Estimation and Sensitivity Analysis of Kinetic Parameters for Plasmid Stability in Continuous Culture of a Recombinant Escherichia coli Harboring trp-operon Plasmid

A model equation to describe the plasmid instability in recombinant Escherichia coli fermentation is proposed. The equation allows one to estimate easily the two model parameters; (1) the difference in the specific growth rates between plasmid-free cells and plasmid-harboring cells ($\delta$), and (2) the probability of plasmid loss by plasmid-harboring cells ($\rho$). The estimated values of $\delta and \rho$ were in the range of 0.02-0.07 and $10^{-3}-10^{-5}$, respectively, and were strongly dependent on the dilution rate. As another parameter, the ratio of specific growth rates of plasmid-free cells and plasmid-harboring cells ($\alha$) was calculated and the result showed the highest value of 1.28 at the lowest dilution rate of 0.075 $hr^{-l}$, examined in this work. By the sensitivity analyses on the estimates of $\delta and \rho$, it was found that the growth rate difference ($\delta$) affected the plasmid instability more seriously than the probability of plasmid loss ($\rho$). Furthermore, the profound instability of plasmid at low dilution rate could be explained by the high values of $\alpha and \rho$.