Quantitative Analysis of the Key Factors Affecting Yeast Growth

Ind. Eng. Chem. Res. 2003, 42, 5109-5116

5109

Quantitative Analysis of the Key Factors Affecting Yeast Growth M. Di Serio,† P. Aramo,† E. de Alteriis,‡ R. Tesser,† and E. Santacesaria*,† Dipartimento di Chimica, Universita` degli Studi di Napoli Federico II, via Cinthia, 80126 Napoli, Italy, and Dipartimento di Fisiologia Generale ed Ambientale, Sez. Igiene e Microbiologia, Universita` degli Studi di Napoli Federico II, via Mezzocannone 16, 80134 Napoli

Yeast growth is affected not only by the operative conditions (temperature, pH, sugar concentration) but also by the intrinsic properties of the investigated system, namely, type of strain, culture medium, and physiological state of the inoculum. Several authors describe the influence of the operative conditions quantitatively, whereas the effects of the intrinsic properties are in general reported as qualitative observations. In order to investigate these aspects, which are very important in the optimization of industrial baker’s yeast production, several yeast growth runs were carried out varying the type of strain, the culture medium, and the physiological state of the inoculum employed. Experimental data on both batch and fed-batch baker’s yeast growth were interpreted quantitatively using a modified and improved suitable cybernetic model. The results of a sensitivity analysis performed on the kinetic parameters of the model have shown that parameters related to the different culture medium and strain can be obtained by mathematical regression on experimental data. The parameters relating to the different physiological state of the inoculum are independent from strain and culture medium employed, so that one batch and one fed-batch growth run, carried out in defined operative conditions, are sufficient to determine the whole set of model parameters. Moreover, the improved model has been tested by simulating fed-batch growth runs, performed under different operative conditions, demonstrating its predictive power. Introduction Saccharomyces cerevisiae biomass, mainly in the form of baker’s yeast, represents the largest bulk production of any single-cell microorganism in the world. Several million tons of fresh baker’s yeast cells are produced yearly for human food use.1 The production of baker’s yeast involves the multistage propagation of the selected yeast strain on sugar as a carbon source. Baker’s yeast is usually produced starting from a small quantity of yeast added to a liquid solution of essential nutrients (molasses, ammonia or ammonium salts, phosphate, and vitamins), at a suitable temperature and pH. Once the cell population has grown enough, it is transferred into a larger bioreactor for a new growth stage; 4 or 5 stages are usually necessary to reach a satisfactory production quantity. Therefore, the bioreactor volume changes from 1/10 dm3 to 100/150 m3. The smaller bioreactors used for the initial stages operate in batch and anaerobic conditions, whereas, in the larger bioreactors used for the later stages, aeration is provided and the fed-batch cultivation mode is adopted, i.e., the nutrients are fed to the culture medium at a variable rate. The plant configuration and operative choices are the consequence of the effects that S. cerevisiae metabolism has on biomass yield and growth rate.2 During the aerobic growth of S. cerevisiae, both sugars and ethanol can be used as carbon and energy sources. Sugars can be metabolized via two different energy-producing * To whom correspondence should be addressed. Phone: ++39+81674027. Fax: ++39+81674026. E-mail: [email protected]. † Dipartimento di Chimica. ‡ Dipartimento di Fisiologia Generale ed Ambientale, Sez. Igiene e Microbiologia.

pathwayssfermentation or oxidationsdepending on the sugar concentration in the medium. Indeed, at a high sugar concentration, oxidation is suppressed and fermentation takes place (the Crabtree effect); oxidation predominates when sugar concentration is below 50100 mg/dm3. On the other hand, under oxygen-limited growth conditions, the fermentative pathway leading to ethanol production predominates, even at a low sugar concentration. During aerobic growth on sugars, the ethanol produced during the initial fermentative metabolic pathway is consumed when sugars are no longer available in the medium. Biomass yields on sugars (gcells/ gsugars) are strongly related to the prevailing metabolic pathway, being maximal only when sugar is oxidized, i.e., when its concentration remains below 0.05-0.1 g/dm3. Contrarily, volumetric biomass productivity (gcells/ dm3 h) is maximal if the specific growth rate is maximal, i.e., at a high sugar concentration, when the fermentative pathway is operative.2 In the first stages of industrial production, a batch cultivation mode is employed, thus favoring productivity instead of biomass yield, since the total biomass produced in small reactors is low. In the following stages carried out in larger reactors, it is necessary to optimize both yield and productivity, and a fed-batch cultivation mode is employed. Therefore, the initial feed profile is selected to give a high growth rate when total biomass is still low (low yield/high productivity); under these conditions some ethanol is produced. Later, the feed profile is fixed in such a way as to favor oxidative metabolism (high yield/low productivity),2 and the ethanol initially formed is also consumed. The control of the molasses feed profile, performed with a feedback loop based on data collected from exhaust gas analysis (O2 and CO2) and/or ethanol sensors,3-5 has not proved to be economically advanta-

