Biotechnol. Prog. IWQ, 6, 7-12
7
Continuous Recombinant Bacterial Fermentations Utilizing Selective Flocculation and Recycle Kimberly L. Henry and Robert H. Davis* Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80309-0424
Austin L. Taylor Department of Microbiology and Immunology, University of Colorado Health Sciences Center, Denver, Colorado 80262
Selective recycle has successfully been used t o maintain an unstable plasmid-bearing bacterial strain as dominant in a continuous reactor, whereas the culture reverts to 100% segregant cells when selective recycle is not used. The plasmid-bearing strain is slower growing and flocculent; however, when the cells lose their plasmid, the resulting segregant cells are nonflocculent and grow a t a faster rate due t o their decreased metabolic burden. Both types of cells exit a chemostat and enter an inclined settler where the flocculent plasmid-bearing cells are separated from the nonflocculent segregant cells by differential sedimentation. The underflow from the cell separator, which is enriched with plasmid-bearing cells, is recycled back to the chemostat, while the segregant cells are withdrawn off the top of the settler and discarded. The experimental results agree well with selective recycle reactor theory. On the basis of the theory, a criterion is presented that has been shown to successfully predict whether or not a selective recycle reactor can maintain a plasmid-bearing strain.
1. Introduction Most recombinant products today are produced by batch processes, even though continuous processes are usually more economical and efficient for the production of most chemicals. A major reason for the preferred use of batch processes for recombinant DNA products is the problem of plasmid loss. Upon cell division, a daughter cell has a finite possibility of not receiving a plasmid even though its parent cell contained one or more plasmids. The resulting cell is called a segregant. Although this phenomenon only occurs about 1 out of every 100 new cells, the decreased metabolic burden of the non-plasmid-bearing cells will result in an increased growth rate.' This means that, even if a chemostat is inoculated with 100% plasmid-bearing cells, segregants can result, and after a few generations, they can take over the reactor. Another reason why continuous fermentations are not used extensively in industry is because of contamination problems. Researchers have tried to combat the problem of plasmid loss by using bacteria with high copy numbers of plasmid DNA2 or by limiting the expression of the plasmid gene, thereby decreasing the selective growth rate advantage of segregant cells (i.e., controlling foreign protein production by using an inducer that allows for protein production at one condition and not under different conditions'). Although these techniques minimize the problem of plasmid loss, they do not eliminate it. Therefore, the stability of a plasmid in host cells cannot be assured in a continuous culture. The maintenance of plasmid-bearing cells is commonly obtained in the laboratory by incorporating antibiotic-resistant genes into plasmids and then growing the cells in media that contain the antibiotic. However, for batch and continuous pro-
* To whom correspondence should be addressed. 8756-7938/90/3006-0007$02.50/0
cesses on the industrial scale, this becomes expensive due to the high cost of the antibiotics. Another selective pressure method is to construct a plasmid that produces an amino acid which is necessary for growth and grow the cells in a medium that does not contain this amino acid. However, Dibiasio and Sardonini3 found that this is a poor method since the plasmid-free cells can obtain sufficient amounts of the particular amino acid, which is being produced by and possibly excreted from the plasmid-bearing cells. Other researchers are incorporating the gene of interest into the chromosomal DNA. Current research in our laboratory overcomes the problem of plasmid loss by using selective recycle based on flocculation and sedimentation properties. Selective recycle for the maintenance of recombinant cells in a continuous reactor was first proposed by O l l i ~who , ~ developed a theory that predicted the degree of selection necessary in a recycle stream. However, he did not comment extensively on a method for achieving the selectivity. Stephanopoulos et al.5 noted that plasmid-bearing cells contain more protein and are larger than segregants and proposed that the two types of cells could be separated by differential sedimentation. Due to the small sizes and relative densities of the cells, such a separation is expected to be difficult and perhaps impractical for larger, continuous fermentations. They were, however, able to successfully maintain a yeast culture in the presence of a bacteria culture with inclined settling to achieve selective recycle: but they did not attempt to separate recombinant cells from host cells of the same species. Recently, Davis and Parnha" showed that slower growing, flocculent yeast cells in competition with faster growing, nonflocculent yeast cells can be maintained in a continuous fermentor that uses an inclined settler to selectively recycle the flocculent cells. The theory they developed will be reviewed in this paper and applied to a plasmid-containing, flocculent bacterial strain.
