A LOGISTIC FEEDING PROFILE FOR A FED-BATCH BAKER'S YEAST PROCESS

Tadeusz Miśkiewicz, Daniel Borowiak
Department of Bioprocess Engineering, Wroclaw University of Economics, Poland

ABSTRACT

The study reported on in this paper has shown that the optimisation of the fed-batch baker’s yeast process by maximising the biomass yield needs a feeding profile differing from the one used in the optimisation of this process by maximising the specific growth rate. Both the profiles can be described by a logistic function of the formula F(t) = a/(1+b·exp(-c·t)), where F(t) denotes the moment of the glucose feed entering the bioreactor in time t, and a, b and c are parameters of the equation. The parameters take different values, depending on the objective of the optimisation process. It has also been demonstrated that the two objectives, maximisation of the biomass yield and maximisation of the specific growth rate, conflict with each other. A compromise feeding profile was proposed, thus enabling the maximisation of the criterion which was the product of the biomass yield and specific growth rate (Y·µ). The criterion reached its maximal value in the baker’s yeast process with a biomass yield and specific growth rate of 0.58 g·g^-1and 0.129 h^-1, respectively.

Key words: baker?s yeast process, biomass yield, logistic feeding profile, Saccharomyces cerevisiae, specific growth rate.

INTRODUCTION

The production of baker’s yeast is a complex, time-variant, nonlinear process, which involves fed-batch methods, the optimisation issue being linked with the feed rate profile. Finding the optimal feeding profile raises serious problems, which are primarily due to the non-linearity and time-dependence of the process itself, as well as to the complexity of the concomitant metabolism. Another serious obstacle to the optimisation of the feed-rate profile is the need to simultaneously achieve many objectives, which conflict with one another. That is why many researchers have focused their interests on the methods of optimising fed-batch processes [4; 8; 11; 13; 15; 18; 20; 25]. In the past decade much attention has been given to the use of artificial intelligence (AI) techniques [17; 22], especially knowledge-based systems [23], artificial neural networks [9; 10; 19], fuzzy logic [5; 6], evolutionary algorithms [21] and hybrid systems [24]. Using AI techniques it is possible to attain reliable results even if some unexpected complications occur in the course of the process, or if the available information which characterises the process is incomplete or uncertain, etc.

The optimisation of the feeding profile is also a key issue in baker’s yeast production, as the results depend on the objective adopted, e.g. maximisation of biomass yield, maximisation of productivity or development of defined biomass properties, such as fermentation activity. But there are many more factors that affect the results of baker’s yeast production, e.g. the occurrence and intensity of complex biochemical changes (referred to as Pasteur effect, Crabtree effect or glucose effect), the composition of the feed, the genetic properties of the yeasts used, the design of the bioreactor and the method of aeration, etc. etc. The diversity of the impacts involved is an obstacle to the optimisation of the baker’s yeast process. The available models are highly sophisticated and therefore of little practical use, if at all. Hence the need to develop straightforward and customized methods has taken on a sense of urgency.

The objective of our study was to derive a simple mathematical formula, which describes feed inflow into the fed-batch culture of baker’s yeast and is able to provide a maximal biomass yield and the highest possible specific growth rate.

The objective of our study was to derive a simple mathematical formula, which describes feed inflow into the fed-batch culture of baker’s yeast and is able to provide a maximal biomass yield and the highest possible specific growth rate.

MATERIALS AND METHODS

Yeast and glucose feed

A pure culture of baker’s yeast (Saccharomyces cerevisiae species B₁) was used in this study. The feed for the yeast culture consisted of glucose (360 g·l^-1), (NH₄)₂SO₄ (104 g·l^-1), KH₂PO₄ (60 g·l^-1), MgSO_4×7H₂O (5 g·l^-1), CaCl_2×6H₂O (5 g·l^-1), yeast extract from Merck (2 g·l^-1), vitamin B₁ hydrochloride (72 mg·l^-1), vitamin B₆ hydrochloride (18 mg·l^-1), d-pantothenic acid calcium salt (360 mg·l^-1), biotin (0.36 mg·l^-1) and meso-inositol (720 mg·l^-1). The solution was sterilised using a 0.2 µm pore size cellulose membrane filter made by Sartorius AG.

Bioreactor and cultivation conditions

The experiments were carried out in a computer-aided laboratory setup (Fig. 1). The reactor had an overall volume of 7 l (its working volume amounting to 3.5 l). Temperature was maintained at 30±0.5°C. The pH was adjusted to 4.75-5.0 using 25% ammonia water. Dissolved oxygen concentration (DOC), as well as the volumes of CO₂ and O₂ in the gases leaving the bioreactor, was determined on-line. Revolutions and the volumetric rate of air inflow were measured throughout. Feed was dosed in portions with a peristaltic pump (12A) every 5 minutes. The volume of each portion and the time of starting each dosing procedure depended on the feeding profile used.

