Analysis of Metabolic Fluxes in Batch and Continuo us Cu It u res of Bacillus subtilr’s

Akshay Goel, Jerome Ferrance, Jinwook Jeong, and Mohammed M. Ataai* Chemical and Petroleum Engineering Department and Center for Biotechnolog y and Bioengineering, University of Pittsburgh, Pittsburgh, Pennsylvania

Received September 1 I , 1992/Accepted April 2, 1993

It is well recognized that metabolic fluxes are the key variables that must be determined in order to under- stand metabolic regulation and patterns. However, ow- ing to difficulties in measuring the flux values, evaluation of metabolic fluxes has not been an integral part of the most metabolic studies. Flux values for metabolites of glycolysis, tricarboxylic acid (TCA) cycle, and hexose monophosphate (HMP) pathway were obtained for batch and g I ucose-l i m ited continuous cu Itu res of Bacillus sub- tilis by combining the information from the stoichiome- try of key biosynthetic reactions with the experimental data on concentrations of glucose and metabolic by- products, COz evolution, and oxygen uptake rates. The results indicate that (1) the metabolic fluxes and ener- getic yield as well as the extent of flux mismatch in metabolic activity of glycolysis and the TCA cycle reac- tions can be accurately quantified; (2) the flux through the TCA cycle in continuous culture is much in excess of cell energetic and biosynthetic demands for precursors; (3) for the range of growth rates examined the TCA cycle flux increases almost in proportion to growth rate and is significantly repressed only a t very high growth rates of batch cultures; and (4) for continuous cultures the isocitrate dehydrogenase catalyzed reaction of the TCA cycle is the major source of the reduced form of nicotinamide-adenine dinucleotide phosphate (NADPH) used in biosynthesis. 0 1993 John Wiley & Sons, Inc. Key words: metabolic fluxes Bacillus subtilis- TCA cycle

glycolysis growth rate

INTRODUCTION

Although a vast number of metabolic reactions occur within cells, the glycolytic, hexose monophosphate (HMP), re- duced nicotinamide-adenine dinucleotide (NADH) turnover, and tricarboxylic acid (TCA) reactions are logical places to thoroughly investigate because, together, they provide key precursors for the synthesis of macromolecules and energy to the cell. It has been demonstrated that the enzymes of the TCA cycle are repressed in cultures of exponentially growing Bacillus specie^.'^'^ Moreover, it has been found from chemostat studies with Escherichia coli that as the growth rate increases, some enzyme activities de~rease .~ , ” The studies on enzyme levels have identified some poten- tially interesting trends. However, generating a coherent picture based on the existing information is difficult for two reasons. First, the culture conditions in many of the experiments were not fully characterized. Second, and more

* To whom all correspondence should be addressed.

importantly, the metabolic fluxes were not determined. Thus, complete closure between fluxes and enzyme regu- lation has not been attained. For example, W e i t ~ m a n ~ ~ notes the regulatory control maintaining balanced metabolic flux and accommodating both energetic and biosynthetic demands, and many other facets of TCA cycle regulations are in their infancy.

Radiolabeled substrates can be employed to attain flux data (involving extraction and separation of metabolites), but they are expensive and the procedures used to employ them are demanding.2s,26 Likewise, I3C nuclear magnetic resonance (NMR) studies can be illuminating, but it is currently difficult to maintain a cell suspension in a desired physiological state during an experiment. Thus, much fewer flux studies have been performed despite their importance.

Alternately, the analysis of the stoichiometry of the metabolic pathways24 could provide significant information on cell metabolism and overall distribution of carbon flow among various metabolic reactions. Conducting overall carbon balances, without resorting to detailed presentation of the metabolic reactions, has also been proved useful in the analysis of fermentation data and implementing process control strategy for obtaining productive fermentation^.^,^ The first comprehensive applications of the metabolic path- ways for analysis of the fermentation data and product yields were reported by Papoutsakis. 19z20 Furthermore, the metabolic pathway balances have been successfully ap- plied to lysine fermentation for obtaining fluxes in batch cultures23 and to citric acid fermentation in continuous cultures.’ The potential applications and the methodology of the stoichiometrically based analysis of metabolic reac- tions for identifying critical branch points in the overall flux distribution have been described in an excellent article by Stephanopoulos and Vallino.21 Moreover, recently, a study on the effect of gene expression on fluxes for a recombinant E. coli growing under anaerobic conditions in batch cultures has been reported.6

In this article, the flux values for continuous cultures of the wild-type Bacillus subtilis at different growth rates and feed glucose concentrations are discussed. Moreover, the continuous culture results are compared to those obtained for batch cultures with different initial glucose concentra- tions. The fluxes were obtained by applying the pseudo- steady-state (PSS) assumption to the metabolic pools and using the information on cell mass, COz evolution rate,

Biotechnology and Bioengineering, Vol. 42, Pp. 686-696 (1993) 0 1993 John Wiley & Sons, Inc. CCC 0006-3592/93/060686-11

oxygen uptake rate, glucose consumption rate, rates of formation of major organic by-products, and the cell com- position in terms of the monomer content. It was found that the actual metabolic fluxes (mmole/g cell h) obtained for batch cultures, using the stoichiometrically based models, may be less reliable than those for continuous cultures, due to the sensitivity of the actual fluxes in batch to the curve-fitting procedure and thus slight measurement errors. Therefore, instead of the actual fluxes for batch cultures, the total flow of each metabolite normalized by the amounts of glucose consumed will be reported.