0 1990 American Chemical Society and American Institute of Chemical Engineers
a
Biotechnol. Prog., 1990,Vol. 6, No. 1
is given by Of
-
00
4
Figure 1. Schematic diagram of a selective recycle reactor and separator.
Bacterial flocculation has been achieved when a plasmid, pORN108, which contains the cloned pi1 operon and a regulatory mutation of that operon, is inserted into a Pil- bacterial strain.' These cells overproduce type 1pili, proteinaceous surface appendages that are assembled by the polymerization of pilin, a protein that is rich in nonpolar amino acid side chains. These cells form aggregates as large as 100 pm in size due to the hydrophobic interactions between the pili that cover the cell surface. In this work, the Pil- bacterial strain containing the plasmid pORN108 is maintained in a continuous fermentor by utilizing an inclined settler to separate and selectively recycle these plasmid-bearing cells to the reactor, while faster growing segregants are discarded. This paper reviews selective recycle reactor theory and inclined settling theory in sections 2 and 3, respectively. In section 4, the experimental materials and methods are described. The experimental results are given in section 5 and are compared with the theoretical predictions. Concluding remarks are given in section 6.
80
p = 1- (1- 7)-
The quantity y is the cell dilution factor, defined as the ratio of the cell concentration in the diluted stream exiting the inclined settler to that entering it (if the reactor is well stirred, the cell concentration entering the settler is the same as that in the reactor). The quantity Q, is the flow rate of the cell broth exiting the top of the cell separator. Equations 1 and 2 assume sterile feed, negligible cell maintenance and death terms, and negligible cell growth in the cell separator. The latter assumption is a reasonable approximation when the separator volume is small compared to the fermentor volume, which is the case for the experiments described later in this paper. It is also assumed that there are no physiological differences between the recycle cells and those in the bioreactor. Monod kinetics were assumed, with p+ and p- having the following forms: (4)
where p m is the maximum specific growth rate, K is the Monod constant, and S is the limiting substrate concentration. The final equation needed is the mass balance on the limiting substrate: p+x+ p-xdS = D ( S , - S) - -- -
(5) dt Y+ Ywhere So is the limiting substrate concentration in the feed and Y and Y - are the yield coefficients for cell growth. There exists a point of stable maintenance for the plasmid-bearing strain, which can be found from the steadystate versions of eq 1 and 2. The following result is obtained: +
P- P+ P+ 1-
--(1-p)
2. Selective Recycle Reactor Theory Selective recycle reactor theory for two competitive species, one faster growing and nonflocculent and one slower growing and flocculent, was developed by Davis and Parnham' and is summarized here. A schematic diagram of the reactor is shown in Figure l. The reactor is continuous with two product lines. One product line passes through an inclined settler (or other suitable separator), where the flocculent cells are separated from the nonflocculent cells. A concentrated stream exits the bottom of the settler and is recycled to the reactor, while a diluted stream is removed from the top of the settler and discarded. The other product line acts as a level controller and withdraws cell broth directly from the bioreactor, where the cell concentration remains unchanged. The desired plasmid-bearing strain is denoted by a superscript +, while a superscript - denotes the segregant or host strain. Unsteady-state mass balances about the entire system (reactor and cell separator) are
dX +/dt = (p+ - /3+D)X+- p+pX + (1) d X -ldt = (p- - p-D)X - - p+pX + (2) where p is the specific growth rate, D = Qf/ V is the dilution rate, Qf is the feed rate, V is the reactor volume, p is the segregation probability, and 0 is an effective cell dilution factor accounting for the direct product line and
(3)
Qf
p+
x+
p-
x-
= 1 +p---
(6)
