Jo~rrrd ofBiorec/trlo/ogy, 20 (1991) 0 1991 Elsevier Science Publishers ADONIS 0168165691001231


1 17- 130 B.V. 016&1656/91/$03.50



Production of cell mass and pertussis toxin by Bordetella pertussis Peter Licari, George R. Siber and Randall Swartz


16 March

1990; revision


16 July



The cultivation of Bordetelln pertussis affects production of pertussis toxin and biomass. Comparison of batch mode, chemostat operation and pHstat-turbidostatic control showed that productivities for the continuous process were greater than that for the batch operation. Continuous operation in balanced growth at the maximum specific growth rate, provided by the pHstat, resulted in the maximum specific production rate. Because of the strong association of pertussis toxin synthesis and cell growth, the concentration of toxin in the effluent of the continuous processes was greater than the maximum obtained in the batch biopro-

Corres~ontle~e U.S.A. Nonte~lnr’tr~:

IO: P. Licari. DCW

= d’y

Biotechnology cell weight


(g); J.Si = quantity



of substrate

University, i used

(g I-‘);



YE = yield

02155. of cells

on substrate (g 6-l): Y,, = growth yield of cells on substrate (g g-‘); X= cell density (g I-‘); S = effluent substrate concentration (g I -I): I = time (Ii): p = specific growth rate (h-l); (dS/df)jn = consumption of substrate for maintenance (g I-’ II-‘); 1)’ = maintenance energy. carbon per DCW per time (g g-’ Ii-‘); QE = specific substrate consumption rate (X-’ (dS/dr); N = nitrogen concentration (g I-‘): Y,,, = yield of cells from nitrogen, DCW per N (g g -I): & = specific product formation rate X-’ (dP/d/); Y p,s = yield of product from cells, toxin per DCW (mg g - ’ ); p = non growth associated product ion feed capacity I-‘); Pr llzlF = lag

formation: D = dilution rate (I~-‘): S, = substrate feed concentration (g I-‘): H, = hydrogen concentration (mol I-‘); H = hydrogen ion effluent concentration (mol I-‘): BC = buffering (mol I-‘); Y,,/, - acid yield constant, H per DCW (mol g-l): P = product concentration (mg = volumetric productivity. toxin per vol. per time (mg I-’ Ii-‘); f,,‘= time of culture (Ii); time (Ii): I, = turnaround time (Ii).


cess. An expanded Luedeking-Piret model of product formation kinetics fits the observed chemostat data and demonstrates that the production of pertussis toxin from the culture of B. perfussis is predominantly growth associated. Bordetella pertussis; Pertussis toxin; Chemostat; pHstat

Introduction Bordetella pertussis is the bacterium responsible for pertussis (commonly referred to as the whooping cough), a disease of the respiratory tract which may be life threatening in infants and young children. A whole cell vaccine was developed shortly after isolation and in vitro cultivation of the organism in 1906. Mass immunization with a killed whole cell vaccine was introduced in the United States circa 1940, resulting in a marked decrease in the number of infections and deaths from B. pertussis. Although effective in providing immunity, the whole cell pertussis vaccine has been associated with adverse reactions at a low frequency. These reactions range from mild local reactions or fever to severe systemic reactions including convulsions and hypotonic-hyporesponsive episodes. Whether severe neurologic reactions such as encephalopathy are caused by the vaccine remains controversial, but fear of such reactions has led to decreased acceptance of the vaccine in Great Britain and suspension of its use temporarily in Japan and permanently in Sweden. In all three countries, there has been a resurgence of pertussis. Current research focuses on developing an acellular vaccine composed of one or more antigenic proteins that have been purified and inactivated in all potentially toxic biological activities. In particular, lipopolysaccharide (endotoxin) and cell wall material, which cause toxicity but contribute no protective activity, are removed from the vaccine. Although the number of components to be included in an optimally protective pertussis vaccine remains to be established, there is general agreement that inactivated pertussis toxin will be an essential constituent. Pertussis toxin is a multisubunit protein that is believed to play a major role in the pathogenesis of pertussis (Pittman, 1984). Recent clinical studies in Sweden demonstrated that a vaccine containing only formalinized pertussis toxin was 80% effective in preventing clinically severe pertussis (Ad Hoc Group for the Study of Pertussis Vaccines, 1988). The development of a vaccine based on this toxin will require a high yield of pertussis toxin from cultures of B. pertussis. This paper describes the growth of B. pertussis and the synthesis of toxin in batch and continuous cultivation. Energy and carbon source requirements are related to engineering design parameters of yield of cells on substrate, (Yno) and a maintenance coefficient (ml. Growth and non-growth associated parameters are used to describe product synthesis in balanced growth (via a turbidostat or a pHstat) and in substrate limited growth (via a chemostat).



