A Mathematical Method for Analysing Plasmid Stability in Micro-organisms

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Abstract
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..mchgt.R, and E. coli RV308(pHSG415), where R.mchgt.d.mu., are analysed in order to demonstrate the method.