10.1021/ie030078z CCC: $25.00 © 2003 American Chemical Society Published on Web 09/19/2003

5110 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 Table 1. Operative Conditions of Experimental Runs Performed run type strain medium initial liquid vol (dm3) inoculum type inoculum (d.w. (dry weight)/dm3) initial sugar concd (g of glucose equiv/dm3) sugar concd in fed (g of glucose equiv/dm3) feed profile dm3/h

1 batch S288C YEPG 0.5 1.00 ferment. 0.1 5.0

2 batch 168/9 YEPG 0.5 1.00 ferment. 0.1 5.0

3 batch 168/9 synthetic 1.00 ferment. 0.1 5.0

geous,6 so industrial fed-batch production of baker’s yeast is still carried out in open loop conditions, and the empirically established molasses feed profiles are kept as manufacturing secrets.7,8 Other than feed control, optimization of the entire bioprocess through the choice of optimal bioreactor size, process duration, and initial concentration of inoculum is the goal of industrial production.6 Major problems arise from the fact that yeast growth rate depends on both the strain employed and composition of molasses, the latter varying considerably according to the refinery technology and agricultural and climate conditions.2,9 This limits the use of an expert program for optimization which requires that the information acquired in previous runs should be stored in the system database.7 A dynamic approach to bioprocess optimization could be carried out by the employment of a mathematical model developed to describe yeast growth in an industrial bioreactor, together with a finite-horizon cost criterion.6 The reliability of the mathematical model proposed should be therefore tested under different operative conditions. Though many different models have been proposed to describe S. cerevisiae growth in batch, fed-batch, and continuous laboratory reactors,10-16 only the models based on the so-called “bottleneck” hypothesis12 and on the “cybernetic” approach developed by Ramkrishna and co-workers17,18 have been tested on industrial data of baker’s yeast production.15,19 Pertev et al.19 tested the model based on the “bottleneck” hypothesis by simulating batch and fed-batch industrial reactor runs, but the results obtained showed some discrepancies attributed to the inability of the model to take into account the behavior of yeast under transient conditions. Di Serio et al.15 showed that the cybernetic approach is suitable for the simulation of baker’s yeast growth in laboratory and industrial bioreactors. In the present paper we have investigated the effects that factors such as type of strain, culture medium, and physiological state of the inoculum exert on yeast growth, by carrying out experimental batch and fedbatch runs. The quantitative analysis of the obtained data was performed by means of an improved version of the previously proposed cybernetic model.15 A sensitivity analysis of the model’s kinetic parameters was also performed to establish the parameters that could be determined by mathematical regression on the experimental data. Furthermore, the improved model has been verified by simulating fed-batch growth runs, carried out in operative conditions different from those used to determine the model’s kinetic parameters, so demonstrating its predictive power.

4 batch 168/9 industrial 1.00 ferment. 0.1 5.0

5 fed-batch 168/9 industrial 0.95 oxidative on ethanol 0.22

6 fed-batch 168/9 industrial 0.95 ferment. 0.22

7 fed-batch 168/9 industrial 0.90 ferment. 0.32

41.65

41.65

60.11

(7.5 × 10-4)e(0.21t)

(7.5 × 10-4)e(0.21t) (7.5 × 10-4)e(0.35t)