Analytical methods

Biomass was analysed turbidometrically with a UV/VIS spectrometer (Ultrospec III made by Pharmacia LKB) at λ=575 nm. Glucose and ethanol concentrations were measured by the HPLC method (model D-7000 HSM made by Merck Hitachi; column type: BIO-RAD HPX-87H; column size: 7.8 mm i.d. x 300 mm; temperature: 60°C; IR detection). The microbiological purity of the reactor was checked every two weeks, using nutrient agar.

Mathematical and statistical analysis

Fitting procedures were performed with TableCurve 2D v 5.01 software (made by SYSTAT Software Inc.). Student’s t-test was used to examine the statistical significance of the difference between the means of two data sets. The level of significance was set at α=0.05.

RESULTS AND DISCUSSION

The procedures of fitting the functions to the time profile of the feed inflow to the baker’s yeast process involved data coming from previous studies [7; 14 and unpublished results], where DOC was the parameter that controlled the inflow of glucose feed (laboratory cultures) or molasses (technical-scale cultures). Attempts were made to find a function for which the coefficient of determination would be greater than 0.99, and all parameters would be statistically significant. Of the many functions that satisfied these conditions, a logistic function was chosen, which had the form of:

F(t) = a/(1+b·exp(-c·t))        (1)

where F(t) denotes the rate of glucose inflow [g∙h^-1] or molasses inflow [l·h^-1], a, b and c are parameters, and t stands for cultivation time [h].

The decision about the choice of the logistic function was supported not only by the authors’ previous investigations but also by relevant data reported in the literature. They indicate that the function well describes the kinetics of microbial growth in fed-batch cultures [1; 12; 16]. A characteristic feature of these processes is the inhibition of feed inflow, which increases with time and is due to the increasing concentration of natural growth-inhibiting substances in the wort, as well as to the accumulation of metabolites following a similar pattern of inhibitory behaviour [3]. The removal of such substances by centrifugation brought about a very high harvest of the baker’s yeast biomass [2]. Table 1 shows the goodness-of-fit statistics (logistic function of equation 1) for the data from three baker’s yeast cultures of choice, and Fig. 2 includes a graphical representation of the goodness-of-fit statistics for the logistic function and the baker’s yeast culture in a 30 m³ volume reactor with DOC as the parameter of molasses inflow control.

The first experimental series was carried out with the aim of choosing appropriate values for the parameters of the logistic function (equation 1) such that the corresponding feed rate profiles would enable the maximisation of both biomass yield (Y) and specific growth rate (µ). In the first experiment of the series the feed was dosed using a logistic function fitted to the results of previous (unpublished) experiments involving the same reactor (profile no. 6; Fig. 3), where use was made of the same yeast and glucose feed, which was dosed in portions according to DOC variations (biomass yield and specific growth rate amounting to 0.55 g·g^-1 and 0.13 h^-1, respectively). In successive experiments (cultures no. 1; 2; 3; 4; 5; 7; 8; 9; 10; 11; Fig. 3), the feeding profiles were obtained by an appropriate choice of the parameters (a, b and c) for profile no. 6. The first portion of the feed and the initial content of the biomass were the same in each experiment of this series in order to provide identical initial conditions, since any change is known to have a significant impact on the course and results of a bioprocess.

The results of this experimental series are summarised in Table 2 and plotted in Fig.4. As shown by these data, biomass yield was the highest (0.59 g·g^-1) in experiments 5 and 6, where glucose concentration in the wort did not exceed 156 mg·l^-1. Under such conditions, ethanol concentration in the medium was below 42 mg·l^-1. The specific growth rate reached the maximum value (0.141 h^-1) in experiment 2, where glucose concentration rose in some instances to 500 mg·l^-1, thus supporting ethanol production. Ethanol concentration amounted to 2.37 g·l^-1, which implied the occurrence of the Crabtree effect. The high rate of biomass increment was achieved on the cost of biomass yield, which did not exceed 0.48 g·g^-1. With an even higher glucose concentration (culture no. 1), there was a decrease in both Y and µ values. The results of this experimental series showed that simultaneous maximisation of biomass yield and specific growth rate included two objectives that conflicted with each other (Fig. 4). It was also observed that, at low glucose concentrations, biomass yield was comparatively low. This is likely to be due to the disadvantageous (in terms of biomass yield) structure of carbon (glucose) utilisation by the cells for growth and maintenance.

