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A pseudo-exponential feeding method for control of specific growth rate in fed-batch cultures
Biochemical Engineering Journal 10 (2002) 227–232
A pseudo-exponential feeding method for control of specific growth rate in fed-batch cultures Li-Chun Cheng a , Jau-Yann Wu b , Teh-Liang Chen a,∗ b
a Department of Chemical Engineering, National Cheng Kung University, Tainan 701, Taiwan Department of Chemical Engineering, I-Shou University, Ta-Hsu Hsiang, Kaohsiung County 840, Taiwan
Received 21 October 2001; accepted after revision 27 December 2001
Abstract A simple feeding method for controlling specific growth rate in fed-batch culture was developed. This method applies a constant feed rate using a concentrate reservoir and two mixing chambers in series to simulate the exponential feeding. Fed-batch cultures with Escherichia coli showed that the present feeding method could sustain the cells growing at predetermined specific growth rates, where the time length for exponential growth was dependent on the magnitude of the growth rate. The present feeding method is convenient to operate, requires no computerized control equipments, and thus could expect an extensive application in fed-batch culture. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Fed-batch culture; Feeding method; Escherichia coli
1. Introduction The use of genetically engineered microorganisms for producing recombinant proteins is an important practice in the biotechnology industry. To enhance the volumetric productivity, high cell concentration and high cell productivity are required, where the former is usually achieved through fed-batch cultivation. In the operation of a fed-batch culture, the control of specific growth rate has been critical because formation of inhibitory byproducts (e.g., acetic acid), cell productivity, and plasmid stability are related to it [1–3]. Owing to the inherent feature of cell growth, exponential feeding is required to sustain a constant specific growth rate. However, exponential feeding needs sophisticated control techniques, and many laboratory works used step changes in the feed rate to simulate the desired exponential profile [4–6]. A drawback of the step changed feeding is that, the cells might experience repeated cycles of large-extent excessive-to-insufficient nutritive environments. As a result, inhibitory effects, such as formation of acetic acid in cultures of Escherichia coli, might be induced during the over-dosed period, and cell concentration as well as cell
productivity would accelerate to fall behind the expected profiles as the fermentation proceeds. In the present work, we propose a simple increased feeding method, which needs no computerized control equipments and can closely simulate exponential feeding. The validity of the method in controlling specific growth rate is examined with E. coli.
2. Development of the feeding method The mass balance for cells in fed-batch cultivation can be expressed as: d(XV) = µXV dt
where X is the cell concentration, V the culture volume, t the time, and µ the specific growth rate. If the fed-batch culture is operated under a condition that the substrate feed rate is equal to its consumption rate, then the mass balance for limiting substrate is described by [3,6,7]: FS0 −
∗ Corresponding author. Tel.: +886-6275-7575x62660; fax: +886-6234-4496. E-mail address: [email protected] (T.-L. Chen).
(1)
µXV =0 YX/S
(2)
where F is the volumetric feed rate, S0 the feeding concentration of the limiting substrate, and YX/S the yield coefficient
1369-703X/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 6 9 - 7 0 3 X ( 0 2 ) 0 0 0 0 2 - 5
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L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
(assumed constant). In addition, the rate of increase in culture volume is dV =F (3) dt From Eqs. (1) and (2) with µ = constant, we have FS0 =
µX0 V0 eµt YX/S
(4)
where X0 and V0 are the cell concentration and the culture volume at the beginning of the fed-batch operation, respectively. It should be noted that for the cells to grow at a predetermined µ, the substrate concentration S in the fermentor must be zero at the fed-batch phase. Eq. (4) indicates that the mass feed rate of the limiting substrate, FS0 , needs to increase exponentially with time if a constant µ is to be sustained. Exponential feeding can be achieved by changing F exponentially while keeping S0 constant, or vice versa. At present, only the former is feasible; nevertheless, we still can increase S0 with time, keep F constant, and make the feeding coincide with an exponential function to a certain extent.
