Data and knowledge based experimental design for fermentation process optimization

Data and knowledge based experimental design for fermentation process optimization

Enzyme and Microbial Technology 27 (2000) 784 –788 www.elsevier.com/locate/enzmictec Data and knowledge based experimental design for fermentation p...

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Enzyme and Microbial Technology 27 (2000) 784 –788

www.elsevier.com/locate/enzmictec

Data and knowledge based experimental design for fermentation process optimization Ralph Berkholza,*, Dirk Ro¨hligb, Reinhard Guthkeb a

b

BioControl Jena GmbH, D-07745 Jena, Germany Hans Kno¨ll Institute for Natural Product Research, D-07745 Jena, Germany Received 29 February 2000

Abstract A novel method for the sequential experimental design in order to optimize fed-batch fermentations was applied to a hyaluronidase fermentation by Streptococcus agalactiae. A ⌳-optimal design was introduced to minimize the model parameter estimation error and to maximize the performance of the fermentation process. The method employs hybrid models that contain mechanistic, fuzzy and neural network components. © 2000 Elsevier Science Inc. All rights reserved. Keywords: Sequential experimental design; Optimization; Fed-batch fermentation

1. Introduction During bioprocess development experiments are designed by skilled biologists and engineers who apply experience, general and associative knowledge as well as simple methods of data analysis. Statistical experimental design methods (e.g. [1]) were applied to optimize nutrient media. This approach however fails with respect to the optimization of feeding rates in fed-batch fermentations. Munack [2] calculated the optimal feeding strategy for the identification of Monod-type models using the Fisher Information Matrix and the modified E-criterion. Syddall et al. [3] applied the same approach using a structured model of a fed-batch penicillin-G fermentation. Takors et al. [4] designed and carried out nutristat cultivations for optimal parameter identification and model discrimination. The purpose of this paper is to apply a novel approach to this problem by sequential experimental design to combine optimal parameter identification with optimal process performance.

Braun Biotech International, Melsungen, 34°C; pH 7; 300 rpm; without aeration). The initial culture volume was 5 liter after inoculation of the strain into a complex medium consisting of 12 g/liter casein-peptone (Difco), 22 g/liter yeast extract (Ohly), glucose (40 g/liter) and mineral salts (0.03 g/liter MgSO4*7 H2O, 0.6 g/liter KH2PO4). During the second and third experiment 1 liter of complex medium (24 g/liter casein-peptone, 44 g/liter yeast extract, 40 g/liter glucose, 0.06 g/liter MgSO4*7 H20, 1.2 g/liter KH2PO4) was fed at different times ␶ with a rate of FM ⫽ 20 liters/h for 0.05 h. A series of three fermentation runs with different times ␶ was designed and performed step by step. Glucose and alkali were fed at concentrations of cGF ⫽ 500 g/liter and cNaOHF ⫽ 200 g/liter, respectively. The alkali feeding was applied to control pH. The volumetric feeding rate of glucose FG was equal to the alkali feeding rate FNaOH in order to maintain the glucose concentration at an almost constant level: F G ⫽ F NaOH

2. Material and methods Streptococcus agalactiae was cultivated discontinuously in a 10 liter fermenter (stirred tank reactor Biostat ED10, B.

* Corresponding author.

(1)

The biomass concentration cX was measured turbidometrically at 600 nm (UV-vis-Spectrophotometer Spekol 1100 Carl Zeiss, Jena). The concentration cP of the product hyaluronidase (hyaluronate lyase, EC 4.2.2.1, [5]) was measured according to Di Ferrante [6]. L-Lactate concentration cL was measured enzymatically (YSI Analyzer 2300 with the kit YSI 2329, YSI, Yellow Spring). Model simulations

0141-0229/00/$ – see front matter © 2000 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 0 2 2 9 ( 0 0 ) 0 0 3 0 1 - X

R. Berkholz et al. / Enzyme and Microbial Technology 27 (2000) 784 –788

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Fig. 1. Measured data of the first experiment and kinetics of the model fitted with identified parameters as shown in Table 1, row 3. Left: Concentrations of biomass (cX, E, solid line) and lactate (cL, 䊐, dotted line). Right: Weight of alkali in the feeding reservoir (wNaOH, E, solid line) and hyaluronidase concentration (cP, 䊐, dotted line).

and other calculations were carried out using MATLAB toolboxes (version 5.0; MathWorks Inc.). 3. Results

Fig. 1 shows measured data of the first experiment as well as simulated kinetics of the following described dynamic model. The dynamics of the concentrations of the biomass cX, the by-product lactate cL and the desired product hyaluronidase cP are modeled by the differential Eqs. (2)–(4): dc X FT ⫽ ␮ 䡠 cX ⫺ 䡠 cX dt V

