Inheritability of plasmids and population dynamics of cultured cells

The compositions of growing bacterial cultures containing F' plasmids are developed in theoretical terms that will be helpful in designating experiments to determine the genetic and physiological parameters involved. The genetic parameter is the inheritability of the plasmid defined as the probability, h, that a daughter bacterium will inherit the plasmid and thus be F' rather than F-. The value of h determines the chance that the plasmid will survive in a clone initiated by a single F' bacterium. If 0 less than or equal to h less than 0.5, the probability of plasmid survival is zero, whereas if 0.5 less than h less than 1 the survival is (2h - 1)/h2. While clone sizes are demonstrated to be erratic, the proportion of F' bacteria does converge to an equilibrium value if log2 h greater than alpha - 1, where the physiological factor, alpha, is the ratio between the division times of F' and F- bacteria. A general expression of this equilibrium is derived. The two cases of alpha = 0, implying that only the F' bacteria multiply on a selective medium, and alpha = 1, implying a completely nonselective medium, are analyzed in detail. It is shown that the above considerations apply generally to growing cultures of cells in which irreversible mutations occur.