Lysine production from methanol at 50°C using Bacillus methanolicus: Modeling volume control,...

Lysine Production from Methanol at 50°C Using Bacillus methanolicus: Modeling Volume Control, Lysine Concentration, and Productivity Using a Three-Phase Continuous Simulation

Grace H. Lee,'** Won Hur,',t Craig E. Bremmon,' and Michael C. Flickinger',z$ ' Institute for Advanced Studies in Biological Process Technology, and Department of Biochemistry, University of Minnesota, St. Paul, Minnesota

55 108-6 106

Received May 24, 1995,LAccepted October 4, 1995

A simulation was developed based on experimental data obtained in a 14-L reactor t o predict the growth and L- lysine accumulation kinetics, and change in volume of a large-scale (250-m3) Bacillus methanolicus methanol- based process. Homoserine auxotrophs of B. methanolicus MGA3 are unique methylotrophs because of the ability to secrete lysine during aerobic growth and threonine starvation at 50°C. Dissolved methanol (100 mM), pH, dissolved oxygen tension (0.063 atm), and threonine levels were controlled to obtain threonine-limited conditions and high-cell density (25 g dry cell weight/L) in a 14-L reactor. As a fed-batch process, the additions of neat methanol (fed on demand), threonine, and other nutrients cause the volume of the fermentation to increase and the final lysine concentration to decrease. In addition, water produced as a result of methanol metabolism contributes to the increase in the volume of the reactor. Athree-phase approach was used to predict the rate of change of culture volume based on carbon dioxide production and methanol consumption. This model was used for the evaluation of volume control strategies to optimize lysine productivity. A constant volume reactor process with variable feeding and continuous removal of broth and cells (VFcstr) resulted in higher lysine productivity than a fed-batch process without volume control. This model predicts the variation in productivity of lysine with changes in growth and in specific lysine productivity. Simple modifications of the model allows one to investigate other high-lysine- secreting strains with different growth and lysine productivity characteristics. Strain NOA2#13A5-2 which secretes lysine and other end-products were modeled using both growth and non-growth-associated lysine productivity. A modified version of this model was used to simulate the change in culture volume of another L-lysine producing mutant (NOA2#13A52-8A66) with reduced secretion of end-products. The modified simulation indicated that growth-associated production dominates in strain NOA2#13A52-8A66. 0 1996 John Wiley & Sons, Inc. Key words: lysine thermotolerant methylotroph Bacil- /us methanolicus - kinetic model, three-phase

* Current address: Lifecore Biomedical, Chaska, Minnesota 55318. t Current address: Department of Fermentation Engineering, Kan-

gwon National University, Hyoja-dong, Chuncheon, Kangwon-do 200-701 Korea.

To whom all correspondence should be addressed.

INTRODUCTION

A new route for the large-scale production of L-lysine is from methanol using auxotrophic mutants of thermotolerant Bacillus methanolicus. 5,31 The advantages of this approach are a readily available, stable, inexpensive substrate and existing large-scale fermentation technology for methylotrophic organisms.'0J' This high temperature process has the advantage of lower cooling costs.2 For a 50°C fermentation, the cooling requirements may be reduced by 18% to 40% of the cooling requirements of a 30°C pro~ess . '~ Lysine is currently being produced industrially at 30°C from carbohydrates by auxotrophic and regulatory mutants of Corynebacteriurn and Brevi- b a c t e r i ~ r n ~ ~ ' ~ . ~ ~ ~ ~ ~ with mass yields of more than 43% and 50%, re~pec t ive ly .~~ Demand for lysine as a dietary supplement in poultry and swine production increased at an annual growth rate of 14.6% during the 1980s.12 In 1989, the worldwide demand for lysine was 115,200 metric tons, and continued growth is expected.'* As demand increases, processes which utilize alternative substrates, such as this methanol process, may become important, and a model of this fermentation would be very useful in optimizing lysine production.

Prior to the report of Schendel et al.,31 there were no reports of thermotolerant, methylotrophic Bacillus systems for the overproduction of L-amino acids.Ig Ba- cillus methanolicus strains are type I methylotrophs, and lysine secreting mutants derived from B. methanolicus MGA3 (ATCC 53907) do not sporulate when nutrient limited at high temperatures (50"C).31 Schendel et al.31 generated homoserine auxotrophic mutant strains of B. rnethanolicus MGA3:' which overproduce lysine during threonine-limited growth. The feedback control of the lysine biosynthetic pathway in Bacillus differs from the regulation found in Corynebacterium, Brevibacter- ium, and Escherichia ~ o l i . ~ ~ The genes for two key en- zymes in the lysine biosynthetic pathway (aspartokinase I1 and diaminopimelate decarboxylase) have recently

Biotechnology and Bioengineering, Vol. 49, Pp. 639-653 (1996) 0 1996 John Wiley & Sons, Inc. CCC 0006-3592/96/060639-15

been cloned from B. m e t h a n ~ l i c u s ~ ~ ~ ~ ~ and feedback- resistant mutants of aspartokinase I1 have been generated.33 Protocols for genetic manipulation of this B. methanolicus are currently being developed in this laboratory to apply metabolic engineering techniques to optimize lysine production.

A kinetic model would be useful to optimize the process of L-lysine production by mutants of B. methanolicus and to predict the design of a large-scale process. However, there are no models of amino acid production by bacilli from a liquid substrate such as methanol. A variety of methylotrophic fermentations have been stud- ied using kinetic modeling appro ache^.'.^^.^^ In general, previous fermentation models of fed-batch processes have been based on carbohydrate substrates and have not been applied to amino acid p r o d ~ c t i o n . ~ ~ ~ ~ ~ ~ ~ ~ ~ ” ~ ~ ~ There are no kinetic models for the optimization of commodity products using Bacillus. Structured models have been developed for some Bacillus specie^,'^.^^.^^ but these are for growth on glucose during protein production or sporulation. Previous models of Bacillus processes do not describe the production of amino acids or the production or water which results from the complete oxidation of methanol (Fig. 1).

Continuous cultures with variable nutrient feed rates based upon methanol demand are used in this investiga- tion to optimize the overproduction of L-lysine by B. methanolicus mutants. The optimization of this Bacillus process differs from previous approaches for the optimization of single cell protein (SCP) from methanol because L-lysine overproduction also requires threonine and methionine feeding. Previous models do not take into account this additional feed and do not include the ability to predict the overproduction of secreted low- molecular-weight products such as amino acids.

