coli TG1 under non-selective, selective and modified selective conditions in a chemostat The model was formulated on the basis of experimental investigations.
Acta Biotechnol. 16 (1996) 4, 271-282
Akademie Verlag
Modelling the Stability of the pBR322 Plasmid Derivative pBBZ10 in Escherichiu coli TG1 under Non-Selective and Selective Conditions LOSER 1,
’ *
c.. RAY 2, P.
Vm.- Umweltforschungszentm Leipzig-Halle GmbH Sektion Sanierungsforschung Permosemr. 15 04318 Leipzig, Germany Dresdner Grundwasser Consulting GmbH Meraner Str. 10 01217 Dresden, Germany
A mathematical model has been developed to describe the stability behaviour of the pBR322 plasmid derivative pBB210 with the plactamase gene and the human interferon-a1 gene in Ercherichia coli TG1 under non-selective, selective and modified selective conditions in a chemostat The model was formulated on the basis of experimental investigations. It includes the interaction between plactam antibiotics (ampicillin and sulbactam) and cells (with and without plasmids). in particular the correlation between the growth rate of plasmid-free cells and ampicillin concentration in the medium; ampicillin transport into the periplasm of the plasmid-bearing cells, ampicillin degradation in the periplasm by plasmid-encoded plactamase and the inhibition of the latter by sulbactam. The results obtained by the simulation of chemostat cultivations under various conditions and by steady state analyses are closely related to the results of experiments. Under non-selective conditions, the fraction of plasmid-bearing cells was approaching zero. Under selective and modified selective conditions, a coexistence between plasmid-free and plasmid-bearing cells was reached at steady state. Under these conditions, the steady state fraction of plasmid-bearing cells was proportional to the ampicillin concentration in the feed and inversely proportional to the cell concentration in the chemostat. During highdensity cultivation, a large amount of ampicillin is necessary to suppress plasmid-free cells. Even small concentrations of the plactamase inhihitor sulhactam in the feed increased the steady state fraction of plasmid-bearing cells (from 17.2% to 99.6% at sulbactam-Na concentrations of0 to 5 mg/l).
Introduction
Models describing biotechnological processes serve as tools for experimental planning, for the interpretation of experimental results as well as for predicting the process behaviour under specific conditions. The productivity of large-scale fermentation processes for the production of plasmidencoded gene products is decisively influenced by the proportion of productive cells
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in the cell population, Since, in practice, important large-copy plasmids are randomly partitioned into daughter cells, plasmid-free cells arise at cell division. The growth rate disadvantage of the plasmid-bearing cells, owing to the metabolic burden of the plasmids [ 1, 21, inevitably results in a decrease in the proportion of plasmid-bearing cells in time. Mathematical models have been derived to describe this behaviour [3,4,51. Various concepts have been developed to prevent the accumulation of unproductive plasmid-free segregants during long-term cultivations. In most cases, they are either aimed at turning the growth rate advantage of the plasmid-free cells into a growth rate disadvantage, or at killing the plasmid-free cells which are formed by segregation. The two most important concepts are the plasmidal compensation of a host awotrophy [6, 7, 81 and the use of plasmid-mediated antibiotic resistance [l, 2, 9, 10, 111. By using the antibiotic-resistance concept, the complete suppression of plasmid-free cells is not possible despite the application of antibiotics; and during continuous cultivation, there is a coexistence between plasmid-free and plasmid-bearing cells at steady state, as observed in experimental investigations [ l , 2, 91 and predicted by mathematical models [lo, 111. In this work, a mathematical model is derived to describe the plasmid stability behaviour found in experimental investigations of chemostat cultures with a population consisting of Escherichia coli TGl and Escherichia coli TG1(pBB210) under non-selective, selective and modified selective conditions [9]. Since the plasmid pBB210 contains a plactamase gene, encoding for ampicillin resistance, selective conditions are created on the basis of the antibiotic resistance concept by the addition of ampicillin, and modified selective conditions were obtained by adding both ampicillin and the plactamase inhibitor sulbactam to the fermentation medium. The model differs from other models which have so far been described for this concept [ 10, 111 in that the model structure can be causally explained or confirmed by the results of experimental investigations. Mathematical Model