The feed concentration S0 can be increased linearly with a gradient maker usually used in gradient elution of chromatography [8], as shown in Fig. 1a. The gradient maker consists of a concentrate reservoir and a mixing chamber. These two vessels are connected by means of tubing at their bases. The feed concentration has been shown to be [9]: F S0 = SB = SB0 + (SA − SB0 )t (5) 2VB0 where the subscripts A and B denote the reservoir and the mixing chamber, respectively; SB0 and VB0 are the initial substrate concentration and the initial volume of the mixing chamber, respectively. As one expects, the linear-gradient feeding coincides with the exponential feeding only for a short time length, and the duration of coincidence decreases sharply with increasing µ. In contrast to Fig. 1a, if the concentrated medium is pumped from the reservoir A to the mixing chamber B, and the volume of the mixing chamber VB is maintained constant (see Fig. 1b), then the feed concentration S0 can be derived as: S0 = SB = SA − (SA − SB0 ) e−Ft/VB
(6)
Fig. 1. Schematic representations of three increased feeding methods: (a) linear-gradient feeding; (b) asymptotic feeding; (c) pseudo-exponential feeding. A: the concentrate reservoir, B and C: the mixing chamber.
L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
229
Fig. 2. Comparison of substrate feed rates for various feeding methods.
According to Eq. (6), the time profile of S0 is an asymptote, which approaches SA rapidly. It is interesting to note that the linear-gradient feeding results in a negative deviation from the exponential feeding, while the asymptotic feeding results in a positive deviation initially (see Fig. 2). Therefore, if we slow down the rate of increase of SB , we can generate a feeding profile that has better coincidence with the exponential feeding. Fig. 1c shows the increased feeding method using two mixing chambers in series; nutrient is pumped from the reservoir A to the mixing chamber B and then to the mixing chamber C. For simplicity, all of the volumetric flow rates between vessels are set equal, and the volumes of the two mixing chambers are also equal (V B = V C ). The mass balances for the limiting substrate in the mixing chambers give: d(SB VB ) = FSA − FSB dt
(7)
and d(SC VC ) = FSB − FSC dt
(8)
From Eqs. (7) and (8), the feed concentration S0 can be obtained as: Ft −Ft/VC S0 = SC = SA − e SA + (SA − SB0 ) − SC0 VC (9) Eq. (9) provides the theoretical basis for the search for appropriate operating conditions, so that FS0 can match the desired exponential profile, Eq. (4), as good as possible. Fig. 2 shows that the proposed feeding method (referred as the pseudo-exponential feeding) can have a much better fit to the exponential profile than both the linear-gradient and the asymptotic feedings within a certain time length. It should
Fig. 3. Designation of SB0 in the pseudo-exponential feeding method to fit the exponential feed profile.
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L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
be emphasized that in reality, a genuine exponential feeding can only be operated for a limited time length, and we are developing a feeding method that could simulate exponential feeding also for a limited time length. The designation of the operating conditions (SA , F, SB0 , SC0 and VC ) for the pseudo-exponential feeding is described as follows. The time profile of the desired exponential feeding requires data of X0 , V0 , and YX/S , which is obtained from an average of corresponding batch cultures. SA is set at its upper limit, so that maximal duration of coincidence with the exponential profile can be obtained. F is selected for convenience of operation. The initial feed concentration SC0 is calculated from Eq. (4) with t = 0, i.e. SC0 =
µX0 V0 FYX/S
(10)
The most suitable value of SB0 is SB0 = SC0 . If SB0 < SC0 , the feeding profile will lie below that of exponential feeding, and in contrast, if SB0 > SC0 , the feeding profile will have a positive deviation from the exponential feeding (see Fig. 3). The last parameter, VC , is designed by comparing the resulted feeding profile with the desired exponential curve; the value of VC determines how long the feeding can be regarded as being exponential.