Flux analyses using stoichiometric approaches have been done for growth of Bacillus subtilis” and for lysine production by Cornyebacterium g E ~ t a m i c u m . ~ ~ - ~ ~ Both analyses were completed for glucose-based processes. Application of this type of analysis depends on the knowledge of the complete carbon pathway through the organism to produce biomass and other products. This

MeOH

Methionine and Threonine

c - Biomass

Other End-products: Glutamate,

Bacillus rnetlioiioliciis + homoserine auxotroph

approach cannot be used to predict the rate of change in the volume of the process. While a stoichiometric approach would be useful in analyzing regulation of carbon flow in B. methanolicus to direct metabolic engineering, the purpose of this process model is to under- stand how changes in process volume, lysine, and biomass production affect final lysine concentration and productivity.

A model of lysine overproduction from B. methanolicus would be useful to predict strategies for the optimization of lysine accumulation and maximum volumetric productivity in a fed-batch or continuous process. A process simulation would be helpful to predict and com- pare the results of various volume control strategies on the final concentration of lysine and to predict process productivity as a function of cell growth rate and final cell density. Volume control of this process is not trivial due to the liquid substrate which is fed on demand, the additional amino acid feedstream needed to satisfy the auxotrophy, pH control, and the water produced by the complete oxidation of methanol to carbon dioxide (Fig. 1). The maximum production of carbon dioxide and water [Eq. (l)] from B. methanolicus occurs when methanol is not assimilated into biomass, lysine, or other byproducts:

(1) 3 2

CH30H i- - 0 2 -+ COz i- 2 H20

The water that is generated, and the continuous addition of a liquid substrate along with a threonine and methionine solution increases the volume of the culture. To minimize the change in culture volume, gaseous ammonia is used instead of a liquid base to control the pH. To avoid further additions to the culture volume, exhaust gas condensate can be removed from the system instead of being returned to the reactor broth.

We report the development of a useful model that can be applied to choose the most beneficial volume control strategy for the optimization of lysine accumulation by mutants of B. methanolicus MGA3 based on data obtained in a 14-L system. The modeling of this system is complicated by the production of multiple products, including glutamate, diaminopimelate, alanine, and water (Fig. l ) . I 3 3 l 4 To accurately describe the growth kinetics and metabolic activity of this Bacillus process, simulations used a three-phase approach to model the three different metabolic phases observed (Fig. 2). This three phase-model is used to evaluate the effect of metabolic changes and different volume control strategies on lysine productivity. Different approaches to volume control are considered: a fed-batch reactor without a condensor; a fed-batch reactor with a perfect condensor; and a variable feed continuous reactor with a constant volume achieved by removing cells and broth. Changes in growth and lysine production kinetics are also investigated.

Alanine, etc.

640 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 49, NO. 6, MARCH 20, 1996

25

20

15

10

5

0

150

100

50

0

Phase 111 Decreasing Metabolic ~ Activity

/ve

I ,

*

0 10 20 30 40 50 60 70 Time (hr)

Figure 2. Typical three-phase fermentation data. Phase I: exponential growth; Phase 11: threonine-limited phase; Phase 111: phase of decreasing metabolic activity. (.) dry cell weight; (I) simulated dry cell weight; (-) oxygen uptake rate; (---) carbon dioxide evolution rate.

MATERIALS AND METHODS

Medium

The minimal salts seed medium used is described in Table I. For 14-L fermentations, 50 mL of seed medium (Table I ) was inoculated with 3 mL of the stock culture in a 250-mL baffled flask. After overnight cultivation in a shaker incubator at 50°C and 300 rpm, the 50-mL culture was added to 500 mL of seed medium and evenly distributed into two 1-L baffled flasks. The inoculated seed medium was then allowed to grow at 50°C and 300 rpm for an additional 12 h before inoculating the fermentor. Table I summarizes the media used for both B. methmolicus strains NOA2#13A5-2 (mutant A) and NOA2#13A52-8A66 (mutant B).

Microorganisms

Stock cultures of homoserine auxotrophic mutants of B. methanolizus MGA3 (ATCC 53907) were developed as previousl!, de~cribed.~ ' During the development of strain NOA2#13A5-2 (obtained from R. S. Hanson), diepoxyoctane and ultraviolet irradiation were also used as mutagens. Isolates were selected by screening mutagenized cells surviving for 6 h in seed medium for mutant A (Table Ib) contained 0.5 g/L of yeast extract instead of individual amino acids. Also present in this outgrowth

Table Ia. Fermentation media.

Chemical Per L deionized

water

Minimal salts solution for seed medium

K2HP04 NaH2P04 . H 2 0 (NH4)zS04

Concentrated vitamin solution

Biotin Vitamin Biz

Concentrated metals solution FeC12 .4H2O MnCI2 . 4 H 2 0 CaCI2 . 2H20 ZnCI2

CoCl2 . 6H20 Na2Mo04 . 2H20 H$O3

CUC12.2H20

Fermentation medium (NH4)2 ' so4 K2HP04 '3H20 KH2P04 NaH,P04. H 2 0 Na2HP04. H 2 0 Threonine Methionine Leucine Biotin Conc. vitamin s o h Conc. metals soh .

3.8 g" 4.9 gb 2.8 g" 1.9 gb 3.6 g" 3.6 gh

20 mg 1 mg

3.967 g 9.896 g 7.350 g 136.3 mg 27.28 mg 40.44 mg 48.40 mg 30.30 mg

2.45 g" 2.65 g"

0.77 g" 0 g"

0 g" 0.21 g" 0.21 g"

0 g" 14.4 mg"

1 mLa 1 mLa

2.114 gh 4.094 gh 0.179 gh 1.527 gh 0.883 gh 0.119 gh 0.075 gh 0.050 gh

1 mLb 1 mLh

90 Mh

Table Ib. Fermentation media: seed medium

Chemical Per L medium

Minimal salts medium Conc. vitamin soh. Conc. metals soh. 1 M MgS04 Threonine Methionine Leucine Neat methanol

1000 mL" 1 mL" 1 mLa 1 mLa

1 mmol" 0.5 mmol"

0 mg" 10 mL"

"Mutant A (NOA2 13A5-2). hMutant B (NOA2 13A52-8A66).

broth were 0.2 g/L aminoethyl-cysteine (AEC), 0.04 g/L 5-hydroxy-~~-lysine . HC1, 0.01 g/L N-c-methyl-L-lysine * HC1 and 40 g/L L-lysine. Stock cultures of this strain were stored at -20°C in 5% v/v methanol.

Strain NOA2#13A52-8A66 (obtained from R. S. Hanson) was isolated after further exposure of NOA2#13A5-2 to N-methyl-N'-nitro-N-nitrosoguan-

LEE ET AL.: MODEL OF LYSINE FROM METHANOL USING A BAClLLUS SP. 64 1

dine and mitomycin C. Isolates were selected by screening mutagenized cells surviving for 6 h in seed medium for mutant A (Table Ib) which contained 0.5 g/L of yeast extract instead of individual amino acids, and then overnight growth in this medium with 60 g/L lysine and 5 g/L alanine. AEC-resistant strains were screened on agar plates with 10 glL theonine, and 0.5 g/L diamino- butyrate in the presence of a filter disk soaked in 100 mglL AEC. The resulting mutant no longer has the phenotype of spontaneous lysing, but is a leaky leucine auxotroph. Stock cultures of this strain were stored at -80°C in 10% v/v glycerol.