and Methods

Bacterial strain. medium and culture conditions Bordeteffa pertussis strain SKlOl, a mod (- > kanamycin resistant strain (Knapp and Mekalanos, 1988) was obtained from the Massachusetts Public Health Biologic Laboratories (Boston, MA). This mutant does not modulate to the avirulent phase in the presence of 20 mM MgSO, or 5 mM nicotinic acid (i.e. it does not downregulate synthesis of virulence factors such as pertussin toxin). The medium used in the cultivation was based on that proposed by Stainer and Scholte (1971). Modifications included the addition of cyclodextrin and Difco Casamino Acids. The growth medium was iron-limited and consisted of 1.0 g I-’ heptakis (2,6-di-0-methyl)-P-cyclodextrin; 6.1 g I-’ Tris; 3.0 g I-’ Difco Casamino Acids; 17.0 g I-’ monosodium glutamate; 2.5 g 1-l NaCl; 0.5 g I-’ KCI; 0.1 g 1-l MgCl,. 6Hz0; 0.02 g I-’ CaC12; 0.24 g I-’ L-proline; 0.004 g I-’ niacin; 0.001 g 1-l FeSO, .7H,O; 0.04 g I-’ L-cysteine hydrochloride monohydrate; 0.15 g 1-l glutathione; 0.4 g I-’ ascorbic acid; 0.06 g I-’ kanamycin sulfate. The medium was filter sterilized. Cultivation in a 2 1 BioFlo unit (New Brunswick Scientific, Edison) was at 36 o C. pH was controlled at 7.6 by the addition of 2 M H,SO,. Air flow rate was maintained at 0.8 SLPM by the use of a Tylan mass flow controller while the agitation rate was maintained at 500 rpm. Cell growth was monitored by the optical density at 530 nm with a Beckman Spectrophotometer (model DU-50). Samples were removed and centrifuged at 15,000 rpm for 10 min. The supernatant was saved to assay for toxin, Dry cell weight was measured with the remaining biomass. Tosin analysis Culture supernatant samples were assayed for pertussis toxin by a fetuin ELISA developed at the Massachusetts Public Health Biologic Laboratories. The assay consists of sensitizing ELISA plates with fetuin, a bovine serum glycoprotein, to which toxin selectively binds. Mouse monoclonal antibodies, specific for the Sl subunit of the toxin, are then allowed to bind to the pertussis toxin. This is followed by the addition of alkaline phosphatase-labeled goat anti-mouse IgG. After sufficient color develops from the addition of p-nitrophenyl phosphate, the reaction is stopped with 1.0 M NaOH and the OD,,,S recorded. The optical densities are converted to a toxin concentration by the use of a standard curve generated with purified pertussis toxin. Amino acid analysis Concentrations of 20 different amino acids in the broth supernatants were determined with an amino acid analyzer. These analyses were performed by Dr.


Harvey Levy at the amino acid laboratory, Massachusetts General Hospital (Boston, MA).

The concentration of ammonia in the supernatants Sigma ammonia diagnostic kit (Procedure 170-UV).

was determined

with a

Results and Discussion Cell growth nrd substrate utilizatiotz

Pirt (1975) has reasoned that cells require substrate for cell carbon, energy for growth and energy for maintenance. The term “maintenance energy” refers to the energy needed to maintain concentration gradients between the cell and its environment, for turnover of cell materials and for cell motility.




j-Ah-‘) Fig.

1. The



of glutamate DCW

per time

as a function (g g-’


of the specific = 0.01+4.65

growth cr.