3. Materials and methods E. coli DH5␣ was employed in this study to examine the feasibility of the pseudo-exponential feeding method. Fermentations were carried out in a 2.5 l laboratory tank fermentor (Model M-100, Tokyo Rikakikai, Japan) with a starting volume of 1 l. The fermentation medium used was described in Table 1, which was according to Riesenberg et al. [10]. The inoculum size was 100 ml; the inoculum was prepared by growing the cells in LB (Luria–Bertani) medium overnight at 37 ◦ C in a shaker. The culture temperature was maintained at 37 ◦ C, and pH was controlled at 7.0 with 6 N H2 SO4 and 28% ammonium hydroxide. To ensure a sufficient capability of oxygen transfer, the agitator
Table 1 Medium composition Component
Concentration
Glucose KH2 PO4 (NH4 )2 HPO4 Citric acid MgSO4 ·7H2 O Thiamin HCl Trace metal solutiona
27.5 g/l 13.3 g/l 4.0 g/l 1.7 g/l 1.2 g/l 4.5 mg/l 10 ml/l
a
The trace metal solution contained (per liter) 6 g of Fe(III) citrate, 1.5 g of MnCl2 ·4H2 O, 0.8 g of Zn(CH3 COO)2 ·2H2 O, 0.3 g of H3 BO3 , 0.25 g of Na2 MoO4 ·2H2 O, 0.25 g of CoCl2 ·6H2 O, 0.15 g of CuCl2 ·2H2 O, and 0.84 g of (ethylenedinitrilo)tetraacetic acid disodium salt·2H2 O.
was equipped with two six-blade flat blade turbines, with a diameter of 6.8 cm and a spacing of 3.7 cm. The agitation speed was 400 rpm and air was sparged into the fermentor at a rate of 1 l/min. The dissolved oxygen concentration was maintained above 10% of air saturation by automatic supplementation of pure oxygen to the aeration stream. Silicone antifoam agent KM-72 (Shin-Etsu, Japan) was used for foam control if necessary. The fed-batch phase was started when glucose in the fermentor was depleted, which was indicated by a rapid increase of the dissolved oxygen concentration (to over 80% of air saturation in 10 min). The glucose concentration in the reservoir SA was 700 g/l. The volumetric feed rate, F, and the initial glucose concentration and the volume of mixing chamber C, SC0 and VC , were designed in accordance with the desired specific growth rate. Other nutrients than glucose (referred as the supplemental nutrients) were added to the fermentor in proportion to the total amount of glucose to be fed, which was calculated through integration of Eq. (9). The proportionality of each component to glucose was based on the medium composition given in Table 1. Cell concentration was measured by turbidimetry (600 nm) and correlated with dry cell weight. Glucose was assayed as reducing sugar by the DNS method [11]. Acetate was analyzed by a gas chromatograph (Shimadzu, GC-14A) equipped with a Porapak Q column. The injector and column temperatures were 150 and 180 ◦ C, respectively. Nitrogen was used as the carrier gas at a flow rate of 30 ml/min. A flame ionization detector was used at 180 ◦ C. Acetate peak appeared 5.3 min after sample injection. A calibration curve constructed from acetic acid standards was used to obtain the acetate concentration.
4. Results and discussion From preliminary experiments, it was found that the batch cultivation proceeded for 12.5 h with X0 = 13.0 g/l, V0 = 1 l, and YX/S = 0.55 g cell/g glucose, where YX/S was calculated from the data of the exponential growth phase (6–12 h). The exponential growth phase had a specific growth rate of 0.34 h−1 . We also found that the agitator was shut down when the culture approached a volume of 1.6 l and a cell concentration of 25 g/l; therefore, the limitation of the agitation capability of the fermentor was considered in the assessment of the fed-batch operation. For a specific growth rate of 0.15 h−1 , a value that has been considered popular [3], the pseudo-exponential feeding method with F = 60 ml/h, SC0 = 59.1 g glucose/l, and V C = 525 ml could have a 10 h coincidence with the exponential feeding. By coincidence with the exponential feeding, we meant a ±10% error in FS0 . The purpose of the experiment was to examine the effect of the error in the substrate feed rate on the control of cell growth. The total amount of glucose fed to the fermentor was calculated to
L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
231
Fig. 4. Fed-batch culture performed with an expected specific growth rate of 0.15 h−1 . Upper panel: (䊉) cell concentration; (䊊) glucose concentration; () volume of NH4 OH added; (䊏) concentration of acetic acid. Lower panel: (—) expected; (䊉) experimental.
