Implications of stochastic inheritance

Abstract

Imperfect coordination between an autonomous genetic element, or plasmid, and a host bacterium reproducing by binary fission is shown to have two effects. The proportion of cells which have lost the plasmid completely tends to a constant for populations growing under constant selective pressure. At the same time, the average number of copies of the plasmid per cell—averaged over those cells which inherit one or more—tends to a constant, which is determined essentially by the ratio of two characteristic probabilities: that of failure of the plasmid to duplicate before a cell divides, and that of failure—of any two copies of the plasmid resulting from the same act of duplication—to separate to opposite halves of a dividing cell. The theory given predicts the proportion of cells which fail to inherit plasmid-like particles after any number of generations of bacterial growth. The manner in which the mean number of particles per particle-containing cell approaches its final constant value is also predicted. The effect of non-random inheritance on cells containing non-replicating particles is determined. Application of the theory is illustrated by experimental data from the literature.