The maintenance ratio, G = p - p + ( l - p ) / P + p - , determines whether a selective recycle reactor will fail (become 100% undesired cells) or not. For nonsegregating cultures ( p = 0), complete washout of the desired (+) strain occurs if G < 1 , whereas complete washout of the undesired (-) strain occurs if G > 1. Coexistence (metastable) is possible only if G = 1. In contrast, stable maintenance for segregating cultures ( p z 0) occurs for all G > 1. The mass ratio, X + / X -, at steady state is given as a function of G by eq 6 and increases with increasing G. For G < 1, however, complete washout of the desired strain ( X = 0) occurs for all possible values of the segregation probability, p . (Note that p is constrained within the range 0 5 p 5 1, and is typically on the order of for recombinant culture^.^) +
3. Inclined Settler Theory An inclined settler is used in this reactor scheme to selectively separate and recycle cells. This settler design, when compared to conventional settlers, enhances the sedimentation rate of particles or cells due to an increase in the available settling area. Not only can flocs of cells settle onto the bottom of a vessel, but they can also settle onto the upward facing inclined wall. These flocs then form a thin sediment layer which slides down to the bottom of the vessel due to gravity. Details of inclined set-
Blotechnol. Prog., 1990, Vol. 6, No. 1
9
h
Figure 2. Schematic diagram of an inclined settler used for selective recycle.
tier theory and enhanced sedimentation are reviewed by Davis and Acrivos." Figure 2 shows a schematic diagram of a rectangular inclined settler. The equation for the volumetric rate of production of fluid which is free from particles or flocs of cells that settle with a vertical settling velocity u is Q(u) = uw(L sin (e)
+ b cos (0))
(7)
where L is the length of the inclined wall, w is the width of the inclined wall, b is the spacing between the plates of the settler, and 0 is the angle of inclination of the settler walls from the vertical. The inclined settler can be used continuously to separate two kinds of bacteria, provided that they have different sedimentation properties. In this work, flocs settle a t an average sedimentation velocity of approximately m/h, while the smaller single cells settle at a rate of approximately lo4 m/h. I t is necessary to determine the distribution of settling velocities in order to design an inclined settler for the selective recycle reactor. Davis et al." used eq 7 along with mass balances to analyze inclined settlers operating continuously to separate faster settling particles from slower settling particles, predicting that
phenicol and kanamycin. Its isolation and characterization are described by Orndorff and Falkow.' The average plasmid copy number for the plasmid pORN108, when it is present in the strain ORN103, was experimentally determined to be 3.8 copies/cell. This was done by isolating the plasmid and chromosomal DNA from the cells, running the DNA on an agarose gel, and then scanning a photograph of the gel on a Beckman DU-50 spectrophotometer to obtain the relative amounts of chromosomal and plasmid DNA. Once these values are known and the cell mass has been determined, the average plasmid copy number can be calculated. The details of the methodology can be found in Henry.g Determination of p i . The value of p i was determined experimentally from batch shake flask experiments. Sterile M9CA medium (6 g of Na,HPO,, 3 g of KH,PO,, 0.5 g of NaC1, 1 g of NH,Cl, 2 g of casamino acids, 2 mL of 1M MgSO,, 0.1 mL of 1M CaCl,, 2 g of glucose, 4.1 mL of 1% L-leucine, 4.1 mL of 4% L-proline, and 0.166 mL of 0.1% vitamin B1, in 1L of water) was inoculated with ORN103 and placed in a water bath at 37 "C. Samples were withdrawn with a sterile pipet every 15 min, and an OD reading was taken at 600 nm on a spectrophotometer. The growth rate was determined to be 1.14 f 0.12 h-' at the 90% confidence level by plotting the logarithm of the cell mass versus time and determining the slope of the line by using linear regression techniques. The details of the statistics are given by Henry.g Determination of p i and p . To determine p: and p , MSCA medium was inoculated with plasmid-bearing cells and placed in a 37 "C water bath. Samples were taken every 15 min, a cell mass reading was taken, and the cells were diluted and plated on LB medium (10 g of tryptone, 5 g of yeast extract, 10 g of NaC1, and 15 g of agar, in 1L of water). Since pili have a ligandlike affinity for mannose, the first dilution was done in 1 M mannose to break apart the flocs. Samples that were read on the spectrophotometer