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A Simplified Model for the Disruption of Escherichia coli: The Effect of Cell Septation Anton P. J. Middelberg' and Brian K. O'Neill Co-operative Research Centre for Tissue Growth and Repair, Department of Chemical Engineering, The University of Adelaide, Adelaide, South Australia, 5005,Australia
Connor J. Thomas Department of Microbiology and Immunology, The University of Adelaide, Adelaide, South Australia, 5005,Australia
A new model for the disruption of Escherichia coli by high-pressure homogenization has been previously presented. Initial model development assumed a bimodal distribution of effective cell strengths to allow for a possible difference in strength between septated and nonseptated cells. A considerably simpler model is obtained when any difference in strength is neglected and a normal distribution is employed. In this article, the disruption of a culture with an abnormally high septated fraction is examined. Disruption versus pressure curves are predicted using both the bimodal and normal approximations to the strength distribution. An examination of disrupted cultures by optical and electron microscopy suggests that septated cells are indeed weaker, thus implying that a bimodal approximation is strictly correct. However, comparison of the model predictions with the experimental results suggests that the simple normal distribution provides sufficient predictive accuracy even for cultures with a high septated fraction.
Introduction The modern biotechnology industry is beginning to commercialize products for high-volume markets demanding a low-cost product (e.g., porcine somatotropin; Petrides et al., 1989). The engineering challenge in such an environment is not to scale up existing laboratory processes, but rather to develop new integrated processes for optimal large-scale production. Accurate predictive models of biochemical unit and process operations are required if optimal design is to be achieved without extensive pilot plant trials. Escherichia coli is the preferred host for many largescale processes, as strongly inducible promoters are readily available and cloning techniques are well established. Furthermore, highly productive fed-batch fermentation protocols have been developed to maximize protein production. Unfortunately, proteins expressed in E. coli are generally not excreted to the culture medium, with the exception of a small class of proteins such as toxins (Hiret et al., 1984) and hemolysins (Goebl and Hedgpeth, 1982). Insome instances, fusion proteins may bedeveloped for excretion (e.g., human growth hormone; Kat0 et al., 1987). Regardless, the majority of proteins remain intracellular, and the first step in protein recovery is therefore disruption of the cell wall. Many techniques are available for protein release, and these have been previously reviewed (Hughes et al., 1971). The high-pressure homogenizer is generally preferred for the large-scale disruption of nonfilamentous organisms (Hopkins, 1991). It offers the advantages of continuous operation, short residence times to minimize product degradation, and contained operation (Keshavarz et al., 1987).
* Corresponding author. 8756-7938/94/3010-0109$04.50/0
A new model for high-pressure homogenization, which overcomes some of the deficiencies of earlier models, has been presented (Middelberg et al., 1992a,b). Cells are proposed to possess a distribution of effective strengths, fs(S). Disruption occurs in response to stress applied by the homogenizer. Disruption (the volume fraction of cells destroyed, D)is calculated by
where fD@) is the probability that a cell of effective strength S is disrupted (i.e., the stress distribution). Application of eq 1 requires functions describing the strength and stress distributions. The stress distribution, fD(s), is described by
where S, is the median maximum stress during homogenization (Le., the stress at which 50% of the cells experience a stress greater than S,) and d is a general coefficient. A power law dependenceof median maximum stress on homogenizer pressure, P, gives the following: (3) The parameters m,n, and d are system-specific and will therefore change with the homogenizer system and valve employed. Initial model development assumed that effective cell
0 1994 American Chemical Society and American Institute of Chemical Engineers
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Table 1. Model Parameters for Use with a Bimodal Strength Distribution (Middelberg, 1992) (E. coli B Homogenized with an APV-Gaulin 15M Homogenizer Using a CD Valve)
Table 2. Model Parameters for Use with a Normal Strength Distribution (Middelberg, 1992) (E. coli B Homogenized with an APV-Gaulin 15M Homogenizer Using a CD Valve)
parameter
value 3.82 18.8, P < 35 MPa 12.6, P 1 35 MPa 0.284, P < 35 MPa 0.393, P 2 35 MPa 7.27,P < 35 MPa 7.85,P 1 35 MPa
d
m
parameter
2
value independently measured for each culture 17.2, P < 35 MPa 12.6, P L 35 MPa 0.307, P < 35 MPa 0.390, P 1 35 MPa 7.53,P < 35 MPa 7.88, P 2 35 MPa 1.86 3.02 18.4
s, (XI 0.562)a
S,
S, ( X > 0.562)"
S, = L, + 3.047
31.3
m n d 0 8
=
sL, + 3.047
d
n d
v
256.9
This correlation is for the mean effective strength of the nonseptated subpopulation in terms of the cross-linkageof the cellwall peptidoglycan ( X )and the average nonseptated cell length (&,).