be 84.4 g. The required supplemental nutrient was divided into two equal parts (each had a volume of 30 ml), which were added separately to the fermentor at 0 and 5 h of the fed-batch phase. The fermentation profiles are shown in the upper panel of Fig. 4. The fed-batch phase started at 12.5 h, glucose concentration remained undetectable throughout this phase, suggesting that the assumption of Eq. (2), i.e., equivalent rates for substrate addition and consumption, was valid. When the supplemental nutrients were added to the fermentor, the pH decreased, and 25 ml of ammonium hydroxide was fed, through the pH control loop, to the fermentor for neutralization. Cell concentration increased from 13.0 to 20.0 g/l in 6 h and thereafter, cell growth rate declined rapidly while formation of acetic acid increased markedly. In the lower panel of Fig. 4, the present feeding method is shown to assure the desired specific growth rate (0.15 h−1 ) for 6 h. In the calculation of cell mass (XV),
the additional volumes of ammonium hydroxide (for pH control) and the supplemental nutrients were taken into account. The negative deviation of the cell mass profile from the expected one was attributed to ineffectiveness of agitation. At 6 h of the fed-batch phase, the culture volume reached around 1.5 l (initially 1 l, feeding 360 ml, supplemental nutrients 60 ml, ammonium hydroxide 60 ml) and the cell concentration was 20 g/l, and a significant reduction in turbulence at the liquid surface was observed. The deviation was not likely due to the feeding method itself because at that time the glucose feed rate was quite agreeable with the exponential one. Table 2 demonstrates some results of fed-batch cultures with the pseudo-exponential feeding method; the fermentation profiles were similar to that of Fig. 4 and thus are omitted. It should be noted that the designation of the operating conditions could be done at the convenience of the
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L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
Table 2 Fed-batch cultures with the pseudo-exponential feeding methoda µdesired (h−1 )
0.05 0.1 0.15 0.2 0.25 a
X0 (g/l)
13.0 13.0 13.0 13.0 13.0
V0 (l)
1 1 1 1 1
YX /S
0.55 0.55 0.55 0.55 0.55
F (ml/h)
20 40 60 80 100
SC0 (g/l)
59.1 59.1 59.1 59.1 59.1
VC (ml)
525 525 525 525 525
Time length of coincidence with exponential growth (h) Expected
Experimental
30 15 10 7.5 6
18 9 6 4 3
S A = 700 g/l, SB0 = SC0 .
experimenter. It can be seen that the higher the specific growth rate, the shorter the time length that the present feeding method could assure the exponential growth. As mentioned above, the shortage in the expected time length for the cells to grow exponentially was due to ineffective agitation of the fermentor; in all cases, the deviation occurred when the culture volume was around 1.5 l and cell density around 20 g/l. In addition, it was found that acetic acid was not formed when the cells grew exponentially, while acetic acid accumulated to over 5 g/l when cell growth deviated significantly from the exponential profile. In summary, the proposed pseudo-exponential feeding method is capable of controlling cell growth at predetermined specific growth rates for various time durations depending on the magnitude of the rate. Owing to the use of constant-rate feeding, the feeding method is convenient, reliable, and not requiring computerized control equipments. This method, therefore, could have extensive applications at least in laboratory fed-batch culture, where the effect of specific growth rate on the culture performance is to be assessed. Acknowledgements This study was supported by Research Grant NSC902214-E-006-002, National Science Council of Taiwan.
