Cell Segregation and Lysis Have Profound Effects on the Growth ofEscherichia coli in High Cell Density Fed Batch Cultures

Lena Andersson,* Lars Strandberg,† and Sven-Olof Enfors

Department of Biochemistry and Biotechnology, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Cell segregation into nondividing states and lysis was found to dominate the growthbehavior of high cell density fed batch cultures of Escherichia coli. When the specificgrowth rate declined below a critical value, the biomass production, oxygen consump-tion, and carbon dioxide formation rates declined sharply. Concomitantly, an extensiveloss of colony-forming ability (cfu) and accumulation of extracellular proteins wasobserved. A segregated model that considered different physiological states, includingdividing, nondividing, and lysed cells, was developed and applied to experimental datafrom high cell density cultures of E. coli.

Introduction

Fed batch cultures are widely employed in bioprocessesto achieve high cell concentrations and improved volu-metric productivity. In contrast to conventional batchcultures, fed batch cultures are growth limited by asubstrate component continuously fed into the bioreactor.The main objective of restricting the substrate consump-tion rate, and thus controlling the specific growth rate,is to avoid inhibitory mechanisms such as substrateinhibition, overflow metabolism and catabolite repression(Yamane and Shimizu, 1984). Moreover, and of equalimportance, restriction of the energy consumption rateoffers an effective tool for preventing conditions of exces-sive heat evolution and oxygen limitation. In fact, theboundary conditions of mass transfer in the bioprocesswill set a limit to the maximal substrate flow rate. Athigh cell concentrations, the specific substrate consump-tion rate will be very restricted and the cells may beexposed to severe energy limitation.Whereas much effort has been made to control and find

feeding strategies for high cell density cultures (Landwalland Holme, 1977; Gleiser and Bauer, 1981; Pan et al.,1987; Riesenberg et al., 1991; O’Connor et al., 1992), therehave been few articles covering microbial death inenergy-limited cultures (Postgate and Hunter, 1962;Tempest et al., 1967; Mason et al., 1986b). During thelast years researchers in the field of environmentalmicrobiology have provided new and important informa-tion on starvation and survival strategies of exponentiallygrowing bacteria that enter stationary phases (Kjelleberg,1993). Several publications have re-established the term“dormant” cells (Gilbert et al., 1990; Kaprelyants et al.,1993, 1994), and others have used the expression “viablebut nonculturable cells” (VBNC) (Byrd et al., 1991;Nilsson, 1991; Oliver et al., 1991) as a physiological statefor nonsporulating bacteria, induced by unfavorableconditions, in which cells do not form colonies on nutrientagar plates but still exhibit metabolic activity.Cell physiology of microorganisms growing in excess

of all required nutrients (batch phase) will however differfrom when cells are exposed to progressively increasingenergy limitation (as in fed batch cultivations), and

consequently, it is not obvious that the cellular responsesto starvation conditions will be the same. In this paperwe have focused on growth kinetics and viability at slowgrowth rates in the fed batch growth system. A segre-gated model that considered different physiological stateswas developed and applied to experimental data fromhigh cell density fed batch cultivations of E. coli.

Materials and Methods

Microorganism. The bacterial strain used, E. coliKA197 (relA1 spoT1), was obtained from ABP Interna-tional, Lund.Media. Composition of medium and feed solutions are

shown in Table 1. pH was controlled with 2 M H2SO4and 25% NH4OH. Additional antifoam was added whennecessary. The cultivations were started as batch cul-tures, and the feed was started when the initially addedglucose was almost exhausted.Cultivation Conditions. Inoculum was prepared

from shake flask cultures grown overnight at 37 °C. Theexperiments were carried out in a 7 L bioreactor (Chemap

* Corresponding author.† Current address: Pharmacia AB, Biopharmaceuticals, Pre-

clinical R&D, S-112 87 Stockholm, Sweden.