strength is distributed according to
1-x, & -exp[ ,a
-(S -
sJ2
2an
]
(4)
which is a bimodal-normal distribution. The choice of a bimodal distribution is based on the fact that any population of E. coli will be heterogeneous as it consists of cells undergoing division (the septated fraction) and cells which have not yet commenced cross-wallformation (the nonseptated fraction). These subpopulations may possess different resistances to disruption, as the division site may act as a point of stress concentration. In eq 4, x sis the volume fraction of the population that is septated, S is the mean effective strength of each subpopulation, and a2is the subpopulation variance. Subscripts s and n denote the septated and nonseptated subpopulations, respectively. Recent work has suggested that an adequate prediction of disruption for cultures with a low septated fraction ( x , 5 20 76 ) may be obtained by assuming a simple normal distribution for effectivecell strength (Middelberg, 1992)
This has the advantage that the strength distribution is now described by two parameters ( S and a) rather than five (Sn,a,, S,, a,, and x,). Furthermore, an experimental measure of the septated volume fraction,x s , is not required. Disruption may be predicted provided the model parameters are known. The parameters for E. coli B disrupted in an APV-Gaulin 15M homogenizer with a CD valve are summarized in Table 1 (assuming a bimodal strength distribution) and Table 2 (assuming a normal strength distribution). Note that all system-specific
S (X I0.563)a
S = -L^128 /5' .23 1X + 2.99
3 (X> 0.563)'
3 = 254.9 L + 2.99
- 10.91In (X/1- x)
-
"This correlation is for the mean effective strength of the population in terms of the cross-linkageof the cell-wallpeptidoglycan ( X ) and the average cell length (&),
parameters (i.e., those describing the stress distribution) are independent of the mean effective cell strength. Furthermore, mean strength is correlated with measurable culture characteristics, namely, peptidoglycan cross-linkage and average cell length. Disruption may therefore be predicted with zero degrees of freedom for the specific system examined. This article examines whether the normal approximation to the effective strength distribution gives an adequate prediction of disruption for a culture with a high septated fraction. Implicitly, we are testing whether or not septated cells are indeed weaker. A culture with an abnormally high septated fraction is obtained by growing E. coli B in the presence of cephalexin, a &lactam antibiotic. At low levels, cephalexin inhibits cell division and causes cells to grow as long filaments (Spratt, 1980). Disruption versus pressure curves are predicted for this culture using both the original assumption of a bimodal strength distribution and the simplified normal approximation. Predictions are compared with experimental disruption results. Additional evidence that septated cells are weaker is sought using optical and electron microscopy. Experimental Procedures Fermentation. A single fermentation was conducted using a 16-L(workingvolume) Chemap CF2000 fermenter. Wild-type E. coli B (P903, Department of Microbiology and Immunology, The University of Adelaide) was inoculated from a shake flask into 16L of modified C1 minimal media (Middelberg et al., 1992a) containing 6.25 g L-l D-glucose to give an initial absorbance ( A m ) of approximately 0.06. Culture pH was automatically controlled at 6.8 with 4 M NaOH. The temperature was controlled a t 37 "C. Cephalexin (5 Mg mL-l, Sigma Chemical) was added when the broth reached an absorbance of 0.8. The culture growth rate remained approximately constant a t 1.12 h-l. A t an absorbance of 3.3, the fermenter's temperature set point was adjusted to 5 "C. Additional growth while the culture was cooling gave a final absorbance of 4.4. Homogenization. The culture was homogenized at various different pressures up to 75 MPa using an APVGaulin 15M-8TA high-pressure homogenizer with a ceramic cell disruption (CD) valve. The homogenizer feed
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100%
100%
c
0
.r( Y
75%
Curve Discontinuity Results from the DiscontinuousS t n s s Function
cn
n
.r(
Experimental
-Bimodal
50%
50%
0
20
40
60
80
Homogenizer Pressure (MPa) Figure 1. Predicted disruption versus pressure curves for a cephalexin-treated culture of E. coli using either a normal or bimodal representation of effective cell strength. Experimental dataareshown for com arison. (Bimodaldistributionparameters are from Table 1with = 36.3 and x = 0.55; normal distribution parameters are from Table 2 with 8 = 29.4.)