The process model, which describes the process taking place in the balance space under investigation, is obtained by linking the kinetic model of cell growth with the reactor model. The specific growth rates of cells are influenced not only by the growth limiting carbon source glucose but, under selective conditions, also by antibiotics. According to experimental results, the correlation between the specific growth rate and the glucose concentration is described by the MONODkinetics (the kinetic constants of plasmid-bearing and plasmid-free cells are different because of the metabolic burden of the plasmids). The ampicillin resistance of the plasmid-containing cells is very high (ampicillin-Na concentrations of up to 1,OOO mg/l have no influence on growth) and so the model needs only to consider the influence of ampicillin on the specific growth rate of plasmid-free cells (phenomenological model fitted to experimentally determined p-C, values of E. coli TGl). The influence of sulbactam on the growth
WR, C., RAY,P., Modelling the Stability of the pBR322 Plasmid Derivative pBB2IO
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of both strains is ngt considered in the model because of its very low concentration in the chemostat experiments. The following equations describe the specific growth rates of the plasmid-bearing cells, p +, and of the plasmid-free cells, p-: "
Within a cell population consisting of plasmid-free and plasmid-bearing fraction of plasmid-containing cells is defined as follows: F =-
c; q+C;
The cell concentrations of the plasmid-bearing and plasmid-free cells, C,+and C;. are calculated from the differential equations describing the time-related changes in the concentrations of all relevant components within the balance space, i.e. the chemostat. These differential equations are constructed for the system under investigation, assuming the following conditions are fulfilled: the process is isothermal, taking place at 6 = 29 "C;the reaction space is ideally mixed; the medium fed to the chemostat is free of cells; the plasmid pBB210 is randomly partitioned at cell division and no plasmid transfer occurs (ColEl plasmids are not autotransferable [12]); the antibiotics do not cause cell lysis; the consumption of glucose is growth-associated and maintenance metabolism is neglected; the dilution rate, D. the concentrations of the incoming medium flow, the working volume of the reactor and all kinetic parameters are independent of time.
In these equations, Ci and C,, mark the concentrations of component i (X = cells, S = glucose, A = ampicillin-Na, I = sulbactam-Na) in the chemostat or its inlet. Yx I denotes the yield coefficient, p the plasmid loss probability, a the specific cell surface and PAthe permeability coefficient of the outer membrane for ampicillin.
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Equations 7 and 8 have to be constructed to calculate c A ( f ) and CI(f), which are required for the calculation of p- (compare Equation 1) and of plactamase inhibition (see below). The diffusion term PA* a - C; (C,- C&) in Equation 7 describes the ampicillin flow into the periplasm of the plasmid-bearing cells. Here, ampicillin is hydrolyzed by the plasmid-encoded plactamase to ampicilloic acid, which has no antibacterial effect. To solve Equation 7, it is necessary to construct an equation describing the ampicillin concentration in the periplasm of the plasmid-beaxing cells, Cip: -= dc;; dt
-vm.
c;.x+ -
c;,
C , + KA+ K A / K ,- C ,
+ x+
f
PA . a .
c;.(CA- c,)-/l+. c ,
(9)
The differential equation contains a reaction term describing ampicillin hydrolysis by plactamase; a diffusion term describing ampicillin transport into the periplasm and the term p+ . CG,which takes into consideration the influence on Cip of the increase in periplasm volume as a result of cell growth. Confirmed by investigations of pBB210-encoded plactamase, hydrolysis of ampicillin takes place according to MICHAELIS-ME” kinetics, and sulbactam acts as a competitive inhibitor. Since the differential quotient on the left-hand side and the term p+ . Cip on the right-hand side of Equation 9 are negligible in comparison with the reaction and diffusion terms, rearrangement provides an equation for the ampicillin concentration in the periplasm of the plasmid-bearing cells (C; = CI, since sulbactam is not consumed in the periplasm):
Model Parameters
The maximum specific growth rates, kX, and yield coefficients, YX/s, of both strains were examined in shake flask cultures under non-selective conditions (composition of the medium, as described in [9], free of antibiotics, 0.8 g/l glucose as the carbon source, 29 “C). The maximum specific growth rates were calculated from the photometrically measured OD-t values of the logarithmic growth phase. The yield coefficients were obtained through dry weight estimations of stationary growth phase cultures with the help of micropore filters. The MONODhalf saturation constants for glucose, K,, were estimated during the glucose-limited chemostat cultivation of plasmid-free and plasmid-bearing cells (compare [9]). Samples were taken at different dilution rates and after the adjustment of the steady state. The glucose concentrations, C,, of the heat-fixed samples were measured by the use of an enzyme electrode. The K, values were obtained by adapting the MONODmodel to the C,-D values. The kinetic parameter k, was calculated by the adaptation of the g(CJ model to the p-4, values obtained in shake flask growth experiments of E. coli TGl
