A stochastic model for cell populations with circadian rhythms

A mathematical model for cell kinetics, based on a random walk, is developed. The model allows variations with time of the rates of passage of proliferating cells through the four phases of the mitotic cycle. Circadian variations in the mitotic and labelling indices of the Syrian hamster cheek pouch epithelium have previously been observed, and the random walk model has been used to simulate this phenomenon. Assuming that all basal cells are proliferative and that these cells leave the basal layer randomly throughout the mitotic cycle to become differentiated cells, it was found that the experimentally observed circadian rhythms of the mitotic and labelling indices could be reproduced in the model by postulating a circadian rhythm in the rate of passage of cells through the G1 and S phases only. Moreover, the growth activity of cells in both the G1 and S phases appears to reach a peak during the dark hours of the light-dark cycle, and to fall off rapidly in the early hours of daylight. The postulate of Møller, Larsen & Faber (1974) that injection of the animals with tritiated thymidine causes a shortening of the G2 phase duration has been qualitatively confirmed by using the random walk model to simulate the FLM and MI curves after injection with tritiated thymidine.