Mathematics of microbial plasmid instability and subsequent differential growth of plasmid-free and plasmid-containing cells, relevant to the analysis of experimental colony number data.

Differential growth of plasmid-containing and plasmid-free microbial cells occurs in many and probably most plasmid systems. Misinterpretation of differential growth as replicational, recombinational, or segregational stability or instability can unfortunately result in grossly erroneous conclusions about replication, recombination, or segregation in plasmid model systems for studies of such phenomena. The differential growth rate should ideally be measured every time that the rate of loss due to instability per se is measured. Unfortunately, the possibility of differential growth has been ignored in most plasmid model systems, since the mathematics of instability and differential growth has not usually been dealt with in ways that are intuitively understandable to experimental microbiologists. Nevertheless, rapid diagnosis of differential growth, and accurate estimation of differential growth rate and rate of loss due to instability per se, can be done by analysis of colony number data using only the relatively simple mathematics described in this review. This review is intended for experimental microbiologists rather than for theoretical population geneticists or for pure mathematicians. However, the same mathematics described in this review is also applicable to certain simple model systems for plasmid ecology or evolution in natural or clinical environments.