L i j s ~C., ~ , RAY,P., Modelling the Stability of the pBR322 Plasmid Derivative pBB210
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(composition of the medium as described in [91, different ampicillin-Na contents, 0.8 g / l glucose, 29 “C). The specific growth rates of the batch cultures were calculated from photometrically measured OD-t values. The plasmid loss probability p is the probability of a plasmid-free cell emerging from a plasmid-bearing cell at cell division. As a ColEl plasmid derivative, the plasmid pBB210 is randomly partitioned into both daughter cells in accordance with the binomial distribution [13, 141. The plasmid loss probability is p = 2‘l-V) [13, 151, where npis the number of separately divisible segregation units. Plasmid pBB210 has a higher plasmid loss probability than calculated using this equation because of plasmid multimerization. Agarose gel electrophoresis [161 gave an average plasmid copy number of about 20 copies per cell and demonstrated the presence of plasmid multimers. In the case of multimerization, np is not identical with the plasmid copy number (number of plasmid monomers). Replication control of ColEl plasmids ensures a certain plasmid copy number before cell division [13]. Hence the formation of multimers with ColEl plasmids does not change the plasmid copy number, but it reduces the number of segregation units. This results in a higher plasmid loss probability [13, 14, 151. Therefore p was obtained by the adaptation of the F(t) course to the F-t values under non-selective conditions rather than by calculation using the above-mentioned equation. The specific cell surface a was calculated from the geometric dimensions of the cells (by using light microscopy), from cell number counts of a stationary growth phase culture (by cultivation of a diluted cell suspension on Pnar dishes), from the yield coefficient and glucose concentration of the medium used a = (main cell surface) . (number of cells per litre medium)/( Y;,s-Cso)
The maximum ampicillin hydrolysis rate, vmax,and the half saturation constant, KA, of the plactamase encoded by plasmid pBB210, in respect of ampicillin were obtained by the adaptation of the MICHAELIS-ME” model to the CA-fvalues. These were determined in ampicillin hydrolysis experiments with crude cell extracts of plasmid-bearing cells. The plactamase-mediated ampicillin degradation in reaction mixtures was measured with the iodometric method described in PERnnet al. [17]. The permeability coefficient of the cell wall, PA, and the inhibitory coefficient, K,, were estimated by fitting the model to the F(t) course obtained under selective and modified selective conditions.
Comparison of Experimental and Simulation Results and Steady State Analysis
The cultivation processes are simulated by the numerical solution of the system of differential Equations 4 to 8, using the p(Cs, C,) models and the algebraic Equations 3 and l l. For this purpose the differentials were converted into differences and the equations were transposed (dCj/dt =fi( ...) + C j ( t+ A t ) = GCt) + A t.fi( ...,t)). In Figs. 1 to 3 and 5, the experimental results from [9] are compared with the simulation results. The relatively good overall agreement of the model calculations with the experimental data confirms the model concept.
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Tab.1. Model parameters Parameter
Symbol
Maximum specific growth rue
Value 0.4733 h-'
of p l a s m i d - M n g cells Maximum specific growth rate Of PliUmid-fW cells
0.4906 h-'
Yield coefficient for glucose of plasmid-bearing cells
0.433
glg
Yield coefficient for glucose of plasmid-free cells
0.451
glg
MONODhalfsaturation constant for glucose of plasmid-bearing cells MONODhalf saturation constant for glucose Of Plasmid-fE cells
0.0025 g/l 0.0024 g/l
Parameter of the p function of plasmid-free cells
0.0015 g/l
Plasmid loss probability Specific cell surface
O.OOO4 12.5 m2/g
Permeability coefficient of the outer membrane for ampicillin
0.027
Maximum specific ampicillin hydrolysis rate of p1aCtamw
370
m/h h-'
MICHAELIS constant of plactamase for ampicillin-Na
0.059
Inhibition constant of plactamase for sulhactam-Na
O.ooOo4 gll
gll
Non-Selective Conditions
Simulation of the fraction of plasmid-bearing cells, F, under non-selective conditions produces a result which closely correlates to the experimental results (Fig. 1). The initially slow decrease of F can be explained by the small plasmid loss rate p of plasmid pBB210 in E.coZi TGl, and the slowly progressing decrease of F is caused by the small p- difference between plasmid-bearing and plasmid-free cells. An analysis of the differential Equations 4 to 6 for the case of t 3 gives the steady state value F* = 0.
