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A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations.

Original publication




Journal article


Phys Rev E Stat Nonlin Soft Matter Phys

Publication Date





Algorithms, Apoptosis, Biophysics, Cell Differentiation, Cell Proliferation, Colon, Disease Progression, Humans, Models, Statistical, Models, Theoretical, Neoplasms, Neoplastic Stem Cells, Stem Cells