The waste-product theory of aging: waste dilution by cell division.

When cells divide, the quantity of waste material per cell decreases because the wastes are "diluted" by apportionment between the daughters which result from the division. The quantity of waste present in a symmetrically or asymmetrically dividing population of cells is governed by a first-order non-linear differential equation. In the derivation of the equation, it is assumed (a) that waste is created at a rate which is either constant or proportional to the amount of waste already formed, (b) that waste is neither destroyed nor transported across cell walls, and (c) that the rate of cell division at large values of time is inversely proportional to the amount of waste per cell raised to a power. Relations among the parameters of the differential equation specify conditions under which its solutions rise to a critical value. If the amount of waste per cell given by a solution of the differential equation exceeds this value, it is assumed that deleterious effects become evident and that cell death follows. Decreases in the cell division rate leading to a cessation of population growth may occur at lower levels of waste accumulation.