(2)

FT dc L ⫽ ␲L 䡠 cX ⫺ 䡠 cL dt V

(3)

FT dc P ⫽ ␲P 䡠 cX ⫺ 䡠 cP dt V

(4)

Using data analysis and dialysis cultivation (not shown in this paper) it was found that growth and by-product formation are inhibited by lactate:

冉 冉

␲ L ⫽ ␤ L 䡠 exp ⫺



c L2 共0.5 䡠 K I兲 2

c L2 共K I兲 2



(7)

The volume of cultivation broth is increasing by the total feeding rate FT: dV ⫽ F T ⫽ F NaOH ⫹ F G ⫹ F M dt

3.1. First experiment and modeling of the process

␮ ⫽ ␮ m 䡠 exp ⫺

␲P ⫽ ␣P 䡠 ␮

(8)

It is assumed that 1 mol of NaOH neutralizes 1 mol of lactate: F NaOH ⫽ ␲ L 䡠 c X 䡠 V 䡠

M NaOH F ML 䡠 cNaOH

(9)

The molar masses of NaOH and lactate are MNaOH ⫽ 40 and ML ⫽ 90, respectively. For the concentration cFNaOH as well as the feeding rates FNaOH, FG and FM see the previous capture and Eq. (1). The weight wNaOH of alkali in the reservoir decreases by the feeding rate FNaOH: dw NaOH ⫽ ⫺FNaOH dt

(10)

The initial values for the product and by-product are set to zero: cP(0) ⫽ cL(0) ⫽ 0. The initial values V(0) and wNaOH(0) of the volume V and the weight of alkali in the reservoir are set according to the values measured. Fitting the model Eqs. (1) to (10) to the data of the first experiment provides the parameters shown in row 3 of Table 1.

(5)

3.2. ⌳-Optimal design and performance of the second experiment

(6)

The model Eqs. (1) to (10) together with the model parameters identified by the fit to the first experiment (see Table 1, row 3) is now applied to design the second experiment. For this purpose a novel criterion is employed:

The hyaluronidase formation was found to be growth associated:

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Table 1 Model parameters identified by fit to the data of one, two or three experiments Parameter dimension

cX(0) [g 䡠 l⫺1]

Experiment 1 (Figure 1) Experiment 1 and 2 (Figure 3) Experiment 1 2 and 3 (Figure 5)

0.015 0.0501 0.02543 0.0547 0.02812 0.0444

␮m [h⫺1]

J ⌳ ⫽ ␻ 䡠 J P /max共 JP兲 ⫹ 共1⫺␻兲 䡠 JS /max共 JS兲 ␶

␤L [h⫺1]

␣P [kU 䡠 g⫺1]

0.8984

67.9005

3.9834

11.9517

0.6742

87.8415

3.2783

12.5236

0.6545

88.3729

3.2397

13.2979

(11)



This criterion is a weighted and normalized sum of the final mass mP of the product J P ⫽ m P共t f兲 ⫽ c P共t f兲 䡠 V共t f兲 at the end tf ⫽ 12 h of the fermentation process and the well-known modified E-criterion function Emod [2] defined by the quotient of the minimum and maximum eigenvalues ␭min and ␭max of the Fisher Information Matrix F: J S ⫽ 1/E mod ⫽

KI [g 䡠 l⫺1]

␭ min共F兲 ␭ max共F兲

Maximizing the component JP provides an optimal process performance whereas maximizing JS provides an optimal process parameters identification (i.e. the error ellipsoid is as spherical as possible). Starting a sequential process development the next experiment should be designed in a way that the minimization of the parameter estimation error should be prior. Therefore, the second experiment is designed using a small weight ␻ ⫽ 0.2. The resulting criterion J⌳ as a function of the process parameter ␶ is shown in Fig.

2. Due to the fact that the function J⌳ reaches its maximum at ␶ ⫽ 9 h the second experiment is designed so that the complex medium will be fed 9 h after inoculation. Fig. 3 shows the data of the second experiment. The model parameters are identified as shown in the row 4 of Table 1 by simultaneous fitting of the simulated model kinetics to the experiments 1 and 2. The initial values cX(0) are identified separately for both experiments. 3.3. ⌳-Optimal design and performance of the third experiment The model Eqs. (1) to (10) together with the model parameters identified by the fit to the first and second experiment as shown in row 4 of Table 1 are applied now to design the third experiment. For this the ⌳-criterion as defined by Eq. (11) is used with the weight factor ␻ ⫽ 0.4. An increased weight factor ␻ was used in order to design an experiment with more emphasis on maximum product yield and less emphasis on parameter estimation. The resulting criterion J⌳ as a function of the process parameter ␶ is shown in Fig. 4. The function J⌳ reaches its maximum at ␶ ⫽ 8 h. Therefore, the third experiment is designed to feed

Fig. 2. Criterion functions JP(␶) (solid line) and JS(␶) (dashed line) vs. feeding time ␶ (left) and combined function J⌳(␶) calculated by Eq. (11) with ␻ ⫽ 0.2 (right) as used to design the second experiment.