were also diluted with 1 M mannose to disperse the flocs and eliminate reading errors due to the fact that flocculent cells adsorb less light than the same number of individual cells because many of the cells in a floc are in the shadow of other cells." After the colonies on the agar plates had grown, they were transferred, using cotton velvet, to an LB plate both with antibiotics to determine the number of plasmid-containing cells and without to check the efficiency of the transfer. When the colonies on these plates were grown, they were counted to determine the fraction of plasmid-bearing cells, F + = X +/(X + X -). (Note that the number fraction is assumed to be the same as the mass fraction, since plasmid-bearing and plasmid-free cells were observed to be of virtually the same size.) The values of p i and p were determined by rearranging the integrated batch fermentation equations for two competitive species in a reactor, as derived by Imanaka and Aiba.' The resulting equations are +
The quantity u, is the cutoff sedimentation velocity for flocs or particles reaching the overflow and is given by Q(u,) = 8,. All flocs with settling velocities of u 1 u, will settle and be recycled to the reactor, whereas a portion of those with u < u, will be carried out in the overflow. P(u) is the normalized probability density function representing the distribution of settling velocities of particles fed into the settler. It can be experimentally determined by using the sedimentation/li ht extinction apparatus designed by Davis and Hunt. 18
4. Materials and Methods Bacterial Strains and Plasmids. E . coli strain ORN103 (recA lacU169 derivative of P678-54) was the host strain for the plasmid used in this study. The plasmid PORN108 is a 15.6-kb (kilobase) fragment and is a regulatory mutant of the pi1 operon inserted into the vector pACYC184.13 It confers resistance to both chloram-
x + = x o+e(l-P)':t x
-(?-'it
PFi 1; - (1- P
hi
(Xo+ - X
(9) +e-':')
+X
(IO)
The variables X ; and Xi are the concentrations of plasmid-bearing and plasmid-free cells at the end of the lag phase ( t = 0). A plot of In X versus time results in a slope of (1- p ) & and a plot of X -e-&' versus (X,'X gives a slope of pp:/ ( p i - (1- p ) p i ) . These plots were analyzed to find that p i = 0.72 f 0.12 h-' and p = +
10
Table I. Model Parameters
bm7h-'
K,g/L P y, gig
+
Fraction X'
Exper~mental
__
Fraction X'
Theoretical
a - .
Y
+
/
10101 Cell MOSS T h e O r e i i C O l
02
X
z
0 0.0
U
1 5
20
0.004 0.03 f 0.02 0.45 0.45-0.7 (varied)
segregant cells (-) 1.14 f 0.12 0.004 n/a 0.48 1.0
Tala1 Cell Moss Experimenlol
n 4
plasmid-bearing cells (+) 0.72 f 0.12
30
2.5
LL
3.5
4.0
4.5
50
5.5
6.0
TIME (HR)
Figure 3. Data from a typical batch experiment used to determine w i and p . 0.03 f 0.02 at the 90% confidence level. The results for a typical experiment are shown in Figure 3. The symbols represent the experimental data points, and the theoretical curves represent a fit of the data to batch reactor theory using the best-fit values of p:, p i , andp. Details of the experiments and the statistics are given by Henrysg Continuous Fermentations. Continuous experiments were performed in a 1-L, 500 Series LH fermentor (0.6-L working volume), which has dissolved oxygen, pH, temperature, and foam controls. The temperature was kept at 37 "C and the pH at 7.0. The inclined settler was made from rectangular glass tubing with L = 51 cm, b = 0.5 cm, and w = 5.0 cm, and it was coated internally with dichlorodimethylsilane to help alleviate the problem of cell adhesion to the glass. The angle of inclination from the vertical was varied from 30" to 45'. The design of the settler was based on eq 8 using experimentally determined settling velocity distributions measured with a sedimentationllight extinction apparatus,12 with the design goal of y - close to unity (all plasmid-free cells passing through the separator without settling) and y + close to zero (all plasmid-bearing cells settling in the separator and subsequently recycled). The fermentor was inoculated with plasmid-bearingcells and run in batch mode with antibiotics to select for the plasmid, until the cells were well into the exponential growth phase. A t this time, the reactor was run continuously with or without selective recycle, depending on the experiment. Samples were taken at least four times daily from the