METHODS

Bacterial Strain and Medium

Wild-type Bacillus subtilis 168 was a generous gift from A. L. Sonenshein (Tufts University, Medical School). The medium composition was the same as the one in the study by Dawes and Mandelstam5 for glucose-limited experiments. One liter of medium contains either 1 or 3 g/L glucose; 1.0 g NH4Cl; 0.04 g tryptophan; 2.72 g KH2PO4; 0.284 g Na2S04; 0.17 g NaN03; 0.15 g KCl; 0.049 g MgC12 * 6H2O; 2.16 mg FeC13 - 6H2O; 0.158 g MnC12 * 4H20; and 0.438 g CaC12 6H2O.

Cultivation System

The cultivation system3 is equipped with a quadrupole mass spectrometer (Ametek Themox Division, Pittsburgh, PA) for gas analyses (CO2 and 0 2 were followed); Cole Parmer (Cole Parmer, Chicago, IL) computerized pumps; a pH probe and controller; and an accurate air flow meter (Brooks, Hatfield, PA). A 2.4-L New Brunswick fermentor with a working volume of 1.5 L (New Brunswick, Edison, NJ) was employed with an air flow rate of 2 L/min for both batch and continuous culture experiments. Batch studies were also conducted with a lower air flow rate of 0.07 L/min in a fermentor with a working volume of about 900 mL. Steady state is assumed in continuous culture when at least five residence times have passed and the optical density, extracellular glucose, and CO2 evolution rate remain constant for two subsequent residence times.

Cell Mass and Residual Glucose Concentration

Cell mass is calculated from our calibration curve relat- ing the culture optical density to biomass concentration (1 OD660 = 0.35 g cell (dry weight)/L). The glucose con- centration is measured enzymatically (Sigma Chemicals, St. Louis, MO).

Analysis of Organic Acids

Organic acids (lactate, acetate, acetoin, formate, pyruvate, and citrate) are measured using a Bio-Rad high- performance liquid chromatography (HPLC) gradient mod-

ule (Bio-Rad, CA, model 401) equipped with UV/Vis monitor. An Aminex 87H organic acid column from Bio- Rad is used for the analysis. A 0.02 N H2SO4 solution with a flow rate of 0.4 mL/min at 63°C is passed through the column and the eluant absorbance is monitored at 210 nm. All samples and buffers are filtered through a 2.2-pm filter.

RESULTS AND DISCUSSION

Evaluation of Metabolic Fluxes for Continuous Cultures

A detailed stoichiometric approach was used to calculate the carbon flux through glycolysis, the TCA cycle, the HMP pathway, and various biosynthetic pathways (see Fig. 1). Key intermediates considered in the model are glucose-6-phosphate (glucose-6-P), ribulose-5-phosphate (ribulose-5-P), fructose-6-phosphate (fructose-6-P), triose phosphate (TP), phosphoenol pyruvate (PEP), pyruvate, acetyl coenzyme A (ACoA), isocitrate, a-ketoglutarate (a-KetoG), and oxaloacetate (OAA). The fluxes were determined by (1) applying the PSS assumption to the metabolic pools of intermediates (i.e., no accumulation of metabolic pools); ( 2 ) measuring cell mass, CO2 evolution rate, oxygen uptake rate, glucose consumption rate, and rates of formation of major organic by-products; and ( 3 ) using the cell composition data of Table I. The metabolic reactions are modeled by the set of reactions listed in the appendix. A balance is constructed around each of the species (also listed in the appendix) using these reactions. This results in 32 equations which need to be solved simultaneously to obtain the fluxes. These equations are listed in Table 11.

The flux of each of the 30 reactions (r, , mmol/g cell 9

h) would be of the form

xi = a i r ,

In this formulation x; is the accumulation vector for the species i , a is the stoichiometric coefficient determined by the stoichiometry of the species under consideration, and j spans the reactions in which species i occurs. For example, x8, the accumulation term for the species TP, is obtained by combining reactions 6, 8, 9, and 10 listed in the appendix:

x8 = 218 + (1/3) r6 - r9 - r10

This system of equations may be represented in a matrix form by

Ax = r

where A is the matrix of coefficients (30 X 32) . The 30 elements of vector x can be divided into three

subgroups: biosynthetic precursors, extracellular products, and intracellular intermediates. The biosynthesis accumu- lation terms are estimated using the cell composition data from Table I. These are comprised of xq, x7, x9, x11, x12, X 1 4 ,

x16, x19, x20, ~ 2 4 , x26, and ~ 2 7 . Table I lists typical composi- tion data of E. coli which were used in these calculations.