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Fig. 3. Measured data of the second experiment and kinetics of the model fitted simultaneously to experiments 1 and 2 with identified parameters as shown in Table 1, row 4 (for explanation of symbols and lines see Fig. 1).

the complex medium 8 h after inoculation. Fig. 5 shows the data of this third experiment. The model parameters are identified by simultaneous fitting of the simulated model kinetics to experiments 1, 2 and 3 as shown in the row 5 of Table 1. Table 2 shows the product yield mP at the final time tf ⫽ 12 h for all three experiments.

4. Discussion The novel concept of sequential experimental design reflects a typical situation in bioprocess development: Knowledge is increasing step by step. Using available

knowledge about the growth associated formation of the desired enzyme and inhibition of growth and by-product formation by the by-product a sequence of two fed-batch experiments was designed for both, the identification of parameters of a dynamic model and the optimization of productivity. The experiments 1 to 3 represent a series of fermentation runs with increasing product yield: Table 2 shows that the process performance increases from 570 kU via 919 kU to 965 kU from the first to the third experiment. Table 1 shows that the identified model parameters ␮ m , K I , ␤ L and ␣ P were changed from the first to the second experiment, but were quite similar when the third experiment was taken into account for model fitting. Therefore,

Fig. 4. Criterion functions JP(␶) (solid line) and JS(␶) (dashed line) vs. feeding time ␶ (left) and combined function J⌳(␶) calculated by Eq. (11) with ␻ ⫽ 0.4 (right) as used to design the third experiment.

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Fig. 5. Measured data of the third experiment and kinetics of the model fitted simultaneously to experiments 1, 2 and 3 with identified parameters as shown in Table 1, row 5 (for explanation of symbols and lines see Fig. 1)

the sequential experimental design using the novel criterion function J⌳ as defined by Eq. (11) allowed for both, the improvement of process performance and model parameter identification. The calculation of all variables and functions (J⌳ etc.) was carried out numerically without any analytical solutions. Therefore, the method is also applicable when hybrid models are used which consist of mechanistic components, fuzzy rules and artificial neural network (ANN) components. Instead of the exponential functions in Eqs. (5) and (6) that describe the inhibition characteristics of growth and by-product formation by high lactate concentrations fuzzy rules and ANN were also applied. This kind of hybrid modeling results in a quite similar design of experiments. In order to support bioprocess development software tools for Table 2 Weight ␻ for ␭-optimal design of the second and third experiment, the calculated optimal and realized process parameter ␶ (i.e. the instant of complex medium feed) and the obtained final product amount mP (⫽C P 䡠 V) Parameter dimension

␻ [⫺]

␶ [h]

mP [kU]

Experiment 1 Experiment 2 Experiment 3

⫺ 0.2 0.4

⫺ 9.0 8.0

570 919 965

the sequential experimental design of fed- batch fermentations using hybrid dynamic models are now available. Acknowledgments The authors would like to thank Dr Peter-Ju¨rgen Mu¨ller and his co-workers of the Hans Kno¨ll Institute for Natural Products Research for their experimental support and to Dr Michael Pfaff from BioControl Jena GmbH for helpful discussions. References [1] Plackett RL, Burman JP. The design of optimum multifactorial experiments. Biometrika 1946;33:305–25. [2] Munack A. Optimal feeding strategy for identification of Monod-type models by fed-batch experiments. In: Fish NM, Fox RI, Thornhill NF, editors. Computer applications in fermentation technology. London, New York: Elsevier, 1989. p. 195–204. [3] Syddall MT, Paul GC, Kent CA. Improving the estimation of parameters of penicillin fermentation models. Proc 7th Int Conf on Computer Applications in Biotechnol. Osaka, Japan, 1998, May 31-June 4. [4] Takors R, Wiechert W, Weuster-Botz D. Experimental design for the identification of macrokinetic models and model discrimination. Biotechnol Bioeng 1997;56:564 –76. [5] Rodig H, Ozegowski JH, Peschel G, Mu¨ller P-J. Complementary characterization of a hyaluronic acid splitting enzyme from Streptococcus agalactiae. Zentralblatt fu¨r Bakteriologie 1999;289:835– 43. [6] Di Ferrante N. Turbidimetric measurement of acid mucopolysaccharides and hyaluronidase activity. J Biol Chem 1956;220:303– 6.