References [1] S.Y. Lee, High cell-density culture of Escherichia coli, Trends Biotechnol. 14 (1996) 98–105. [2] D. Riesenberg, R. Guthke, High-cell-density cultivation of microorganisms, Appl. Microbiol. Biotechnol. 51 (1999) 422–430. [3] L. Yee, H.W. Blanch, Recombinant protein expression in high cell density fed-batch cultures of Escherichia coli, Biotechnology 10 (1992) 1550–1556. [4] J. Lee, S.T. Lee, S. Park, Fed-batch culture of Escherichia coli W by exponential feeding of sucrose as a carbon source, Biotechnol. Tech. 11 (1997) 59–62. [5] Y. Li, J. Chen, Y.Y. Mao, S.Y. Lun, Y.M. Koo, Effect of additives and fed-batch culture strategies on the production of glutathione by recombinant Escherichia coli, Process Biochem. 33 (1998) 709–714. [6] L. Yee, H.W. Blanch, Recombinant trypsin production in high cell density fed-batch cultures in Escherichia coli, Biotechnol. Bioeng. 41 (1993) 781–790. [7] T. Paalme, K. Tiisma, A. Kahru, K. Vanatalu, R. Vilu, Glucose-limited fed-batch cultivation of Escherichia coli with computer-controlled fixed growth rate, Biotechnol. Bioeng. 35 (1990) 312–319. [8] V.R. Srinivasan, M.B. Fleenor, R.J. Summers, Gradient-feed method of growing high cell density cultures of Cellulomonas in a bench-scale fermentor, Biotechnol. Bioeng. 19 (1997) 153–155. [9] C.F. Mignone, C.A. Rossa, Simple method for designing fed-batch cultures with linear gradient feed of nutrient, Process Biochem. 28 (1993) 405–410. [10] D. Riesenberg, V. Schulz, W.A. Knorre, H.D. Pohl, D. Korz, E.A. Sanders, A. Roß, W.D. Deckwer, High cell density cultivation of Escherichia coli at controlled specific growth rate, J. Biotechnol. 20 (1991) 17–28. [11] G.L. Miller, Use of dinitrosalicylic acid reagent for determination of reducing sugar, Anal. Chem. 31 (1959) 426–428.
A pseudo-exponential feeding method for control of specific growth rate in fed-batch cultures Li-Chun Cheng a , Jau-Yann Wu b , Teh-Liang Chen a,∗ b
a Department of Chemical Engineering, National Cheng Kung University, Tainan 701, Taiwan Department of Chemical Engineering, I-Shou University, Ta-Hsu Hsiang, Kaohsiung County 840, Taiwan
Received 21 October 2001; accepted after revision 27 December 2001
Abstract A simple feeding method for controlling specific growth rate in fed-batch culture was developed. This method applies a constant feed rate using a concentrate reservoir and two mixing chambers in series to simulate the exponential feeding. Fed-batch cultures with Escherichia coli showed that the present feeding method could sustain the cells growing at predetermined specific growth rates, where the time length for exponential growth was dependent on the magnitude of the growth rate. The present feeding method is convenient to operate, requires no computerized control equipments, and thus could expect an extensive application in fed-batch culture. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Fed-batch culture; Feeding method; Escherichia coli
1. Introduction The use of genetically engineered microorganisms for producing recombinant proteins is an important practice in the biotechnology industry. To enhance the volumetric productivity, high cell concentration and high cell productivity are required, where the former is usually achieved through fed-batch cultivation. In the operation of a fed-batch culture, the control of specific growth rate has been critical because formation of inhibitory byproducts (e.g., acetic acid), cell productivity, and plasmid stability are related to it [1–3]. Owing to the inherent feature of cell growth, exponential feeding is required to sustain a constant specific growth rate. However, exponential feeding needs sophisticated control techniques, and many laboratory works used step changes in the feed rate to simulate the desired exponential profile [4–6]. A drawback of the step changed feeding is that, the cells might experience repeated cycles of large-extent excessive-to-insufficient nutritive environments. As a result, inhibitory effects, such as formation of acetic acid in cultures of Escherichia coli, might be induced during the over-dosed period, and cell concentration as well as cell
productivity would accelerate to fall behind the expected profiles as the fermentation proceeds. In the present work, we propose a simple increased feeding method, which needs no computerized control equipments and can closely simulate exponential feeding. The validity of the method in controlling specific growth rate is examined with E. coli.
2. Development of the feeding method The mass balance for cells in fed-batch cultivation can be expressed as: d(XV) = µXV dt
where X is the cell concentration, V the culture volume, t the time, and µ the specific growth rate. If the fed-batch culture is operated under a condition that the substrate feed rate is equal to its consumption rate, then the mass balance for limiting substrate is described by [3,6,7]: FS0 −
∗ Corresponding author. Tel.: +886-6275-7575x62660; fax: +886-6234-4496. E-mail address: [email protected] (T.-L. Chen).