GOEL ET AL.: METABOLIC FLUXES IN BACILLUS CULTURES 687

Ribose for Nucleic Acid

r2 t r5/( Cell Wall Glucose 6-P ___t Ribulose-5P

Fructose 6P AA 13

TP -TriGlycerides I r9

ri i + "",2 AA f-------- I% - Nucleic Acid

i r i 3

r i 4 AA - PEP

' 1 5 1 r Y A A > Organics P yruvate -> Z A A

A CoA ___t Membrane

Acetate

rzz l r 2 2

Nucleic rate Acid

AA - a 2 r32

Figure 1. Reaction networks used in the flux analysis for B. subtilis.

Complete composition data are not available for B. subtilis. However, those available, such as the composition of DNA and RNA and the cellular contents of several amino acids, are not significantly different than the numbers reported in Table I." Moreover, variations in cell composition do not, to any significant extent, affect the relative distribution of fluxes between the glycolysis and the TCA cycle. As examples, the calculations for ~ 2 7 and x26 for cells growing in continuous culture at a dilution rate of 0.15 h-' and feed concentration of 3 g/L glucose (summarized in Table 111) are discussed. The value of ~ 2 7 is obtained by adding the numbers in the oxaloacetate (OAA) column of Table I, which corresponds to OAA conversion to amino acids and multiplying the sum by the dilution rate [i.e., ~ 2 7 = (0.201 + 0.101 + 0.252 + 0.403 + 0.201 + 0.252) X 0.15 = 0.2115 mmol/g cell * h]. Similarly, the accumulation term xz6, which represents the conversion of OAA to RNA and

DNA, is calculated by adding the numbers that correspond to conversion of O M to DNA and RNA precursors and multiplying the sum by the dilution rate (i.e., x26 = 0.115 + 0.024 + 0.115 + 0.024) X 0.15 = 0.042). To estimate x6 (the cell wall biosynthesis flux from glucose), the following information is used. The fraction of biomass as cell wall (about 15%) is represented by fw, and 2700 is the aver- age molecular weight of a peptidoglycan unit which con- sists of approximately 12 glucose molecules and 5 amino acids.

The extracellular accumulation quantities which include glucose uptake rate (XI), organics ( ~ 1 7 and x21), CO2 evo- lution rate (x~I), and 0 2 uptake rate ( ~ 3 2 ) are those which were measured experimentally. Using the pseudo-steady- state assumption, the intracellular accumulation terms ( x ~ ,

are set to zero. x3, x.5, XB, x10, x13, XIS, x18, x22, x237 x25, x28, x29, and x30)

688 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 42, NO. 6, SEPTEMBER 5, 1993

Table I. Synthesis of monomers from metabolic precursorsa used for biosynthesis.

Monomer Monomer content G6P TP PG PEP PYR OAA KG ACoA

Ala A% ASP Asn cys Glu Gln GlY His Ile Leu

Met Phe Pro Ser Thr

Lys

TIP TY r Val

AMP dAMP GMP dGMP CMP dCMP UMP dTM P

cl6 fatty acid GIYPh

0.454 0.252 0.201 0.101 0.101 0.353 0.201 0.403 0.050 0.252 0.403 0.403 0.201 0.151 0.252 0.302 0.252 0.050 0.101 0.302 0.115 0.024 0.11s 0.024 0.1 1s 0.024 0.1 15 0.024 0.280 0.140

0.151

0.101b

0.403 0.050

0.302

0.100 0.101

0.11s 0.024 0.115 0.024 0.115 0.024 0.115 0.024

0.454 0.252

0.201 0.101

0.353 0.201

0.252 0.252 0.806 0.403 0.403

0.201 0.302b

0.252

0.252 0.100b 0.202

0.604 0.115 0.024 0.115 0.024

0.115 0.024 0.115 0.024

0.403

1.40 0.140

All numbers arc mmol/g dry weight biomass. Abbreviations: TP, triose phosphate; PG, phosphoglycerate; GP, glycerolphosphate; PEP, phospho-

a The values are taken in part from ref. 16. ’ Values indicate that they are different than those of ref. 16. The values differ because our inspection of biosynthetic reactions revealed that some values were placed in the wrong column or the stoichiometry was in error. For example, ref. 16 indicates that Phe is derived from PG while Phe is a derivative of PEP.

enolpyruvate; PYR, pyruvate; OAA, oxaloacetate; KG, a-ketoglutarate; ACoA, acetyl-CoA; AA, amino acid.