Fermentation

B. methanolicus mutants were cultivated at 50°C in a modified 14-L fermentor (Chemap, S. Plainfield, NJ) with an 11-L working volume, an air sparge rate of 5.5 L/min (0.5 vol/vol 1 min), and an agitation rate of 374 cm/s (900 rpm) (Fig. 3). The pH was maintained at 6.7 by automatic addition of gaseous ammonia (Air Products, Inc., Allentown, PA), into the air sparge line. Vessel pressure was maintained at 4.0 psig. The fermentation medium is described in Table Ia. The concentrated vitamin solution and concentrated trace metals solution (Table Ia) were added after the reactor cooled, along with 0.25 g MgS04 7H20 per liter of medium. A 1-L reservoir contained the amino acid feed. The methanol feed reservoir also contained 33 mL of concentrated trace metals (Table Ia) for every 2 L of neat methanol.

Dissolved oxygen was monitored using a galvanic probe with a 2-mil Teflon-laminated membrane (Chem Fab, West Palm Beach, FL) and was maintained at 30% of air saturation (0.063 atm) by oxygen-enriched aera- tion. Feeding of oxygen was monitored and controlled by a 0-10 SLPM mass flow controller (Sierra Instruments Inc., Carmel Valley, CA) interfaced with a proportional- integral-derivative (PID) controller (LFE Corp., Clin- ton, MA).

Optical density was monitored off-line by the absorb- ance (ABS) at 500 nm (ABS 1.00 = 0.31 g dry cell weightll). Foaming was controlled with a liquid level controller (Cole-Parmer, Chicago, IL) by the automatic addition of an aqueous 10% emulsion of SAG-471 (Union Carbide).

Inlet and exhaust gases (nitrogen, oxygen, argon, water, carbon dioxide, methanol, and ammonia) were monitored by a Questor quadrupole mass spectrometer (Ex- trel Corp., Pittsburgh, PA). The gases were transported to the Questor, first through a 0.5-mm stainless multi- tube Mott filter (Series 3600, Mott Metallurgical Corp., Farmington, CT) then through 1/8-in. and 1/16-in. outer diameter (0.d.) stainless-steel tubing, heat-traced with 110°C self-regulating heating tape (Type 3515, Decoron, Inc., Aurora, OH), and insulated with a 1.5-in. fiberglass insulation (Fig. 4). Transport time for the exhaust gases to flow to the Questor was approximately 1 min. The inlet and exhaust gases were alternately sampled for 2.5 min (sample rate 0.166 s-') after a 30-s delay to purge the ionization chamber.

Figure 3. sion line.

Schematic of 14-L fermentation system: (-) gas or liquid line; (----) electrical transmis-


Figure 4. Simplified diagram of condensate removal system for the modified 14-L fermentation system. (A) Dissolved methanol sensor. (B) Dissolved methanol sensor exhaust (insulated) to hydrocarbon sensor. (C) Inlet air for dissolved methanol sensor. (D) Head-space exhaust line to ihe mass spectrometer. (E) Heat tape for temperature control on the head-space exhaust line to the mass spectrometer. (F) Insulation. c G) Glass funnel for collection of exhaust gas condensate. (H) Line to pump for continuous removal of condensate from the exhaust condensor. (I) Exhaust filter (scintered stainless-steel). (J) Exhaust gas condensor. (K) Head-space exhaust. (L) Liquid level controlled by scnsor (not shown).

The data were collected with an IBM-PCIAT running a program written in the Asyst programming language for data acquisition and control (Keithly Asyst, Taun- ton, MA). Data were averaged every 5 min, stored, and used in the calculation of oxygen uptake and carbon dioxide evolution rates.

Methanol levels in the reactor were continuously monitored by using an in situ methanol sensor consisting of 1-m long silicone tubing (0.062-inch inner diameter [i.d.] X 0.095-in. OD) probe3' connected to a TGS 822 hydrocarbon sensor (Figaro USA, Inc., Wilemette, IL) (Fig. 4). The flow rate of air through the probe was 220 mL/min. The tubing connected to the hydrocarbon sensor was heat-traced with 50°C self-regulating heating tape (Type 2505, Decoron) and insulated. A peristaltic pump for methanol addition (501U Watson-Marlow, Wilmington, MA) was controlled by a PID control loop in a pMAC-5000 computer monitor and control system (Analog Devices, Norwood, MA). The PID control loop was used with the hydrocarbon sensor to maintain a dissolved methanol concentration of 100 mM. A plat- form scale (LC133, Omega Engineering, Inc., Stamford, CT) was used to determine the methanol feed rate.

The amino acid nutrient mixture was fed using a peristaltic pump (503U Watson-Marlow), with the control

signal connected in parallel with the methanol feed pump, thus controlled by the same PID controller. This resulted in an amino feeding rate which was proportional to the methanol feed rate. Amino acid feeding was changed by adjusting the amino acid concentration in the feed reservoir. Amino acid consumption was monitored with an electronic balance. Fermentations were carried out under conditions of different threonine and methionine concentrations in the feed reservoir; both at a concentration of 11.7 g/L, 23.4 g/L, or 46.8 g/L for strain NOA2#13A5-2. Strain NOA2#13A52-8A66 was fed threonine, methionine, and leucine at a mass ratio of 4 : 1 : 2 and a concentration of 23.7 g/L threonine.

During the fermentation, methanol, amino acids, and antifoam were added to the reactor. To maintain a constant culture volume of 11 L, cells and broth were removed at an average rate of 55.2 mL/h by a 6-rpm fixed- speed peristaltic pump (Cole-Parmer) connected to a dip tube (Fig. 3). An additional fixed-speed pump was attached to a 1-in.-diameter glass funnel located directly under the point of return of the exhaust condensate to continuously remove 15 mL/h of condensate from the exhaust gas condensor (Fig. 4). In addition to the above, the reactor volume was also affected by the periodic removal of five 50-mL samples per day for analysis of cell density and amino acid concentrations.

Amino Acid Analysis

Amino acids in the broth were assayed by high-perfor- mance liquid chromatography using a precolumn deri- vatization fluorodetection method, as modified from Jarrett et al.15 Solvent A was 2.5 mM sodium acetate (pH 6.0) and 5% acetonitrile in deionized water. Solvent B was 100% acetonitrile. The derivatizing solution was made by mixing 2 pL 6-mercaptoethanol with each mil- liliter of o-phthaldaldehyde reagent (incomplete solution [l mg/mL], Sigma, St. Louis, MO). Sample mixing and loading of multiple samples onto a C8 reverse-phase column (Alltech Econosphere Cg 5p, 150 mm, Alltech Associates, Inc., Deerfield, IL) were done using an automated injection system (Gilson Model 231, Gilson Medi- cal Electronics, Middleton, WI). A linear gradient from 5% to 65% of solvent B was controlled by an automated gradient controller (Waters, Milford, MA). The deriva- tized amino acids were detected using a Gilson Model 121 filter fluorometer (Gilson), and the chromatograms were printed and integrated by a Waters 740 data mod- ule (Waters). Norleucine at a concentration of 5 mg/L was used as an internal standard.