(1)
µXV =0 YX/S
(2)
where F is the volumetric feed rate, S0 the feeding concentration of the limiting substrate, and YX/S the yield coefficient
1369-703X/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 6 9 - 7 0 3 X ( 0 2 ) 0 0 0 0 2 - 5
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L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
(assumed constant). In addition, the rate of increase in culture volume is dV =F (3) dt From Eqs. (1) and (2) with µ = constant, we have FS0 =
µX0 V0 eµt YX/S
(4)
where X0 and V0 are the cell concentration and the culture volume at the beginning of the fed-batch operation, respectively. It should be noted that for the cells to grow at a predetermined µ, the substrate concentration S in the fermentor must be zero at the fed-batch phase. Eq. (4) indicates that the mass feed rate of the limiting substrate, FS0 , needs to increase exponentially with time if a constant µ is to be sustained. Exponential feeding can be achieved by changing F exponentially while keeping S0 constant, or vice versa. At present, only the former is feasible; nevertheless, we still can increase S0 with time, keep F constant, and make the feeding coincide with an exponential function to a certain extent.
The feed concentration S0 can be increased linearly with a gradient maker usually used in gradient elution of chromatography [8], as shown in Fig. 1a. The gradient maker consists of a concentrate reservoir and a mixing chamber. These two vessels are connected by means of tubing at their bases. The feed concentration has been shown to be [9]: F S0 = SB = SB0 + (SA − SB0 )t (5) 2VB0 where the subscripts A and B denote the reservoir and the mixing chamber, respectively; SB0 and VB0 are the initial substrate concentration and the initial volume of the mixing chamber, respectively. As one expects, the linear-gradient feeding coincides with the exponential feeding only for a short time length, and the duration of coincidence decreases sharply with increasing µ. In contrast to Fig. 1a, if the concentrated medium is pumped from the reservoir A to the mixing chamber B, and the volume of the mixing chamber VB is maintained constant (see Fig. 1b), then the feed concentration S0 can be derived as: S0 = SB = SA − (SA − SB0 ) e−Ft/VB
(6)
Fig. 1. Schematic representations of three increased feeding methods: (a) linear-gradient feeding; (b) asymptotic feeding; (c) pseudo-exponential feeding. A: the concentrate reservoir, B and C: the mixing chamber.
L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
229
Fig. 2. Comparison of substrate feed rates for various feeding methods.
According to Eq. (6), the time profile of S0 is an asymptote, which approaches SA rapidly. It is interesting to note that the linear-gradient feeding results in a negative deviation from the exponential feeding, while the asymptotic feeding results in a positive deviation initially (see Fig. 2). Therefore, if we slow down the rate of increase of SB , we can generate a feeding profile that has better coincidence with the exponential feeding. Fig. 1c shows the increased feeding method using two mixing chambers in series; nutrient is pumped from the reservoir A to the mixing chamber B and then to the mixing chamber C. For simplicity, all of the volumetric flow rates between vessels are set equal, and the volumes of the two mixing chambers are also equal (V B = V C ). The mass balances for the limiting substrate in the mixing chambers give: d(SB VB ) = FSA − FSB dt
(7)
and d(SC VC ) = FSB − FSC dt
(8)
From Eqs. (7) and (8), the feed concentration S0 can be obtained as: Ft −Ft/VC S0 = SC = SA − e SA + (SA − SB0 ) − SC0 VC (9) Eq. (9) provides the theoretical basis for the search for appropriate operating conditions, so that FS0 can match the desired exponential profile, Eq. (4), as good as possible. Fig. 2 shows that the proposed feeding method (referred as the pseudo-exponential feeding) can have a much better fit to the exponential profile than both the linear-gradient and the asymptotic feedings within a certain time length. It should
Fig. 3. Designation of SB0 in the pseudo-exponential feeding method to fit the exponential feed profile.
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L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
be emphasized that in reality, a genuine exponential feeding can only be operated for a limited time length, and we are developing a feeding method that could simulate exponential feeding also for a limited time length. The designation of the operating conditions (SA , F, SB0 , SC0 and VC ) for the pseudo-exponential feeding is described as follows. The time profile of the desired exponential feeding requires data of X0 , V0 , and YX/S , which is obtained from an average of corresponding batch cultures. SA is set at its upper limit, so that maximal duration of coincidence with the exponential profile can be obtained. F is selected for convenience of operation. The initial feed concentration SC0 is calculated from Eq. (4) with t = 0, i.e. SC0 =
µX0 V0 FYX/S
(10)
The most suitable value of SB0 is SB0 = SC0 . If SB0 < SC0 , the feeding profile will lie below that of exponential feeding, and in contrast, if SB0 > SC0 , the feeding profile will have a positive deviation from the exponential feeding (see Fig. 3). The last parameter, VC , is designed by comparing the resulted feeding profile with the desired exponential curve; the value of VC determines how long the feeding can be regarded as being exponential.
