An analysis of the instability kinetics of plasmid pHSG415 during continuous culture of Escherichia coli

Abstract

The effect of dilution rate on the instability kinetics of Escherichis coli RV308(pHSG415) during glucose-limited continuous culture is examined. Two nonlinear models are fitted to the data, both of which characterize the plasmid-host system in terms of the rate parameters R (for the plasmid segregation rate) and dp (for the specific growth rate difference between plasmid-free and plasmid-bearing single cells). In the first model, both R and dp have constant values with respect to time. In the second, either R or dp is represented as a time-dependent function. Although both models fit the data equally well, it is demonstrated that the constant rate parameter model gives results which appear to be misleading. A comparison is also made among some of the many plasmid instability models (both mass-balance and segregated) which have appeared in the literature. It is found that all of these give identical trajectories and differ only in the definitions of the rate parameters used.

Estimating the Instability Parameters of Plasmid-Bearing Cells. I. Chemostat Culture

“…This again is not a new result, even though previous estimates have been obtained using not completely verified methods [Method 1 and its derivatives Davidson et al, 1990;Dunn et al, 1995)]. The cost of the plasmid pBR322 in these conditions varies from 0.10 to 0.40.…”

“…In order to evaluate the quality of methods developed in this paper and the method suggested previously (Walmsley et al, 1983;Lenski & Bouma, 1987;Davidson et al, 1990;Dunn et al, 1995), we have generated two sets of data from numerical solutions of the basic mathema- Fig. 1(A)] and fitted these data by (i) previously suggested solution (14), (ii) solution (17) found in this paper at the approximation a ¼ const; and (iii) solutions (11) and (12) found when aaconst: The results of the fitting are summarized in Table 1.…”

“…Assuming that m þ ðSÞ ¼ D and a ¼ const we find its explicit solution Walmsley et al, 1983;Lenski & Bouma, 1987;Davidson et al, 1990;Proctor, 1994;Dunn et al, 1995).…”

“…The general approach previously applied to estimate parameters a and t 0 at the approximation a ¼ const has been done by assuming a constant steady state in chemostat with m þ ðSÞ ¼ D (Davidson et al, 1990;Dunn et al, 1995). Rewriting eqn (7) by replacing zðtÞ with n þ ðtÞ we obtain…”

“…Growth rates of y t 0 Ey=2; where y is the probability that a plasmidbearing cell gives rise to a plasmid-free cell at cell division (Bailey et al, 1986;Dunn et al, 1995;Boe & Rasmussen, 1996). V. V. GANUSOV AND A. V. BRILKOV plasmid-bearing and plasmid-free cell populations are assumed in the form suggested by Monod (Monod, 1949;Pirt, 1975):…”