Table 1. Media Composition for High Cell Density FedBatch Cultivations

componentinitial concn

(g L-1)feed soln I(g L-1)

feed soln II(g L-1)

Na2SO4 2.0 2.0(NH4)2SO4 2.0NH4Cl 0.5 0.5K2HPO4 14.6 14.6NaH2PO4‚H2O 3.6 3.6(NH4)2-H-citrate 1.0 1.01 M MgSO4 2.0 (mL L-1)glucoseexpt 1 20 600expt 2 10 600expt 3 20 600expt 4 20 600

trace elements(Holme et al., 1970)

2.0 (mL L-1) 12 (mL L-1) 12 (mL L-1)

thiamine 0.1adecanol LG-109 0.05 (mL L-1)

composition oftrace element solution

concn(g L-1)

composition oftrace element solution

concn(g L-1)

CaCl2‚2H2O 0.5 MnSO4‚4H2O 0.15FeCl3‚6H2O 16.7 CoCl2‚6H2O 0.18ZnSO4‚7H2O 0.18 Na-EDTA 20.1CuSO4‚5H2O 0.16

190 Biotechnol. Prog. 1996, 12, 190−195

8756-7938/96/3012-0190$12.00/0 © 1996 American Chemical Society and American Institute of Chemical Engineers

SG7). The initial working volume was 3.5 L. Thetemperature was kept at 37 °C. The air flow rate waszero at the time of inoculation but after a short period ofadaptation increased to a final value of 2.0 L min-1. Thestirrer speed was kept at 800 rpm. The dissolved oxygentension was always maintained above 20%.Analyses. Dry weight was determined by centrifuging

3× 5 mL of cell suspension in preweighed tubes, washingthe samples with distilled water, and drying overnightat 105 °C before weighing.Analysis of number of dividing cells (colony-forming

units, cfu) was performed on nutrient agar plates,incubated at 37 °C for 24 h.Metabolic potential was assessed microscopically using

reduction of iodonitrotetrazolium (INT) to cell-boundformazan as the criterion (Zimmerman et al., 1978).Diluted cell samples (1 mL) were added to test tubescontaining 0.25 mL of 2% INT aqueous solution togetherwith mineral salts (see Media) and 2 g L-1 glucose. Aftermixing, the samples were incubated for 20 min at 37 °Cand the fraction of respirating cells was determined usingphase contrast microscopy.Oxygen and carbon dioxide contents of the effluent gas

were analyzed with a paramagnetic analyzer (ServomexOxygen Analyser 540A, Sybron/Taylor, U.K.) and an IRanalyzer (Binos, Leybold-Hereaus, Germany), respec-tively. The dissolved oxygen tension was continuouslymeasured with a polarographic oxygen electrode (Ingold,Switzerland).Protein concentration in the culture medium was by

measured by the Bradford method (Bradford, 1976).Samples were taken from the fermenter, centrifuged, andfiltered before freezing at -20 °C.Parameters used in simulations were estimated from

experimental data by a computer program written in Cemploying the simplex algorithm (Strang, 1986). Thecost function (fit) used was the square root of the summedsquared differences between normalized values calcu-lated from the model and experimental data divided bythe number of fitted points. The program finds optimumvalues for the variable parameters by minimizing the costfunction with respect to each parameter simultaneously.It was used for analyzing the combination of totalbiomass formation (cell mass values), oxygen consump-tion and carbon dioxide production rates, and the fractionof dividing biomass (Xv). This fraction was estimatedfrom cfu values using a conversion factor of 0.10 g ofbiomass/cfu × 10-12. An exponential function was fittedto the calculated Xv values and used as a data set in thesimulations.The elemental composition of biomass used in the

simulations was CH1.72O0.47N0.24, estimated from previouswork [not published].