The balance on NADPH (species 28) needs some further explanation. The HMP pathway has two major functions: to provide precursors for the nucleic acid biosynthesis, flux r 5 , and to generate NADPH. The NADPH requirement for cell mass biosynthesis is estimated to be 18 mmol NADPH/g cell.17 For continuous cultures, the rate of NADPH consumption in biosynthesis would be given by 18D mmol/g cell 1 h where D is the dilution rate. Reac- tions 4 and 23 are assumed to be the only source of NADPH in the model. Let ~ N A D P H represent the cell NADPH re- quirements. Thus, for continuous culture, rNADpH = 18 D. If (TNADPH > r23), then the TCA flux is insufficient to fulfill the cell NADPH biosynthesis needs, and thus the balance has to be provided by the HMP flux r4. Since based on the overall reaction for the biosynthesis of NADPH via the HMP pathway, 3 glucose 6-P - 2 fructose 6-P + TP + 3 C02 + 6 NADPH, 2 mol of NADPH is produced per mole glucose entering this pathway, the accumulation term

r23, then the second function of the HMP pathway is not required, and thus r 6 is set to zero.

x28 becomes rNADpH -r23 - 2r4). If, however, rNADpH 5

There are 30 unknowns and 32 equations. The system of equations are solved by a least-squares procedure23 of the first 31 equations. The least-squares solution was based on the first 31 equations because of oxygen uptake rate (OUR) values were unreliable due to the high air flow rate of 2 L/min (the difference between inlet and outlet oxygen partial pressure approaching the limit of the sensitivity of the instrument). The flux values presented in Tables 111 and IV are for three different dilution rates with the feed glucose concentration of 1 g/L and for one dilution rate with the feed glucose concentration of 3 g/L. As example of the growth profile, the data on optical density, glucose concentration, and COz evolution rate for 3 g/L glucose in the feed are shown in Figure 2.

Calculations of Fluxes for Batch Cultures

Obtaining the flux values for cells growing in a batch culture is more difficult than those for the chemostat grown cells. This is because the slopes of time-dependent variations (on a log scale) for cell density, glucose uptake

689 GOEL ET AL.: METABOLIC FLUXES IN BACILLUS CULTURES

Table 11. Equations for flux determination and consistency analysis.

*D is the dilution rate for continuous cultures and X is the cell concentration (g/L); C denote concentrations of the metabolites in the reactor and Cfglucose is the feed glucose concentration; CER and OUR represent the measured C02 evolution rate and the oxygen uptake rate, respectively.

For batch calculations see discussion in the text.

and CO;! evolution rate, and rates of formation of organic by-products were not identical for the exponential growth phase of the batch culture, as shown in Figures 3-5. Thus, the flux values for the exponential phase of growth will not be time invariant. Moreover, the batch data, in particular

Table 111. rates.

Continous culture fluxes (mmol/g cell h) for different dilution

SO = 3.0 g/L, So = 1.0 g/L, So = 1.0 g/L, So = 1.0 g/L, Flux D = 0.15 h-' D = 0.15 h-I D = 0.3 h-' D = 0.5 h-'

2.69 (2.68)

0.06 (0.06) 0.08 (0.08) 0.08 (0.08)

2.44 (2.44) 2.44 (2.44)

4.87 (4.86)

0.04 (0.04) 4.70 (4.70) 0.09 (0.09) 4.61 (4.50) 0.38 (0.38)

3.82 (3.82) 0.06 (0.06)

0.10 (0.10)

0.00 (0.00)

0.02 (0.02)

0.12 (0.12)

0.00 (0.00)

0.21 (0.21) 0.21 (0.21) 3.34 (3.34) 3.34 (3.34) 0.16 (0.16) 3.19 (3.18) 0.04 (0.04)

0.41 (0.41) 0.21 (0.21)

3.21 (2.94)

0.06 (0.06) 0.08 (0.08) 0.08 (0.08)

2.97 (2.71) 2.97 (2.71)

5.91 (5.40)

0.04 (0.04) 5.74 (5.23) 0.09 (0.09) 5.65 (5.15) 0.38 (0.38)

4.86 (4.28) 0.06 (0.06)

0.00 (0.09) 4.59 (3.92) 4.59 (3.92) 0.16 (0.16) 4.43 (3.76) 0.04 (0.04)

0.41 (0.40)

0.10 (0.10)

0.00 (0.00)

0.02 (0.02)

0.12 (0.12)

0.00 (0.09)

0.21 (0.21)

0.21 (0.21)

5.94 (5.37) 0.20 (0.20) 0.12 (0.12) 0.17 (0.16) 0.17 (0.16)

5.46 (4.89) 5.46 (4.89) 0.04 (0.04)

10.87 (9.76) 0.25 (0.25) 0.08 (0.08)

10.54 (9.43) 0.18 (0.18)

10.36 (9.25) 0.76 (0.75)

8.77 (7.50)

0.42 (0.42) 0.00 (0.19) 8.23 (6.77) 8.23 (6.77) 0.32 (0.32) 7.92 (6.46)