Materials and Methods Experimental Runs. All the experimental runs performed and the relative operative conditions used are shown in Table 1. S. cerevisiae strains S288C (MATR, SUC2, Mal, gal2, CUP1)20 and 168/9 were used in the experiments of this paper. S288C is a laboratory strain, whereas the 168/9 strain was isolated from commercial baker’s yeast (Eridania, Genova, Italy). Strains were stored at 4 °C on agar slants. The media used in batch experiments were (a) YEPG 0.5 (10 g/dm3 yeast extract, 5 g/dm3 bactopeptone, 5 g/dm3glucose; (b) the synthetic medium according to von Meyemburg21 (5 g/dm3 glucose, 3.75 g/dm3 (NH4)2HPO4, 0.50 g/dm3 KH2PO4, 0.15 g/dm3 MgSO4‚7H2O, 0.020 g/dm3 CaCl2, 7.5 mg/dm3 FeSO4(NH4)2SO4‚6H2O, 2.0 mg/dm3 ZnSO4‚7H2O, 0.3 mg/dm3 CuSO4‚5H2O, 20 mg/ dm3 inositol, 4.4 mg/dm3 thiamine chlorhydrate; 1.2 mg/ dm3 pyridoxine, 0.5 mg/dm3 calcium D-pantotenate, 0.03 mg/dm3 biotin); and (c) and an industrial medium with molasses as the carbon source, prepared by diluting a 50% v/v beet molasses and 50% v/v cane molasses stock solution, so that the total sugar concentration was 5 g of glucose equiv/dm3, with 10 dm3 of (NH4)2HPO4, 10 g/dm3 KH2PO4, and 3 g/dm3 MgSO4‚7H2O added. In fed-batch experiments, a solution having the same inorganic salt concentration as that of the previously mentioned industrial medium was used. The fed solution was prepared by diluting a 50% v/v beet molasses and 50% v/v cane molasses stock solution. Both batch and fed-batch experiments were carried out at 30 °C, pH 5.0, and 700 rpm in a 2-L stirred tank reactor (New Brunswick), equipped with electrodes and control systems for pH, temperature, and dissolved oxygen concentration, and a peristaltic pump and control software for feed profile setting. As regards the physiological state, two different types of inoculum were used: a fermentative and an oxidative inoculum, obtained by collecting cells from a preculture at the exponential phase of growth on glucose and ethanol, respectively. Oxygen was supplied by sparging the fermenter with air at a flow rate of 110 N L h-1, so that dissolved oxygen concentration was always higher than 15% air saturation.4 kLa of the fermenter in the operative conditions of the experiments performed was determined by the dynamic method and resulted as 180 h-1. Samples of culture medium were withdrawn from the reactor at fixed time intervals during growth experiments to determine biomass, residual sugar, and ethanol concentrations in the medium.

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5111

For biomass determination, cells were harvested by centrifugation, washed with distilled water, and heated at 105 °C for dry weight determination. Residual glucose and ethanol determinations were made on culture supernatants using the GOD-Perid and Ethanol-UV enzymatic kit (Roche Diagnostics GmbH, Mannheim, Germany), respectively. The concentration of total sugars in the industrial medium was determined with the phenol sulfate method (see Dubais et al.22). A fraction (22%) of the total sugar concentration present in the industrial medium was shown to have not been metabolized by yeast cells, as demonstrated by determining the residual sugar concentration in the industrial medium after yeast cells (168/9 strain) were allowed to grow in that medium until the end of the first exponential phase of growth. The determination errors were experimentally estimated to be about 5% maximum on the basis of several measurements employing the error propagation. The Cybernetic Model. As previously described, S. cerevisiae has internal regulating mechanisms which direct the microorganism toward the most convenient metabolic pathway able to optimize the use of available resources. The kinetic modeling of the growth behavior of S. cerevisiae requires a detailed knowledge of the intracellular control mechanisms that the Monod classical model is not able to describe. As a general rule, none of the unstructured models are able to predict complicated dynamics, e.g., the diauxic growth. Ramkrishna and co-workers have simplified these problems: invoking the cybernetic viewpoint, they developed a general modeling framework.18 The cybernetic modeling framework is based on the hypothesis that microorganisms optimize the utilization of available substrates to maximize their growth rate at all times. The values of the single growth rates of the different metabolic pathways are calculated by means of a modified Monod equation rate, where each growth rate is proportional to the concentration of the “key” enzyme (ei) of the single metabolic pathway. The cybernetic modeling framework replaces the detailed modeling of regulating processes with the cybernetic variables ui and vi representing the optimal strategies for the synthesis and activity, respectively, of the enzymes of the metabolic pathway, i. The value of ui can be assessed assuming that cell resources will be allocated in such a way as to obtain the maximum biomass growth rate. A law of resource allocation can be derived from the economic theory of marginal utility:18