The Model

Theoretical Background. A simple unstructuredmodel for a glucose-limited fed batch culture can es-sentially be represented by the following equation:

Biomass and carbon dioxide are assumed to be the mainproducts (expressed in c-mole). The total mass (g) of cellsand substrate are considered in the following rateexpressions:

The maintenance rate in the model is assumed to beindependent of the specific growth rate, µ (Pirt, 1965):

Since the substrate fed into the fermenter is immediatelyconsumed in a constantly fed batch culture, the assump-tion can be made that dS/dt , Fs. During these condi-tions, eq 3 can be rewritten as

and the specific growth rate is given by

In the case of aerobic growth on glucose with ammoniaas the nitrogen source, the following equations (Roels,1983) can be applied for the rates of oxygen consumptionand carbon dioxide production (expressed in mol h-1):

The degree of reduction of substrate and biomass, γs andγx, is estimated from the stoichiometry of the reactiondescribed in eq 1 and by using the elemental compositionof CH1.72O0.47N0.24 for the biomass. The rate equationsfor RO2 and RCO2 can be simplified by using the relation-ship from eq 4 and inserting values on γs and γx(expressed in g h-1):

Segregated Model. An unsegregated model of aculture treats the microorganisms as one homogeneouspopulation with the same physiological state. Incorpora-tion of cells with different physiological states leads to adifferentiation of the total biomass. In this study celldivision, conversion of cells from dividing to nondividingbut metabolically active cells and lysis of dividing andnondividing cells are considered as the four reactionsinvolved the in segregation, as shown in Figure 1. Theoccurrence of dead but nonlysed cells without any res-piration was found to be negligible for the investigatedsystem. Consequently, the three fractions that analyti-cally comprise the flow of biomass are dividing biomass,nondividing biomass, and lysed cells. Dividing biomass(Xv) consists of intact cells that have a metabolic activity(respiration) and replicate. Nondividing biomass (Xnd)is comprised of cells that have metabolic activity but havelost the ability to divide, and finally, lysed biomass (Xl)originates from lysis of Xv and Xnd. Differentiation is

CH2O + ANH3 + BO2 f

YsxCHeOfNg + CH2O + DCO2 (1)

dXdt

) µX (2)

dSdt

) Fs - Rs (3)

Rs ) µXYsx

+ mX (4)

Rs ) Fs (5)

µ ) (Fs

X- m)Ysx (6)

RO2) 14[( γs

Ysx

Mx

Ms- γx)µX

Mx+ γsm

XMs

] (7)

RCO2) [( 1Ysx

Mx

Ms- 1)µX

Mx+ m X

Ms] (8)

RO2) 32[Rs

Ms- 1.02µX

Mx] (γs ) 4.0, γx ) 4.06) (9)

RCO2) 44[Rs

Ms- µXMx

] (10)

Biotechnol. Prog., 1996, Vol. 12, No. 2 191

further assumed to be induced at some critical specificgrowth rate, µcrit, at which the culture is subjected tosevere energy limitation. The biomass balance equationsthen become

Xv is converted to Xnd at a specific rate of knd. Nondi-viding (Xnd) and dividing biomass (Xv) are subjected tocell lysis at specific rates of klnd and klv, respectively.According to eq 4 the maintenance rate is substrate

consumption that does not lead to an increase in biomass.From this definition the assumption is made that thenondividing fraction of the biomass has the same main-tenance rate as the viable fraction. Accordingly, the rateexpression of glucose consumption becomes

from which the specific growth rate, µ, is obtained:

The gas exchange rates, in units of g h-1, are obtainedfrom eqs 9 and 10:

A tabular representation of the equations used in thesimulations is given in Table 2.

Experimental ResultsGrowth Pattern of High Cell Density Cultures.

A number of high cell density fed batch cultivations of

E. coli KA197 with different constant feed rates wereperformed. All cultures showed the same characteristicgrowth behavior with two distinct growth phases. In thefirst phase, the biomass formation (Rx), oxygen consump-tion (RO2), and carbon dioxide production (RCO2) rates werealmost constant. In the successive growth phase thevalues on growth and gas exchange rates drasticallydeclined. An example of a cultivation with a glucose fedrate of 11.1 g h-1 is shown in Figure 2.Concurrently with changed growth pattern an increas-

