate as a travelling wave converting undifferentiated cells into differentiated ones. We suggest a model of this process which takes into account intracellular regulation, extracellular regulation and different cell types. They include undifferentiated cells and two types of differentiated cells. When a cell differentiates, its choice between two types of differentiated cells is determined by the concentrations of intracellular proteins. Differentiated cells can either stimulate differentiation into their own cell lineage or into another cell lineage. In the case of the positive feedback, only one lineage of differentiated cells will finally appear. In the case of negative feedback, both of them can coexist. In this case a periodic spatial pattern emerges behind the wave.


Cell differentiation Lineage choice Reaction-diffusion waves Pattern formation 

Mathematics Subject Classification

92C15 35K57 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • M. Benmir
    • 1
  • N. Bessonov
    • 2
  • S. Boujena
    • 1
  • V. Volpert
    • 3
  1. 1.Faculté des SciencesUniversity Hassan II of CasablancaCasablancaMaroc
  2. 2.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSaint PetersburgRussia
  3. 3.Institut Camille Jordan, UMR 5208 CNRSUniversity Lyon 1VilleurbanneFrance

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