B. pertussis cells are unable to utilize carbohydrates, pyruvate, lactate and intermediates of glycolysis (Jebb and Tomlinson, 1957; Rowatt, 1957; Parker, 1976). Instead, the organisms use amino acids as their carbon and energy source. The specific substrate utilization rate, Qn, for each amino acid was calculated at several dilution rates by operating a chemostat. A plot was made of QE versus the specific growth rate. The analysis for glutamate, the main carbon and energy source, is included in Fig. 1 as a typical analysis. The linear fit is described by the equation: QE = 0.01 + 4.65( /.L) where QE is in units of g glutamate (g DCW-h)-’ and p is in inverse hours. Thus the value for the maintenance requirement, 177, is 0.01 g glutamate g DCW per h. The value for the true growth yield of cells on glutamate, Y,,, is 0.22 g g-‘. A similar analysis was completed for each amino acid. From this data it was desirable to calculate overall coefficients in which all of the amino acids utilized were accounted for in one parameter. Since the bacteria utilize more than one substrate, the above analysis must be expanded to account for this multiplicity. The overall yield, denoted Y,, is defined as AX Y, = ~ S( ASi) where i indicates all of the amino acids consumed by the bacteria. This may be written in the form 1


+ AS,,,,

+ AS,,,

+ .. . )



In terms of the individual yields this reduces to 1 YE=


1 +






Similarly the overall “true”

+ ...

growth yield may be defined as 1

YE, =


I +



Since the maintenance




.. .

term for each amino acid, i, is defined as

1 dSi ??7i =



X dt

the overall maintenance dS,,, -I?7



dS,qo + -117



may be expanded to

“SV,L + -I?7



.. .









per amino

egg-‘) Glutamate Proline Valine Leucine Isoleucine Alanine Methionine Lysine

0.22 5.0 12 14 3s 82

amino (gg-’

acid h-‘)

per DCW

per time

0.01 0.00 0.00 0.00 0.00 0.00

100 140

Simplifying ~72=nz,,“+,n,,,+n2”,,+


0.00 0.00

.. .

The individual analysis of each amino acid indicated that glutamate and proline were metabolized efficiently, with glutamate being the main substrate. The data for several amino acids are presented in Table 1. Although misleading when presented alone, these values provided enough information to calculate an overall growth yield and maintenance parameter for the growth of Borderelfa perrussis cells. Prior to calculating any cumulative parameters, a common unit of measure was needed since the amino acids consumed have different molecular weights. Hence values were expressed in terms of grams and moles of carbon. YE, (DCW per carbon) was calculated to be 0.48 +_0.02 g g-’ or 5.8 g (DCW mol-‘1. The maintenance parameter (carbon per DCW per time) was 0.0043 + 0.0005 g gg’ h-’ or 3.6 x 10-4mol g-’ h-‘. As expected the numerical values for the overall parameters resemble those for glutamate, indicating that glutamic acid is the primary amino acid utilized and accounts for most of the growth in the current medium formulation. The growth yield expressed in units of dry cell weight per g of carbon allows for a more meaningful comparison with other microbes that utilize carbohydrates or intermediates of glycolysis. If this is done, YE, for B. pertussis is 0.50 g DCW per g carbon; as compared to values in the literature of 0.43 to greater than 1 g DCW per g carbon. The yield of cells from nitrogen

The amount of nitrogen incorporated into the organism can be determined from a mass balance on nitrogen in the system. The yield coefficient, YX,N, is a ratio of the mass of cells to the mass of nitrogen utilized by the cells. The balance of nitrogen accounted for the amount of amino acids incorporated into the cells (total amino acids in - total amino acids out) less the amount of nitrogen present in the ammonia of the culture. The yield was calculated to be 5.7 + 0.2 g DCW per g nitrogen.


In terms of the amount of nitrogen incorporated into the microbe, there is 0.12 f 0.01 g nitrogen per g of dry cell weight, i.e., the cells are 12% nitrogen. This figure correlates well with other types of microbial cells (Pirt, 197.5). Product formation

The growth curve and the production of toxin in a batch culture are presented in Fig. 2. Possible conclusions drawn from this figure are: (a> the production of toxin is intimately related to the growth of the organism or (b) the production of toxin depends on the presence of one or more components in the medium. Luedeking and Piret (1959) described product formation kinetics for the production of lactic acid from Lactobacillus defbruekii in terms of both growth and non-growth associated parameters. This may be written as:

Qp = G/,/J


The first term (Y,,,p) accounts for product associated with the growth of the organism and the second term C/3>is a measure of non-growth associated product formation.




