Mathematical modelling of spatio-temporal cell dynamics in colonic crypts following irradiation

Objectives: Modelling the apoptotic process is essential for simulating and understanding tumour growth, as most tumour tissues carry mutations in apoptotic signalling pathways. Thus here, we have aimed to construct a mathematical model of colonic crypts that explicitly incorporates the apoptotic mechanism. Methods: A murine colonic crypt was described as being a two-dimensional rectangular surface model. In this system, three types of cells with different proliferating and differentiating potentials migrate. Apoptosis was described as a process activated by irradiation that progresses in a stepwise manner. Parameter values in the model were determined to be consistent with experimental data for changes in the apoptotic cell ratio within murine transverse colonic crypts following irradiation. Results: First, we constructed a model reproducing cell proliferation dynamics in normal murine colonic crypts; next, we applied the apoptotic mechanism to this model. As a result, we succeeded in simultaneous reproduction of both spatial and temporal changes in distribution of apoptotic cells in murine colonic crypts by determining parameter values in numerical simulations. Through this adjustment process, we were able to predict that stem cells and transit amplifying (TA) cells in each generation must react distinctly from each other, to apoptosis-inducing stimuli. Conclusions: We constructed a mathematical model with which we could quantitatively describe cell proliferative and apoptotic dynamics in a murine colonic crypt. Using this model, we were able to make novel predictions that sensitivity to apoptosis-inducing stimuli is dependent on cell type.