Estimating the instability parameters of plasmid-bearing cells. I. Chemostat culture.

What determines the stability of plasmid-bearing cells in natural and laboratory conditions? In order to answer this question in a quantitative manner, we need tools allowing the estimation of parameters governing plasmid loss in different environments. In the present work, we have developed two methods for the estimation of the instability parameters of plasmid-bearing cells growing in chemostat. These instability parameters are: (i) selection coefficient (or cost of the plasmid)alpha and (ii) the probability of plasmid loss at cell division tau(0). We have found that generally selection coefficient alpha changes during elimination of plasmid-bearing cells due to changes in substrate concentration; hence, methods which assume constancy of alpha are intrinsically imprecise. Instead, one can estimate selection coefficient at the beginning and the end of cultivation when the substrate concentration is approximately constant. Applying developed techniques to two sets of experimental data, we have found that (i) the cost of the plasmid pBR322 depended on the dilution rate in chemostat and was higher at low dilutions; (ii) high levels of plasmid gene expression led to a high cost of the plasmid pPHL-7; (iii) the probability of plasmid loss was lower at high levels of plasmid gene expression and independent of the dilution rate. We have also discussed the application of our results to understanding the basic biology of bacterial plasmids.