ing amount of extracellular proteins was observed in themedium (Figure 2B). Calculated values of C recoverybased on the glucose, carbon dioxide, and biomass flowsstarted to decline systematically from around 95% duringthe first growth phase to final values of about 80% atthe end of the cultivations (not shown). In addition, thenumber of dividing cells measured as colony-formingunits (cfu) started to decrease rapidly (Figure 2B). Inspite of the drastic drop in cfu, less than 3% of the cellshad lost their capacity to respirate throughout thecultivations, according to the INT assay (data not shown).Extracellular protein release, C recovery, and colony-forming ability together indicated that the altered growthkinetics were accompanied by cell lysis and a change inphysiological state of the cells and that a nonsegregatedmodel would not give an adequate description of the highcell density fed batch cultures.Determination of m and Ysx. The growth param-

eters Ysx and m, to be further used in simulations of thesegregated model, were obtained by parameter estima-tion using a simple unsegregated model. This approachto determine kinetic parameters in unstructured growthmodels has been described previously in the literature(van Verseveld et al., 1986; Baltes et al., 1994). Experi-mental data on biomass production, oxygen consumption,and carbon dioxide formation rates from different fedbatch cultivations were used for the fitting procedure.All simulations were terminated before the observedtransitions to the second growth phase (µ > µcrit). Theresults are shown in Table 3.Experimental Verification of the Segregated

Model. Measurements of biomass (Xt) and gas exchange

Figure 1. Schematic representation of a segregated model ofbacterial growth involving cell lysis and segregation into anondividing state.

dXv

dt) (µ - knd - klv)Xv (11)

dXnd

dt) kndXv - klndXnd (12)

dXl

dt) klndXnd + klvXv (13)

Xt ) Xv + Xnd (14)

Rs,seg )µXv

Ysx+ m(Xv + Xnd) (15)

µseg )Ysx

Xv[Rs - m(Xv + Xnd)] (16)

RO2,seg) 32[Rs,seg

Ms- 1.02

µXv

Mx] (γs ) 4.0, γx ) 4.06)

(17)

RCO2,seg) 44[Rs,seg

Ms-

µXv

Mx] (18)

Table 2. Segregated Model of Bacterial GrowthDescribing Cell Segregation to Nondividing State andLysis

param-eter description equation

Xv cells that have metabolicactivity and replicate

dXv

dt) (µ - knd - klv)Xv

Xnd cells that have metabolicactivity but are notdividing

dXnd

dt) kndXv - klndXnd

Xl cell debris that originatesfrom lysis of Xv and Xnd

dXl

dt) klndXnd + klvXv

Xt total amount of cell mass Xt ) Xv + Xnd

Rs substrate utilization rateduring quasi-steadystate

Rs ) Fs

µ specific growth rateµ )

Ysx

Xv[Rs - m(Xv + Xnd)]

RO2 oxygen consumption rateRCO2 carbon dioxide formation

rate RO2) 32[Rs

Ms- 1.02

µXv

Mx]

µcrit critical specific growthrate for the onset ofsegregation

RCO2) 44[Rs

Ms-

µXv

Mx]

192 Biotechnol. Prog., 1996, Vol. 12, No. 2

(RCO2, RO2) together with calculated values on dividingbiomass (Xv), based on cfu values, were compared withsimulations based on the segregated model (Figure 3).This model was tested against two fed batch cultures,experiments 1 and 2, performed with different initialglucose concentrations and constant feed rates. Theinitial glucose concentration was decreased in experiment2 with the intention of obtaining the same specific growthrate for the two cultures in the beginning of the fed batchcultures. The kinetic parameters, knd, klnd, klv, and µcrit,which were estimated from simulations, are presentedin Table 4.

An attempt was also made to correlate the amount ofextracellular proteins to lysed biomass (Xl) simply byassuming that all proteins that originate from lysed cellsare accessible to analysis and that the cellular proteincontent is 50% of the total biomass. Figure 4 shows thatthe amount of lysed cells according to the extracellularprotein analysis was much lower than predicted by themodel.