MODEL DEVELOPMENT

A simulation of this process must account for all the liquid feedstreams and the generation of water by cell metabolism. Because the Bacillus methanolicus strains used for lysine overproduction are homoserine auxo-

LEE ET AL.: MODEL OF LYSINE FROM METHANOL USING A BAClLLUS SP. 643

trophs, the main carbon source, methanol, is not the only feedstream (Fig. 1). The volume of the reactor is increased by the feeding of methanol, and a solution of threonine and methionine, all of which are required for growth. However, feeding too much threonine will inhibit and repress aspartokinase activity and lysine production will be reduced.27 Control of threonine feeding is an important aspect in optimizing lysine production by B. methanolicus.

Water generated by the complete oxidation of methanol [Eq. ( l ) ] adds to the total volume of the system. If only 1 mol of carbon dioxide and 1 rnol of lysine are produced from methanol, the stoichiometric ratio is 1.36 mol of water produced per mole of methanol consumed [Eq. (211:

7 CH3OH + 3.25 0 2 + 2NH3 + CO2 + CtjH15N202 + 9.5 H20 (2)

The same mass balance can be made including biomass production, using an average elemental composition for a bacterial ell.^,^' When the final products are carbon dioxide, lysine, and biomass, assuming only 1 mol of each is made, the stoichiometric ratio of water generated per mol of methanol consumed is 1.39 [Eq. (3)]:

8 CH3OH + 3.71 0 2 + 2.22 NH3 + COZ + CdfisN202 + CH1.sNo2200.34 + 11.08 H20 (3)

The actual proportion of products from the fermentation cannot accurately be determined, due to the secretion of byproducts, such as glutamate, alanine, and dia- min~pimela te , '~ . '~ which vary with different strains. These additional byproducts were accounted for in this model by a nonspecific consumption term. In initial simulations, a stoichiometric ratio of water produced per mole of methanol oxidized between 1.35 and 2 was used. A value of 2 would be the maximum number of moles of water produced from 1 rnol of methanol [Eq. (l)]. The minimum would be zero and could only occur if all the water produced during the oxidation of methanol to carbon dioxide were consumed by the organism to produce cell mass or other metabolic products.

Because the 14-L reactor total volume could be filled with culture in the absence of volume control, a significant volume of broth with respect to an 11-L culture volume was removed for both sampling and volume control. However, as the scale and volume of the process increases, the effect of sample removal on volume control becomes insignificant. Because cell density and methanol demand was low during the initial hours of the fermentation, volume could be removed by the pump which removed exhaust condensate from the system (Fig. 4). This pump was on for the first 48 h of the fermentation. However, after the first 24 h of incubation, until the end of the reactor run, a second pump was needed to remove cells and broth to maintain an 11-L culture volume.

An average volumetric rate of broth removal was used in the model based on the average of five separate runs: three runs at a threonine and methionine concentration in the amino acid reservoir of 23.4 giL; one run at a concentration of 11.7 g/L; and one at a concentration of 46.8 g/L. The initial dry cell weight concentration used in the program was an average from the level of inoculum used in these five runs.

Based on experiments at three different amino acid feed concentrations (as described above), initial model parameters for B. methanolicus strain NOA2#13A5-2 were determined as a function of threonine feed levels for the carbon dioxide evolution rate (CER), dry cell weight concentration, specific lysine production, and methanol consumption (using a specific consumption term and a nonspecific consumption term). The CER and methanol consumption were modeled using a three-phase approach (Fig. 2): I-exponential growth; 11-threonine-limited growth; and 111-decreasing metabolic activity. During phase I, the methanol consumed by the organism is used to produce cells, lysine, carbon dioxide, and other byproducts. At the end of exponential growth, the threonine initially added to the fermentor was depleted, and the metabolism of B. methanolicus mutants changed to threonine-limited growth. This shift in metabolism was indicated by a reproducible change in the CER data which occurred after 9.2 h for each fermentation and for other fermentations done in this laboratory using the same initial conditions. During threonine-limited growth (phase II), methanol is consumed at a different rate to produce cells, lysine, carbon dioxide, and other byproducts.

When the organism enters phase 111, a period of decreasing metabolic activity, the dry cell weight is constant. In most Bacillus species, spores are usually formed under nutrient-limiting conditions. When mutants of B. methanolicus MGA3 are grown to high-cell density under threonine-limited conditions at high temperatures (50°C to 65"C), spores are not formed,31 but the cells enter a phase of decreasing metabolic activity. The transition from threonine-limited growth (phase 11) to the phase of decreasing metabolic activity (phase 111) occurred as the dry cell weight approached 19 g/L and the specific growth rate decreased to less than 0.06 h-' for B. methanolicus strain NOA2#13A5-2. This transition point was determined based on gas data (CER and OUR) obtained from multiple fermentations with this organism. During this third phase, biomass is not produced, but methanol is consumed to produce carbon dioxide, lysine, and other byproducts.

To describe multiple liquid feeds, three growth phases, and nonspecific consumption, a mathematical model based on a modified version of the fermentation model of Parulekar and Lim26 was used. Computer simulations consist of four differential equations describing culture volume, dry cell weight, lysine concentration, and substrate concentration in the reactor.


Culture Volume The rate of change in the culture volume, V, is described in Eq. (4). The volumetric flow rate into the reactor (Fin) is the sum of the methanol, amino acid and antifoam feed rates. The volumetric flowrate out of the reactor (FOut) represents the removal of broth from the reactor by evaporation, sample removal, condensate removal, and removal of cells and broth to maintain a constant volume. The rate of water produced by the complete oxidation of methanol to carbon dioxide ( d V,,,,,/dt) is taken into consideration when calculating the culture volume.

dvmetah -- dV - F,, - F,,, + ___ dt dt (4)

Using the volumetric data from each fermentation, the methanol feed rate and the antifoam feed rate were fit to arbitrary functions of time and threonine concentration in the amino acid feed reservoir. The amino acid feed rate was calculated to be 28% of the methanol feed rate due to the proportional amino acid feeding strategy. The water produced by the oxidation of methanol was calculated based on the three-phase simulation of the carbon dioxide evolution rate.