fermentor and once a day from the overflow line exiting the settler. The cell mass and fraction of plasmid-bearing cells were determined as described in the batch experiment methodology. For the experiments with recycle, y and y - were calculated by dividing the experimentally determined values of X and X -, respectively, in the overflow from the settler by the corresponding values in the fermentor. It was found that y - = 1.0 in all the experiments, as desired, indicating that the nonflocculent cells did not settle in the inclined settler. In contrast, significant sedimentation of the flocculent cells occurred, with dilution factors observed in the range 0.45 Iy I0.7. The actual value for y measured during the reactor experiments was higher than the one predicted by the sedimentationllight experiments. This means that more flocculent cells were leav+
+
+
+
ing the top of the inclined settler than desired. This is due to the agitation in the fermentor, which breaks apart the flocs, decreasing their size. Since the flocs were smaller than predicted, less of them settled over the length of the separator than predicted, resulting in higher values of y + * Yield coefficients were calculated by determining the dry cell mass and the concentration of cells in a batch culture for a given limiting substrate concentration, once the cells had reaced the stationary phase. Y + was found to equal 0.45 g/g and Y - to equal 0.48 g/g. The Monod coefficients, K + and K -, were assumed to equal 0.004 g/L, which is a typical value for E. coli strains growing in glucose-limited medium.14 The feed flow rate, and thus the dilution rate, was varied from experiment to experiment. All of the parameter values are summarized in Table I, along with the 90% confidence intervals when known.
5. Results The first continuous fermentation was done without recycle to demonstrate that the plasmid-bearing strain is washed out of the reactor by the faster growing segregant cells. The data, depicted in Figure 4, clearly show that this is the case. The theoretical curve is also shown, and there is good agreement between theory and experiment. The dilution rate for this experiment was 0.45 h-l, and the maintenance ratio was 0.61. This value of G < 1 correctly predicts the washout of the plasmidbearing strain. The second experiment was performed with selective recycle, with nearly all of the product stream exiting through the inclined settler (98% recycle). In this case, the selective recycle maintained the plasmid-bearingstrain in the fermentor, in spite of its ability to segregate and its growth-rate disadvantage (Figure 5). The desired strain was the dominant strain in the continuous reactor until the experiment was stopped after 180 h, whereas in the first experiment without recycle, it was washed out of the reactor after about 50 h. The maintenance ratio in the second experiment was greater than unity (G = 1.33), so the observed maintenance of the desired strain was expected. Again, there is very good agreement between theory and experiment. The third experiment demonstrates the strength of the selective recycle reactor (Figure 6). The reactor was allowed to fail to the point where it contained about 20% plasmid-bearing cells and 80% segregants. A t this time ( t = 0 on the graph), the dilution rate was lowered, which caused the value of y + to decrease due to the increased hold-up time in the settler, placing the system in favorable conditions for recovery (G > 1). This shows that selective recycle can be used to recover a failing reactor that would otherwise have to be shut down. There are seven theoretical curves shown in this figure. These curves use the experimentally determined values of p , p i : and y and the plus and minus 90% confidence limits of each. This graph shows that segregation (the value of p ) has less effect on the overall dynamics of the system than +
Biotechnol. Pmg., 1990,Vol. 6, No. 1
-t
11 10
Change in Angle of Inclination
v
9 =
D
0.45 hr-'
G = 0.61
30
m
G = 0.87
e
..4 -
___ "-0.t
y* = 0 7 y- = 1 0
0
04
I
0
Experimental Data T h e a r e k a l Curve ( G = l 0 ) . . . TieoretNcal C u r v e ( G = O 87) 0
- _
Theoretical Curve Experimental Dolo
a LL
P
00 0
30
20
10
50
40
70
60
80
Figure 4. Washout of the plasmid-bearingbacterial strain when recycle was not used. 1
O~_.I?..-.--%..--
* - I -.c=
L v
D = 0.16 G+ = 1.33
- 0-
-
,-*.-=-,a.