Discussion

E. coli KA197 growing in glucose-limited fed batchcultures exhibited two distinct growth phases. In thefirst growth phase the biomass production and gasexchange increased almost linearly, which is in agree-ment with the linear equation for substrate consumption(eq 4). During the transition between the growth phases,the rates of oxygen consumption, carbon dioxide forma-tion, and biomass production (dX/dt) changed drasticallyand then stabilized at new and lower values. Disconti-nuities in the growth pattern of carbon/energy limitedsystems have been observed for a variety of microorgan-isms, e.g. E. coli, Paracoccus denitrificans, and Bacilluslicheniformis (Tempest et al., 1967; Esener et al., 1983;Chesbro et al., 1990). van Verseveld et al. (1986) provideda mathematical description for an energy-limited recy-cling fermenter with 100% biomass feedback. In themodel, the second growth phase was assigned extremelylow m values and constant overall growth yields (Rx/Rs).Stringent regulation was suggested to cause the alteredgrowth behavior in the second phase, and this is a likelyexplanation, as evidence for involvement of stringentregulation has been observed in other studies of energy-limited cultures (Arbige and Chesbro, 1982). The maxi-mum cellular level of the main effector of stringentresponse, guanosine 5′-diphosphate 3′-diphosphate(ppGpp), was reached simultaneously with a drop in dX/dt at a critical specific growth rate.In the present study, the amount of extracellular

proteins increased significantly concurrently with thechange in growth pattern, indicating cell lysis. Despitethe fact that no direct method was applied to distinguishbetween growing and nondividing cells, the presenteddata strongly indicate that an increasing fraction of thebiomass consisted of nondividing but respirating cells.All cells that were microscopically assessed throughoutthe cultivations showed respiratory activity suggestingthat the presence of dead nonlysed cells was negligible.This observation has previously been done in studies ofviability (Mason et al., 1986a). The data on biomassproduction rate and RO2 did not show any drops causedby death that could account for the distinct decline incfu. Thus, the ability of the cells to divide was ceasingprogressively, while the cellular metabolic potential fordissimilation remained. The loss of colony-forming abil-ity and the substantial increase of extracellular proteinswas encountered at a low specific growth rate (0.022 gg-1 h-1), reflecting a considerable degree of starvation.The rel status of the strain used in this study (relA

spoT) may have an effect on the responses. It has beenshown that stringent strains outcompete relaxed strains

Figure 2. Example of the growth behavior from a fed batchcultivation with a constant glucose feed rate of 11.1 g h-1. Thefigure shows (A) dry weight (g L-1), carbon dioxide formationrate, RCO2 (g L-1 h-1), oxygen consumption rate, RO2 (g L-1 h-1),and specific growth rate (g g-1 h-1) and (B) colony-forming units(cfu mL-1) and extracellular protein content (g L-1).

Table 3. Comparison of Model Predictions of m and YsxEstimated from Different Experimentsa

expt

glucosefeed rate(g h-1)

m(g g-1 h-1)

Ysx(g g-1) fit

1 11.1 0.030 0.53 0.06392 5.8 0.023 0.50 0.06803 11.7 0.024 0.52 0.13774 5.9 0.020 0.50 0.1019

a Data on RCO2, Xt, and RO2 from 0-22 h of glucose-limited fedbatch cultivations were used for the fitting procedures

Table 4. Model Predictions of Growth Parameters Estimated from Data on RCO2, RO2, Xt, and Xv from 2 to 80 h ofGlucose-Limited Fed Batch Cultivationsa

expt

initialglucose concn

(g L-1)

glucosefeed rate(g h-1)

knd(g g-1 h-1)

klnd(g g-1 h-1)

klv(g g-1 h-1)

µcrit(g g-1 h-1) fit

1 20 11.1 0.077 0.003 0.027 0.023 0.2062 10 5.8 0.129 0.002 0.016 0.022 0.148

a Segregation was assumed to be induced at µcrit.