2 c




.c ;: I-




20 Time(h)

Fig. 2. Toxin


and dry cell weight

as a function

of time

for batch


l toxin,

0 In( X ).


The effect of contirzuous culture on product formation B. pertussis was cultivated continuously in a chemostat. Several dilution rates were examined in an effort to fit the above model to the production of toxin by Bordetella per-tussis. The culture was assumed to be steady when the cell density was constant for a period of at least ten doublings of the bacterial population. Values for Q,, were calculated and plotted as a function of growth rate (Fig. 3). The Luedeking-Piret product formation kinetics of pertussis toxin are characterized by the equation

Qp = 6.81(/~) - 0.09 where the units of Q,, are toxin per DCW per time (mg g-’ hh’). The yield of product from cells, Yr,x, is 6.81 mg toxin per g DCW. This term is associated with the energy used for growth. The coefficient, /3, is an indication of the amount of product formed that is not growth related and is therefore associated with the energy consumed for maintenance. The fact that this term is negative is an indication that the product may be degraded or that the LuedekingPiret:t model may be an oversimplification for the B. bertussis Pire pertussis system. 0.5 0.5 1_1 1_1 77cc

m E”

0.4 -

.-E L :

0.3 -

3 x L it .c ; (_ z

0.2 -

0.1 -

0.0 0.04




pu(“-I) Fig. 3. The effect

of growth rate on toxin production. 0 chemostat data, n pHstat Q, (mg toxin per g DCW per h) is plotted against p (h-‘).

data (QP at prnLIX),


In an analysis on Agrobacterium turnefaciens, Kurowski (1974) expanded the Luedeking-Piret model by defining the yield term as a function of growth rate, i.e., Y ,,,x = Kp. Hence the equation for the growth-linked product was:


= Y,, X/J, = K’CL

Although unstructured, this model demonstrated that the yield may not be a constant but may be proportional to the growth rate. In an attempt to describe the B. pertussis system better, the following equation was used: Q,, = 0.00 + 1.76(p) + 55.2( 4’ The data presented here are similar to that of Kurowski in that Yp,x is not a constant but instead increases with the specific growth rate. This fit is preferred over the straight-line Luedeking-Piret model because the non-growth associated term is zero and not a negative value. No degradation of product was witnessed in the batch culture to confirm the negative value of the Luedeking-Piret kinetics. The data indicate that the non-growth-associated term is effectively zero and that the production of toxin is entirely growth-associated. The batch data of Fig. 2 should not be interpreted as toxin production being directly nutrient dependent, but rather that cell growth depends on nutrient availability and toxin production depends on cell growth. In an effort to maximize the specific rate of toxin production one would like to keep the cells dividing as rapidly as possible and for as long as possible, a task best suited for a continuous process. The pHstat: twbidostatic

control based on pH changes

The underlying theme governing the operation of a chemostat is that the cells are dividing at a rate lower than the maximum growth rate due to substrate limitation. The uptake of the limiting nutrient proves to be the rate limiting process in the growth of the organism. This may result in several alterations in cellular properties, including size, morphology, physiological activity, the amount of intracellular DNA and RNA, and in the production and secretion of various proteins. Thus, it was of interest to operate a continuous culture in which the cells were not substrate-limited but were growing at the maximum specific growth rate to determine if any fundamental differences existed. Balanced continuous growth can be obtained by operating the system under turbidostatic control. Since the metabolism of amino acids by B. pertcrssis results in the release of ammonium ions, it appeared that the operation of a pHstat, turbidostatic control based on changes in pH due to growth, would be an effective means of control. The fundamentals of a pHstat are discussed thoroughly in the literature (Martin and Hempfling, 1976; MacBean et al., 1979). The steady state equations describing such a system are:

YE x=(S,-S) (H,-H)