&
temperature was 5 "C. The machine was equipped with a second stage which remained set to zero pressure during all tests. Pressures were set using the fitted gauge. Approximate maximum average pressures (Pin eq 3) were calculated from the nominal gauge pressure (Pg):
P = 1.015Pg+ 3.2
(6) Equation 6 was determined by the regression of experimental data obtained using a pressure transducer (Middelberg, 1992). This was necessary as the original model was developed using maximum average pressure rather than average gauge pressure (Middelberg et al., 1992a). Analysis. Disruption was determined using an analytical disk centrifuge (Middelberg et al., 1992a). Cellwall structure was analyzed by reverse-phase, highperformance liquid chromatography (Middelberg et al., 1992b), giving a measured peptidoglycan cross-linkage, X,of 0.452. The undisrupted culture was photographed using a phase-contrast microscope a t lOOX magnification. Developed negatives were mounted as slides, projected onto a screen,and digitizedfor image analysis. Captured images were analyzed using Syzcount (Middelberggt al.,199213) to give L = 5.21 pm, L, = 3.65 pm, and xB = 0.55. MicroscopicExamination. Cultures homogenized at low pressure were examined using a phase-contrast microscope at lOOX magnification. Disrupted cultures were also examined by transmission electron microscopy, using a Philips EM300 transmission electron microscope.
Results and Discussion The culture is characterized by a very high septated fraction of 55 % This is a result of the action of cephalexin (Spratt, 1980). The culture mean effective strength was redicted using the correlations in Tables 1and 2, giving = 29.4 and S, = 36.3. These predictions allow disruption versus pressure curves to be predicted for the culture. These are shown in Figure 1, with experimental data superimposed for comparison. The bimodal distribution apparently provides a better prediction than the normal distribution. However, much of the prediction error is due to the limited accuracy of the correlations for mean effectivestrength (approximately*6 % ;Middelberg et al.,
.
5
0
20
40
60
80
Homogenizer Pressure (MPa) Figure 2. Disruption versus pressure curves for a cephalexintreated culture of E. coli using either a normal or bimodal representation of effective cell strength. Experimental data are shown for comparison. (Bimodal distribution parameters are from Table 1with x , = 0.55 and &,= 35.4 by nonlinear re ession; normal distribution parameters are from Table 2 withg = 31.2 by nonlinear regression.)