0.42 (0.42) 0.82 (0.81)

0.00 (0.00)

0.00 (0.19)

0.12 (0.12)

0.08 (0.08)

8.96 (8.29) 0.33 (0.33)

0.28 (0.27) 0.28 (0.27)

8.15 (7.49) 8.15 (7.50) 0.07 (0.07)

16.23 (14.94) 0.42 (0.41) 0.14 (0.14)

15.68 (14.39) 0.30 (0.30)

15.37 (14.09) 1.26 (1.26)

12.74 (11.26)

0.07 (0.07)

11.84 (10.14) 11.84 (10.15) 0.53 (0.53)

11.31 (9.62) 0.14 (0.14) 0.71 (0.70)

0.20 (0.20)

0.00 (0.00)

0.00 (0.22)

0.20 (0.20)

0.00 (0.22)

1.37 (1.35)

Numbers in parentheses are the least-squares solutions and numbers before them are obtained by solving Equations (1)-(30) in Table 11.

for the 2 and 3 g/L glucose in the feed, reveal that at the onset of acetate production, the specific slope (on a log scale) drops considerably for the C 0 2 evolution rate and the cell density.

At attempt was made to obtain actual fluxes (mmol/g cell h) by curve-fitting the experimental data to appro- priate exponential functions for the entire growth phase or segments of it. The resulting fluxes showed high sensitivity to the shape of the curve. This dependence implies that the actual flux values would be very sensitive to the curve- fitting procedure and thus to slight measurement errors. Therefore, instead of obtaining actual fluxes (mmol/g cell . h) as representative of the entire exponential phase or determining fluxes at different times during the growth, the total flows (mmol/L of culture), which provide an average picture of flux distribution in batch cultures, were determined. The equations listed in Table I1 are also used for the calculation of metabolic flows in batch cultures with the modifications that the dilution rate (0) is replaced by the amount of biomass produced during the period for which the balances were conducted.

The results for batch culture experiments are presented in Tables V and VI. To obtain reliable OUR values in the batch experiments, an air flow rate lower than continuous culture experiments was used. Thus, the least-squares solution for batch cultures makes use of all the 32 equations. It should

690 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 42, NO. 6, SEPTEMBER 5, 1993

Table IV. Analysis of continuous culture fluxes.

Parameter So = 3.0 g/L, so = 1.0 g/L, so = 1.0 g/L, so = 1.0 g/L,

D = 0.5 h-' D = 0.15 h-' D = 0.15 h- ' D = 0.3 h-'

Glycolysis/TCA (rlo/r23) 1.46 (1.46) 1.29 (1.38) 1.32 (1.44) 1.37 (1.47) TCA for biosynthesis (r24/r23) 0.05 (0.05) 0.03 (0.04) 0.04 (0.05) 0.04 (0.05) C as C0;/6rl 0.62 (0.62) 0.60 (0.66) 0.56 (0.62) 0.56 (0.60)

C as biomass*/6rl 0.35 (0.35) 0.29 (0.32) 0.32 (0.35) 0.35 (0.38) ATP yield coefficient (g cell/mol ATP) 4.58 (4.61) 3.54 (4.02) 3.91 (4.57) 4.48 (5.06)

C as acids*/6rl 0.03 (0.03) 0.00 (0.02) 0.00 (0.03) 0.00 (0.02)

See Table 111 for explanation of numbers in parentheses. * Measured values of CER, biomass, and acids formation rates are used.

be pointed out that the batch experiments with 3 g/L glucose were also conducted with the high air flow rate of 2 L/min (same as the continuous culture air flow rate) and flux values were similar to those reported in Tables V and VI.

Calculation of Adenosine Triphosphate Yield Coefficient

Having the flux values, the adenosine triphosphate (ATP) generation rate can also be determined based on the reported value of P/2e- [the number of adenosine diphosphates (ADPs) phosphorylated per electron pair transferred to oxygen]. The P/2e- value for B. subtilis is reported as 1.3.' The ATP generation rate is calculated as the sum of all the fluxes which are coupled to ATP formation rate (i.e., ATP generation rate = rATp = -(;g) + r10 + r15 + r21 + r25 + r29 X 1.3 + r30 X 1.3 X 3). In these calculations, it is assumed that 1 FADH = NADH and 1 GTP = 1 ATP. Since normally the ATP consumed for transport of glucose is considered as part of biosynthetic requirements,22 the term r l has not been included in the equation for ATP generation. Moreover, because the isocitrate dehydrogenase reaction produces NADPH for use in biosynthetic reactions, its contribution to ATP production is neglected. The ATP

L'

1 '

o ! I I I I I 0 1 0 20 30 40 50

Time (h)

Figure 2. Optical density and COz evolution rate for cells growing in continuous culture at dilution rate of 0.15 h-' and the feed glucose concentration of 3 g/L.

yield coefficient was calculated by dividing the dilution rate by the molar ATP generation rate (YATP = 1000 X

D / TA TP 1.