ui )

ri

∑rj

νi )

maxj(rj)

e1 Z r1 ) µ1,max e1,max K1VL + Z

e3 Ox Z r3 ) µ3,max e3,max K3VL + Z Kox + Ox sugar oxidation (5) Z and E represent the quantity of sugars which can be metabolized and ethanol, respectively, in the bioreactor; Ox is the concentration of dissolved oxygen; VL the volume of the liquid in the bioreactor. µi,max and Ki represent the maximal specific growth rate and saturation constants for the substrate of each metabolic pathway i, respectively. Kox is the saturation constant for the dissolved oxygen which is independent of any single oxidative metabolic pathway. With these growth rate equations, the common balance equations for batch (Fin ) 0; Fout ) 0), fed-batch (Fin * 0; Fout ) 0) and continuous (Fin * 0; Fout * 0) bioreactors can be written as

dB dt

3

)(

B

riνi)B - Fout ∑ V i)1

balance on biomass

(6)

L

(

)

r1ν1 r3ν3 Z dZ ) FinzFed + B - Fout dt Y1 Y3 VL balance on sugar (7)

(

)

r1ν1 r2ν2 E dE ) φ1 B - Fout dt Y1 Y2 VL balance on ethanol (8) dVL ) Fin - Fout dt

( )

d

balance on liquid volume

e1

e1,max dt

3

( (2)

sugar fermentation (3)

e2 Ox E r2 ) µ2,max e2,max K2VL + E Kox + Ox ethanol oxidation (4)

(1)

The variable controlling the inhibition/activation mechanism of the “key” enzyme i (vi) is determined considering a null inhibition effect when the microorganism grows on the substrate which accelerates the biomass growth rate to the utmost, whereas the inhibition effect progressively increases at a decreasing growth rate.18 Therefore,

ri

The “cybernetic approach” has been used by Jones and Kompala18 and by Di Serio et al.14,15 to describe the growth of S. cerevisiae. The model used in this paper is an improvement of that suggested by Di Serio et al.15 The specific growth rates for the different metabolic pathways are modeled according to a modified Monod rate equation, where the modification consists of the fact that each growth rate ri has been assumed proportional to ei/ei,max, the relative intracellular “key” enzyme concentrations:

(

(9)

)

Z ) (µ1,max + β) 1 - 1 + 1u1 K1VL + Z

( )

riνi + β) ∑ e i)1

e1

balance on relative

1,max

concentration of fermentation key enzyme (10)

5112 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003

( )

d

e2

e2,max dt

Ox

)

Kox + Ox

( )

d

dt

( )

3


-(

e2

2,max

balance on relative concentration of ethanol oxidation key enzyme (11)

e3

e3,max

(

E ) (µ2,max + β) 1 - 2 + 2u2 K2VL + E

(

Z ) (µ3,max + β) 1 - 3 + 3u3 K3VL + Z Ox

)

Kox + Ox

( )

3


-(

e3

Figure 1. Experimental data (points) of run 1 and the simulation values (lines) obtained by using the corresponding parameters (see Table 4).

3,max

balance on relative concentration of sugar oxidation key enzyme (12)

(

)

r2ν2 r3ν3 B d(Ox) + φ3 ) kLa(Ox* - Ox) - φ2 dt Y2 Y3 V L balance on liquid concentration of oxygen (13) where B, Fin, zFed, kLa, and Ox* are the biomass quantity in the reactor, the feed flow rate, the sugar concentration in the feed, the coefficient of gas-liquid mass transfer, and the concentration of oxygen at the gasliquid interface, respectively. Yi and φi are the yields and the stoichiometric coefficients for the different metabolic pathways, respectively. β is the enzyme decay rate constant; it is considered independent from the enzyme type and assumed to be 0.2 h-1.13-15,18 The term i is equal to Ri/(Ri + Ri*), where Ri is the i enzyme synthesis rate constant for i metabolism, and Ri* is the constitutive synthesis term of i enzyme which is always operative.13,15,23 In the previous version of the model Di Serio et al.15 considered the same i value for the enzyme of each metabolic pathway, whereas in this paper, with a closer approach to the reality of cell metabolism, we consider that each metabolic pathway has its own characteristic “key” enzyme synthesis rate constant (Ri) and constitutive synthesis term (Ri*).