1992b). To test the effect of this error on the predictions, experimental data were regressed to each model using nonlinear regression packages (Middelberg et al., 1992a). In both regressions, mean effective strength (Sor S,) was the only parameter allowed to vary. Other parameters were set to the values in either Table 1 (bimodal distribution) or Table 2 (normal distribution). For regression with the bimodal distribution, the measured septated fraction was employed (Table 1). The re ression provided the following optimal strength values: = 35.4 and S = 31.2. These optimal values are within 6% of the predictions. The disruption versus pressure curves using these values are shown in Figure 2. The curves predicted assuming a normal or bimodal strength distribution are of comparable accuracy when the optimal mean effective strength is employed. The number of standard deviations separating the experimental disruption from the model predictions and regressions is shown in Figure 3. The results suggest that the bimodal distribution provides a marginally improved description of the disruption data at low pressures. This suggests, somewhat tentatively, that septated cells may indeed be weaker. For predictive purposes, however, the normal and bimodal distributions have virtually equal accuracy due to the error in the predictions of S and S,. Figure 4 presents size distributions of the undisrupted culture and a sample homogenized with a single pass at 9.6 MPa. The undisrupted sample exhibits a definite bimodal size distribution, presumably due to the presence of filamentous cells. The disrupted sample exhibits a single mode at a smaller Stokes diameter than the undisrupted culture. Again, the results suggest that septated cells may be weaker. Figure 5 shows a photograph of the undisrupted feed sample. Filamentous cells are clearly visible for the cephalexin-treated culture. Figure 6 shows a sample disrupted once at 9.6 MPa. Some septated cells are still visible, but at a considerably reduced frequency. Filamentous cells were not present. Disrupted cells are also clearly visible and generallyexhibit fractures perpendicular to the main axis of the cell (i.e., cell fragments have the same diameter as intact cellsbut are considerably shorter). This observation suggestathat peptide bonds are the weak
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71 :=x!
-41
I 20
0
40
60
80
Homogenizer Pressure (MPa) Figure 3. Number of standard deviations separating the experimentaland predicted disruption for a cephalexin-treated cultureofE.co1iusingeitheranormalorhimodalrepresentation of effective strength. Bimodal distribution: m, 3. = 36.3, predicted; 0.3. = 35.4, regressed. Normal distribution: 0 , s = 29.4. predicted 0, 3 = 31.2, regressed.
Figure5. Cephalexin-treatedE. colicells beforehomogenization (phase-contrast microscope, lOOX objective) (top) and a culture grown under the same conditions hut without the addition of cephalexin (bottom).
0.70
0.95
1.20
1.45
1.70
Stokes Diameter (pm) Figure 4. Size distributions of a cephalexin-treated culture of
E. coli before homogenization (feed) and after one pass at 9.6 MPa (homogenate)determinedwiththeanalyticaldiskcentrifuge (Middelberg et al., 199%).
point in the cell (provided peptide bonds are aligned perpendicular to the main axis, as proposed by Verwer et al. (1978)).Cultures were also examined after disruption byonepassat24MPa (photographnotsbown). Noclearly septated cells could be found. Further, the debris was of a smaller size than that after disruption at 9.6 MPa, and it was not clear that the debris resulted from breakage perpendicular to the main bacterial axis. This may simply he due to the harsher homogenization conditions, leading to demadation of the debris or to the action of a different disruption mechanism. Examination of the culture homogenized at 9.6 MPa bv transmission electron microscopy (+EM) clearly revealed many cells fractured at a division site. Whether such fracture is a general phenomenon cannot, however, he deduced from such limited evidence.
Concluding Remarks Combined, the preceding evidence supports the suggestion that septated cells are weaker. The assertion is not proved. For the culture examined, the normal
Figure 6. Cephalexin-treated E. coli cells nlrerone homogenizer pass at 9.6 MPa (phase-contrast microscope. IOOX objective). approximation to the true strength distribution provides sufficient predictive accuracy despite the high septated fraction. It islikelythat thiswill be trueformostsituations of practical interest. However, in cases where a different stress functionisused (e.g.,a homogenizerhavinganalmost
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Bbtechnol. Rog., 1994, Vol. 10, No. 1
step-function stress distribution), t h e septated volume fraction may be a critical model parameter, and a more accurate approximation of the true strength distribution (e.g., a bimodal representation) will be required. In conclusion, the bimodal representation of t h e effective strength distribution would appear to be a closer approximation to the true strength distribution. However, for modeling purposes, a simple normal approximation is sufficient. The simplified model also has the advantages that fewer parameters are required to predict disruption and that a measure of the septated fraction of t h e population is not required.