Discussion of Flux Data

Overall, the results of Tables 111-VI show that the evolved C02 for batch cultures is significantly lower than the continuous cultures, but the acid formation is substantially higher. Table 111 shows the fluxes for continuous culture experiments. Table IV provides a snapshot of some key trends. The results of the batch experiments are presented in Tables V and VI. Although the inspection of the data in Tables 111-VI allows for comparison of the key fluxes in batch and continuous cultures, we have also included one biochemistry diagram (Fig. 6), labeled with batch and continuous fluxes, only to provide a quick reference. The difference in some of the biosynthetic fluxes between the batch and continuous culture flows reflects the usage of the least-squares solution.

First note that for both batch and continuous culture experiments, the exact solution of the first 30 equations and the least-squares solution, which also make use of the last two equations for oxygen uptake and C02 evolution rates, are only slightly different. (The measured values of oxygen uptake and C02 evolution rates are essentially identical to those which can be obtained from the least- squares solution). In the case of 3 g/L glucose in the feed, however, the exact solution leads to a negative value for r25, the flux of a-ketoglutarate to oxaloacetate, while in the least-squares solution this value is positive. Since the least-squares solution is more reliable, it would be used in our discussion of flux values. Moreover, the positive value for r25 is consistent with the highly irreversible nature of the a-ketoglutarate dehydrogenase catalyzed reaction. Some comments regarding the nature of this negative number may be instructive. The amount of glucose carbon which is used to provide the biosynthetic precursors derived from a-ketoglutarate (124) is small. Because the flux r23 is also a small value for the batch experiment with 3 g/L glucose, the relative value of r24 becomes very sensitive to the measurement errors. For example, a measurement error of +3% for acetate and other organics could affect the value of r23 to the extent that its flux will be sufficient to provide for the a -ketoglutarate derived precursors and hence avoid

GOEL ET AL.: METABOLIC FLUXES IN BACILLUS CULTURES 69 1

10 1 .ooo - -CER ’ +Glucose used

y! . *Cell Density

m

4 h W

a

n

> W

B . &Acetate .- i3 t al

- - al 0 .- W

7 al Y 0 Y

0 0 3 al a

3 8 G

b E E

0 1

.- n r 0

0.1 00 0.000 0.500 1 .ooo 1.500 2.000

W

8

Figure 3. Growth profile for cells grown in a batch culture with the feed glucose concentration of 1 g/L. Time 0 corresponds to 2.5 h after inoculating the batch reactor (no data were taken during the first 2.5 h). The metabolic flow analysis was conducted between the period of 0.15 and 2 h of the figure.

the operation of the TCA cycle in the reverse direction (i.e., negative value of r25 obtained by the exact solution).

The TCA cycle flow for continuous cultures, r 2 3 , in- creases as the growth rate is increased (see Table 111). The TCA cycle flux of continuous cultures is substantially larger than the batch cultures as reflected by the ratio of the glycolysis flux to that of the TCA cycle ( r l o / r 2 3 ) of about 1.4 for the continuous cultures (Table IV) and about 17 for batch cultures with 2 and 3 g glucose/L (Table VI). The substantially higher TCA cycle flux of continuous cultures

is also apparent in the value of 123 , being 20-25 times higher than the key biosynthetic flux derived from the TCA cycle metabolites (i.e., a-ketoglutarate to amino acids, r 2 4 ;

see Table IV) in contrast to 1.3-fold for batch-growing cells with 2 and 3 g/L glucose in the medium.

Fairly proportional increase in TCA flux with increase in dilution rate in continuous cultures and substantially lower TCA cycle flux for the batch cultures may indicate that syn- thesis of TCA cycle enzymes increases in proportion to the rate of growth, and repression occurs at very high growth

1 .ooo 2 U

8 a c 8 m al 0 - -

0.100 ;;

9 B

2 v

B al 0 Y

*

0.01 0

Figure 4. reactor was inoculated. The metabolic flow analysis was conducted between the period of 3.3 and 7.2 h.

Growth profile for cells grown in a batch culture with feed glucose concentration of 2 g/L. Time 0 is the time at which the batch

692 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 42, NO. 6, SEPTEMBER 5, 1993

10.000 1 .ooo

D

3 : 1.000

0.1 00

10.000

1 .ooo cf W 0

0.1 00

I 1 I 1 1 I I I I I 0 1 2 3 4 5 6 7 8 9

Time(h)

(a)

0.100 6 \ d

W

0.010

1.000

.- a t!!