Results and Discussion Batch and Fed-Batch Experiments. By comparing the experimental data from batch runs 1 and 2, carried out with the same culture medium and type of inoculum (fermentative) but different strains (Figures 1 and 2), it is possible to observe that complete depletion of glucose and ethanol in the medium occurred earlier in the case of 168/9, thus revealing that this strain seems better adapted than S288C to both fermentative and oxidative conditions. Additional qualitative information deriving by the two batch experiments considered is that final biomass concentration of strain 168/9 appeared higher than that of S288C, this probably due to the origin of 168/9, which is a strain selected for industrial use. The culture medium employed had a great influence on final biomass concentration, as shown by comparing


the experimental data of runs 2, 3, and 4, carried out with the same strain (168/9) and inoculum type, but different media (Figures 2, 3, and 4). Indeed, the final biomass concentration, obtained with the complex medium (YEPG 0.5), was significantly higher than those obtained with both the synthetic and industrial media. This can be attributed to the fact that YEPG 0.5 contains various organic components, which can be used as carbon sources other than glucose and ethanol by the



Figure 5. Experimental data (points) used feed profile (dashed line) of run 5 and the simulation values (continuous lines) obtained by using the corresponding parameters (see Table 4).

growing yeast. The final biomass concentration value obtained with the industrial medium was intermediate between those obtained with the complex and the synthetic media, since also molasses contains organic compounds which can be consumed by cells,24 but in small amounts. In Figure 4 it is clearly shown that total sugar concentration in the industrial medium did not fall to zero, thus indicating that a percentage of sugars in molasses is not consumed by S. cerevisiae.24 The influence of the physiological state of the inoculum on growth can be evidenced by comparing the experimental data from fed-batch runs 5 and 6, carried out with the same strain (168/9), medium (industrial), and feed profile (Figures 5 and 6), but started with an oxidative and fermentative inoculum, respectively. In the growth run started with the oxidative inoculum (Figure 5), ethanol formation began only form the 12th hour of growth, notwithstanding the fact that after the 6th hour, sugar concentration had already reached a value higher than 0.1 g/dm3, which should give rise to the Crabtree effect. On the contrary, in the growth with a fermentative inoculum (Figure 6), ethanol formation was detected already from the 6th to 7th hour of growth. The lower final biomass concentration obtained in run 6 with respect to run 5 can be attributed to the different type of inoculum employed in the two experiments. These observations show the great influence that the physiological state of inoculum has on growth.



The effect of the feed profile can be seen by comparing the data of fed-batch runs 6 and 7 (Figures 6 and 7), carried out under the same experimental conditions insofar as yeast strain and inoculum type were concerned, but with different molasses concentrations and feed profile. The higher feed profile in run 7 with respect to run 6 determined a higher sugar concentration in the medium all through the run, favoring fermentative metabolism, and consequently higher final biomass and ethanol concentrations. Simulations of Batch and Fed-Batch Runs. In the proposed model we need 15 parameters (Yi, µi,max, Ki, i, φi, i ) 1, 3) and 3 initial values of ei/ei,max (i ) 1, 3) to simulate the experimental runs. The growth runs performed in this work were carried out avoiding oxygen starvation conditions (see Materials and Methods), so that the influence of the oxygen saturation constant (kOx) and oxygen stoichiometric factors (φ2, φ3) on simulations can be neglected. Therefore, these parameters can be derived from the literature (kOx ) 4.6 × 10-5 g/dm3, φ2 ) 1.067, φ3 ) 0.52).15 The values of 1, 2, and 3 were determined by finding the best values that, by using the model (eqs 10-12), gave the experimental ratios (ei/ei,max)stationary in the stationary phase. The (e1/e1,max)stationary and (e2/ e2,max)stationary values were determined considering that the values of e1,max and e2,max were proportional to the