Notation disruption (volume fraction of cells destroyed during homogenization) coefficient determining the stress distribution width cumulative fraction of events during homogenization with a stress greater than S (Le., the probability of disruption) effective strength volume-frequency distribution (or effective strength distribution) average cell length (pm) constant (eq 3) (MPa-”) exponent (eq 3) homogenizer pressure (the maximum average pressure recorded during the transient) (MPa) nominal gauge pressure during homogenization
(ma) effective strength mean effective strength median maximum stress experienced during homogenization (i.e., the stress at which 50% of the events have a stress greater than S,) degree of peptidoglycan cross-linkage volume fraction of the bacterial population that is septated Greek Symbols UZ
variance of the effective strength distribution
Subscripts n 8
nonseptated subpopulation of bacteria septated subpopulation of bacteria
Acknowledgment The authors thank APV-Gaulin for their generosity in providing the valve unit used in this work. We are also indebted to Mr. A. S. Hull and A/Prof. Agarwal for the use of their image analysis hardware a n d their Syzcount
software. The authors also thank Dr.A. H.Rogers and Mr. N. Gully for their assistance in analyzing the cell-wall structure of the culture by HPLC. We are grateful to Prof. J.-V. H6ltje of t h e Max-Planck-Institut fiir Entwicklungsbiologie, Tfibingen, Germany, for providing chromatographic standards. The assistance of Mrs.R. Middelberg during the homogenization testa is also acknowledged.
Literature Cited Goebel, W.; Hedgpeth, J. Cloning and Functional Characterization of the Plasmid-Encoded Hemolysin Determinant of Escherichia coli. J. Bacteriol. 1982,151, 1290-1298. Hirst, T. R.; Randall, L. L.; Hardy, S. J. S. Cellular Location of Heat-Labile Enterotoxin in Escherichia coli. J. Bacteriol. 1984,157, 637-642. Hopkins, T. R. Physical and Chemical Cell Disruption for the Recovery of Intracellular Proteins. In Purification and Analysis of Recombinant Proteins; Seetharam, R., Sharma, S. K., Eds.; Marcel Dekker: New York, 1991;Chapter 3, pp 57-83. Hughes, D. E.; Wimpenny, J. W. T.; Lloyd, D. The disintegration of microorganisms. In Methods in Microbiology; Norris, J. R., Ribbons, D. W., Eds.; Academic: New York, 1971;Vol. 5B, Chapter 1, pp 1-54. Kato, C.; Kobayashi, T.; Kudo, T.; Furusato, T.; Murakami, Y.; Tanaka, T.; Baba, H.; Oishi, T.; Ohtauka, E.; Ikehara, M.; Yanagida, T.; Kato, H.; Moriyama, S.; Horikoehi, K. Construction of an excretion vector and extracellular production of human growth hormone from Escherichia coli. Gene 1987, 54, 197-202. Keshavarz, E.; Hoare, M.; Dunnill, P. Biochemical engineering aspects of cell disruption. In Separations For Biotechnology; Verrall, M. S., Hudson, M. J.,Eds.; Ellis Horwood: Chichester, U.K., 1987;Chapter 3, pp 62-79. Middelberg, A. P. J. A model for the disruption of Escherichia coli by high-pressure homogenization. Ph.D. Dissertation, University of Adelaide, Adelaide, SA, Australia, 1992. Middelberg, A. P. J.; ONeill, B. K.; Bogle, 1. D. L. A new model for the disruption of Escherichia coli by high-pressure homogenisation. I. Model development and verification. Trans. Inst. Chem. Eng. 19928,70 (C4), 205-212. Middelberg, A. P. J.; O’Neill, B. K.; Bogle, I. D. L.; Gully, N. J.; Rogers, A. H.; Thomas, C. J. A new model for the disruption of Escherichia coli by high-pressure homogenieation. 11. A correlation for the effective cell strength. Trans. Znst. Chem. Eng. 199213,70 (C4), 213-218. Petrides, D.; Cooney, C. L.; Evans, L.B.; Field, R. P.; Snoswell, M. Bioprocess Simulation: An Integrated Approach to Process Development. Comput. Chem. Eng. 1989,13,553-561. Spratt, B. G. Biochemical and genetic approaches to the mechanism of action of penicillin. Philos. Trans. R. SOC. London B 1980,289,273-283. Accepted October 12,1993.@ Abstract published in Advance ACS Abstracts, December 16, 1993. @