Prior to operating a successful pHstat several possible shortcomings were considered, including the instability of the medium at a low pH and the possibility of probe drift interfering with the stability of the culture. Medium stored at a pH of 3.95 for up to one week did not exhibit any alterations of growth properties. Although stable, medium was not kept at this pH in excess of one week. pH probe drift was overcome by sampling the bioreactor every 12 h and recalibrating the probe if necessary. Bacterial growth through the metabolism of amino acids is the predominant reason for ammonium ion generation and the concomitant elevation of the pH. This allows information concerning growth to be obtained by measuring the amount of acid needed to neutralize this change. Determining the appropriate acid concentration of the medium inlet for the pHstat was most successful when based on the chemostat data. For each dilution rate at which the chemostat was operated, the ratio of the volume of 2 M sulfuric acid used to maintain a pH of 7.6 to the ratio of effluent produced was calculated. All values were in a narrow range (24-26 ml H,SO, per 1 of effluent) with the higher dilution rates having the higher ratios. From these data it was determined that 22 ml of 2 M sulfuric acid to 1.0 1 of medium at a pH of 7.6 would provide balanced growth. The resulting pH of the medium to feed the pHstat was 3.95. This value allows for the control of pH while maintaining an excess of all nutrients. pHstat operation resulted in a steady continuous culture in which the cells were dividing at ~~~~~while in balanced growth. It was assumed that the cells were dividing at the maximum growth rate in balanced growth because the dilution rate of the pHstat was greater than the critical value of the dilution rate that in chemostat experiments had resulted in washout. This study provided a p,,,,,, value of 0.093 &- 0.002 h-‘, which correlates to a doubling time of approx. 7.5 h. Cell adaptation was ruled out by studies with subsequent batch cultures. The specific toxin production rate for this system was calculated to be 0.48 mg toxin per g DCW per h. This point is presented with the data from the chemostat studies in Fig. 3. The expanded Luedeking-Piret model (based on chemostat data) suggests a higher value for Qr at the maximum specific growth rate. Most likely this is a limitation in the fit of the curve. The value of Q,, at pmns results in a smooth curve if one assumes the toxin production rate begins to level off as the growth rate approaches a maximum. It should be noted that the differences in substrate-limited growth and balanced growth may result in this discrepancy between the data. Based on these results it may be beneficial to operate a fed batch or a repeated fed batch process. A comparison of productivity

in batch, chemostat and turbidostat cultures

From the data presented in Fig. 3 it appears that the operation of a continuous culture is the most effective means for producing pertussis toxin. A measure of how suitable a system is may be obtained by comparing the productivities of each process. Volumetric productivity is defined in units of milligrams of toxin per liter of reactor working volume per hour,


For a batch and fed batch process the productivity, Pr =

Pr, is defined as


where P is the final concentration of product, t,,, is the time of cell growth at P ,,,oX, flss is the time the cells spend in the lag phase, and t, is the turnaround time. The turnaround time includes vessel preparation, medium preparation and inoculum development. Parameters for the batch culture of Bordetella pertussis were: P = 15 mg I-‘, t cUI= 25 h, flElp= 5 h, and tt = 15 h. The resulting batch productivity of toxin is 0.33 mg I-’ hh’. Thes e values are based on the data from the operation of a 10-l vessel. One would expect that a larger production vessel will require extended lengths of time for vessel and medium preparation, the net effect being a reduction in the batch productivity. ’ For a continuous process the productivity is calculated as Pr=PD

For the cultivation of B. pertussis in a chemostat operating at a dilution rate of 0.075 hh’ and with a pertussis toxin concentration in the effluent of 16 mg I-‘, Pr = 1.2 mg I-’ h-‘. Inherent in the operation of a chemostat is the fact that it must be operated below pma, or washout tends to occur. The dilution rate of 0.075 h- ’ was chosen from its demonstrated stability in the laboratory. Since turbidostatic control allows for operation at the maximum specific growth rate, one expects an increase in productivity over chemostat operation. The productivity for a continuous culture utilizing pHstat-turbidostatic control and operating at I-L,,;,, is 1.3 mg I-’ hh’. It is clear that the concentration of pertussis toxin in the effluent of a continuous reactor must be comparable to that in the batch cultivation in order to use an efficient recovery process. Fortunately, the concentration of toxin in the effluent of the continuous processes is slightly greater than for the batch process. One must conclude that continuous operation is the process best suited for the production of pertussis toxin due to the strong growth association. Feasibility of continuous operation in scale-up