3. Materials and methods E. coli DH5␣ was employed in this study to examine the feasibility of the pseudo-exponential feeding method. Fermentations were carried out in a 2.5 l laboratory tank fermentor (Model M-100, Tokyo Rikakikai, Japan) with a starting volume of 1 l. The fermentation medium used was described in Table 1, which was according to Riesenberg et al. [10]. The inoculum size was 100 ml; the inoculum was prepared by growing the cells in LB (Luria–Bertani) medium overnight at 37 ◦ C in a shaker. The culture temperature was maintained at 37 ◦ C, and pH was controlled at 7.0 with 6 N H2 SO4 and 28% ammonium hydroxide. To ensure a sufficient capability of oxygen transfer, the agitator
Table 1 Medium composition Component
Concentration
Glucose KH2 PO4 (NH4 )2 HPO4 Citric acid MgSO4 ·7H2 O Thiamin HCl Trace metal solutiona
27.5 g/l 13.3 g/l 4.0 g/l 1.7 g/l 1.2 g/l 4.5 mg/l 10 ml/l
a
The trace metal solution contained (per liter) 6 g of Fe(III) citrate, 1.5 g of MnCl2 ·4H2 O, 0.8 g of Zn(CH3 COO)2 ·2H2 O, 0.3 g of H3 BO3 , 0.25 g of Na2 MoO4 ·2H2 O, 0.25 g of CoCl2 ·6H2 O, 0.15 g of CuCl2 ·2H2 O, and 0.84 g of (ethylenedinitrilo)tetraacetic acid disodium salt·2H2 O.
was equipped with two six-blade flat blade turbines, with a diameter of 6.8 cm and a spacing of 3.7 cm. The agitation speed was 400 rpm and air was sparged into the fermentor at a rate of 1 l/min. The dissolved oxygen concentration was maintained above 10% of air saturation by automatic supplementation of pure oxygen to the aeration stream. Silicone antifoam agent KM-72 (Shin-Etsu, Japan) was used for foam control if necessary. The fed-batch phase was started when glucose in the fermentor was depleted, which was indicated by a rapid increase of the dissolved oxygen concentration (to over 80% of air saturation in 10 min). The glucose concentration in the reservoir SA was 700 g/l. The volumetric feed rate, F, and the initial glucose concentration and the volume of mixing chamber C, SC0 and VC , were designed in accordance with the desired specific growth rate. Other nutrients than glucose (referred as the supplemental nutrients) were added to the fermentor in proportion to the total amount of glucose to be fed, which was calculated through integration of Eq. (9). The proportionality of each component to glucose was based on the medium composition given in Table 1. Cell concentration was measured by turbidimetry (600 nm) and correlated with dry cell weight. Glucose was assayed as reducing sugar by the DNS method [11]. Acetate was analyzed by a gas chromatograph (Shimadzu, GC-14A) equipped with a Porapak Q column. The injector and column temperatures were 150 and 180 ◦ C, respectively. Nitrogen was used as the carrier gas at a flow rate of 30 ml/min. A flame ionization detector was used at 180 ◦ C. Acetate peak appeared 5.3 min after sample injection. A calibration curve constructed from acetic acid standards was used to obtain the acetate concentration.