-
Selective Conditions
The stability behaviour under selective conditions was experimentally investigated in the chemostat for various ampicillin and glucose concentrations in the feed medium [9].In Figs. 2 and 3 the experimental results are compared with the simulated fraction of plasmid-bearing cells, F, at various glucose and ampicillin-Na concentrations in the feed medium. The higher the ampicillin-Na concentration and the lower the glucose concentration (i.e. the lower the cell concentration in the reactor) in the feed medium, the higher the fraction of plasmid-bearing cells at steady state, F*.was.
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0.8
0.6 k
0.4
-
0.2
-
0.0 0
I
I
I
I
1
I
I
50
100
150
200
250
300
350
--1
400
450
Time [h] Fig. 1. Fraction of plasmid-bearing cells (F)in chemostat culture under non-selective conditions (C,,= 0.8 g/l, C,, = 0 gA. C,, = 0 g/l, -fitted to the experimental data, - - - - model simulation)
1.o
0.8
0.6
cr 0.4
0.2
0.0
0
50
100
150
200
250
300
350
400
450
Time [h] Fig. 2. Fraction of plasmid-hearing cells (F)in chemostat cultures under selective conditions with various glucose concentrationsin the feed (C,,= 0.02 g/l, C, = 0 g/l, -fitted to the experimental data. - - - - model simulation)
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o-sl
0.6 kl
-
-----__
0.2 O - 1
0.0
'
0
I
I
I
I
I
I
I
I
I
50
100
150
200
250
300
350
400
450
Time [h] Fig. 3. Fraction of plasmid-bearing cells (F)in chemostat cultures under selective conditions with various ampicillin-Na concentrations in the feed (C,,= 0.4 gh,C, = 0 g/l,-fitted to the experimental data. - - - - model simulation)
For a better understanding of the process of transition of F from the initial value F(t = 0) to the steady state value F*,the specific growth rates of plasmid-free and plasmid-bearing cells p- and p+as well as the ampicillin concentrations of the medium in the chemostat and in the periplasm of the plasmid-bearing cells C, and CL were simulated (see Fig. 4). Since F a t the beginning of the cultivation is high, ampicillin is intensively degraded by the plasmid-bearing cells, and the ampicillin concentration in the medium is correspondingly low. The low ampicillin concentration does not much affect p -,and therefore p - is distinctly larger than p i (because of p L > p k and K; < Kl). As a result of the growth rate advantage of the plasmid-free cells, their proportion within the population increases so that F decreases in time (see Fig. 2). The decrease in F reduces the degradation of ampicillin and increases the ampicillin concentration in the medium, and so p- decreases. The process continues until the ampicillin concentration in the medium has reached a point where the growth rate advantage of the plasmidfree cells turns into a slight growth rate disadvantage, which compensates for the conversion of plasmid-bearing cells into plasmid-free cells as a result of plasmid segregation at cell division. The system of differential equations was analyzed for dCildr = 0 in order to obtain an equation for F at steady state depending on the parameters Cso, CAoand D. After certain simplifications (only permissible if Yils = Y;ls = Yxls, KJ = Kf, p > Ci, CAo>> C;, and C i >>Cs) the following explicit equation is obtained: 1
F*=
025
'a'y X / S
'kp
*['-P;mx
/PA]
*-
D . c ~ ~ forocpc 1
cso
(1 1)
LijsER, C.,
RAY, P., Modelling the Stability of the pBR322 Plasmid Derivative pBB210
279
Time [h] Fig. 4. Model simulation of the sp5fic growth ntes of the plasrnid-free and plasmidbearing cells orand p+)and the ampicillin-Naconcentrationsin the chemostat and in the periplasm of plasrnid-bearing cells (Ciand under selective conditions (C, = 0.4 a,C,, = 0.02 g/l, C,o= 0 g/l, D = 0.4 h-', F(t = 0) = 0.976)
c,)
The results calculated by simulation and by Equation 11 correlated very well. Using the model it can be predicted that at a high glucose concentration in the feed medium (i.e. at high cell concentrations in the chemostat) despite a high antibiotic supply the steady state fraction of plasmid-bearing cells will be low, and so the rDNA product formation will be accordingly small. The behaviour of E. coli TGl(pBB210) was therefore investigated under modified selective conditions. Modified Selective Conditions
The stability behaviour under modified selective conditions was investigated in the chemostat for various sulbactam concentrations in the feed medium [9]. In Fig. 5 the time-related changes of the fraction of plasmid-bearing cells F received in the experiments are compared with simulation results. In general, there is close agreement between simulation and experimental results, except for the F(t) course at a sulbactam-Na concentration of C,,= 1 mgfl. The addition of sulbactam to the feed medium clearly increases the fraction of plasmid-bearing cells at steady state. The higher the sulbactam-Na concentration in the feed medium, the greater this effect was. This behaviour is to be explained by the inhibiting effect of sulbactam on the plactamase in the periplasm of the plasmid-bearing cells. The partial inhibition of the plactamase reduces the ampicillin degradation by plasmid-bearing cells so that a higher concentration of plasmid-bearing cells is necessary to reduce the ampicillin concentration to a value at which the plasmid-free and plasmid-bearing cells coexist in the chemostat.