.L
-
hr-'
y = 0.45 7 - = 1.0
0
y
0 O 46 I
0
__
U
E
00 2
L
,
I
20
40
I
I
60
BO
,
I
100
120
Experiment01 Data Thearelicol Curve
,
,
160
140
180
TIME (HR)
Figure 5. Maintenance of the plasmid-bearingstrain when selec-
tive recycle was used.
-
1.0-
L
D
=
5
0.1 hr-'
3
-
(L
5
06-
m I
0 02j/&-'
4
c2 L
t
oo!
0
I
,
20
40
I
, 80
60
100
120
TIME (HR)
Figure 6. Recovery of the plasmid-bearing strain by selective recycle. The parameters for curve 1are the experimentallymeasured values: p = 0.03, w: = 0.72 h-', and y = 0.45 (G = 1.3). The remaining theoretical curves use the same parameter values except for the following changes: p = 0.05 (curve 2), p = 0.01 (curve 3,fi: = 0.84 h-' (curve 4), p: = 0.60 h-' (curve 5), y = 0.5 (curve 6), and y = 0.4 (curve 7). +
+
o o
10
/ 20
A 30
40
50
60
70
sa
90
100
iio
TIME (HR)
TIME (HR)
7
o
+
do selective recycle (the value of y relative to y -) and the growth-rate differential (the value of p+ relative to +
P-).
The final experiment is depicted in Figure 7. It demonstrates the utility of the maintenance ratio, G, for predicting the fermentor performance. In the first part of the experiment ( t < 28 h), the reactor was run at a dilution rate of 0.63 h-l, and the angle of inclination from the vertical, 8, was set at 45O. The value of G was calcu-
Figure 7. Continuous fermentation experiment ( D = 0.6 h-') with recycle, which demonstrates the utility of the maintenance ratio, G. lated to be 1.0, which predicts a slow recovery of the plasmid-bearing cells toward a stable coexistence with F + = 0.87. At t = 28 h, the angle of inclination was decreased to 30'. This was done because there was a large amount of adhesion of the flocculent, plasmid-bearing cells to the glass walls of the settler. However, this placed the reactor in an unfavorable state, G = 0.87, and washout of the desired cells ensued. This experiment demonstrates the large sensitivity of the reactor performance to values of the maintenance ratio near unity. Another important advantage of recycle is an increase in cell density in the fermentation vessel. In the third experiment, for example, there was about a 40% increase in cell density before the reactor run was terminated, which agrees with the theoretical prediction. This demonstrates that not only can selective recycle be used to maintain plasmid-bearing cells in continuous fermentations but it can also increase cell density, leading to higher production of speciality recombinant DNA products. 6. Conclusions The theory and experiments described in this paper demonstrate that selective recycle utilizing inclined settling may be used to maintain a plasmid-bearing bacterial strain in a continuous fermentor, when it would otherwise be washed out by faster growing, segregant cells. The plasmid-bearing cells are maintained by using the plasmid pORN108, which encodes for the hyperpiliation of a cell and thus flocculation. When the cells lose their plasmids, they no longer form flocs, and they are separated by differential sedimentation from the plasmidbearing cells. In this way, only the desired plasmid-containing cells are recycled to the fermentation vessel. The recovery of the slower growing desired strain, after a significant takeover by the faster growing segregant strain, was also demonstrated. The selective recycle reactor theory developed by Davis and Parnham' is shown to agree well with the experimental data for all experiments, and the utility of the maintenance ratio, G, is also shown. This ratio provides a simple criterion for predicting whether a selective recycle reactor will recover or fail. In particular, washout of the desired strain occurs for G < 1, whereas partial or complete maintenance of the desired strain occurs for G > 1. The main utility of this is that, knowing only the specific growth rates and the segregation probability constant, selective recycle reactor theory can correctly identify the amount of enrichment needed to maintain a plasmid-bearing strain in a continuous reactor. Inclined set-
Biotechnol. Prog., 1990,Vol. 6, No. 1
12
tling was used in these experiments, but other methods of selectively recycling cells can also be used. Further work in this area includes constructing a plasmid that will allow for the artificial control of a gene that causes flocculation (pil operon). This will allow for the production of a speciality product of interest under one condition and subsequent flocculation and selectivity under different conditions.