Biotechnol. Prog., 1996, Vol. 12, No. 2 193

in chemostat and that this effect is enhanced at lowerdilution rates (Riesenberg and Bergter, 1984). It shouldhowever be emphasized that changes in viability and cellsegregation during slow growth are not unique to E. colior relmutants (Tempest et al., 1967; Mason et al., 1986).Correlated values of Xl, based on analysis of extracel-

lular proteins, did not agree with the amount of lysedcells predicted by the model. The explanation for thisdeviation could be due to errors both in the experimentaland simulated estimations. It is obvious that part of theoverprediction of Xl could have arisen from failure incorrect estimations of, for example cell dry weight,especially at high cell concentrations. The simulations

were performed by parameter estimation which meansthat the values used to correlate Xl in the model werecombined experimental results of total biomass (Xt),oxygen consumption rate (RO2), carbon dioxide formation(RCO2), and dividing cell mass (Xv). These other experi-mental data correlates fairly well with model predi-cationsswhich gives us reason to believe that the majorerror lies in the correlation between measurements ofextracellular protein content and actual amount of lysedbiomass. Sample preparation of extracellular proteinsincluded centrifugation and filtration. Both of thesesteps may have lead to fractional losses due to removalof insoluble proteins and absorption on the filter surface.Also, part of the cellular proteins may not have beenaccessible for sampling as a consequence of insolubilityand foam attachment to the fermenter wall.In the segregated model it was assumed that dividing

and nondividing cells had the same maintenance require-ment. An alternative model had been proposed earlierwhere cells differentiate into dormant cells with zeromaintenance energy at slow growth rates (Pirt, 1987). Itstill remains to be determined whether dividing cells arecapable of lowering their substrate consumption forenergy when entering the nondividing state or not.Occurrence of an increasing part of biomass with loweredmaintenance rate would indeed have extensive effects ongrowth dynamics and energetics.Another assumption made in the model was that no

cell lysis takes place during the first growth phase (beforeµcrit). Experimental results show (Figure 2B) that extra-cellular proteins were accumulated in the medium alsoduring this phase. The low amount observed, however,indicates that it had an insignificant effect on growthkinetics.

Figure 3. Simulation results (lines) and experimental data (symbols) of fed batch experiments 1 and 2. Growth parameters usedfor simulations and estimated parameter values for the segregated model are listed in Tables 3 and 4. (A) Oxygen consumption rate,RO2 (mmol h-1). (B) Carbon dioxide formation rate, RCO2 (mmol h-1). (C) Total biomass, Xt (g). (D) Comparison of estimated andpredicted data on dividing biomass, Xv (g). The calculated values of Xv were estimated from cfu values using a conversion factor 0.10g of biomass/cfu × 10-12.

Figure 4. Comparison of simulation results (lines) and calcu-lated values of lysed cells, Xl (g) (symbols), from experiment 2(Fs ) 5.8 g h-1). The calculated values were estimated fromexperimental data on extracellular protein content using aconversion factor 2.0 g of lysed biomass/g of extracellularprotein.

194 Biotechnol. Prog., 1996, Vol. 12, No. 2

ConclusionCell segregation and lysis were shown to influence

considerably the growth behavior of the high cell densityfed batch cultures of E. coli. The present study isinsufficient for an entire understanding of these phe-nomena but has shown that cell segregation and lysisshould be included in order to model high cell densityfed batch cultures. Finally, an interesting problem thatneeds to be further investigated is what effects thesephenomena might have during industrial production ofproteins. Depending on whether cell segregation into anondividing state results in a complete inability toproduce protein or if it leads to cells that are specializedin production (in favor of cell division), the outcome wouldindeed influence process performance.

NotationFs substrate feed rate (g h-1)ki rate constant (g g-1 h-1)m maintenance coefficient based on substrate

requirement (g g-1 h-1)Mi c-mole molar mass (g-1) of compound iRi conversion rate of compound i (g h-1)S glucose quantity (g)Xi biomass quantity (g)Ysx yield coefficient for biomass per substrate

utilized excl. maintenance (g g-1)γi generalized degree of reduction of compound iµ specific growth rate (g g-1 h-1)

SubscriptCO2 carbon dioxidel lysednd nondividingO2 oxygens substrateseg segregationt totalv dividingx biomass

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Accepted October 5, 1995.X

BP950069O

X Abstract published in Advance ACS Abstracts, December 1,1995.

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