Heuristic Model of Mitotic Autoregulation in Cell Populations

Abstract

THE control of mitosis has general significance only in relation to the effect exerted on cell division within a population by the population itself. For this a signal must pass between cells, enabling the size of the population to be gauged and cell division to be regulated accordingly. It is convenient to assume that this signal is an inhibitor of cell division and that the mitotic index is inversely proportional to the concentration of this inhibitor for any class of cells. The rate of accumulation of this mitotic inhibitor (Ai) is proportional to the formation of the inhibitor, minus its loss. Thus where f₁, f₂ and f₃ represent respectively the rate of generation, the rate of breakdown and the rate of loss of inhibitor from the surface. The rate of generation of inhibitor is a function of the mass of cells and therefore proportional to the volume, and this argument also applies to the rate of its endogenous degradation. The rate of loss from the surface of the cell aggregate is proportional to the surface area.