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The stability of a low-copy-number plasmid, pHSG415, in Escherichia coli, was investigated in batch and continuous culture. The plasmid was unstable in batch culture, but was significantly stabilized by growth in continuous culture with phosphate, nitrogen or potassium limitation. However, the plasmid was very unstable when grown in continuous culture with sulphate limitation. These results contrast with those obtained with multicopy plasmids such as pBR322, which is particularly unstable in carbon- or phosphate-limited continuous culture. The effect of growth rate on the stability of E. coli(pHSG415) grown in continuous culture with glucose limitation was also investigated. The plasmid was significantly more stable in cells grown at higher growth rates. The segregational instability (R) of the plasmid and the difference in growth rate between plasmid-free and plasmid-bearing cells (dmu) were calculated for each condition using the method of Cooper et al. (accompanying paper: Journal of General Microbiology 133, 1871-1880). It was found that the primary cause of the loss of pHSG415 from the cell population was the segregational instability of the plasmid.

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.