The high proportion of the substrate cost in the overall cost of baker’s yeast production suggests that the baker’s yeast process should be optimised by maximising biomass yield, whereas the utilisation of the reactor volume should be optimised by maximising productivity. As these two objectives conflict with each other, a compromise optimisation variant was proposed. In this variant, maximisation is carried out for the criterion which is the product of biomass yield and specific growth rate (Y·µ). As shown by the data in Table 2, the criterion reached a maximal value (0.075) in experiment 3, where biomass yield and specific growth rate amounted to 0.58 g·g^-1 and 0.129 h^-1, respectively.

The experiments have shown that each optimisation variant required another feeding profile. The profiles can be described by a logistic function whose parameters take different values, depending on the optimisation variant used. Thus, for the needs of further studies we chose such a feeding profile that enabled the criterion (Y·µ) to be maximised. The corresponding logistic function takes the form:

F(t) = 160.99/(1+50.93·exp(-0.36·t))     (2)

In the experiments mentioned it was assumed that successive nutrient portions are dosed every 5 minutes. Such approach was adopted on the basis of the results obtained with many previous cultures of the same baker’s yeast where DOC was the feed control parameter. To verify the correctness of the assumption, a series of experiments was carried out in such a way that the feed was dosed according to the same profile (equation 2) and the time between the starts of dosing subsequent feed portions was 0.5; 1; 2; 3; 4; 5; 6; 7; 10; 12 and 15 minutes in successive experiments. Hence, in each experiment the total amount of the feed dosed was the same but the portions differed in size. It was impossible to further shorten the intervals between the starts of dosing subsequent portions or to apply continuous dosing because of the type of the peristaltic pump used. The results of this experimental series are summarised in Table 3.

The intervals between the dosage of subsequent glucose portions ranged from 0.5 to 7 minutes (cultures no. 1; 2; 3; 4; 5; 6; 7 and 8) and had no statistically significant effect on the biomass yield, specific growth rate or the (Y·µ) criterion value, since the relevant coefficients of correlation did not significantly differ from zero for α = 0.05. This is an indication that the 5-minute dosing cycle adopted a priori should not raise objections. Dosing cycles longer than 7 minutes (cultures no. 9; 10 and 11) produced a statistically significant deterioration of the results obtained. Student’s t-test was used to examine the statistical significance of the difference between the means of two data sets. This deterioration was observed both with biomass yield and specific growth rate and resulted from the dosage of such glucose amounts that produced the Crabtree effect, as it may be inferred from the ethanol concentrations measured in the wort (Table 3). The concentrations of ethanol concomitant with elevated concentrations of glucose were not as high as in the first experimental series. This finding seems to be linked with the difference in the frequency of occurrence of high glucose concentrations between the two experimental series. In the first series, high glucose concentrations occurred every 5 minutes. In the second series, the occurrence of increased glucose concentrations was far less frequent because of the longer intervals between glucose dosages. In this way, the yeast cells had enough time for the assimilation of glucose and thereafter of a considerable portion of the ethanol produced.

The presented method for the control of the baker’s yeast process is not very complicated. What it needs is a digital dosing pump fitted with a microprocessor. With such a pump it is possible to carry out different optimisation variants. The biomass yield and specific growth rate values obtained are comparable to the highest ones achieved with the same yeast cultures, when use was made of a fuzzy logic controller to optimise and control feed dosage [7].

CONCLUSIONS

On the basis of the results obtained the following conclusions can be drawn:

1. The logistic function of the form F(t) = a/(1+b·exp(-c·t)) well describes the feeding profile for the baker’s yeast process involving a glucose-based substrate.

2. The maximisation of biomass yield and the maximisation of specific growth rate are two objectives that conflict with each other. The specific growth rate value is maximised at the cost of the biomass yield value. A compromise solution is a feeding profile enabling the maximisation of the criterion (Y·µ), which is the product of the biomass yield and the specific growth rate. The criterion reached the maximal value in the baker’s yeast culture when biomass yield and specific growth rate amounted to 0.58 g·g^-1 and 0.129 h^-1, respectively.

REFERENCES

1. Fang B. (1994): Application of a generalized logistic equation to simulate a fed-batch process. Chin. J. Biotechnol., Vol. 10, No. 3, 179-186.

2. Fukuda H., Shiotani T., Okada W., Morikawa H. (1978a): A new culture method of baker’s yeast to remove growth-inhibitory substances. J. Ferment. Technol., Vol. 56, No. 4, 354-360.

3. Fukuda H., Shiotani T., Okada W., Morikawa H. (1978b): A mathematical model of the growth of baker’s yeast: subject to product inhibition. J. Ferment. Technol., Vol. 56, No. 4, 361-368.

