Time correlations in a model of tissue growth

CHARA OSVALDO; LAVALLE, NATALIA; GRIGERA, TOMAS

Congreso; XLIX Reunión Anual de la Sociedad Argentina de Biofísica 2021; 2021

Sociedad Argentina de Biofísica (SAB)

Tissue growth is controlled by cell proliferation and apoptosis. The interplay between both cellular processes is crucial during physiological embryonic development as well as in pathophysiological conditions like cancer, among many other examples of biological and medical importance. In this study, we investigate the problem of tissue growth with a minimal Markovian mathematical model of the number of cells in a tissue subjected toboth, cell proliferation and apoptosis. The model shows three dynamical phases, depending on the difference between the two relevant model parameters, the proliferation and the apoptosis rates: a growth phase and a decline phase in which proliferation is greater than apoptosis and vice versa, respectively, together with ahomeostatic phase, where both rates are identical. The extinction probability is one in the decline phase and it is less than one (but not zero) in the growth phase. In the homeostatic phase, the extinction probability is one while the average number of cells is constant. To quantitatively characterize tissue growth dynamics, we computed the time correlation function for our model in these three regimes. We found that the time correlation is clearly different in the three dynamical phases and we verified this result numerically. Noteworthy, we found that that time correlations follow a power-law behavior in the homeostatic phase, suggesting that this phase is critical. We discuss the implications of this minimal model in the context of biophysics of tissue growth.