0.100

0.01 0 0 1 2 3 4 5 6 7 a 9

Time(h)

(b) Figure 5. Growth profile for cells grown in a batch culture with feed glucose concentration of 3 g/L. Time 0 corresponds to 3.5 h after inoculating the batch reactor (no data were taken during the first 3.5 h, the first value is for time 0.15 h in Figure 3 at which the OD was 0.04). The metabolic flow analysis was conducted between the period of 1.5 and 6.2 h of the figure.

rates, such as exponentially growing cells in batch cultures (the maximum growth rate of B. subtilis in batch culture with 1 g/L glucose in feed is about 0.6 h-'). Experiments which will entail making enzymatic activity measurements and analysis of intracellular metabolites would allow for

a comprehensive assessment of these observations to be made.

Regarding the trend for batch data, the ratio of the glycolysis flux to that of the TCA cycle ( T ~ o / Q ~ ) increases as the glucose concentration of the medium is increased

693 GOEL ET AL.: METABOLIC FLUXES IN BACILLUS CULTURES

Table V. Normalized fluxes for batch cultures.

Flux so = 1.0 g/L so = 2.0 g/L So = 3.0 g/L

100 (100) 5 (6) 3 (4)

4 (5 )

53 (35)

1 (2)

6 (6) 2 (2)

4 (4)

40 (53)

36 (47)

77 (66)

164 (145)

157 (138)

152 (134) 17 (18)

116 (104) 0 (1)

3 (4) 10 (1 1) 57 (62) 46 (27) 46 (28)

38 (23) 7 (7)

2 (0) 10 (8) 19 (11)

100 (100) 5 (5 ) 3 (3)

4 (4) 61 (68)

57 (63) 31 (26) 69 (68)

155 (156) 1(1)

6 (6) 2 (2)

5 ( 5 ) 147 (148)

142 (144) 19 (20) 20 (23) 82 (81) 3 (3)

11 (11)

15 (9)

8 (8) 7 (2) 2 (2)

11 (11) 21 (20)

54 (58)

15 (10)

100 (100) 4 ( 5 ) 2 (3)

49 (45) 3 (4)

44 (44)

1 0 )

5 (4) 2 (1)

3 (3)

46 (43)

7.5 (72)

165 (156)

159 (150)

155 (147) 14 (14)

77 (80) 49 (45)

2 (3) 8 (8 )

4 (8) 4 (8) 5 (6)

-2 (5 ) 2 (0) 8 (6)

16 (9)

63 (60)

See Table 111 for explanation of numbers in parentheses.

(Table VI). The results of Table VI clearly highlight much reduced TCA cycle activities in the batch cultures of 2 and 3 g glucose/L. These cells have become glycolytic and the TCA cycle may no longer operate as a cycle since the flux of a-ketoglutarate to oxaloacetate has essentially diminished. The batch grown cells with 1 g/L glucose exhibit a behavior somewhat in between that of continuous cultures and the batch cultures with 2 and 3 g/L glucose in the medium. As a consequence of high TCA flux in continuous cultures, the NADPH requirement for biosynthesis is provided by the isocitrate catalyzed reaction of the TCA cycle ( ~ 3 ) which is coupled to NADPH formation. In batch cultures, however, the NADPH requirement is primarily satisfied by the HMP pathway (flux rq). The results of our experiments with the continuous and batch cultures of both E. coli K-12 and E. coli B

Table VI. Flux analysis for batch cultures.

strains have also revealed the same trend as with B. subtilis regarding the utilization of the HMP pathway.

The ATP yield coefficient, presented in Tables IV and VI, is higher in batch culture due to the lower flux through the TCA cycle (which leads to lower ATP production). The low ATP yield coefficients in continuous cultures of B. subtilis are comparable with the values reported for continuous cultures of E. coli under aerobic condition^.'^ The batch values of about 10 for the ATP yield coefficient are also in the range of the ATP yields reported in the literature.22

The significant mismatching activities of the glycolysis and TCA cycle reactions, as observed by about 12-fold variation in this ratio, may imply that performing anabolic and catabolic functions under a wide range of growth conditions requires regulatory compromises. In particular, the batch flux through the TCA cycle is essentially large enough to provide for biosynthetic precursors derived from a-ketoglutarate leading to significant acid formation. In continuous cultures this flux is, however, much in excess of biosynthetic and energetic demands resulting in significant excess C02 formation. It appears that there might exist a “regulation cost” as part of maintenance energy (such as membrane energization, macromolecular turnover, etc.), which has been cited as a possible cause of the several-fold difference between the theoretical ATP yield coefficient and the observed values.