4. He R.Q., Xu J., Li C.Y., Zhao X.A. (1993): The principle of parabolic feed for a fed-batch culture of baker’s yeast. Appl. Biochem. Biotechnol., Vol. 41, No. 3, 145-155.

5. Hisbullah, Hussain M.A., Ramachandran K.B. (2003): Design of a fuzzy logic controller for regulating substrate feed to fed-batch fermentation. Food Bioprod. Processing, Vol. 81, No. C2, 138-146.

6. Karakuzu C., Öztürk S., Türker M. (2004): Design and simulation of a fuzzy substrate feeding controller for an industrial scale fed-batch baker yeast fermentor. In: Lecture Notes in Computer Science. Publisher: Springer-Verlag GmbH, Vol. 2715/2003, 458-465.

7. Kasperski A., Miœkiewicz T. (2002): An adaptive fuzzy logic controller using the respiratory quotient as an indicator of overdosage in the baker’s yeast process. Biotechnol. Lett., Vol. 24, No. 1, 17-21.

8. Kishimoto M., Sawano T., Yoshida T., Taguchi H. (1984): Application of a statistical procedure for the control of yeast production. Biotechnol. Bioeng., Vol. 26, No. 8, 871-876.

9. Kurtanjek Z. (1998): Principal component ANN for modelling and control of baker's yeast production. J. Biotechnol., Vol. 65, No.1, 23-35.

10. Lee J., Lee S.Y., Park S., Middelberg P.J. (1999): Control of fed-batch fermentations. Biotechnol. Adv., Vol. 17, 29- 48.

11. Li Y., Chen J., Song Q., Lun S., Katakura Y. (1997): Fed-batch culture strategy for high yield of baker's yeast with high fermentative activity. Chin. J. Biotechnol., Vol. 13, No. 2, 105-113.

12. Liu G., Zheng Z., Song D., Cen P. (1995): Kinetic models of batch and fed-batch culture of single-cell protein with double carbon sources. Chin. J. Biotechnol., Vol. 11, No. 3, 163-170.

13. Lübbert A., Jørgensen S.B. (2001): Bioreactor performance: a more scientific approach for practice. J. Biotechnol., Vol. 85, 187-212.

14. Miœkiewicz T., Wilczyński S. (1996): A real-time feed rate control system for pilot plant baker's yeast production. Biotechnol. Lett., Vol. 18, No.1, 1-6.

15. O’Connor G.M., Sanchez-Riera F., Cooney C.L. (1992): Design and evaluation of control strategies for high cell density fermentations. Biotechnol. Bioeng., Vol. 39, No. 3, 293-304.

16. Özadali F., Özilgen M. (1988): Microbial growth kinetics of fed-batch fermentations. Appl. Microbiol. Biotechnol., Vol. 29, No. 2/3, 203-207.

17. Patniak P.R. (1997): Artificial intelligence as a tool for automatic state estimation and control of bioreactors. Lab. Robotics Automat., Vol. 9, 297-304.

18. Pertev C., Türker M., Berber R. (1997): Dynamic modeling: Sensitivity analysis and parameter estimation of industrial fermenters. Comput. Chem. Eng., Vol. 21, Supplement, 739-744.

19. Petrova M., Koprinkova P., Patarinska T. (1997): Neural network modeling of fermentation process. Microorganisms cultivation model. Bioproc. Biosyst. Eng., Vol. 16, No. 3, 145-149.

20. Rani K.Y., Rao V.S.R. (1999): Control of fermenters: a review. Bioproc. Biosyst. Eng., Vol. 21, No. 1, 77- 88.

21. Ronen M., Shabtai Y., Guterman H. (2002): Optimization of feeding profile for a fed-batch bioreactor by an evolutionary algorithm. J. Biotechnol., Vol. 97, 253-263.

22. Shimizu K., Ye K. (1995): Development of intelligent bioreactor systems. Sensor Mater., Vol. 7, No. 4, 233-247.

23. Suzuki H., Kishimoto M., Kamoshita Y., Omasa T., Katakura Y., Kenn-ichi S. (2000): On-line control of feeding of medium components to attain high cell density. Bioproc. Biosyst. Eng., Vol. 22, No. 5, 433-440.

24. Thibault J., Acuña G., Pérez-Correa R., Jorquera H., Molin P., Agosin E. (2000): A hybrid representation approach for modelling complex dynamic bioprocesses. Bioproc. Biosyst. Eng., Vol. 22, No. 6, 547-556.

25. Ündey C., Tatara E., Çinar A. (2004): Intelligent read-time performance monitoring and quality prediction for batch/fed-batch cultivations. J. Biotechnol., Vol. 108, 61-77.

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