In general, the benefits of continuous operation over a batch process for the production of a primary metabolite are numerous. Chemostat operation on an industrial scale might pose contamination problems; however, continuous cultivation of B. pertcmis on the bench top was conducted in excess of one month. The fact that the SK101 mod(-) strain is kanamycin resistant was instrumental in maintaining sterility. Bordetella perfussis has been shown to undergo a genetic mutation termed phase variation (Leslie and Gardner, 1931). This mutation from a virulent to an avirulent organism is pertinent in that the degraded cells are unable to express pertussis


toxin. If such a mutation is demonstrated to be a problem, it is feasible to operate the chemostat for shorter periods of time. The literature suggests that Bordetelln per-tussis in the virulent phase is relatively unstable when maintained in laboratory cultures (Field and Parker, 1978). This antigenic cultural modulation may be induced by a variety of means, including high salt or nicotinic acid concentrations. Such a shift to the avirulent phase results in loss of several virulence factors, including toxin production. The particular strain used in this work, SK101 mod (- >, is a mutant strain selected based on its resistance to modulation. In the presence of high salt or nicotinic acid concentration the SK101 mod(-) strain has shown a greater ability to remain in the virulent phase than wild type organisms. It should be noted that the chemostat population never had a shift in virulence, either due to phase variation or cultural modulation, in the greater than 2000 h of operation. This stability of the virulent organism is further support of continuous culture for the production of pertussis toxin. Acknowledgements

This work was funded by the Massachusetts Health Research Institute. We are grateful to Dr. Larry Winberry, Ms. Leslie Wettorlow, Dr. Elizabeth Eubanks and the staff at the Massachusetts Public Health Biologic Laboratories for their support and assistance. We also thank James G. Kenimer of the Center for Biologics Research and Review, FDA, Bethesda, MD, for the use of clone 3CX4 which produces the monoclonal antibody specific for the Sl toxin subunit. Finally we express special thanks to Dr. H. Levy at the Massachusetts General Hospital for the amino acid analysis of the medium. References Ad

Hoc Group for the Study of Pertussis Vaccines (1988) Placebo-controlled trial of two acellular pertussis vaccines in Sweden. Protective efficacy and adverse events. Lancet 1, 950-960. Field, L.H. and Parker, C.D. (1978). Differences observed between fresh isolates of Eor&e//(r pemssir and their laboratory passaged derivatives. Third International Symposium on Pertussis. ed. Manclark and Hill, U.S. Department of Health, Education and Welfare, Washington, D.C. Jebb, W.H. and Tomlinson, A.H. (1957) The minimal amino acid requirements of Hnmop/~i/~rs pe~~lrssis. J. Gen. Microbial. 17, 59-63. Knapp, S. and Mekalanos, J.J. (19SS) Two Ircrrrs-acting regulatory genes (c,;r and /nod) control antigenic modulation in Bot&re/ln permsis. J. Bacterial. 170, 5059-5066. Kurowski, W.M. (1974) Transformation of sucrose to 3 keto-sucrose by Agrobocre&/n twm$xiens and stability of the glucoside-3-hydrogenase activity in non-growing cells. Ph.D. Thesis, University of London. Leslie, P.H., and Gardner, A.D. (1931). The phases of Haetnophihrs prrmsis. Am. J. Hyg. 31, 423-434. Luedeking, R. and Piret, E.L. (1959) A kinetic study of the lactic acid fermentation. J. Biochem. Microbial. Technol. Eng. 1, 393. MacBean, R., Hall, R. and Linklater, P.M. (1979) Analysis of pH stat continuous cultivation and stability of the mixed fermentation in continuous yogurt production. Biotechnol. Bioeng. 21, 1517-1541.

129 Martin, G.A. and Hempfling, during continuous culture Parker, CD. (1976) Role of

W.P. (1976) A method for at high growth rates. Arch. the genetics and physiology

the regulation of microbial population density Microbial. 107, 41-47. of Borcietelln pertussis in the production of

vaccine and the study of the host-parasite relationship in pertussis. S.J. (1975) Principles of Microbe and Cell Cultivation. Blackwell England. Pittman, M. (1984) The concept of pertussis as a toxin-mediated 367-386. Rowatt, E. (1957) Some factors affecting the growth of Bor~letelln Pirt,

279-296. Stainer, D.W. and Scholte, M.J. (1971) A simple phase I Borr/c~e//n pertttssis. J. Gen. Microbial.

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Microbial. production

3, 17, of

Production of cell mass and pertussis toxin by Bordetella pertussis.

The cultivation of Bordetella pertussis affects production of pertussis toxin and biomass. Comparison of batch mode, chemostat operation and pHstat-tu...
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