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---____
v----CIO
= 0.002 gn
0.6 -
cr 0.4
-
0.2 a
0.0
0
I
I
I
I
I
I
50
100
150
200
250
300
-
-
-
CIO = 0.000 g/1 350
I
I
400
450
Time [h] Fig. 5. Fraction ofplasmid-bearing cells (F)in chemostat cultures under modified selective conditions with variouS sulhactiun-Naconcentrationsin the feed (Cso= 0.4 g/l, C,, = 0.02 g/l. -fitted to the experimental data, - - - model simulation)
-
To obtain an equation for the fraction of plasmid-bearing cells at steady state as a function of the parameters Cso,C,,, C,,and D, a steady state analysis was carried out in the same way as under selective conditions. In this case, however, CL is no longer negligible compared with C,, since the presence of sulbactam reduces the ampicillin degradation in the periplasm and thereby increases CL. After certain simplifications (only permissible if Y;ls = Yl,s= Yxls, Ki = Ki,p > Ci,C ,, >> C;), the analysis of Equations 1 to 8 for dC, /dt = 0 gives the following explicit equation:
The steady state concentrations C s and C; in Equation 12 are calculated using Equation 11 at C, = C; and C,= C,, and by setting C; = k,, . (1 - pk / p-)o.25 (obtained from Equations 1 and 2). Conclusions
This work was aimed at drawing conclusions from experimental and theoretical investigations into the plasmid stability behaviour for efficient technologies in largescale fermentation processes using recombinant microorganisms. A large productivity of cloned gene product formation requires high-density cultivation and a large fraction of plasmid-bearing cells. From the model it can be predicted that using high
LOSER,C., RAY,P., Modelling the Stability of the pBR322 Plasmid Derivative pBB210
28 1
cell concentration4 in the chemostat, despite the high antibiotic concentration in the feed, the fraction of productive plasmid-bearing cells will be low. The behaviour was therefore investigated under modified selective conditions. The experimental results showed that the additional use of the plactamase inhibitor sulbactam suppressed the plasmid-free segregants. But model calculations, on the other hand, indicated that using high cell concentrations, the fraction of plasmid-bearing cells at steady state was low even if sulbactam was present. From these results it could be concluded that large-scale fermentation processes for rDNA product formation should not be conducted in continuous but in batch culture. When batch cultivation is used under non-selective conditions, the decrease in the fraction of plasmid-bearing cells during cultivation has to be accepted. This strategy is possible because the plasmid loss rate of pBB210 in E coli TG1 is low and the growth rate disadvantage of E. coli TGI(pBB210) over E. coli TGI is small, but only if a fraction of plasmid-bearing cells near F = 1 at the beginning of batch fermentation is ensured. Symbols u
- specific cell surface [m*/g]
Ci Ci,
-concentration of component i in the cultivation medium within the chemostat [@I - concentration of component i in the feed medium of the chemostat cultull: [@I -concentration of component i in the periplasm of plasmid-bearing cells [@I - dilution rate of the chemostat [h- '1 - fraction of plasmid-bearing cells in the cell population of the chemostat culture [-I -MICHAELISconstant of /3lactamase for ampicillin-Na [@I - inhibition constant of plactamase for sulbactam-Na [gA] - MONODhalf satuntion constant for glucose [gill -parameter of the p function of plasmid-free cells [@I - number of separately divisible segregation units [-I - plasmid loss probability [-I -permeability coefficient of the outer membrane for ampicillin-Na [m/h] -cultivation time - maximum specific ampicillin hydrolysis rate of plactamase [h- '1 - ratio of the media volume to the periplasm volume of the plasmid-bearing cells [MI - yield coefficient for glucose [dg] - specific growth rate [h- '1 - maximum specific growth rate [h- '1