The carbon dioxide evolution rate (CER) was calculated from mass spectrometer data. In each of the three phases, the CER or the specific carbon dioxide production rate (carbon dioxide produced per gram of dry cell weight per unit time) was fit to the equations in Table 11. This calculated CER was then used to determine the amount of water produced by the metabolism of methanol.

Dry Cell Weight Although some methylotrophs are known to be subject to substrate inhibition.3 the level of methanol used for

this study was maintained at 100 mM, far below 400 mM which is the inhibitory level for growth of B. methanolicus. Therefore, dry cell weight accumulation was modeled as independent of substrate concentration. The dry cell weight data ( X ) , based on optical density measurements, was initially fit using the logistic equati0n,6.~~ where growth inhibition is proportional to the square of the dry cell weight concentration (x). Unfortunately, use of the logistic equation relates the final concentration to the final volume of the system. To decouple the dry cell weight concentration and the volume, the data were recalculated according to total dry cell weight (x) and fit to a modified logistic equation [Eqs. ( 5 ) and (6)]:

d x dt - - - a X ( l -

xoeai 1 - y xo(l - ear)

X =

The initial total dry cell weight is represented by xo. The parameter, a, was then fit to a function of threonine feed concentration [Eq. (7)]:

amax thr 8.12424 + thr a = (7)

The specific growth rate of B. methanolicus NOA2#13A5-2 was calculated using parameters of the above-modified logistic equation [Eqs. ( 5 ) and (6)]:

= d(x/V) V dt x

-_

dV dt

- - a(l - y x V ) - -/v

Table 11. Calculation of carbon dioxide evolution rate (CER) during each phase of the fermentation of methanol to lysine by B. methanolicus.

Phase I: CERlX = a, + bl * X -3.4801 + 3.5933 [thr]

t = 0 to t = 9.2 h -9.3794 + [thr]

0.33942 [thr] - 0.004723 [thr]'

Phase 11: CER/X = a2 + b2 * X 0.75937 + -0.019028 - t = 9.2 h to 0.31541 [thr] - 0.0074553 [thr] +

prier = 0.06 h-' 0.0042629 0.00014010 [thrI2

Phase 111: CER = a3 + b3 * t -24.9347 + 0.022384 - pnet = 0.06 h-' to end ( t = 70 h) 0.059678 [thrIZ 1.3337e-5 [thr]'

7.47017 [thr] - 0.0022764 [thr] +

Equations to describe the carbon dioxide production during each of the three growth phases of the fermentation. Carbon dioxide evolution rate (CER) = mmol of carbon dioxide produced per liter of culture volumelmin. Specific carbon dioxide production (mmollg dry cell weighthin) is equal to CER divided by dry cell weight concentration ( X ) . a, and b, are functions of the threonine feed level in the reactor based on the amino acid feed concentration. a, are in units of mmol/g dry cell weighthin. b, and b2 are in units of mmoliL per minute. b7 is in units of mmol/Llmin2.


The rate of change in the dry cell weight concentration (DCW) in the fermentor of this variable feed continuous process (VFcstr) is calculated by using Eq. (9). The concentration of dry cell weight ( X ) is a function of the simulated specific growth rate (pnet) of the organism, the dilution rate due to the feedstreams, and the dilution rate due to water produced by the metabolism of methanol:

By using the parameters from the modified logistic equation to calculate the specific growth rate [Eq. (S)], it is assumed that the decrease in dry cell weight concentration due to dilution is negligible.

Lysine Concentration

Specific lysine production (nnet = lysine produced per mass of dry cell weight per unit time) was calculated from dry cell weight and lysine concentration measurements taken over the time of the fermentation for each amino acid feed concentration and fit to a linear function of the apparent specific growth rate (paPp) which was also calculated from dry cell weight measurements:

nnci = m P a p p + k (10)

The first term describes growth-associated lysine production, and the second term describes non-growth-associated production.26 Apparent non-growth-associated production can be due to continued synthesis by the organism, leakage of lysine from the cells, or release of lysine from the cells when lysis occurs. The slope ( m ) and intercept ( k ) of Eq. (10) were then fit to arbitrary functions of threonine feed concentration. For the simulations, paPp is equal to pnet from Eq. (8).

Lysine concentration in the culture ( P ) depends on the dry cell weight concentration ( X ) , the specific production rate, nnet [Eq. (lo)], the dilution rate due to the feedstreams, and the dilution rate due to water produced by the metabolism of methanol. Lysi’ne is only produced and removed from the reactor (no lysine is added to the fermentation by the feedstreams):

Substrate Concentration and Consumption

The rate of methanol fed into the reactor is equal to the concentration of the methanol feed (So) times the methanol feed rate (FMeOH). Methanol is removed from the reactor by evaporation, consumption, or broth removal as previously described. The rate of evaporation is equal to the flowrate of the exhaust gas (G) times the concentration of substrate in the exhaust (S,). When including evaporation in the calculation of the decrease

in volume, an additional term results which is the rate of volume lost through evaporation (Fexh) times the substrate concentration. The specific rate of substrate consumption, unet, is the amount of methanol consumed per mass of dry cell weight per unit time and takes into account the methanol consumed to produce cells, carbon dioxide, and lysine. The nonspecific consumption (cons) is used to describe the consumption of methanol for the formation of other byproducts such as glutamate and diaminopimelate (Table 111). Based on the mass balance equation for the system, several terms in the calculation of the substrate concentration are divided by the culture volume.

The specific rate of consumption (unet) varies for each phase. During both exponential growth (Phase I) and threonine-limited growth (Phase I]), methanol is consumed to produce cells, carbon dioxide, and lysine. Dur- ing the period of decreasing metabolic activity (Phase III), methanol is consumed only to make carbon dioxide and lysine. Eq. (13) describes the methanol consumption for these three products using stoichiometric yields for carbon dioxide ( Yco,n), lysine ( Ypl.y), and biomass (YxIs) based on an average elemental composition of bacterial celWqO:

CER -

where pnet = 0 for Phase 111. The purpose of this model is to predict the production rate and concentration of lysine. Therefore, the production of other byproducts was combined into a single nonspecific consumption term (cons). This term is used to account for the carbon flow used to generate end-products other than lysine. The nonspecific consumption for each phase was calculated to maintain the substrate concentration equal to 100 mM in the reactor. Table 111 summarizes the functions used for the nonspecific consumption term and the parameters involved as a function of amino acid feed concentration. During each phase, the nonspecific consumption term is a linear function of methanol concentration in the fermentor. Nonspecific consumption during these phases takes into account other metabolites such as glutamate, diaminopimelate, and alanine, which are excreted by some mutants. The nonspecific consumption term takes this into account as well as the inaccuracy in using a theoretical stoichiometric yield of average biomass.

Process Scale-Up For modeling the scale-up of the culture volume of this process, the program was adjusted to calculate the


Table 111. lysine by B. methanolicus.