5114 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 Table 2. Initial Enzyme Concentration Values for the Different Types of Inocula inoculum fermentative oxidative on ethanol oxidative on sugar stationary

(e1/e1,max)0

biomass collected in fermentative exponential phase on sugar biomass collected in oxidative exponential phase on ethanol biomass collected in oxidative exponential phase on sugar Biomass collected after long-term stationary phase (ei/ei,max)stationary

sensitivity

φ1 Y1 Y2 Y3 µ1,max (h-1) µ2,max (h-1) µ3,max (h-1) K1 (g/dm3) K2 (g/dm3) K3 (g/dm3) a

value 0.41 0.15 0.74 0.5 0.45 0.20 0.33 1.0 0.08 0.001

batch g/dm3

4.15 16.61 g/dm3 8.59 g/dm3 0.01 g/dm3 19.71 g h/dm3 12.22 g h/dm3 0.01 g h/dm3 2.52 2.53 0.

(e3/e3,max)0

0.8

(e2/e2,max)stationary



0.8




0.8

0.01

0.11

0.46

Since the other model parameters related to the strain type and culture medium (Yi, µi,max, Ki, i ) 1, 3, φ1) had to be obtained by mathematical regression on experimental data, a sensitivity analysis was performed on them.27 The study of parametric sensitivity was carried out with the parameters used by Di Serio et al.15 to simulate the experimental data of von Meyemburg.28 The parameters are reported in Table 3, together with the maximal relative sensitivity of each of them, both in batch and in fed-batch growth runs. From the results of the parametric analysis it is clear that the determination of the parameters of the first two metabolic pathways (sugar fermentation and ethanol oxidation) can be obtained by carrying out one batch growth run, whereas for the determination of the parameters of the third metabolic pathway (sugar oxidation) it is necessary to examine one fed-batch growth run, i.e., considering an experimental condition where the Crabtree effect did not occur. The seven parameters (Y1, Y2, µ1,max, µ2,max, K1, K2, and φ1), obtained by nonlinear regression analysis on the experimental data29 for batch runs 1-4, are reported in Table 4. Since batch run simulations resulted unaffected by the values of the parameters related to oxidative metabolism (Y3, µ3,max, and K3), those derived from the literature15 were employed. The agreement between simulations and experimental data is shown in Figures 1-4. The parameter values obtained reflect the properties of both the yeast strain and culture medium employed. In fact, the values of biomass yields (Y1, Y2) of the 168/9 strain are higher than those of S288C. In particular, Y2 resulted equal to 1.26 ( 0.11, indicating that the industrial strain 168/9 is able to metabolize other nutrients present in the complex medium more efficiently than S288C. Also µ1,max and µ2,max resulted higher in the case of the industrial strain, thus confirming the qualitative observations previously discussed. The different values of Y1, Y2, µ1,max, µ2,max, K1, and K2 of runs 2, 3, and 4 of Table 4 evidenced the effect of culture medium on yeast growth. The higher values of biomass yields and growth rates were obtained with the

Table 3. Kinetic Parameter Values Used by Di Serio et al.15 To Simulate the von Meyemburg Experimental Data28 and Maximum Parametric Sensitivity in Batch and Fed-Batch Runsa parameter

(e2/e2,max)0

fed-batch 0.01 g/dm3 0.01 g/dm3 0.01 g/dm3 8.73 g/dm3 0.01 g h/dm3 0.01 g h/dm3 14.24 g h/dm3 0.01 0.01 2.24

Sensitivity, Si ) ∂(Z/VI)/∂πi.

