A mathematical method for analysing plasmid stability in micro-organisms

A mathematical model describing the instability of plasmids in micro-organisms has been developed. The model is based on the assumption that the overall causes of plasmid instability are described by the segregational instability of the plasmid, R (i.e. the rate at which plasmid-free cells are generated from plasmid-bearing cells), and the growth rate difference, d mu (i.e. the difference in growth rate between plasmid-free and plasmid-bearing cells). A method for determining the values of R and d mu (accompanied by 95% confidence limits) for any plasmid-bearing micro-organism is described. This method is based on the observation that, depending on the plasmid, various exponential patterns of plasmid instability are observed. The stability of Escherichia coli 1B373(pMG169), where d mu much greater than R, and E. coli RV308(pHSG415), where R much greater than d mu, are analysed in order to demonstrate the method.