Calculation of nonspecific consumption during each phase of the fermentation of methanol to

- ~~~ ~~

Nonspecific consumption C, d,

-3792.72 + 450.689 [thr] - 12.753 [thrj2 0.127517 [thrI2

Phase I: I = 0 to t = 9.2 h

Phase 11: cons = c2 + d2 * [S] -153859.333 + 1538.573 - 120.70256 [thr] I = 9.2 h to 12070.47 [thr] - 1-2.81618 [thr]’

cons = cI + dl * [S] 37.9227 - 4.50632 [thr] +

pnet = 0.06 h-’ 281.6215 [thr]’

-6261.4 - 11.843 [thr] Phase 111: cons = c3 + d3 * [S] 62.617 + 0.11849 [thr] pnet i= 0.06 h-’ to

end (t = 70 h)

Equations used to describe the nonspecific consumption during each of the three growth phases of the fermentation. The nonspecific consumption term is denoted by “cons,” and is a linear function of methanol concentration (S). The units for “cons” are mM methanohin. c, and d, are functions of the threonine feed level in the reactor based on the amino acid feed concentration. c, are in units of mM methanol/min. d, are in units of min-’.

methanol feed for each simulation based on the consumption terms, and a constant dissolved methanol concentration of 100 mM. To predict lysine productivity at the pilot plant and commercial scales,’8 simulations were done at the 2.5-m3, 25-m3, and 250-m3 scale. The initial culture volume for these simulations was equal to 80% of the capacity of the reactor.

Model Simulation Using the Three- Phase Approach

The model equations were integrated using the Gear method of implicit in tegra t i~n .~ During the simulation, the three-phase approach introduced discontinuities into the computer program when calculating the change in volume and methanol consumption. Discontinuities in both the CER and methanol consumption descrip- tions occur at the transition from phase I1 to phase I11 (specific growth rate = 0.06 h-’) and can be too large for the integration program to overcome. Under these circumstances, the program would be reset to the last completed integration step and only the Phase 111 model of the CER and methanol consumption would be used (Fig. 5).

The total time of the simulation was chosen to be 70 h, which was the longest culture time of the fermentations considered. Using a data file, the user inputs nine parameters: amax [from Eq. (7)], y [from Eqs. ( 5 ) and (6)], amino acid feed concentration, amino acid feed levels, initial dry cell weight concentration (Xo), initial culture volume (Vo), volume control options (variable feed with a constant volume ( VFcstr), a fed-batch process without a condensor. a fed-batch process with a perfect condensor), reactor volume, and initial methanol reservoir volume. Also, the total simulation time and total number of points to calculate for the simulation are input through this data file.

RESULTS AND DISCUSSION

The results of a series of fermentations using strain NOA2#13A5-2 at increasing threonine feed rates illustrates the need for controlling threonine and methionine feeding (Fig. 6). As the concentration of threonine in the feed reservoir increased, the dry cell weight increased, and lysine production peaked with the middle feed rate. The rate of water generated during the complete oxidation of methanol (dV,,,,,/dt) was calculated based on the carbon dioxide evolution rate (Fig. 7). Variation of lysine production as a function of threonine feeding level, water generated by metabolism of methanol, and multiple feedstreams were taken into account while developing this three-phase simulation.

Figure 8 illustrates the results for a fermentation using strain NOA2#13A5-2 with 23.4 g/L of methionine and threonine feed. The simulation reasonably describes the experimental data of an 11-L constant volume continuous process for each of the three amino acid feeding levels. For the dry cell weight and lysine production, the simulation varies from the data by at most 23%. Using the parameters from the modified logistic equation [Eqs. ( 5 ) and (6)] to calculate specific growth rate produced acceptable results. This indicates that the assumption of negligible dilution effect in the calculation of dry cell weight is acceptable. The lysine concentration of the simulation is lower than the experimental data due to errors in fitting the specific production rate as a linear function of specific growth rate and due to the overestimation of volume by the simulation. The simulated culture volume increased by 23% over the setpoint of 11 L. This overestimation is due to the complex broth removal system used during the experiment and the assumption of the maximum stoichiometric ratio of two between the water produced by the system and the methanol consumed.

The culture volume is a function of the feedstreams, broth removal and the amount of water produced from


Y(at t=ti), t=ti, t f = t i + l L Phase I -

Exponential Growth

Phase I1 - Thrionine Limited Growth

vnet= 6.0e -2 hr-'

Metabolic Activity

I I

Yes

1 idjusted Model

1 Phase 111 - Decreasing Metabolic Activity i Phase

Figure 5. Schematic of simulation using three phases to describe growth and methanol consumption. Mathematical description of Phases, I, 11, and I11 are the same except for the equations used to describe carbon dioxide production and methanol consumption. Y is the array of state variables: volume, dry cell weight concentration, lysine concentration, and substrate concentration. When a discontinuity occurs, the values from the last completed integration step are used as the initial value inputs to an adjusted model which only describes Phase 111.

,p 3"' 'f

yr: /

f" 0 20 40 60 80

Time (hr)

Figure 6. Dry cell weight concentration and lysine concentration data from three 14-L fermentations at different amino acid feed concentrations. Threonine and methionine feed concentrations (each): (A) 11.7 g/L; (0) 23.4 g/L; (0 ) 46.8 g/L. Open symbols denote dry cell weight concentration at these amino acid reservoir concentrations. Closed symbols denote lysine concentration at these amino acid reservoir concentrations.

Phase I Phase I1 Phase I11 ~ l ~ ~ , L t d [ e c r e a s i n g Metabolic A ivity

0 10 20 30 40 50 60 70 80 Time (hr)

Figure 7. Three phases of fermentation used in the computer simulation: (-) Phase I; (---) Phase 11; (----) Phase 111. (-------) Observed CER from a 14-L fermentation using a threonine and methionine feed of 23.4 g/L each. The upper plot is simulated specific growth rate. The lower plot is carbon dioxide evolution, both observed and simulated.

U


0 10 20 3 0 4 0 50 6 0 70 80 Time (hr)

Figure 8. Fit of simulation to data from a 14-L fermentation using an amino acid feed of 23.4 g/L. (-------) Simulated lysine concentration; e) measured lysine concentration; (-) Simulated dry cell weight; ( 0 ) observed dry cell weight; (-) simulated methanol reservoir volume; (A) observed methanol reservoir volume; (-) simulated volume; (----) volume setpoint.

the metabolism of methanol. Figure 9 compares the simulated culture volume using different stoichiometric ratios of moles of water produced per mole of methanol consumed. The initial 1.5% decrease in simulated culture volume indicates that using a constant average rate of broth removal slightly overestimates the amount of broth removed during the first 10 h. The stoichiometric ratio of moles of water produced per mole of methanol

14.0

0 10 20 30 40 50 60 70 80 Time (hr)

Figure 9. Simulation of culture volume for a 14-L reactor using different ratios of water generated from methanol consumed. Culture volume equal to 11 L. Threonine feed concentration equal to 23.4 gl L. Watedmethanol ratio: (A) 0.0; (B) 1.4; (C) 1.6; (D) 2.0; (E) setpoint.

consumed does not affect the first 10 h of the fermentation simulation, because the volume increase due to methanol metabolism is small due to a low cell density.

After the first 10 h, the ratio has a dramatic affect on the simulated culture volume. When assuming a ratio of 2, the simulation rises over the setpoint by 23%. Using ratios of 1.6 and 1.4 result in an increase of 17% and 14% over the setpoint, respectively. If no water is produced, the final volume of the reactor would decrease by 7% due to the volumetric rate of broth removal by sampling and evaporation and removal of condensate and of broth. This indicates that a substantial amount of water can be produced by the metabolism of methanol resulting in an increase in broth volume. Since the actual proportion of products from the fermentation cannot accurately be determined, due to a number of secreted byproducts other than L-lysine, all the following results use a molar ratio of 2 (water produced/methanol consumed), resulting in the maximum predicted culture volume change.

Model Simulations for the Process at the 250-m3 Scale

Seventy-hour fermentations were simulated with 40 time steps calculated using different volume control strategies and different cell growth characteristics. The amino acid feeding rate was 28% of the methanol feed for the simulation of the experimental data. To decrease the volume added by this additional feedstream during scale-up, the amino acid feed rate was adjusted to acco- modate an increased concentration of 54 g/L in the amino acid reservoir without increasing the feed level of the reactor. Simulations for the 2.5-m3, 25-m3, and 250-m3 scale all had the same general characteristics for equivalent initial conditions: culture volume, dry cell weight concentration, lysine concentration, and methanol consumption when assuming the same cell growth and lysine production characteristics. Only the results of the 250-m3 reactor simulations are presented here (Table IV and V). It was assumed as a first approxima- tion that there is a constant rate of evaporation per unit of reactor volume equal to that in the 11-L culture.

Evaluation of Culture Volume Control Strategies

Using this simulation, different approaches to reactor volume control were investigated. A continuous constant culture volume approach (VF,,,,) adds nutrients on demand and removes both broth and cells from the reactor to maintain the volume at the initial level. Figure 10 compares the change in culture volume of a fed- batch reactor with a perfect condensor and one without a condensor compared to a continuous constant volume process. In a simulation of a fed-batch process with no condensor, all the evaporated liquid in the exhaust is removed from the reactor, and no condensate is re-


Table IV. The results of altering volume control on lysine concentration, yield, and process productivity.

Final lysine concentration Final yield Max. productivity Conditions WL) (g lysinelg MeOH) (g lysinelllh)

~~

Constant volume 27.22 0.128 0.475 at 35 h

No condensor 19.06 0.122 0.398 at 32 h

Perfect condensor 17.51 0.120 0.381 at 32 h

Comparison of different fermentation conditions in terms of final concentration, final yield, and maximum productivity for a 2SO-m3 reactor. Culture volume = 200,000 L.

turned to the system. Under these conditions, the volume would increase 53% from the initial starting volume. Although this process would be simple, such a procedure is not feasible because methanol would be released into the atmosphere. Using a perfect condensor, no liquid evaporates from the culture volume, and the volume would increase 69% relative to a constant volume system.

The difference between the fed-batch process with a perfect condensor and one without a condensor (16%) shows that evaporative losses at 50°C can be significant, but cannot totally compensate for the increases in volume due to the addition of feedstreams and methanol metabolism. This increase in volume results in a decrease in the final lysine concentration of 30% and 36% in a system without a condensor and a system with a perfect condensor, respectively. These simulations indicate that fed-batch processes would allow the culture volume to increase and would dilute the final product concentration and decrease the productivity of the system. A constant volume control strategy which continuously removes cells and broth results in a higher maximum productivity and final lysine concentration (Table IV).

A constant volume process also removes complications which can occur when considering a variable volume system for aerobic fermentations. If the culture volume of a reactor changes during the fermentation,

other key characteristics can change, such as mixing patterns and oxygen transfer rates. Changes in these parameters can greatly affect microbial metabolism and, in the end, affect final product yield. Maintaining a constant volume process will eliminate these complications and, for this methanol process, result in a higher final lysine concentration.

Evaluation of Cell Growth and Lysine Production

Ideally, in a microbial process, substrate would be consumed to synthesize more product and less biomass. A constant volume process was used to investigate possible changes in metabolism on the productivity of the fermentation. Table V summarizes the results of altering the final dry cell weight concentration and specific lysine productivity. Decreasing the final dry cell weight also decreases the yield and final lysine concentration of the process. However, doubling the specific lysine productivity while maintaining a lower final biomass concentration resulted in only a 10% increase in yield. If byproduct formation is suppressed, the lysine yield would increase by 44% from the original metabolic conditions and by 60% for the final altered condition. This large increase would be due to decreasing the dilution effect of the amino acid stream because less methanol is consumed and there is more efficient usage of methanol for lysine production.

Table V. The results of altering metabolism on lysine concentration and yield. ~~~~ ~

Cons f 0.0 Cons = 0.0

Final lysine concentration Final yield Final lysine concentration Final yield Conditions (g/L) (g lysine/g MeOH) (g/l) (g lysine/g MeOH)

Original 27.22 0.128 27.67 0.185 (+44%)

Final DCW = 0.5 X, 14.02 0.078 (-39%) 14.25 0.119 (-7%)

Final DCW = 0.5 X, 27.89 0.141 (+lo%) 28.35 0.205 (+60%) (7inet = double original 7inet)