rate of protein synthesis, the former in the fermentative exponential phase on sugar and the latter in the oxidative exponential phase on ethanol.25 Meanwhile e1 and e2 were proportional to the rate of protein synthesis in the long-term stationary phase.25 The resulting values were (e1/e1,max)stationary ) 0.01 and (e2/e2,max)stationary ) 0.11. The value of (e3/e3,max)stationary equal to 0.46 was determined by considering the ratio between the values of total enzyme concentrations in baker’s yeast during the oxidative exponential phase on sugar and in the stationary phase.26 The corresponding i values were calculated: 1 ) 0.997, 2 ) 0.943, and 3 ) 0.804. To simulate growth runs of the present work carried out with different types of inoculum, the initial relative enzyme concentrations (ei/ei,max)0 reported in Table 2 were employed. Since the physiological state of the inoculum is characterized by the different values of enzyme concentrations related to the three different metabolic pathways, it was assumed that the enzyme concentrations of the nonpredominant metabolic pathways were those corresponding to the stationary phase, whereas the one related to the predominant pathway was higher, so a 0.8 value was used for the simulation, the system being poorly sensitive to this parameter in a range of 20%.

Table 4. Kinetic Parameters Obtained by Regression Analysis and Used To Simulate the Different Runs with the Cybernetic Model run

1

2

3

4

5

6

7

φ1 Y1 Y2 Y3 µ1,max (1/h) µ2,max (1/h) µ3,max (1/h) K1 (g/dm3) K2 (g/dm3) K3 (g/dm3)

0.373 ( 0.016 0.199 ( 0.007 0.803 ( 0.038 0.5a 0.659 ( 0.064 0.172 ( 0.041 0.23a 0.692 ( 0.064 0.277 ( 0.054 0.001a

0.355 ( 0.019 0.212 ( 0.010 1.26 ( 0.11 0.5a 0.723 ( 0.069 0.275 ( 0.066 0.23a 0.604 ( 0.070 0.272 ( 0.054 0.001a

0.374 ( 0.018 0.1425 ( 0.0048 0.419 ( 0.032 0.5a 0.422 ( 0.038 0.111( 0.005 0.23a 0.217 ( 0.041 0.0234 ( 0.038 0.001a

0.451 ( 0.002 0.210 ( 0.005 0.583 ( 0.002 0.5a 0.580 ( 0.012 0.175 ( 0.003 0.23a 0.229 ( 0.002 0.218 ( 0.001 0.001a

0.451 ( 0.210 ( 0.005(4) 0.583 ( 0.002(4) 0.675 ( 0.005 0.580 ( 0.012(4) 0.175 ( 0.003(4) 0.217( 0.006 0.229 ( 0.002(4) 0.218 ( 0.001(4) 0.0385 ( 0.0004

0.451 ( 0.210 ( 0.005(4) 0.583 ( 0.002(4) 0.675 ( 0.005(5) 0.580 ( 0.012(4) 0.175 ( 0.003(4) 0.217( 0.006(5) 0.229 ( 0.002(4) 0.218 ( 0.001(4) 0.0385 ( 0.0004(5)

0.451 ( 0.002(4) 0.210 ( 0.005(4) 0.583 ( 0.002(4) 0.675 ( 0.005(5) 0.580 ( 0.012(4) 0.175 ( 0.003(4) 0.217( 0.006(5) 0.229 ( 0.002(4) 0.218 ( 0.001(4) 0.0385 ( 0.0004(5)

a

From Di Serio et al.15 (4) From run 4 and (5) from run 5.

0.002(4)

0.002(4)