4. Results and discussion From preliminary experiments, it was found that the batch cultivation proceeded for 12.5 h with X0 = 13.0 g/l, V0 = 1 l, and YX/S = 0.55 g cell/g glucose, where YX/S was calculated from the data of the exponential growth phase (6–12 h). The exponential growth phase had a specific growth rate of 0.34 h−1 . We also found that the agitator was shut down when the culture approached a volume of 1.6 l and a cell concentration of 25 g/l; therefore, the limitation of the agitation capability of the fermentor was considered in the assessment of the fed-batch operation. For a specific growth rate of 0.15 h−1 , a value that has been considered popular [3], the pseudo-exponential feeding method with F = 60 ml/h, SC0 = 59.1 g glucose/l, and V C = 525 ml could have a 10 h coincidence with the exponential feeding. By coincidence with the exponential feeding, we meant a ±10% error in FS0 . The purpose of the experiment was to examine the effect of the error in the substrate feed rate on the control of cell growth. The total amount of glucose fed to the fermentor was calculated to
L.-C. Cheng et al. / Biochemical Engineering Journal 10 (2002) 227–232
231
Fig. 4. Fed-batch culture performed with an expected specific growth rate of 0.15 h−1 . Upper panel: (䊉) cell concentration; (䊊) glucose concentration; () volume of NH4 OH added; (䊏) concentration of acetic acid. Lower panel: (—) expected; (䊉) experimental.
be 84.4 g. The required supplemental nutrient was divided into two equal parts (each had a volume of 30 ml), which were added separately to the fermentor at 0 and 5 h of the fed-batch phase. The fermentation profiles are shown in the upper panel of Fig. 4. The fed-batch phase started at 12.5 h, glucose concentration remained undetectable throughout this phase, suggesting that the assumption of Eq. (2), i.e., equivalent rates for substrate addition and consumption, was valid. When the supplemental nutrients were added to the fermentor, the pH decreased, and 25 ml of ammonium hydroxide was fed, through the pH control loop, to the fermentor for neutralization. Cell concentration increased from 13.0 to 20.0 g/l in 6 h and thereafter, cell growth rate declined rapidly while formation of acetic acid increased markedly. In the lower panel of Fig. 4, the present feeding method is shown to assure the desired specific growth rate (0.15 h−1 ) for 6 h. In the calculation of cell mass (XV),
the additional volumes of ammonium hydroxide (for pH control) and the supplemental nutrients were taken into account. The negative deviation of the cell mass profile from the expected one was attributed to ineffectiveness of agitation. At 6 h of the fed-batch phase, the culture volume reached around 1.5 l (initially 1 l, feeding 360 ml, supplemental nutrients 60 ml, ammonium hydroxide 60 ml) and the cell concentration was 20 g/l, and a significant reduction in turbulence at the liquid surface was observed. The deviation was not likely due to the feeding method itself because at that time the glucose feed rate was quite agreeable with the exponential one. Table 2 demonstrates some results of fed-batch cultures with the pseudo-exponential feeding method; the fermentation profiles were similar to that of Fig. 4 and thus are omitted. It should be noted that the designation of the operating conditions could be done at the convenience of the
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Table 2 Fed-batch cultures with the pseudo-exponential feeding methoda µdesired (h−1 )
0.05 0.1 0.15 0.2 0.25 a
X0 (g/l)
13.0 13.0 13.0 13.0 13.0
V0 (l)
1 1 1 1 1
YX /S
0.55 0.55 0.55 0.55 0.55
F (ml/h)
20 40 60 80 100
SC0 (g/l)
59.1 59.1 59.1 59.1 59.1
VC (ml)
525 525 525 525 525
Time length of coincidence with exponential growth (h) Expected
Experimental
30 15 10 7.5 6
18 9 6 4 3
S A = 700 g/l, SB0 = SC0 .
experimenter. It can be seen that the higher the specific growth rate, the shorter the time length that the present feeding method could assure the exponential growth. As mentioned above, the shortage in the expected time length for the cells to grow exponentially was due to ineffective agitation of the fermentor; in all cases, the deviation occurred when the culture volume was around 1.5 l and cell density around 20 g/l. In addition, it was found that acetic acid was not formed when the cells grew exponentially, while acetic acid accumulated to over 5 g/l when cell growth deviated significantly from the exponential profile. In summary, the proposed pseudo-exponential feeding method is capable of controlling cell growth at predetermined specific growth rates for various time durations depending on the magnitude of the rate. Owing to the use of constant-rate feeding, the feeding method is convenient, reliable, and not requiring computerized control equipments. This method, therefore, could have extensive applications at least in laboratory fed-batch culture, where the effect of specific growth rate on the culture performance is to be assessed. Acknowledgements This study was supported by Research Grant NSC902214-E-006-002, National Science Council of Taiwan.
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