~~~~~

Comparison of different fermentation conditions in terms of final concentration, and final yield for a 250-m3 reactor. Culture volume = 200,000 L. Numbers in parentheses indicate the percentage change relative to the original conditions.


a 30 I r(

aJ

&

8 2

5

d

5 L 0

m I

18 1 I I I I 0 10 20 30 40 50 60 70 80

Time (hr)

Figure 10. Comparison of volume control strategies for a 250-m3 reactor (culture volume 200,000 L). (-) Constant volume strategy; (----) perfect condensor; (----) no condensor.

Modification of Simulation to Describe a Mutant (NOA2#13A52-8A66) With Decreased Production of Side Products

The nonlysing strain, NOA2#13A52-8A66, was grown under slightly different conditions (see Materials and Methods) and had different growth and lysine productivity characteristics. Evidence that this new mutant did not tend to lyse during the phase of decreasing metabolic activity was supported by the reactor exhaust gas data and the characteristics of the cell pellet. With strain NOA2#13A5-2, two layers would appear in the cell pellet: one resulted from whole cells and another layer due to cell debris. When using strain NOA2#13A52-8A66, this additional layer of cell debris was not visible. Fewer byproducts relative to lysine were also secreted by this mutant compared to strain NOA2#13A5-2 (Fig. 11). Most notably. the production of diaminopimelate was substantially decreased.