Acknowledgment This work was supported by the Biotechnology Program of the National Science Foundation under grant EET-8611305, and by a graduate student fellowship to K. L. Henry by the Colorado Institute for Research in Biotechnology. We would also like to thank Dr. Paul Orndorff for the bacterial strains that he provided, and both Laura McBurney and Tina Ellis for their assistance with carrying out the experiments, while supported by the Research Experiences for Undergraduates grant EET-8842370 from the National Science Foundation.
Notation b
D F+ G K
L P P(V) Q(V) Qt Qo
S S O
t v V W
spacing between plates in the inclined settler, cm dilution rate, Qr/V, h-' fraction of desired cells, X +/(X+ + X -) stable coexistence ratio, (Fp+/fl+/.l-)(lp) Monod constant, g/L length of inclined settler, cm segregation probability normalized probability density function representing the distribution of settling velocities, (cm1hI-l inclined settling clarification rate given by eq 8, L/h volumetric feed rate to fermentor, L/h volumetric overflow rate through separator, L/h substrate concentration in the fermentor, g/L substrate concentration in the feed, g/L time, h settling velocity, cm/h fermentor volume, L width of inclined walls of settler, cm
X Y
cell concentration in fermentor, g/L yield coefficient, g of cells/g of substrate effective cell dilution factor given by eq 3 P cell dilution factor equal to ratio of cell concenY tration in diluted stream exiting cell separator to that in the fermentor /.l specific growth rate, h-' maximum specific growth rate, h-l /.lm e angle of inclination of settler walls from the vertical Superscripts + desired or plasmid-bearing strain undesired or segregant strain
Literature Cited (1)Imanaka, T.; Aiba, S. Ann. N . Y.Acad. Sci. 1981,369,114. (2)Uhlin, B. E.; Molin, S.; Gustafsson, P.; Nordotrom, K.Gene 1979,6,91-106. (3)Dibiasio, D.; Sardonini,C. Ann. N . Y. Acad. Sci. 1986,469, 111-117. (4)Ollis, D. F. Phil. Trans. R. SOC.London 1982,B297, 617629. (5)Stephanopoulos, G.; San, K. Y.; Davison, B. H. Biotechnol. Prog. 1985,I , 250-259. (6)Davison, B.H.; San, K. Y.; Stephanopoulos, G. Biotechnol. Prog. 1985,1, 260-269. (7)Davis, R. H.; Parnham, C. S. BiotechnoL Bioeng. 1989,33, 767-776. (8)Orndorff,P. E.; Falkow, S. J . Bacteriol. 1984,160,61-66. (9)Henry, K.L.Selective Recycle of Flocculent Bacteria Using Continuous Bioreactors. M.S. Thesis, University of Colorado, Boulder, 1988. (10)Davis, R. H.; Acrivos, A. Ann. Rev. Fluid Mech. 1985,17, 91-118. (11)Davis, R. H.; Zhang, X.; Agarwala, J. P. Ind. Eng. Chem. Res. 1989,28,785-793. (12)Davis, R.H.;Hunt, T. P. Biotechnol. Prog. 1986,2,91-97. (13)Chang, A. C. Y.; Cohen, S. N. J . Bacteriol. 1978,134,11411158. (14)Shinier, R.Y.;Doudoroff, M.; Adelberg, E. A. The Microbial World, 3rd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1970; p 317.
Accepted September 20,1989
