Cell cycle control at the first restriction point and its effect on tissue growth.

Cell cycle is controlled at two restriction points, R (1) and R (2). At both points the cell will commit apoptosis if it detects irreparable damage. But at R (1) an undamaged cell also decides whether to proceed to the S phase or go into a quiescent mode, depending on the environmental conditions (e.g., overpopulation, hypoxia). We consider the effect of this decision at the population level in a spherical tissue {r < R(t)}. We prove that if the cells have full control at R (1), they can manipulate the size of R(t) to ensure that 0 < c <or= R(t) <or= C < infinity; simulations further show that R(t) can be made nearly stationary. In the absence of such control, R(t) will either increase to infinity or decrease to 0. The mathematical model and analysis involve a system of PDEs in {r < R(t)}.