C& D F KA K, K, k,
np p
PA
r ,v x+
Yx,s p H,
m]
Indices i
+ *
-component (X= microorganisms, S = glucos, A = ampicillin-Na, I = sulbactam-Na) - symbolizes plasmid-free cells -symbolizes plasmid-bearing cells - symbolizes smdy-state values
Received 29 January 1996 Received in revised form 16 !September 1996 Accepted 24 September 1996
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References [l] ScHWAR?Z. L. S., JANSEN, N. B., Ho, N. W.Y.,TSAO, G. T.: Plasmid Instability Kinetics of the Yeast S288C pUCKm8 [cir+l in Non-Selective and Selective Medium. Biotechnol. Bioeng. 32 (1988). 733-740. L , Plasmid Instabilities of Single [2] MASCHKE.H.-E., KUMAR,P. K. R.. GEIGER,R., S C H ~ E RK.: and Three-Plasmid Systems in Eschenchia coli during Continuous Cultivation. J. Biotechnol 24 (1994). 235-251. [3] H s ~ .S.-B., WALIMAN,p.. W ~ ~ W I CG.Z ,S. K-: Global Analysis of a Model of PlasmidBearing, Plasmid-Free Competition in a Chemostat. J. Math. Biol, 32 (1994). 731-742. 141 PAR(IAK,P. R: A Simple Analytical Solution of a Model for Probabilistic Plasmid Loss. and its Implications in Continuous Cultures. Biotechnol. Tech. 7 (1993). 357-360. [5] PARK,S.H., RW, D. Y.. LEE.S. B.: Determination of Kinetic Parameters Related to the Plasmid Instability: For the Recomhinant Fermentation under Repressed Condition. Biotechnol. Bioeng. 37 (1991). 404414. [6] SRIENC, F., CAMPBELL,J. L., BAILEY,J. E.: Analysis of Unstable Recombinant Saccharomyces cerevisiue Population Growth in Selective Medium. Biotechnol. Bioeng. 28 (1986). 996-1006. [7] SARDONINI. C. A., BIASIO,D. D.: A Model for Growth of Succhuromyces cerevisiue Containing a Recomhinant Plasmid in Selective Medium. Biotechnol. Biwng. 29 (1987). 469-475. A.. GREENFELD, P. F.. D. A.: Data Analysis of Plasmid [8] SYMSU, K.. IMPOOLSUP, Stability in Continuous Culture of Recomhinant Succhuromyces cerevisiue. Biotechnol, Tech. 6 (1992), 393-398. C.: Stability of the pBR322 Plasmid Derivative pBB210 in Escherichiu coli TG1 under [9] USER, Non-Selective and Selective Conditions. Acta Biotechnol. 15 (1995). 375-380. [lo] OLLIS,D. F.: Competition hetween Two Specie when Only One Has Antibiotic Resistance: Chemostat Analysis. AIChE Meeting in San Francisco, 1984. [l 11 CHANG,Y. K.. LIM, H. C.: Static Characteristics of a Continuous Flow Bioreactor Containing Antibiotic-ResistantRecomhinant Cells. Biottxhnol. Biwng. 29 (1987). 950-961. J.: Characterization of the ColEl Mobilization [12] BOYD,A. C., ARCHER,J. A. K., SHERRATT, Region and its Protein Products. Mol. Gen. Genet. 217 (1989). 488498. [13] SUMMERS, D. K.. SHERRATT, D. J.: Multimerization of High Copy Number Plasmids Causes Plasmid Instability: ColEl Encodes a Determinant Essential for Plasmid Monomerimtion and Stability. Cell 36 (1984). 1097-1 103. [14] SHERRA'IT, D. J.: Novel Recombination Mechanisms in the Maintenance and Propagation of Plasmid Genes. In: Banbury Report 24 - Antihiotic Resistance Genes - Ecology, Transfer, and Expression. Cold Spring Harbor, New York Cold Spring Harhor Laboratory, 1986,263-273. [151 MA", N. H.: Plasmid Partitioning in Escherichiu coli. Microbiol. Sci. 2 (1985). 299-302. [ 161 MANIATIS,T., FRITSCH,E. F., SMROOK, J.: Molecular Cloning - A Laboratory Manual. New York Cold Spring Harbor Laboratory. 1982. [17] RRETII. S. W.,BAILEY, J. E., LEE,J. J.: Transcription from Plasmid Genes, Macromolecular Stahility, and Cell-Specific Productivity in EFcherichiu coli Carrying Copy Number Mutant Plasmids. Biotechnol. Biwng. 34 (1989). "2-908.