If the acid formation in batch culture were to be minimized, the biosynthetic fluxes must increase rather substantially. Thus, identifying factor(s) that limit the biosynthetic flux will be necessary. Based on the flux data which we have presented, a possible bottleneck in biosynthesis in batch cultures could be the formation of amino acids derived from a-ketoglutarate as the flux to this metabolite is significantly reduced. For continuous cultures, the TCA cycle flux, rather than the HMP, provides for most of the NADPH used in biosynthesis. Hence, conditions which increase the HMP flux might slow down the TCA cycle flux. We are currently examining the regulations at the glucose-6-P-dehydrogenase and a-ketoglutarate dehydro- genase branch points of E. coli and B. subtilis by subjecting the wild-type and mutants of the TCA cycle enzymes to various feeding strategies (i.e., glucose supplemented with various TCA cycle precursors) for obtaining regulatory insights and developing optimal growth conditions. Finally, the regulatory insights which will be obtained from analysis of enzyme activity, fluxes, and intracellular concentrations

Parameter so = 1.0 g/L so = 2.0 g/L So = 3.0 g/L

Glycolysis/TCA (r,o/r23) 3.59 (5.16) 10.49 (16.35) 42.22 (17.80) TCA for biosynthesis (r24/r23) 0.16 (0.23) 0.54 (0.85) 1.55 (0.57) C as COza/6rl 0.32 (0.33) 0.22 (0.23) 0.28 (0.22) C as acids/6rl 0.19 (0.21) 0.25 (0.31) 0.45 (0.43) C as biomass/6rl 0.44 (0.46) 0.47 (0.50) 0.36 (0.35) ATP yield coefficient 8.36 (10.39) 12.19 (13.12) 9.31 (8.97)

See Table 111 for explanation of numbers in parentheses. a Measured values of CER, biomass, and acids formation rates are used.

694 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 42, NO. 6, SEPTEMBER 5, 1993

G1ur 1 OO[ 1001 Ribose for Nucleic Acid

Cell

AA

Nucleic Acid

4151 Wall - AA

TP - TriGlycerides I 1111 . . I 182[156]

4141 1111 AA - ffi - Nucleic Acid

I 175[150]

Ic AA

168[147] 7 Organics

Pyruvate -7 f A A

15191 A CoA 8181 +Membrane f I &Acetate

125181

Figure 6. and D = 0.15 h- ' for continuous culture, and SO = 3.0 g/L for the batch culture. The batch numbers are in square brackets.

Comparison of batch and continuous fluxes normalized with respect to r l . The data are from the experiments with SO = 3.0 g/L

will also be used for assessing the potential applications of metabolic engineering strategies2 for constructing cells which will attain high growth rate and high cellular yields with minimum acid or excess C02 formation.

4. Glucose-6-P + 2NADP = ribulose-5-P + C02 + 2NADPH

5. Ribulose-5-P = ribose for nucleic acid 6. Ribulose-5-P = 3 fructose-6-P + 5 TP 2 1

7. Glucose-6-P = fructose-6-P 8. Fructose-6-P + ATP = 2 TP + ADP 9. TP = triglycerides

10. TP + NAD + ADP = PG + NADH + ATP

We are thankful to one of the reviewers for his/her instructive comments. This work was supported, in part, by National Science Foundation grants (BCS-8907371 and BCS-9207614).

APPENDIX 11. PG = AA (from PG pool) 12. PG = NA (from PG pool) 13. PG = PEP 14. PEP = AA (from PEP pool) Reactions considered for the flux estimation are as follows:

1. Glucose + ATP = glucose-6-P + ADP 2. Glucose-6-P = cell wall 3. Glucose-6-P = AA (from glucose 6-P pool)

15. PEP = pyruvate + ATP 16. Pyruvate = AA (from pyruvate pool) 17. Pyruvate = organics (other than acetate)

GOEL ET AL.: METABOLIC FLUXES IN BAClLLUS CULTURES 695

18. Pyruvate + NAD = ACoA + C02 + NADH 19. ACoA = AA (from ACoA pool) 20. ACoA = membrane 21. ACoA + ADP = acetate + ATP 22. ACoA + O M = isocitrate 23. Isocitrate + NADP = a-KetoG + C02 + NADPH 24. a-KetoG = AA (from a-KetoG pool) 25. a-KetoG + FAD + GDP + 2NAD = OAA + C02 +

FADH + GTP + 2NADH 26. OAA = NA (from OAA pool) 27. OAA = AA (from OAA pool) 28. Pyruvate + C02 = OAA 29. NADH + 1.3 ADP + iy = 1.3 ATP + NAD 30. FADH + ;(1.3 ADP) + 502 = ;(1.3 ATP) + FAD

The species considered are as follows:

1. Glucose 2. Glucose 6-P 3. Ribulose 5-P 4. NA (from ribose) 5. Fructose 6-P 6. Cell wall 7. AA (from Glucose pool) 8. TP 9. Triglycerides

10. PG 11. AA (from PG pool) 12. NA (from PG pool) 13. PEP 14. AA (from PEP) 15. Pyruvate 16. AA (from pyruvate) 17. Organics (other than acetate) 18. ACoA 19. AA (from ACoA pool) 20. Membrane 21. Acetate 22. Isocitrate 23. a-KetoG 24. AA (from a-KetoG pool) 25. OAA 26. Nucleic acid (from OAA pool) 27. AA (from OAA pool) 28. NADPH 29. NADH 30. FADH 31. C02 32. 0 2

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