complex medium, which contains a high amount of components which can be metabolized by yeast. It must be pointed out that the model does not take into account the fact that yeast cells may metabolize nutrients other than sugars and ethanol, so that the values of Y1, Y2, µ1,max, µ2,max, K1, and K2, reported in Table 4 and related to runs 1 and 2, should be considered apparent. To simulate fed-batch run 5, the three parameters related to oxidative metabolism (Y3, µ3,max, and K3) were obtained by nonlinear regression on experimental data, whereas the other parameters were derived from run 4, where the same yeast strain and culture medium were employed. In run 5 an oxidative inoculum was employed. The agreement between the simulation obtained and experimental data is shown in Figure 5. Indeed, the cybernetic model developed can describe both batch and fed-batch runs. Moreover, a fed-batch run, namely, run 6, performed with the same yeast strain and medium as those employed in run 5, but with a fermentative inoculum, was simulated with the same parameters used for run 5, except for the initial enzyme concentrations, which obviously were chosen in agreement with the fermentative inoculum employed (Table 2). The agreement between the simulation and experimental data (Figure 6), notwithstanding the different experimental behavior shown in the two runs (Figures 5 and 6), demonstrated the predictive power of the cybernetic model with respect to the physiological state of the inoculum. In order to study the effect of the different operative choices, run 7 was carried out under the same experimental conditions as run 6 with respect to the type of strain, culture medium, and physiological state of the inoculum employed, but changing the feed profile and molasses concentration. To simulate run 7 the same kinetic parameters and initial enzyme concentrations of run 6 were used. Also in this case, the predictive power of the model employed could be noted by the satisfactory agreement between simulation curves and experimental data (Figure 7). Conclusions The results of the present work represent a further demonstration that the growth of S. cerevisiae is strongly influenced by the intrinsic properties of the investigated system, that is, the type of strain and the culture medium, and the physiological state of the inoculum. Therefore, all these factors should be carefully checked in an industrial process for baker’s yeast production. The quantitative analysis of the key factors affecting yeast growth was performed by means of an improved version of the cybernetic model previously proposed. In fact, the qualitative differences observed in the growth runs carried out in various experimental conditions were quantified by estimating the model’s kinetic parameters. Moreover, the interpretation of the experimental runs performed has revealed the predictive power of the cybernetic model. Its employment should allow the scaling-up and optimization of the conduction of the industrial bioreactors for a given type of yeast strain and medium, starting from data derived from one batch and one fed-batch run. This type of investigation will be developed in a further paper. The results reported in this work support Bailey’s idea30 of “cybernetic modeling” as a powerful approach to the description of biological phenomena, even if it

represents a big conceptual leap from the traditional point of view of chemical reaction engineering. However, the large amount of experimental data reported in this paper could also be useful for testing simulation models proposed by other authors. Acknowledgment Thanks are due to Consiglio Nazionale delle Ricerche (Target Project on Biotechnology) and to Murst (MurstCofin 40% to Palma Parascandola No. MM05C63814) for the financial support. Nomenclature B ) yeast mass (g) E ) ethanol mass (g) ei/ei,max ) relative concentration of the key enzyme of the i metabolic pathway (1 ) glucose fermentation, 2 ) ethanol respiration, 3 ) glucose respiration) Fin ) liquid feed (dm3/h) Ki ) saturation constant of the metabolic way i K1 ) saturation constant of sugar fermentation (g/ dm3) K2 ) saturation constant of ethanol oxidation (g/ dm3) K3 ) saturation constant of sugar oxidation (g/ dm3) kLa ) oxygen mass transfer coefficient (h-1) Ox* ) oxygen solubility (g/dm3) Ox ) oxygen concentration in liquid bulk (g/dm3) ri ) specific growth rates for the metabolic pathway i Si ) parametric sensitivity of sugar concentration with respect to ith parameter t ) time (h) ui ) cybernetic variables ui controlling the synthesis of the “key” enzyme i VL ) liquid volume (dm3) Y1 ) sugar fermentation yeast yield (g of biomass/g of sugar consumed) Y2 ) ethanol oxidation yeast yield (g of biomass/g of sugar consumed) Y3 ) sugar oxidation yeast yield (g of biomass/g of sugar consumed) Z ) metabolizing sugar mass (g) zFed ) metabolizing sugar feed concentration (g/ dm3) Ri ) constant of the i enzyme synthesis (h-1) Ri* ) constant of the i enzyme constitutive synthesis (h-1) β ) constant of the enzyme degradation (h-1) i ) Ri/(Ri + Ri*) µ1,max ) maximum specific rate of growth of fermentation (h-1) µ2,max ) maximum specific rate of growth of ethanol oxidation (h-1) µ3,max ) maximum specific rate of growth of sugar oxidation (h-1) νi ) cybernetic variable controlling the inhibition/activation mechanism of the “key” enzyme i πi ) ith parameter of the model φ1 ) stoichiometric coefficient of ethanol production in fermentative pathway φ2 ) stoichiometric coefficient of oxygen consumption in oxidation ethanol pathway φ3 ) stoichiometric coefficient of oxygen consumption in oxidation sugar pathway

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Received for review January 27, 2003 Revised manuscript received June 19, 2003 Accepted July 23, 2003 IE030078Z

Quantitative Analysis of the Key Factors Affecting Yeast Growth

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