The dry cell weight data for this strain was fit to a modified logistic equation, and the parameters of lysine production were determined assuming a linear function of specific growth rate. The effect of threonine feed rate and the specific carbon dioxide production were assumed to be the same as with strain NOA2#13A5-2. Volume control was simulated as a constant volume reactor with variable feed (VFcstr). Figure 12 shows a comparison of the simulation with both growth and non- growth-associated productivity as well as only growth- associated productivity. The simulation with both growth- and non-growth-associated productivity overestimates the data by 53%. When only growth-associated productivity is considered, the simulation underesti- mated the final concentration by only 7%, and follows the general trend of the data much better. This indicates that NOA2#13A52-8A66 does not have substantial non- growth-associated lysine productivity, and that the apparent non-growth-associated lysine production in the previous strain may have been due to release of lysine during cell lysis. The variation between the simulation

f"

0 1 0 20 30 40 50 6 0 70 Time (hr)

Figure 11. Amino acid concentration data for NOA2#13A5-2 and NOA2#13A52-8A66. (A) Open symbols denote amino acid concentrations for NOA2#13A5-2. (B) Closed symbols denote amino acid concentrations for NOA2#13A52-8A66. (A) Lysine; (0) glutamate; ( 0 ) diaminopimelate; (0) alanine.

and the data is due to the previously mentioned assump- tions.

CONCLUSIONS

The three-phase kinetic model developed is useful for predicting process scale-up and indicates the need to run the fermentation as a variable feed constant volume process (VF,,,,) to achieve maximum lysine productivity. The model can be applied to predict the changes in process characteristics due to changes in metabolism and can be easily modified to describe other high-lysine- producing mutants. Decreasing biomass production while increasing specific lysine productivity increases the final yield of a variable feed constant volume process. Suppression of byproduct formation would also increase the productivity of the process due to more efficient usage of methanol and decrease of the dilution effect by the addition of the amino acid feed. While strain NOA2#13A5-2 appeared to produce lysine by both growth and non-growth-associated production, strain NOA2#13A52-8A66 depends only on growth- associated production. The simulations of these two strains as well as observations during the fermentation indicate that the non-growth-associated lysine production in strain NOA2#13A5-2 is probably due to cell ly-

LEE ET AL.: MODEL OF LYSINE FROM METHANOL USING A BACILLUS SP. 65 1

80 j

60 70 - 1 0 0

0 0

15

10 ~

5 I 0 10 20 30 40 50 60 70 80

Time (hr)

Figure 12. Comparison of NOA2#13A52-8A66 data with modified simulation. (----) Lysine production according to simulation using growth and non-growth-associated productivity; (-) lysine production according to simulation using only growth-associated productivity; (--11) simulation of dry cell weight; (.) measured lysine concentration; (0) observed dry cell weight.

sis, a phenotype which does not describe strain NOA2#13A52-8A66. This three-phase kinetic model has been shown to be useful in describing this complicated methanol-based process and in predicting the effect of metabolic changes and volume control strategies on lysine production.

The authors thank Dr. Warren E. Stewart and Dr. Roderick Bain (Department of Chemical Engineering, University of Wisconsin, Madison, WI) for use of the integration package (Double Precision Differential Algebraic Sensitivity Analy- sis Code) and the parameter estimation code (General REGression code). Mutant B. rnefhunolicus strains were kindly provided by Professor R. S. Hanson (Gray Freshwater Biological Institute, University of Minnesota, Navarra, MN). Helpful suggestions were also provided by Professor James C. Liao on modeling of growth-associated lysine accumulation. Funding for this project has been provided by The Blandin Foundation (Grand Rapids, MN) Kyowa Hakko Kogyo, Co., Ltd. (Tokyo, Japan) and the Institute for Ad- vanced Studies in Biological Process Technology at the Uni- versity of Minnesota (St. Paul, MN).

NOMENCLATURE

al, a*, a3 intercept for linear correlation of specific carbon dioxide evolution rate for each phase of growth (Table 11) (mass of C 0 2 produced per mass of dry cell weightltime) slope for linear correlation of specific carbon dioxide evolution rate for Phases I and I1 (Table 11) (mass of

bl, bZ

COz produced per culture volumeltime) slope for linear correlation of specific carbon dioxide evolution rate for Phase 111 (Table 11) (mass of COz produced per culture volumeltimeltime) intercept for linear correlation of nonspecific consumption for each phase of growth (Table III) (mass of methanol consumedlvolumeltime) carbon dioxide evolution rate (mass of C02 produced per culture volumeltime) nonspecific consumption term (mass of methanol consumedlvolumeltime) slope for linear correlation of nonspecific consumption for Phases I (Table 111) (mass of methanol consumed per mass of dry cell weightltime) slope for linear correlation of nonspecific consumption for growth phases I1 and 111 (Table 111) (time ') dry cell weight (masslvolume) volumetric flow rate lost through evaporation (volumel time) total volumetric Row rate into the reactor (volumeltime) volumetric flow rate of methanol feed (volumeltime) total volumetric Row rate out of the reactor (volumel time) volumetric flow rate of exhaust gas (volumeltime) intercept of an equation for specific lysine productivity as a linear function of specific growth rate (masslmassi time) slope of an equation for specific lysine productivity as a linear function of specific growth rate (masdmass) oxygen uptake rate (mass of O2 consumed per culture volumeltime) lysine concentration in the reactor (masslvolume) methanol concentration in the reactor (massivolume) methanol concentration of the feed (mass/volume) methanol concentration of the exhaust gas (mass/ volume) time threonine feed reservoir concentration (mass/ volume) culture volume initial culture volume volume due to the addition of water produced from the metabolism of methanol to carbon dioxide total dry cell weight (mass) initial total dry cell weight (mass) dry cell weight concentration (masslvolume) initial dry cell weight concentration (masslvolume) final dry cell weight concentration (massivolume) yield of carbon dioxide on methanol (masslmass) yield of lysine on methanol (masslmass) yield of biomass on methanol (masslmass)

Greek symbols

(Y

a,,,

Y

papp

pnet 7rnet

unet

rate of dry cell weight increase in modified logistic equation (time-') maximum rate of dry cell weight increase in modified logistic equation (time-') inverse of final total dry cell weight in modified logistic equation (volumelmass) apparent specific growth rate calculated from data (time-') simulated net specific growth rate (time-') simulated net specific lysine production rate (masslmassl time) simulated net specific consumption rate (masslmassl time)


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LEE ET AL.: MODEL OF LYSINE FROM METHANOL USING A BACILLUS SP. 653

Lysine production from methanol at 50°C using Bacillus methanolicus: Modeling volume control,...

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